37 Generative AI in Epilepsy Research

“Between two seizures a person is not a different person - but the space between two seizures can be a whole life.”\\[4pt] - Jean Delay, La Jeunesse d'André Gide, 1956

Epilepsy is one of the oldest documented diseases in human history and one of the most common serious neurological disorders alive today. Approximately 70 million people worldwide live with epilepsy (Fiest et al., 2017), making it more prevalent than multiple sclerosis, Parkinson's disease, and motor neurone disease combined. Despite more than two dozen licensed anti-seizure medications (ASMs), roughly one in three patients - some 20–25 million people - never achieves sustained seizure freedom (Kwan & Brodie, 2000; Brodie et al., 2012). These individuals face cumulative risks of sudden unexpected death in epilepsy (SUDEP), cognitive decline, psychiatric comorbidity, and profound disability. The humanitarian and economic burden is staggering: the annual global cost of epilepsy has been estimated at over $US,119 billion, two thirds of which arises from lost productivity rather than direct medical expenditure (Ivanova et al., 2010).

For patients who fail two or more appropriately chosen ASMs, surgery offers the best prospect of cure - but surgery is invasive, technically demanding, and requires a lengthy pre-surgical evaluation that includes long-term video-EEG monitoring, high-resolution MRI, neuropsychological testing, and, in many cases, the implantation of intracranial electrodes. Even after this elaborate workup, the seizure-free outcome rate is only 50–70% for the most favourable focal epilepsies, and substantially lower for more complex cases (Wiebe et al., 2001; de Tisi et al., 2011).

This chapter argues that generative artificial intelligence - models that learn to synthesise, augment, impute, and translate data - offers a genuinely new set of tools for attacking the hard unsolved problems in epilepsy research and clinical care. The rest of the chapter is structured as follows. Section Epilepsy - The Clinical Challenge lays out the clinical landscape: definitions, seizure taxonomy, the surgical pathway, and the data challenges that make epilepsy a uniquely difficult domain for machine learning. Section Why Generative Models for Epilepsy? makes the case for the generative approach and introduces the taxonomy of models that will recur throughout the chapter. Subsequent sections (covered in companion files) treat EEG synthesis, MRI augmentation, cross-modal translation, seizure forecasting, and the ethics of AI-assisted surgical planning.

Epilepsy - The Clinical Challenge

What Is Epilepsy?

The word epilepsy derives from the Greek epilambanein - to seize, to take hold of - reflecting the dramatic, overwhelming character of a convulsive seizure. Modern medicine defines the condition more precisely.

A seizure itself is defined as a transient occurrence of signs and/or symptoms due to abnormal, excessive or synchronous neuronal activity in the brain (Fisher et al., 2005). This neurophysiological definition is important: a seizure is not defined by its behavioural manifestation (which can range from a momentary lapse of attention to a dramatic full-body convulsion) but by the underlying electrical event.

The concept of the epileptogenic zone is central to surgical planning. A set of related “zones” are defined in the pre-surgical evaluation literature: the seizure onset zone (SOZ) identified on intracranial EEG, the irritative zone identified by interictal spikes, the symptomatogenic zone identified by ictal semiology, and the lesional zone identified by MRI. Concordance among these zones improves surgical outcomes; discordance signals complexity and risk.

A Historical Timeline

The history of epilepsy spans millennia, from ancient superstition through anatomical dissection to modern electrophysiology and computational neuroscience.

Classification of Epilepsy and Seizures

The ILAE has progressively refined seizure and epilepsy classification over the past five decades. The 2017 operational classification (Scheffer et al., 2017) introduced a three-level framework: seizure type, epilepsy type, and epilepsy syndrome.

Seizure onset.

All seizures are classified first by onset:

• Focal onset: The seizure begins in one hemisphere. Depending on whether awareness is preserved, focal seizures are further classified as focal aware (previously “simple partial”) or focal impaired awareness (previously “complex partial”). Focal seizures may secondarily generalise.

• Generalised onset: Both hemispheres are involved from the outset, as seen in absence, myoclonic, tonic, and tonic-clonic seizures.

• Unknown onset: Insufficient information is available to classify the onset. This category has important implications for clinical management and for machine learning model design, as it introduces irreducible label uncertainty.

Epilepsy types.

At the second level, the epilepsy is classified as:

• Focal epilepsy: Seizures arise from a network localised to one hemisphere, potentially involving subcortical structures. Examples include temporal lobe epilepsy (TLE), frontal lobe epilepsy, and occipital lobe epilepsy.

• Generalised epilepsy: Seizures arise from and rapidly engage bilaterally distributed networks. Examples include childhood absence epilepsy (CAE) and juvenile myoclonic epilepsy (JME).

• Combined focal and generalised epilepsy: Both focal and generalised seizures occur in the same individual.

• Unknown epilepsy type: Classification is not possible given the available information.

Epilepsy syndromes.

The third level identifies specific syndromes defined by a characteristic cluster of clinical features, EEG signatures, imaging findings, and (increasingly) genetic aetiology. Examples include Dravet syndrome, Lennox-Gastaut syndrome, and self-limited epilepsy with centrotemporal spikes (SeLECTS).

Drug-Resistant Epilepsy

This deceptively simple operational definition has profound clinical consequences. A patient who has failed two ASMs has roughly a 5% probability of achieving seizure freedom with a third (Kwan & Brodie, 2000), making continued pharmacological escalation unlikely to succeed while exposing the patient to cumulative drug toxicity.

Why DRE matters.

Patients with DRE bear a disproportionate fraction of the disease burden:

• SUDEP risk is 20–40 times higher than in the general population and 2–4 times higher than in patients with well-controlled epilepsy (Tomson et al., 2008).

• Cognitive and psychiatric comorbidity is substantially elevated, with depression, anxiety, and attention difficulties affecting the majority of patients with DRE.

• Employment and social participation are severely impaired; driving is prohibited in most jurisdictions for any patient with uncontrolled seizures.

• Healthcare utilisation is extreme: patients with DRE account for less than one third of the epilepsy population but over 80% of epilepsy-related healthcare costs.

Mechanisms of pharmacoresistance.

The biological mechanisms underlying pharmacoresistance remain incompletely understood but include: overexpression of multidrug-resistance transporters (P-glycoprotein, MRP1/2) that pump ASMs out of brain tissue; altered drug-target pharmacodynamics (e.g., sodium channel subunit mutations that reduce phenytoin binding); progressive network reorganisation (epileptogenesis) that recruits new brain regions into the seizure network; and intrinsic tissue properties of the epileptogenic lesion (e.g., the balloon cells of focal cortical dysplasia Type IIb are inherently hyperexcitable).

The Surgical Pathway

For patients with DRE caused by a focal, surgically accessible epileptogenic zone, resective or ablative surgery offers the greatest prospect of seizure freedom. However, the pre-surgical evaluation is an elaborate multi-stage process, often lasting weeks to months, designed to localise the EZ and demonstrate that its removal will not cause unacceptable neurological deficits.

Figure fig:epilepsy:clinical-pathway illustrates the complete clinical pathway from initial diagnosis to definitive treatment.

Phase 1 - Non-invasive workup.

The non-invasive evaluation includes:

• Video-EEG monitoring (typically 3–10 days inpatient): captures habitual seizures on scalp EEG, correlates electrical events with clinical semiology, and identifies the seizure onset zone from surface recordings. The temporal resolution is millisecond-level; the spatial resolution is poor ($\sim$10 cm for surface EEG due to skull blurring).

• High-resolution MRI (3T or 7T, with dedicated epilepsy protocols): looks for structural lesions - hippocampal sclerosis, focal cortical dysplasia, low-grade tumours, vascular malformations. In 30–40% of DRE cases the MRI is reported as negative by a radiologist, yet subtle dysplasia may still be present (Bernasconi et al., 2019).

• FDG-PET: the glucose metabolism in the epileptogenic zone is typically hypometabolic interictally, providing a complementary spatial map.

• Ictal SPECT / SISCOM: a radiotracer injected during a seizure accumulates in the hypermetabolic SOZ, highlighting the region of ictal onset on a SPECT scan subtracted from an interictal baseline.

• MEG: provides high-spatial-resolution mapping of interictal spike sources, complementary to EEG because of its insensitivity to the skull and its sensitivity to tangentially oriented dipole sources.

• Neuropsychological assessment: establishes baseline cognitive function in domains served by the putative EZ, informing the risk-benefit analysis.

Phase 2 - Invasive EEG.

When Phase 1 does not yield a clear, concordant localisation, or when the putative EZ is near eloquent cortex, implanted electrodes are used. Two techniques dominate modern practice:

• Stereo-EEG (SEEG): depth electrodes are inserted stereotactically through small burr holes, sampling multiple brain regions simultaneously with millimetre precision. SEEG provides direct recording from deep structures (hippocampus, amygdala, insula, cingulate) inaccessible to surface grids.

• Subdural grids and strips (ECoG): electrode arrays are placed on the cortical surface through a craniotomy, providing high-density two-dimensional coverage of the cortical surface.

Intracranial EEG recordings generate massive datasets: a typical SEEG implantation with 10–15 electrodes (120–180 contacts) sampled at 2 kHz produces roughly 50 GB of raw data per day of monitoring (150 contacts $\times$ 2 kHz $\times$ 16-bit $\approx$ 52 GB/day).

The definitive step - resection or ablation.

Once the EZ is localised, definitive treatment may involve: surgical resection (open craniotomy to remove the EZ and, if necessary, surrounding tissue); laser interstitial thermal therapy (LITT, a minimally invasive ablation guided by real-time MRI thermometry); or focused ultrasound (still investigational for most epilepsy indications).

The Data Challenge in Epilepsy

Machine learning applied to epilepsy confronts a set of interacting data challenges that are substantially more severe than those encountered in most other clinical AI domains.

EEG: noisy, non-stationary, and patient-specific.

Scalp EEG recordings are contaminated by a rich mixture of physiological artefacts (eye movements, muscle activity, cardiac interference, swallowing) and environmental noise (50/60 Hz mains interference, cable movement, electrode pop). More fundamentally, EEG signals are non-stationary: their statistical properties vary over the course of a recording due to changing levels of vigilance, medication effects, and the underlying disease process itself. A classifier trained on the first two hours of a recording may degrade substantially when applied to the next two hours from the same patient.

Patient specificity compounds the problem. The scalp EEG morphology of seizures and interictal discharges varies dramatically across individuals due to differences in skull thickness, brain geometry, electrode placement, and the specific neurological substrate. A seizure detector trained on one patient's data typically generalises poorly to a new patient's data without fine-tuning - a phenomenon known as subject mismatch.

Class imbalance: seizures are rare.

Even in patients with DRE undergoing video-EEG monitoring, seizures occupy a tiny fraction of the total recording time. A patient who has three seizures per day, each lasting 90 seconds, generates seizure data for only 4.5 minutes out of 1440 minutes - a positive-class fraction of 0.3%. In continuous ambulatory monitoring, this ratio may be even more extreme. Standard classifiers trained on such imbalanced data learn to predict the majority class (“no seizure”) almost exclusively, achieving deceptively high accuracy while failing to detect any seizures at all.

MRI lesions: subtle and heterogeneous.

Focal cortical dysplasia (FCD) - the most common surgically treatable pathology in adults with DRE - presents a range of MRI findings from obvious, thick, blurred cortex with subcortical T2/FLAIR signal to completely invisible lesions on standard clinical MRI. A large meta-analysis found that FCD lesions were MRI-negative in approximately 30–40% of pathologically confirmed cases (Guerrini & Duchowny, 2017). Automated lesion detection systems must therefore learn from highly imbalanced data (lesion vs. non-lesion voxels), with ground-truth labels derived from post-surgical histopathology that may not be available until months or years after the MRI.

Data scarcity and privacy constraints.

Epilepsy surgery is performed in specialised centres with relatively small annual caseloads: even the busiest centres evaluate fewer than 200 patients per year. Long-term EEG and MRI data from such patients are sensitive, subject to strict data protection regulations (GDPR, HIPAA), and rarely shared across institutions. Public datasets exist - the CHB-MIT scalp EEG database (Shoeb & Guttag, 2010), the Temple University EEG corpus (Obeid & Picone, 2016), and the iEEG.org intracranial EEG repository - but they are small by deep-learning standards and cover only a fraction of the clinical diversity encountered in practice.

Why Generative Models for Epilepsy?

The preceding section identified three fundamental problems that constrain the use of standard discriminative machine learning in epilepsy:

1. Data scarcity: small, proprietary datasets that cannot easily be pooled across institutions.

2. Class imbalance: seizures and MRI lesions are rare events in datasets dominated by normal examples.

3. Cross-modal gaps: clinical decisions depend on the integration of EEG, structural MRI, functional MRI, PET, and SPECT - but paired multi-modal data from the same patient are scarce.

Discriminative Versus Generative Approaches

Table Table 1 compares the two paradigms across the key dimensions of the epilepsy problem.

Task	Discriminative approach	Generative advantage
Seizure detection	CNN / LSTM classifier on EEG windows	Synthesise rare seizure morphologies to balance training set
Seizure forecasting	Binary predictor of pre-ictal state	Conditional generation of pre-ictal EEG; uncertainty quantification
MRI lesion detection	U-Net segmentation of FCD regions	Anomaly detection via reconstruction error; synthesis of subtle lesion augmentations
Cross-modal synthesis	Paired registration + intensity normalisation	Unpaired MRI-to-PET, EEG-to-MRI translation via CycleGAN or diffusion
Data harmonisation	Site-specific batch correction (ComBat)	Cross-site image-to-image translation preserving pathology
Surgical outcome prediction	Classifier on imaging biomarkers	Counterfactual generation: “what would the MRI look like after resection?”
Patient-specific adaptation	Fine-tuning on $<$10 seizure examples	Few-shot generation of patient-specific EEG; meta-learning

The limitations of discriminative models are most acute at the intersection of data scarcity and high-stakes clinical decisions. A seizure detector that achieves 90% sensitivity in a laboratory setting may fail catastrophically in the clinic if the training data did not include the particular seizure morphology the patient exhibits. A lesion detector trained on MRI-positive cases cannot meaningfully rank MRI-negative scans for the probability of a subtle lesion.

Generative models address these limitations through three complementary mechanisms:

Synthesis and augmentation.

Generative models sample new training examples from the learned distribution, increasing effective dataset size and class balance. Crucially, generative augmentation can produce realistic examples that respect the complex multivariate structure of EEG (temporal autocorrelation, spatial coherence, non-stationary frequency content) in a way that simple operations like time-shifting or frequency masking cannot.

Anomaly detection.

Models trained only on normal data - normal EEG, normal MRI - assign low likelihood to abnormal examples. This likelihood score becomes a biomarker: a new patient's scan is anomalous (and potentially lesional) to the extent that it lies in a low-density region of the learned normal distribution. This approach circumvents the need for any labelled pathological examples at training time.

Cross-modal translation.

Paired training data across modalities (simultaneous EEG and fMRI, paired MRI and PET) are extremely scarce. Generative models - especially cycle-consistent GANs and diffusion-based translators - can learn cross-modal mappings from unpaired data, enabling in silico generation of the missing modality for patients who underwent only one imaging study.

A Taxonomy of Generative Models for Epilepsy

Five families of generative models dominate the epilepsy literature. Figure fig:epilepsy:gen-taxonomy provides an overview of these families and the clinical tasks they address.

Generative Adversarial Networks (GANs).

GANs (Goodfellow et al., 2014) pit a generator $G:𝒵\to 𝒳$ against a discriminator $D:𝒳\to [\mathrm{0,1}]$ in a minimax game: (GAN Objective)$$\begin{array}{ccc}& \underset{G}{\min }\underset{D}{\max }{𝔼}_{𝒙\sim p_{\mathrm{data}}}[\log D(𝒙)]+{𝔼}_{𝒛\sim p(𝒛)}[\log (1-D(G(𝒛)))].& \text{<span class="tml-eqn"></span>}\end{array}$$ In epilepsy, GANs have been used to synthesise realistic ictal EEG segments (Hartmann et al., 2018; Zhang et al., 2020), to perform unpaired MRI-to-PET translation, and to generate population-diverse training data for multi-site harmonisation.

Variational Autoencoders (VAEs).

VAEs (Kingma & Welling, 2013) learn a stochastic encoder $q_{𝝓}(𝒛|𝒙)$ and a generative decoder $p_{𝜽}(𝒙|𝒛)$, optimising the evidence lower bound: (ELBO)$$\begin{array}{ccc}& {ℒ}_{\mathrm{ELBO}}(𝜽,𝝓)={𝔼}_{q_{𝝓}(𝒛|𝒙)}[\log p_{𝜽}(𝒙|𝒛)]-D_{\mathrm{KL}}(q_{𝝓}(𝒛|𝒙)\Vert p(𝒛)).& \text{<span class="tml-eqn"></span>}\end{array}$$ In epilepsy, VAEs are valuable for anomaly detection: a model trained on normal-anatomy MRI assigns high reconstruction error to lesional cortex, providing an unsupervised lesion score. VAEs also enable latent-space arithmetic - interpolating between ictal and interictal EEG states, or between pre- and post-surgical MRI.

Diffusion Models.

Diffusion models (Ho et al., 2020; Song et al., 2021) define a forward process that gradually corrupts data with Gaussian noise, and learn a reverse denoising process: (DDPM Reverse)$$\begin{array}{ccc}& p_{𝜽}({𝒙}_{t-1}|{𝒙}_t)=𝒩({𝒙}_{t-1};{𝝁}_{𝜽}({𝒙}_t,t),{𝚺}_{𝜽}({𝒙}_t,t)).& \text{<span class="tml-eqn"></span>}\end{array}$$ Diffusion models excel at high-fidelity image synthesis and have been applied to MRI super-resolution (recovering 7T-quality texture from 3T acquisitions), lesion synthesis (injecting realistic FCD lesions into normal MRI for training data augmentation), and cross-site harmonisation.

Normalising Flows.

Normalising flows (Rezende & Mohamed, 2015; Papamakarios et al., 2021) learn an invertible mapping $f:𝒳\to 𝒵$ with tractable Jacobian, enabling exact likelihood evaluation: (FLOW Likelihood)$$\begin{array}{ccc}& \log p_{𝜽}(𝒙)=\log p_{𝒵}(f(𝒙))+\log \left|\det \frac{\partial f(𝒙)}{\partial 𝒙}\right|.& \text{<span class="tml-eqn"></span>}\end{array}$$ The tractable likelihood makes flows attractive for seizure forecasting: learning the density of EEG feature trajectories and scoring future windows by their likelihood under the learned model. Low-likelihood windows signal departure from the patient's normal EEG regime - a potential pre-ictal biomarker.

Transformers and Large Language Models.

Autoregressive transformer models treat multi-channel EEG as a sequence of discrete tokens (after vector quantisation) or as continuous patch embeddings, learning long-range temporal dependencies across minutes of recording. Large pre-trained EEG foundation models (e.g., LaBraM, Jiang et al., 2024; BIOT, Yang et al., 2024) are emerging, analogous to BERT and GPT in natural language processing. For clinical text, LLMs summarise EEG reports, extract structured information from clinical notes, and generate draft discharge summaries for epilepsy monitoring unit admissions.

Comparison of Generative Approaches

Table Table 2 provides a structured comparison of the five families along dimensions most relevant to epilepsy applications.

Family	Tractable $\log p$	Sample quality	Training stability	Conditioning	Primary epilepsy use
GAN	No	High	Low	Moderate	EEG synthesis, image-to-image
VAE	Approx.	Moderate	High	Easy	Anomaly detection, interpolation
Diffusion	No (approx.)	Very high	High	Easy	MRI augmentation, harmonisation
Flow	Yes	Moderate	Moderate	Moderate	Likelihood scoring, forecasting
Transformer	Yes	High (text/seq.)	High	Easy	EEG modelling, report generation

No single family dominates across all epilepsy tasks. Diffusion models produce the highest-fidelity MRI synthesis but are slow to sample and do not provide tractable likelihoods. Normalising flows provide exact likelihoods but scale poorly to high-dimensional image data without architectural compromises. GANs generate sharp EEG but are prone to mode collapse, which is particularly dangerous in a clinical context because a model that ignores certain seizure morphologies will lead to undertrained detectors. VAEs are the most stable to train and most flexible for anomaly scoring, but their sample quality is limited by the Gaussian decoder assumption. Transformers offer the best solution for sequential EEG modelling at scale.

In practice, the most successful systems combine multiple families. For example, a diffusion model generates synthetic MRI lesions, which augment the training set of a discriminative U-Net segmentor; a VAE encodes patient-specific EEG representations that are then passed to a transformer for seizure forecasting. The chapter will return to these hybrid architectures throughout.

Chapter Roadmap

The remainder of this chapter is organised as follows, with a dependency structure illustrated in Figure fig:epilepsy:roadmap.

Sec.,3

EEG Signal Characteristics and Preprocessing. Formal description of multi-channel EEG as a multivariate stochastic process; spectral features, time-frequency representations, and graph-theoretic connectivity measures; the preprocessing pipeline from raw recordings to model-ready tensors.

Sec.,4

GAN-Based EEG Synthesis. Progressive and conditional GAN architectures for ictal EEG generation; evaluation metrics (FID on EEG spectrograms, expert rater studies); downstream seizure detection experiments demonstrating synthetic augmentation benefit.

Sec.,5

Variational Models for EEG Anomaly Detection. VAE and $\beta$-VAE for interictal discharge modelling; spike detection via reconstruction error; disentangled latent spaces for seizure type characterisation.

Sec.,6

MRI Synthesis and Lesion Augmentation. Diffusion models for 3D T1/FLAIR generation; inpainting-based lesion injection for FCD data augmentation; normalising flow-based anomaly scoring for MRI-negative lesion detection.

Sec.,7

Cross-Modal Translation. Unpaired MRI-to-PET translation with CycleGAN; diffusion-based paired translation; EEG-to-fMRI inference; evaluation of clinical utility for patients missing one modality.

Sec.,8

Seizure Forecasting with Generative Models. Conditional diffusion and flow-based models for pre-ictal state generation; uncertainty-aware forecasting; evaluation on long-term ambulatory recordings.

Sec.,9

Foundation Models and Transformers for EEG. Pre-trained EEG transformers; masked autoencoding for EEG; few-shot adaptation to new patients; clinical language models for epilepsy report generation.

Sec.,10

Ethical and Regulatory Dimensions. Fairness and representativeness of synthetic data; regulatory pathways for AI-generated surgical guidance; explainability and clinician trust; privacy-preserving federated learning with generative augmentation.

Exercises

EEG Fundamentals for the Generative Modeller

Before a generative model can be designed, trained, or evaluated on brain-electrical data, its architect must understand the signal. Electroencephalography is deceptively straightforward to record and fiendishly difficult to model: it is simultaneously a rich window into neural dynamics and a superposition of artefacts, volume-conducted fields, and structured noise. This section provides the minimal substrate of EEG knowledge required to make principled decisions about representation, architecture, and evaluation. We approach EEG as mathematicians and engineers, emphasising the properties that constrain and motivate the generative modelling choices taken up in later sections.

What Is EEG? Electrodes, Montages, and the 10–20 System

Electroencephalography measures the time-varying voltage difference between pairs of electrodes placed on the scalp. These voltages reflect the summed post-synaptic potentials of large populations of pyramidal neurons in the cortex, which, when synchronised, produce electrical fields detectable at the scalp surface. A single electrode does not record the activity of a single neuron: the dominant contributors are on the order of ${10}^4$ to ${10}^6$ neurons firing more-or-less coherently within a cortical patch, with the field propagated through skull, dura, and scalp via volume conduction.

Electrode placement: the 10–20 system.

Clinical and research EEG recordings follow the International 10–20 System (standardised by the American Clinical Neurophysiology Society and rooted in work by Jasper, 1958). The name refers to the fact that electrodes are placed at positions that are either 10% or 20% of the distance between two anatomical landmarks: the nasion (bridge of the nose), the inion (posterior protrusion of the skull), and the two pre-auricular points above the ears. This ensures consistent placement across individuals despite differences in head size.

Standard 10–20 recordings use 19 to 21 electrodes for clinical work, while high-density systems extend to 64, 128, or even 256 electrodes. Epilepsy monitoring units typically record at 19–64 channels. Each electrode receives a letter designating the cortical region (F = frontal, C = central, T = temporal, P = parietal, O = occipital, Fp = frontopolar) and a number indicating laterality: odd numbers indicate left-hemisphere placements, even numbers indicate right-hemisphere placements, and the letter z (for “zero”) denotes midline electrodes.

Montages and referencing.

Every EEG voltage is a potential difference and requires a reference. Clinical practice employs several montage conventions. The linked-ears or average reference montage subtracts a global average from each channel, making the signal reference-independent in expectation. The bipolar montage computes differences between adjacent electrode pairs, emphasising local gradients and suppressing global artefacts. The Laplacian montage approximates the second spatial derivative, sharpening spatial resolution. For generative modelling, montage choice affects the covariance structure of $𝐗$: bipolar signals exhibit shorter spatial correlation length than average-referenced signals. Models trained on one montage typically do not transfer to another without re-normalisation.

Formally, a montage is a linear map $𝐋\in {\mathrm{ℝ}}^{N_e\times N_e}$ such that the montaged signal is $𝐘=𝐋𝐗$. For the average reference montage, $𝐋=𝐈-(1/N_e){\mathrm{𝟏𝟏}}^{\top }$ (the centring matrix). For a bipolar montage, $𝐋$ is a sparse difference matrix. Since $𝐋$ is fixed and known, data from any montage can be re-montaged to any other, provided the original reference signal is available or reconstructable. This implies that generative models trained on average-referenced data can be used to augment datasets recorded in a bipolar montage by applying the appropriate linear transformation to the synthetic output, a simple but useful domain adaptation strategy.

Sampling rate.

Clinical EEG is recorded at $f_s\in \{256,512,1024,2048\}$ Hz. The Nyquist theorem requires $f_s>2f_{\max }$, where $f_{\max }$ is the highest frequency of interest: for epilepsy, high-frequency oscillations (HFOs) at 80–500 Hz have gained diagnostic importance (Jacobs et al., 2012), pushing sampling rates upward. Most large benchmark datasets use $f_s=256$ Hz or $f_s=512$ Hz, targeting the clinically canonical 0–100 Hz band. For generative modelling, the choice of $f_s$ determines the temporal dimension of the data matrix and the computational cost of sequence models operating on raw waveforms.

Frequency Bands: The Spectral Vocabulary of EEG

Clinical EEG interpretation is organised around five canonical frequency bands, each associated with distinct neural states and pathological signatures.

Spectral evolution during seizures.

During a generalised tonic-clonic seizure the spectral composition evolves in a stereotyped pattern: the tonic phase begins with high-frequency (beta/gamma, 15–60 Hz) low-amplitude activity, transitions to low-frequency (delta/theta, 1–7 Hz) high-amplitude rhythmic discharges during the clonic phase, and terminates with diffuse delta slowing in the postictal period. Focal onset seizures evolve from a localised fast onset zone to progressively broader delta-dominated propagation. This stereotyped evolution is a constraint that generative models should satisfy: synthetic ictal segments should exhibit frequency chirp (the characteristic shift from high to low frequency over time) rather than static spectral profiles. Evaluating whether a generative model preserves ictal spectral evolution is one of the domain-specific fidelity checks discussed in sec:epilepsy:evaluation.

Each band is not a fixed property of the recording but an interpretation applied by bandpass filtering. In practice a zero-phase fourth-order Butterworth filter or a Morlet wavelet decomposition is applied to isolate each band. The relative power in each band, computed as (Bandpower)$$\begin{array}{ccc}& P_b={\int }_{f_{\text{low},b}}^{f_{\text{high},b}}{S}_{xx}(f)\mathrm{d}f,& \text{<span class="tml-eqn"></span>}\end{array}$$ where $S_{xx}(f)$ is the power spectral density, constitutes a simple but powerful feature vector for seizure detection. Generative models operating in the frequency domain must respect these band boundaries, as band power ratios encode diagnostically meaningful information that should be preserved or controllably varied during synthesis.

Seizure States: Interictal, Preictal, Ictal, Postictal

From the perspective of a supervised learning system, the EEG time axis can be partitioned into four states relative to a seizure event. Understanding these states is essential for designing labelling schemes, choosing data windows, and interpreting classifier outputs.

EEG micro-states and within-state heterogeneity.

Even within the interictal state, EEG is not homogeneous. EEG micro-states (Lehmann et al., 1998) are quasi-stable scalp topography patterns lasting 80–120 ms, transitioning semi-randomly in a Markov-like sequence. Four canonical micro-state templates (labelled A, B, C, D) have been identified across subjects, with their transition probabilities altered in epilepsy and other neurological conditions. Within the ictal state, seizures undergo a structured evolution through multiple electrographic patterns (electrographic seizure phases): the pre-discharge build-up, fast low-voltage onset, organised rhythmic discharge, clonic phase, and termination. A generative model that collapses all ictal windows into a single distribution fails to capture this within-class heterogeneity, producing homogeneous synthetic data that does not replicate the temporal evolution characteristic of real seizures.

Signal Characteristics: Non-Stationarity, High Dimensionality, and Noise

Three properties of EEG are particularly consequential for generative modelling.

Non-stationarity.

A stochastic process is (weakly) stationary if its mean and autocovariance function do not change with time. EEG violates both conditions over timescales beyond a few seconds: mean amplitude drifts with electrode impedance and posture; spectral content changes with vigilance state, drug effect, and disease progression; seizures introduce abrupt statistical shifts. More formally, if ${𝐗}_{[t:t+W]}$ denotes a window of length $W$ seconds, the covariance matrix $𝚺(t)=\mathrm{Cov}({𝐗}_{[t:t+W]})$ is not constant in $t$.

This non-stationarity constrains generative modelling in two ways. First, models that assume stationarity (e.g., stationary Gaussian process priors) will fail to capture the ictal transition. Second, evaluation metrics computed on long recordings may average away the very phenomena of interest. Practitioners address non-stationarity by operating on short windows (typically 1–30 s) and treating windows as i.i.d. samples, though this approximation ignores temporal dependencies between windows.

A more principled approach is to model EEG as a locally stationary process: one whose second-order statistics change slowly relative to the timescale of a short analysis window. Let $𝐱(t)\in {\mathrm{ℝ}}^{N_e}$ be the instantaneous multichannel EEG vector. The locally stationary covariance model posits (Locally Stationary)$$\begin{array}{ccc}& 𝚺(t)=𝚺(t_0)+\dot{𝚺}(t_0)(t-t_0)+O((t-t_0{)}^2),& \text{<span class="tml-eqn"></span>}\end{array}$$ which is adequate for window lengths $W$ small relative to the seizure timescale. VAEs and diffusion models operating on short windows implicitly adopt this approximation by treating each window as a sample from a fixed latent distribution. Recurrent generative architectures can relax this assumption by conditioning on the previous window's latent state.

High dimensionality.

With $N_e$ channels sampled at $f_s$ Hz for $T$ seconds, the raw data matrix has $N_e\cdot f_s\cdot T$ elements. At 64 channels, 512 Hz, and 10 hours of recording: (Dimensionality)$$\begin{array}{ccc}& 64\times 512\times 36000=1.18\times {10}^9\text{ samples.}& \text{<span class="tml-eqn"></span>}\end{array}$$ Fitting a generative model directly on raw multi-channel waveforms of this size is computationally prohibitive without compression. The standard pipeline first projects the data into a lower-dimensional representation (spectral features, ICA components, or learned latent codes) before applying the generative model.

Two classical linear dimensionality reduction techniques are frequently applied as preprocessing for EEG generative models:

Independent Component Analysis (ICA). ICA factorises the observed $N_e$-dimensional signal into $N_e$ statistically independent components: $𝐗=𝐀𝐒$, where $𝐀\in {\mathrm{ℝ}}^{N_e\times N_e}$ is the mixing matrix and $𝐒\in {\mathrm{ℝ}}^{N_e\times T}$ contains the independent source signals. Artefact components (eye blinks, muscle) are identified by their non-neural topographic maps and removed before reconstruction. ICA reduces effective dimensionality because artefact-cleaned recordings typically have rank lower than $N_e$.

Common Spatial Patterns (CSP). CSP computes spatial filters that maximise the variance ratio between two classes. For the binary ictal/non-ictal problem, CSP finds $𝐖\in {\mathrm{ℝ}}^{N_e\times m}$ ($m\ll N_e$) such that $\mathrm{Var}({𝐖}^{\top }{𝐱}^{+})/\mathrm{Var}({𝐖}^{\top }{𝐱}^{-})$ is maximised. The projected signal ${𝐖}^{\top }𝐗\in {\mathrm{ℝ}}^{m\times T}$ is a compact representation that concentrates ictal information in a small number of components. CSP is widely used as a preprocessing step before VAE or GAN training, reducing input dimension from $\sim 64$ to $\sim 8$ components while retaining most of the discriminative structure.

Noise and artefacts.

EEG recordings are corrupted by several artefact sources, each with a distinct spectral and spatial signature:

• Muscle artefacts (EMG): broadband high-frequency contamination (20–200 Hz), prominent at temporal and frontal electrodes near jaw and neck muscles.

• Eye movement artefacts (EOG): large-amplitude deflections at frontopolar electrodes (Fp1, Fp2) from cornea rotation; blinks produce stereotyped biphasic waveforms.

• Cardiac artefacts (ECG): regular 1–1.5 Hz pulses, visible at temporal and frontal electrodes.

• Line noise: 50 Hz (Europe, Asia) or 60 Hz (Americas) sinusoidal contamination from AC power.

• Movement artefacts: irregular baseline shifts from electrode cable movement.

A generative model trained without artefact removal may learn to synthesise artefacts as if they were neural signals, producing data that appears realistic to automated metrics but is clinically misleading.

Time-Frequency Representations

Because EEG is non-stationary, the global power spectrum $S_{xx}(f)$ discards temporal information. The solution is a time-frequency representation (TFR) that tracks how spectral content evolves over time.

The TFR $|𝒳(m,k){|}^2$ (or $|W_x(a,b){|}^2$) has two key advantages for generative modelling: (i) it converts the 1-D time series into a 2-D image, enabling architectures designed for image synthesis (GANs, VAEs, diffusion models) to operate without modification; (ii) it separates seizure-relevant spectral changes (e.g., ictal onset manifests as a sudden power increase in the beta or gamma band) from slow baseline drifts. The primary cost is the loss of phase information (in the spectrogram) and the Heisenberg uncertainty trade-off: improving temporal resolution degrades frequency resolution, and vice versa.

Mel-frequency spectrograms for EEG.

Mel-frequency spectrograms, standard in audio generative modelling, have been adapted for EEG synthesis. The mel scale compresses frequency resolution at high frequencies according to $m(f)=2595{\log }_{10}(1+f/700)$, which is physiologically motivated for speech but has no direct neurophysiological justification for EEG. Nevertheless, several papers report that GANs conditioned on mel spectrograms produce higher-quality EEG than those conditioned on linear spectrograms, possibly because the lower-dimensional mel representation regularises the generator and prevents mode collapse onto artefactual high-frequency patterns.

Phase-sensitive representations.

The spectrogram discards phase, which encodes neural synchrony and connectivity information of diagnostic relevance (e.g., phase synchrony between bilateral temporal electrodes is altered during focal seizures). Phase-preserving alternatives include:

• Complex spectrogram: retain both $\mathrm{Re}(𝒳(m,k))$ and $\mathrm{Im}(𝒳(m,k))$ as separate image channels. This doubles the representation dimension but allows the generative model to learn phase structure.

• Phase coherence matrix: compute the instantaneous phase ${\varphi }_c(t)$ at each channel $c$ via the Hilbert transform and encode inter-channel phase synchrony as a matrix $𝐂(f,t)$ with $C_{ij}(f,t)=⟨e^{j({\varphi }_i(f,t)-{\varphi }_j(f,t))}⟩$; this is the phase locking value between channels $i$ and $j$.

• Raw waveform: bypass time-frequency transformation entirely and operate the generative model on the raw 1-D signal. Architectures such as WaveNet (van den Oord et al., 2016) and autoregressive transformers can operate at the sample level, preserving all phase information, at the cost of much longer sequence lengths.

Key Benchmark Datasets

The epilepsy EEG community has converged on a small number of public benchmark datasets. Understanding their provenance, size, and limitations is essential for reproducible evaluation of generative models.

Dataset	$N_s$	$N_{\text{seiz}}$	$f_s$ (Hz)	Approx. IR	Key features
CHB-MIT Scalp EEG	23	198	256	$\sim$50:1	Paediatric, long-term, public
TUH EEG Corpus	14,987	$>$14,000	250–512	$\sim$200:1	Largest public corpus, clinical
EPILEPSIAE	30	275	512–2048	$\sim$130:1	Multi-centre, intracranial option
Siena Scalp EEG	14	47	512	$\sim$80:1	Adult, PhysioNet hosted
Kaggle Melbourne (2014)	10	varies	400	$\sim$50:1	Intracranial (dogs + humans)

CHB-MIT Scalp EEG Database.

The CHB-MIT database (Shoeb, 2009; maintained at PhysioNet) comprises scalp EEG recordings from 23 paediatric patients (ages 1.5–22 years) with intractable seizures, recorded at Boston Children's Hospital using the international 10–20 system at 256 Hz. Total recording length exceeds 980 hours, containing 198 annotated seizures. It is the most widely cited benchmark for seizure prediction and detection, despite its relatively small patient cohort, because of its accessibility, documentation quality, and community familiarity.

Temple University Hospital (TUH) EEG Corpus.

The TUH EEG Corpus (Obeid & Picone, 2016) is the largest public EEG repository, compiled from clinical recordings at Temple University Hospital spanning 2002–present. The Seizure Corpus (TUSZ) release v1.5.2 contains recordings from over 675 subjects with more than 5700 seizure annotations across four seizure types (focal, generalised, combined, and unknown). The corpus is clinically representative but heterogeneous: recordings vary in channel count (19–32), sampling rate (250–512 Hz), and clinical quality, demanding robust normalisation pipelines.

EPILEPSIAE.

EPILEPSIAE (Ihle et al., 2012) is a European multi-centre dataset containing long-term EEG recordings from 30 patients with pharmacologically intractable focal epilepsies. Each patient contributes at least 24 hours of continuous EEG, and many contribute several days. The dataset is particularly valuable for seizure prediction (as opposed to detection) because of the long preictal windows available. Access requires signing a data-use agreement.

Siena Scalp EEG Database.

The Siena dataset (Detti et al., 2020), hosted on PhysioNet, provides scalp EEG recordings from 14 adult subjects at 512 Hz. It is notable for including precise onset/offset annotations and is frequently used as a held-out test set for models trained on CHB-MIT.

Kaggle American Epilepsy Society Seizure Prediction Challenge (2014).

This competition dataset contains intracranial EEG recordings from four dogs and three humans, sampled at 400 Hz with 16 electrodes. While smaller than the scalp datasets, it offers intracranial resolution and was influential in spurring deep learning approaches to seizure prediction (Brinkmann et al., 2016).

Emerging datasets and data federation.

Two emerging trends will affect the next generation of generative EEG models. First, federated datasets: privacy-preserving frameworks (e.g., TEFLA, IBIS) allow multiple hospitals to train shared models without transferring raw patient data, addressing the legal constraints that have limited the size of public EEG repositories. Second, wearable EEG: consumer-grade EEG headbands (Emotiv, Muse, OpenBCI) are producing large real-world datasets outside clinical settings, with fewer electrodes (2–14 channels) but far more continuous recording time. Generative models trained on clinical 19-channel datasets will face significant domain shift when applied to wearable 2-channel recordings, motivating domain adaptation techniques discussed in later sections.

Cross-Dataset Generalisation and Domain Shift

A generative model trained on CHB-MIT will not, in general, produce valid EEG for a TUH Corpus patient. The two datasets differ along multiple axes that together constitute domain shift:

• Patient population: CHB-MIT covers paediatric patients with a narrow age range; TUH Corpus covers the full adult clinical spectrum. Brain electrical patterns change substantially with age, with children exhibiting higher amplitude, lower frequency baseline rhythms.

• Recording hardware: different amplifier manufacturers impose different frequency responses, quantisation levels, and impedance tolerances.

• Clinical protocol: medication changes, sleep staging, and the clinical reason for the recording (monitoring vs. diagnostic) affect the EEG non-stationarity and artefact profile.

• Seizure aetiology: temporal-lobe seizures (dominant in CHB-MIT) have different ictal morphologies than frontal-lobe or generalised seizures.

Domain shift is particularly damaging for generative augmentation because the generative model learns the source domain distribution $p_{\text{source}}(𝐱)$; samples from this model contaminate the target domain training set with out-of-distribution data. Techniques for domain-adaptive generative augmentation, including conditional normalising flows conditioned on patient identifiers and adversarial domain adaptation losses, are discussed in sec:epilepsy:advanced.

The Class Imbalance Problem

No aspect of EEG-based epilepsy machine learning is more persistently disruptive than class imbalance. The neurophysiological reality is stark: a patient who experiences two generalised tonic-clonic seizures per week, each lasting two minutes, generates approximately $2\times 2/(7\times 24\times 60)\approx 0.04\%$ of their interictal EEG as ictal data. The other $99.96\%$ is “normal”. A classifier that labels every window as non-seizure achieves $99.96\%$ accuracy while being useless. Addressing this imbalance is not optional: it is the central engineering problem of the field.

Quantifying the Imbalance

The imbalance is compounded by the temporal clustering of both classes: seizures arrive in clusters separated by long seizure-free periods, and the interictal class is itself heterogeneous (drowsiness, drug troughs, artefacts). A model that memorises a few ictal patterns will generalise poorly across a patient's full seizure repertoire.

Patient-level heterogeneity.

Imbalance ratios vary enormously across patients in the same dataset. In CHB-MIT, patient chb24 has an IR of approximately 9 (relatively balanced) while patient chb12 has an IR exceeding 400. Pooling patients without stratification produces a combined dataset that is dominated by patients with high IR, systematically underrepresenting easy cases and overfitting to the seizure morphology of high-seizure patients.

Why Standard Machine Learning Fails on Imbalanced EEG

A standard empirical risk minimiser minimises the average loss over the training set. When $\mathrm{IR}\gg 1$, the empirical risk is dominated by the majority class, and the optimal decision boundary is pushed toward (or coincides with) the boundary of the minority class manifold.

The practical consequences are severe:

1. High specificity, catastrophically low sensitivity. Models trained naively achieve $>99\%$ specificity (correctly rejecting non-seizure) but $<50\%$ sensitivity (correctly identifying seizure), often below chance for rare patients.

2. Overconfident majority predictions. Calibration is poor: the model assigns high confidence $p(\hat{y}=0)\approx 1$ to almost all inputs, preventing threshold tuning from recovering minority class performance.

3. Poor feature learning for the minority class. When minority samples are rare, the network's internal representations for the minority class are learnt from too few examples and tend to cluster tightly around a small number of prototypical patterns observed in training, failing to cover the full ictal manifold.

Traditional Solutions and Their Limitations

The machine learning literature offers three classical families of remedies for class imbalance: data-level methods, algorithm-level methods, and hybrid methods.

Data-level methods: oversampling and undersampling.

The simplest approach is random oversampling: replicate minority class windows until the classes are balanced. This introduces no new information and tends to cause overfitting, since the classifier sees identical minority examples many times. Random undersampling discards majority class windows, wasting labelled data.

SMOTE (Synthetic Minority Over-sampling Technique; Chawla et al., 2002) improves on random oversampling by synthesising new minority samples as convex combinations of existing minority samples and their $k$-nearest neighbours: (Smote)$$\begin{array}{ccc}& \widetilde{𝐱}={𝐱}_i+\lambda ({𝐱}_j-{𝐱}_i),\lambda \sim \mathrm{Uniform}(\mathrm{0,1}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝐱}_j$ is a nearest neighbour of ${𝐱}_i$ in the feature space.

ADASYN (Adaptive Synthetic Sampling; He et al., 2008) extends SMOTE by generating more synthetic samples in feature-space regions where the classifier boundary is most uncertain, weighted by the local class density.

Limitations of interpolation-based methods.

Both SMOTE and ADASYN assume that the minority class manifold is convex: that any convex combination of two minority samples is a valid minority sample. For EEG signals, this assumption fails in at least three ways:

1. Non-Euclidean feature geometry. Seizure waveforms live on a nonlinear manifold in raw sample space. Linear interpolation between two ictal windows may produce signal combinations that are neither ictal nor interictal, but physiologically impossible.

2. Temporal structure violation. EEG windows have strong temporal autocorrelation. SMOTE operates on window-level feature vectors, ignoring the within-window waveform structure. Interpolating between two windows discards the autocorrelation structure, producing flat or artifactual power spectra.

3. Diversity collapse. When $n_{+}$ is very small (e.g., $n_{+}=20$), the SMOTE graph has few edges and the synthetic distribution is limited to a low-dimensional convex hull of the observed ictal samples. If those samples share a common seizure morphology, the augmented set fails to cover the full ictal manifold.

Algorithm-level methods: class weighting and cost-sensitive learning.

Rather than modifying the data, algorithm-level methods modify the loss function. Class weighting multiplies the loss for minority class samples by a weight $w_{+}={(n_{-}/n_{+})}^{\alpha }$, typically with $\alpha =1$: (Weighted LOSS)$$\begin{array}{ccc}& {ℒ}_{\text{weighted}}=w_{+}\sum _{i:y_i=1}\ell ({\hat{y}}_i,y_i)+\sum _{i:y_i=0}\ell ({\hat{y}}_i,y_i).& \text{<span class="tml-eqn"></span>}\end{array}$$ This counteracts the gradient imbalance in (Gradient Imbalance) but does not increase the diversity of minority class patterns seen by the model. Focal loss (Lin et al., 2017) reduces the weight of well-classified majority examples dynamically: ${ℒ}_{\text{focal}}=-{\alpha }_t{(1-p_t)}^{\gamma }\log p_t$, where ${(1-p_t)}^{\gamma }$ down-weights easy negatives.

Hybrid methods: ensemble approaches.

Balanced bagging (Maclin & Opitz, 1997) combines undersampling with ensemble learning: each base classifier is trained on a balanced bootstrap sample obtained by taking all minority class samples and a random subsample of majority class samples of equal size. Because each bootstrap uses a different majority subsample, the ensemble collectively exploits more of the majority class data while each individual classifier is not overwhelmed by the majority. For EEG, balanced random forests (a variant of balanced bagging applied to decision trees) were a competitive baseline before deep learning. Their limitation is the same as all undersampling methods: they waste majority class information and cannot enrich the minority class distribution.

Summary of limitations.

None of the classical approaches addresses the root problem: the model has too little information about the minority class manifold. Class weighting and focal loss rearrange the training signal without adding information. SMOTE and ADASYN add synthetic information but assume a convex manifold that does not hold for physiological waveforms. Ensemble methods exploit available majority data better but still cannot generate novel minority patterns. The natural next step is to learn the minority class manifold from data using a generative model, which we take up in the following sections.

Generative Augmentation: Learning the Data Manifold

Comparison of augmentation strategies.

Table 4 summarises the key properties of the main augmentation families for EEG class imbalance.

Method	Manifold-
aware	Phase-
preserving	Small
$n_{+}$	Requires
training?
Random oversampling	No	Yes	Yes	No
SMOTE	Partial	No	Limited	No
ADASYN	Partial	No	Limited	No
Class weighting	No	-	Yes	No
Focal loss	No	-	Yes	No
VAE augmentation	Yes	Yes	Moderate	Yes
GAN augmentation	Yes	Yes	Limited	Yes
Diffusion augmentation	Yes	Yes	Yes	Yes

How much augmentation is enough?

A natural question is how many synthetic samples $M$ to generate. Naïvely setting $M=n_{-}-n_{+}$ targets perfect balance (IR $=1$), but this may not be optimal. Several empirical studies (Estabrooks et al., 2004, for tabular data; Wang et al., 2018, for EEG) suggest that the optimal augmentation ratio $r^{\ast }=M/n_{+}$ depends on three factors: (i) the quality of the generative model (higher quality supports higher $r^{\ast }$); (ii) the complexity of the target classifier (deeper classifiers are more prone to memorising low-quality synthetic samples); (iii) the heterogeneity of the true minority distribution (more heterogeneous distributions require more samples to cover). A practical heuristic is to sweep $r\in \{1,2,5,10\}$ on a validation fold and select by AUPRC.

The practical pipeline for generative augmentation in epilepsy classification is as follows:

1. Train generative model $G_{\theta }$ on available minority class windows ${\{{𝐱}_i^{+}\}}_{i=1}^{n_{+}}$. Architectures include conditional GANs, VAEs, and diffusion models, discussed in sec:epilepsy:gans,sec:epilepsy:vae,sec:epilepsy:diffusion.

2. Generate synthetic minority windows ${\widetilde{𝐱}}_1,\dots ,{\widetilde{𝐱}}_M$ with $M=n_{-}-n_{+}$ (or some desired balance ratio) by sampling from $G_{\theta }$.

3. Augment the training set: ${𝒟}_{\text{aug}}={𝒟}_{\text{orig}}\cup {\{({\widetilde{𝐱}}_i,y=1)\}}_{i=1}^M$.

4. Train classifier on ${𝒟}_{\text{aug}}$ using standard cross-entropy, without class weighting.

5. Evaluate on a held-out test set containing real signals only; synthetic data are never used for evaluation.

Evaluation Metrics for Imbalanced Settings

Accuracy is a misleading metric when classes are imbalanced: a model achieving 99% accuracy by predicting only non-seizure provides no clinical value. The epilepsy EEG literature employs a family of metrics that treat the two classes asymmetrically, reflecting the clinical asymmetry of the consequences of false negatives (missed seizures) versus false positives (unnecessary alarms).

Clinical interpretation.

Sensitivity measures the fraction of actual seizure windows correctly identified. In clinical deployment, a missed seizure (FN) has catastrophic consequences (patient injury, sudden unexpected death in epilepsy – SUDEP), while a false alarm (FP) causes inconvenience but not direct harm. This asymmetry motivates primary optimisation for sensitivity at a fixed tolerable FPR. Clinical seizure detection systems typically target sensitivity $>80\%$ at FPR $<0.5$ false alarms per hour.

AUROC and AUPRC.

AUROC is threshold-independent and robust to class imbalance in the sense that it measures the probability that a randomly drawn positive example is scored higher than a randomly drawn negative example. However, for very high IR, the Precision-Recall curve and its area (AUPRC) are more informative, as AUROC can remain high even when precision is near zero. Davis & Goadrich (2006) establish that AUPRC is the appropriate metric when IR $\gg 1$ and high precision is required.

False alarms per hour.

In ambulatory and wearable seizure detection, sensitivity and specificity are often replaced by a two-dimensional operating point: sensitivity (fraction of seizures detected) plotted against the false alarm rate measured in alarms per hour (FAR). This metric is clinically intuitive: a device that triggers 10 alarms per hour is clinically useless regardless of its sensitivity. Clinical targets are typically FAR $<1$ alarm/hour at sensitivity $>80\%$. Receiver Operating Characteristic (ROC) curves parameterised by FAR rather than FPR are sometimes called DETA (Detection Error Trade-off Analysis) curves in the seizure literature.

Event-based vs. window-based metrics.

A subtle but important distinction separates window-based from event-based evaluation. Window-based evaluation treats each time window as an independent sample; event-based evaluation assesses whether the classifier correctly detects each seizure event (onset to offset) with at most $d$ seconds of latency. A model can achieve high window-level sensitivity by firing on many windows within a single seizure, while still missing an entire seizure event at another time. International conference competitions (e.g., EPILEPSIAE, Kaggle) have moved toward event-based scoring, and generative augmentation papers should report both.

Seizure prediction-specific metrics.

Seizure prediction (forecasting a seizure before it occurs) introduces additional metric complexity. A prediction issued in the preictal window of width $\mathrm{\Delta }$ is counted as true positive; a prediction outside the preictal window is a false positive. The time in warning (TIW) metric measures the fraction of time spent in the alarm state, a measure of disruption to patient quality of life. An ideal predictor has high sensitivity, low FPR, and low TIW. The Poisson process benchmark provides a natural baseline: a random predictor that issues alarms at rate $\lambda$ achieves expected sensitivity $1-e^{-\lambda \mathrm{\Delta }}$ and TIW $=1-e^{-\lambda }$ per hour. Any learned predictor should beat this Poisson baseline to be considered non-trivial (Mormann et al., 2006).

Practical Considerations for Imbalanced EEG Pipelines

Stratified cross-validation.

Naive $k$-fold cross-validation over windows can allocate all minority windows to the same fold, creating folds with zero positive examples. Stratified $k$-fold cross-validation ensures that each fold contains approximately $n_{+}/k$ positive windows. For EEG, stratification should be applied at the seizure event level, not the window level, to avoid temporal leakage.

Normalisation and whitening.

Before training either the generative model or the downstream classifier, EEG windows must be normalised. Common choices are:

• Global z-score: subtract the mean and divide by the standard deviation computed over the training set.

• Per-channel z-score: normalise each channel independently to zero mean and unit variance over the training set. This removes amplitude differences between channels while preserving relative channel-to-channel power differences.

• Robust normalisation: subtract the median and divide by the interquartile range; robust to outliers caused by artefact windows.

Normalisation parameters (mean, standard deviation) must be computed on the training fold only and applied without re-fitting to the validation and test folds. Generative models must synthesise data in the normalised space; if the model operates in the raw amplitude space, the synthetic windows must be normalised before being added to the augmented training set.

Validation strategy for generative augmentation.

Evaluating generative augmentation requires a three-way split: (i) a training set on which both the generative model and the downstream classifier are trained; (ii) a validation set used for hyperparameter selection (augmentation ratio, generative model architecture); (iii) a test set reserved for final evaluation. A common mistake is to use the validation set performance to choose the augmentation ratio, then report test set performance as if it were unbiased. Proper practice requires that the test set is touched exactly once, after all hyperparameters have been frozen.

Section Summary

Class imbalance is the central data challenge of EEG-based epilepsy machine learning. The key facts established in this section are:

1. Seizure windows constitute 0.01–2% of total recording time in typical long-term EEG datasets, yielding imbalance ratios of 50:1 to 500:1.

2. Standard empirical risk minimisers converge to majority-class predictors when $\pi \ll 1$, because the minority class contributes fraction $\pi$ of the gradient in expectation.

3. Classical remedies (SMOTE, ADASYN, class weighting) address the symptom (imbalance) without addressing the root cause (too little information about the minority manifold).

4. Generative augmentation learns a probability distribution supported on the minority class manifold, producing diverse synthetic samples that respect the temporal, spectral, and spatial structure of real ictal EEG.

5. Evaluation must use imbalance-robust metrics (sensitivity, AUPRC, event-based detection rate at fixed FAR) and must never include synthetic samples in the test fold.

The remainder of this chapter develops the specific generative architectures (GANs in sec:epilepsy:gans, VAEs in VAEs and Hybrid Generative Models, diffusion models in sec:epilepsy:diffusion) and their application to seizure augmentation, cross-patient transfer, and seizure simulation.

GANs for EEG Synthesis

Electroencephalography records the brain's electrical symphony at millisecond resolution, capturing the rapid depolarisations that mark a seizure's onset, propagation, and cessation. Yet the scarcity of labelled ictal recordings remains the central bottleneck for data-driven epilepsy research: a single patient may seize fewer than a dozen times during a prolonged inpatient monitoring stay, and the recordings that do exist carry identifying biomarkers that preclude free sharing across institutions. Generative Adversarial Networks (GANs) offer a compelling solution to both problems simultaneously-they can synthesise arbitrarily large libraries of realistic seizure-like waveforms and, if properly designed, can replace real patient data with plausible surrogates that share statistical properties without sharing identifiable content.

The adversarial training framework pits a generator $G$ against a discriminator $D$ in a minimax game. For EEG synthesis the generator receives a noise vector $𝒛\sim p(𝒛)$ (often together with a conditioning signal $𝒄$) and produces a synthetic multichannel time-series $\widehat{𝒙}=G(𝒛,𝒄)$. The discriminator evaluates whether a presented waveform is real or synthetic. At the Nash equilibrium the generator's output distribution matches the true data distribution, a goal that is notoriously difficult to reach in practice but has been approached increasingly closely by a succession of architectural and training innovations described in the subsections below.

Conditional GAN for Seizure-Like EEG

The most direct approach to seizure synthesis conditions the generator on a patient's own interictal (seizure-free) EEG, asking the network to transform quiescent background activity into a plausible ictal episode. This interictal-conditioned paradigm was pioneered on the EPILEPSIAE database, one of the largest multi-centre scalp and intracranial EEG repositories, which provided a richly annotated pool of interictal and ictal recordings from over 270 patients.

Architecture.

The generator adopts a U-Net topology, originally devised for biomedical image segmentation, adapted here to one-dimensional multichannel signals. Let ${𝒙}_{\mathrm{ii}}\in {\mathrm{ℝ}}^{C\times T}$ denote an interictal EEG segment with $C$ channels and $T$ time samples. The encoder $E$ maps this input through a cascade of dilated convolutional blocks $\{h_1,h_2,\dots ,h_K\}$, where each $h_k$ halves the temporal resolution and doubles the feature depth: (Encoder)$$\begin{array}{ccc}& h_k=\mathrm{BN}\left(\mathrm{LeakyReLU}\left({\mathrm{Conv}}_{d=2^{k-1}}(h_{k-1})\right)\right),h_0={𝒙}_{\mathrm{ii}}.& \text{<span class="tml-eqn"></span>}\end{array}$$ The conditioning vector $𝒄$ (encoding seizure type, duration target, and frequency band) is injected at the bottleneck via adaptive instance normalisation (AdaIN). The decoder $D_G$ mirrors the encoder with transposed convolutions and U-Net skip connections that re-introduce fine-grained temporal structure from each encoder level: (Decoder)$$\begin{array}{ccc}& {\hat{h}}_k=\mathrm{BN}\left(\mathrm{ReLU}\left(\mathrm{TranspConv}([{\hat{h}}_{k+1};h_{K-k}])\right)\right),\widehat{𝒙}=\tanh (\mathrm{Conv}({\hat{h}}_1)).& \text{<span class="tml-eqn"></span>}\end{array}$$ The discriminator is a PatchGAN that classifies overlapping windows of the output as real or fake, encouraging high-frequency detail to be preserved across the full sequence.

Train-on-Synthetic Paradigm.

A downstream seizure detector is trained exclusively on synthetic data produced by the GAN and tested on real held-out recordings. This “train on synthetic, test on real” (TSTR) protocol evaluates whether the synthetic data captures clinically relevant features. Experiments on EPILEPSIAE demonstrated that a random forest detector trained on 10,000 synthetic ictal segments matched the performance of the same classifier trained on an equal-size sample of real data, achieving a sensitivity of $82.3\%$ at a false-positive rate of $0.15$ per hour-a result that would have required several patient-years of monitoring to obtain from real recordings alone.

DCGAN for Scalp EEG and Intracranial EEG

Deep Convolutional GANs (DCGANs) replace fully connected layers with strided convolutions throughout both generator and discriminator, imposing spatial stationarity that proves beneficial when generating long EEG segments where the same spectral patterns may recur at different time offsets. Applied to the Children's Hospital Boston–MIT (CHB-MIT) scalp EEG corpus-a widely used benchmark comprising $23$ paediatric patients recorded with $23$-channel 10-20 montages-DCGANs have demonstrated the ability to generate patient-specific ictal waveforms that preserve the channel covariance structure of real recordings.

Patient-Specific Generation.

Rather than pooling all patients' data into a single model (which tends to blur patient-specific morphology), the patient-specific approach trains a separate DCGAN for each individual. The generator $G_{\varphi }:{\mathrm{ℝ}}^{128}\to {\mathrm{ℝ}}^{23\times 1024}$ maps a latent vector to a four-second, $23$-channel segment at $256\mathrm{Hz}$ ($1024/256=4$ s). The discriminator $D_{\psi }:{\mathrm{ℝ}}^{23\times 1024}\to [\mathrm{0,1}]$ uses five strided-convolutional layers with spectral normalisation to stabilise training.

Transfer Learning with Pretrained CNNs.

A practical challenge is that per-patient datasets contain as few as $50$–$100$ ictal segments, insufficient to train a GAN from scratch without overfitting. Transfer learning addresses this by initialising the discriminator's feature extractor with weights from ImageNet-pretrained convolutional networks. EEG segments are first converted to time-frequency images (scalograms or Morlet wavelet spectrograms) so that 2D convolutional feature detectors can be re-used. Two architectures have been evaluated:

• VGG16. The final three fully connected layers are replaced with a single linear head. The convolutional body is frozen for the first $50$ epochs and then fine-tuned end-to-end. On CHB-MIT, VGG16-based transfer achieves a Fréchet Inception Distance (FID) of $18.4$ vs. $31.2$ for random initialisation.

• InceptionV3. Multi-scale feature extraction via the Inception modules captures both high-frequency spike morphology (fine scale) and slow wave envelopes (coarse scale) simultaneously. InceptionV3-based transfer yields FID $15.7$, the best result reported on CHB-MIT as of the studies surveyed here.

TripleGAN: Multi-Domain Synthesis across Time, Frequency, and Time-Frequency Representations

A single representation of EEG-whether in the raw time domain, the frequency domain, or a joint time-frequency plane-captures only a partial picture of seizure dynamics. High-frequency oscillations are best distinguished in the frequency domain; rhythmic propagation patterns across channels are clearest in the time domain; and the evolution of spectral content during seizure onset is most visible in the time-frequency plane. The TripleGAN architecture exploits this complementarity by training three coupled generators and three coupled discriminators, one for each representation domain.

Let ${𝒙}_t\in {\mathrm{ℝ}}^{C\times T}$, ${𝒙}_f\in {\mathrm{ℝ}}^{C\times F}$, and ${𝒙}_{tf}\in {\mathrm{ℝ}}^{C\times T^{\prime }\times F^{\prime }}$ denote the time-domain, frequency-domain, and time-frequency representations of a segment, respectively. The three generators $G_t,G_f,G_{tf}$ share a common latent vector $𝒛\sim \mathrm{Normal}(0,𝐈)$ and are trained with a combined adversarial loss plus a consistency regulariser that enforces alignment between domains: (Consistency)$$\begin{array}{ccc}& {ℒ}_{\mathrm{consist}}={\lambda }_1{\Vert ℱ(G_t(𝒛))-G_f(𝒛)\Vert }_1+{\lambda }_2{\Vert \mathrm{STFT}(G_t(𝒛))-G_{tf}(𝒛)\Vert }_F^2,& \text{<span class="tml-eqn"></span>}\end{array}$$ where $ℱ$ denotes the DFT magnitude spectrum and $\mathrm{STFT}$ the short-time Fourier transform. Regularisation weights ${\lambda }_1=0.1$ and ${\lambda }_2=0.05$ were set by grid search.

Evaluated on a five-patient temporal lobe epilepsy cohort using a downstream $k$-nearest-neighbour seizure classifier, the TripleGAN achieves a reported accuracy of $\mathrm{𝟗𝟗.𝟕}\%$-the highest classification accuracy in the literature at the time of that study. This striking result reflects the value of multi-domain training: each representation enforces different structural constraints on the latent space, collectively ruling out mode collapse along any single representational axis.

WGAN-GP: Stable Training and Semi-Supervised Learning

Vanilla GAN training is notoriously unstable: the discriminator's loss can saturate early, leaving the generator without a useful gradient signal. The Wasserstein GAN with Gradient Penalty (WGAN-GP) replaces the standard binary cross-entropy objective with the Wasserstein-1 distance between real and generated distributions, enforcing the Lipschitz constraint on the critic via a gradient penalty rather than weight clipping.

Semi-Supervised Training with Bi-LSTM.

A practical advantage of WGAN-GP in the epilepsy setting is its natural extension to semi-supervised classification. The critic's penultimate features can be shared with a seizure classifier head, trained jointly on both labelled ictal/interictal pairs and the much larger pool of unlabelled continuous EEG. A Bidirectional LSTM (Bi-LSTM) is appended to the shared feature extractor, capturing long-range temporal dependencies that convolutional layers miss: (Bilstm)$$\begin{array}{ccc}& {𝒉}_t=[\overrightarrow{\mathrm{LSTM}}({𝒉}_{t-1},{𝒙}_t);\overleftarrow{\mathrm{LSTM}}({𝒉}_{t+1},{𝒙}_t)].& \text{<span class="tml-eqn"></span>}\end{array}$$ The combined WGAN-GP with Bi-LSTM classifier achieves a balanced accuracy of $93.5\%$ on temporal lobe epilepsy seizure detection when $80\%$ of training labels are withheld-demonstrating that synthetic data can act as a regulariser that reduces the label requirement for clinical deployment.

TimeGAN for Temporal Lobe Epilepsy: SEEG Synthesis

Stereo-EEG (SEEG) records electrical activity from depth electrodes implanted directly within brain parenchyma, providing submillimetre spatial precision at the cost of invasive surgery. SEEG recordings from patients with drug-resistant temporal lobe epilepsy are particularly valuable for mapping the epileptogenic zone, but datasets are tiny-typically fewer than $20$ patients per centre. TimeGAN addresses this scarcity with a generator architecture built around LSTM modules that explicitly model the temporal autoregressive structure of intracranial time-series.

The TimeGAN framework decomposes the synthesis task into a static component (patient identity, electrode placement, seizure type) captured by a learned embedding, and a dynamic component (moment-to-moment state evolution) modelled by a supervised LSTM sequence generator. Formally, the generator consists of:

1. Embedding network $e$: maps a real sequence ${𝒙}_{1:T}$ to a latent code ${𝒉}_{1:T}$ in a low-dimensional temporal embedding space.

2. Recovery network $r$: reconstructs ${\widehat{𝒙}}_{1:T}=r({𝒉}_{1:T})$, trained with ${ℒ}_{\mathrm{recon}}=\Vert {𝒙}_{1:T}-{\widehat{𝒙}}_{1:T}{\Vert }_2^2$.

3. Sequence generator $g$: an LSTM that generates synthetic embeddings ${\widetilde{𝒉}}_{1:T}$ from noise ${𝒛}_{1:T}\sim \mathrm{Normal}{(0,𝐈)}^T$, supervised so that the conditional distribution $p({\tilde{h}}_t|{\tilde{h}}_{1:t-1})$ matches the real embedding distribution estimated by $e$.

4. Discriminator $d$: a bidirectional LSTM that distinguishes real from synthetic embeddings in the latent space.

Applied to SEEG recordings from $15$ patients with mesial temporal lobe epilepsy, TimeGAN produces synthetic ictal sequences whose maximum mean discrepancy (MMD) from real data is $0.023\pm 0.004$, compared to $0.048\pm 0.007$ for a standard DCGAN baseline-a $52\%$ reduction in distributional distance, reflecting the benefit of explicitly modelling temporal autocorrelation.

L-C-WGAN-GP for Compressed-Sensing EEG Reconstruction

Wearable EEG devices designed for ambulatory seizure monitoring must transmit data wirelessly under severe power constraints, motivating compressed sensing (CS) frameworks that acquire a small number of random linear measurements $𝒚=𝚽𝒙+𝐧$ from a high-dimensional signal $𝒙$, where $𝚽\in {\mathrm{ℝ}}^{M\times N}$ with $M\ll N$ is the measurement matrix and $𝐧$ is sensor noise. Classical CS recovery requires sparsity of $𝒙$ in some transform basis, an assumption that holds only approximately for EEG seizure activity. Generative models offer an alternative: use the generator $G$ as a structural prior, seeking $\widehat{𝒛}$ such that $G(\widehat{𝒛})\approx 𝒙$ with $𝚽G(\widehat{𝒛})\approx 𝒚$.

Architecture.

The L-C-WGAN-GP (Local-Conditional Wasserstein GAN with Gradient Penalty) extends WGAN-GP in two ways. First, the generator is conditioned on local context windows of the measurement vector $𝒚$, allowing reconstruction quality to adapt to spatially varying noise levels. Second, the critic includes a local patch discriminator that evaluates whether short overlapping windows of the reconstructed signal are consistent with real EEG morphology, complementing the global Wasserstein critic. The combined objective is: (Objective)$$\begin{array}{ccc}& ℒ={ℒ}_{\mathrm{W}\mathrm{G}\mathrm{A}\mathrm{N}\text{-}\mathrm{G}\mathrm{P}}+\alpha {ℒ}_{\mathrm{local}}+\beta {\Vert 𝒚-𝚽G(𝒛,{𝒚}_{\mathrm{local}})\Vert }_2^2,& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\alpha =0.5$ and $\beta =10$ balance the local critic and the measurement consistency term, respectively.

At a compression ratio $M/N=0.25$ (transmitting $25\%$ of the original samples), L-C-WGAN-GP achieves a signal-to-noise ratio of $19.8\mathrm{dB}$ and a normalised mean squared error of $0.031$, compared to $14.2\mathrm{dB}$ and $0.078$ for LASSO recovery-a substantial improvement driven by the GAN's ability to hallucinate clinically plausible high-frequency content from limited measurements.

TikZ Architecture: Conditional GAN for EEG Generation

Comparative Summary of GAN Variants

Table 5 summarises the principal GAN architectures discussed in this section, their training datasets, loss formulations, and reported downstream classification accuracy.

Model	Dataset	Loss / Key Feature	Metric	Value
Conditional GAN (U-Net)	EPILEPSIAE	Adversarial + $L_1$ recon.	Sensitivity	$82.3\%$
DCGAN + VGG16	CHB-MIT	Standard GAN, transfer	FID	$18.4$
DCGAN + InceptionV3	CHB-MIT	Standard GAN, transfer	FID	$15.7$
TripleGAN	TLE cohort ($n=5$)	Multi-domain consistency	Acc. (kNN)	$99.7\%$
WGAN-GP + Bi-LSTM	TLE cohort	Wasserstein + semi-sup.	Balanced Acc.	$93.5\%$
TimeGAN	SEEG ($n=15$)	Supervised LSTM gen.	MMD	$0.023$
L-C-WGAN-GP	Wearable EEG (CS)	Local critic + meas. cons.	SNR (dB)	$19.8$

VAEs and Hybrid Generative Models

Generative Adversarial Networks excel at perceptual sharpness-their adversarial training pushes generated samples to the edge of the real-data manifold. Yet this very sharpness comes at a cost: the latent space has no guaranteed structure, interpolation between latent codes produces unpredictable outputs, and there is no principled mechanism to obtain a posterior over latent variables given an observed signal. Variational Autoencoders (VAEs) occupy the complementary niche. By framing generation as inference in a latent variable model, VAEs provide a smooth, interpretable latent space, closed-form estimates of the posterior distribution, and a tractable optimisation objective-the Evidence Lower Bound (ELBO)-that does not require adversarial training.

VAE Fundamentals for EEG: Latent Space Smoothness and the ELBO

Let $𝒙\in {\mathrm{ℝ}}^{C\times T}$ denote an EEG segment and $𝒛\in {\mathrm{ℝ}}^d$ a low-dimensional latent code. The VAE posits a generative model $p_{\theta }(𝒙|𝒛)p(𝒛)$ and an approximate posterior $q_{\varphi }(𝒛|𝒙)$. For EEG, the prior is typically $p(𝒛)=\mathrm{Normal}(0,𝐈)$ and the approximate posterior is a factored Gaussian: (Posterior)$$\begin{array}{ccc}& q_{\varphi }(𝒛|𝒙)=\mathrm{Normal}({𝝁}_{\varphi }(𝒙),\mathrm{diag}({𝝈}_{\varphi }^2(𝒙))),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝝁}_{\varphi }$ and ${𝝈}_{\varphi }$ are outputs of the encoder network. Training maximises the ELBO: (ELBO)$$\begin{array}{ccc}& {ℒ}_{\mathrm{ELBO}}(\theta ,\varphi ;𝒙)=\underset{\text{reconstruction term}}{\underbrace{{𝔼}_{q_{\varphi }(𝒛|𝒙)}\left[\log p_{\theta }(𝒙|𝒛)\right]}}-\underset{\text{regularisation term}}{\underbrace{D_{\mathrm{KL}}\left(q_{\varphi }(𝒛|𝒙)\Vert p(𝒛)\right)}}.& \text{<span class="tml-eqn"></span>}\end{array}$$ The reconstruction term encourages the decoder to faithfully reproduce the input EEG segment. For continuous EEG, this is typically implemented as a mean squared error under a diagonal Gaussian decoder: $-\log p_{\theta }(𝒙|𝒛)=\frac{1}{2{\sigma }_r^2}\Vert 𝒙-{𝝁}_{\theta }(𝒛){\Vert }_2^2+\mathrm{const}$. The KL divergence regularises the posterior toward the prior, inducing the latent space smoothness that makes interpolation between seizure types meaningful: nearby points in $𝒛$-space correspond to EEG segments with similar morphology.

Conditional VAE for Motor Imagery EEG and Interictal Epileptiform Discharges

The Conditional VAE (CVAE) augments the standard VAE with a label $y$ (or a richer condition vector $𝒄$) that is injected into both encoder and decoder, enabling class-conditional generation without the need for separate models per class.

For the motor imagery task-distinguishing imagined left-hand from right-hand movements from scalp EEG, a benchmark for brain-computer interfaces-the CVAE synthesises class-balanced training sets for subjects with few labelled trials. The condition $y\in \{0,1\}$ (left vs. right) is appended as a one-hot vector to both $𝒙$ at the encoder input and to $𝒛$ at the decoder input. The conditional ELBO is: (ELBO)$$\begin{array}{ccc}& {ℒ}_{\mathrm{CVAE}}={𝔼}_{q_{\varphi }(𝒛|𝒙,y)}\left[\log p_{\theta }(𝒙|𝒛,y)\right]-D_{\mathrm{KL}}\left(q_{\varphi }(𝒛|𝒙,y)\Vert p(𝒛|y)\right).& \text{<span class="tml-eqn"></span>}\end{array}$$ A study on the BCI Competition IV Dataset 2a (nine subjects, four motor imagery classes) found that a CVAE trained on $70\%$ of trials and used to synthesise a $3\times$ data augmentation increased the mean subject accuracy of a CSP-LDA baseline from $68.2\%$ to $74.9\%$-a $6.7$ percentage-point improvement without any change to the classifier.

For interictal epileptiform discharges (IEDs)-the sharp waves and spike-and-slow-wave complexes that mark inter-seizure epileptic activity-a CVAE conditioned on IED subtype (generalised vs. focal vs. multifocal) generates synthetic IED events that are visually indistinguishable from real events in blind review by board-certified neurologists. Synthetic IEDs are used to up-sample the minority class in automated IED detectors, reducing the false-negative rate by $18\%$ on held-out evaluation data.

VAE-cGAN: Scalp-to-iEEG Translation for IED Detection

Intracranial EEG (iEEG) offers far superior spatial resolution and signal-to-noise ratio compared to scalp EEG, but requires invasive surgery that is only performed when patients are candidates for resective surgery. For the much larger population with non-surgical epilepsy, only scalp EEG is available. The VAE-cGAN bridges this gap by learning a translation function from scalp EEG to a synthetic iEEG representation that preserves clinically relevant features of interictal epileptiform discharges.

Architecture.

The VAE-cGAN hybridises a Conditional VAE (providing a structured latent space and stable training) with a conditional GAN (providing perceptual sharpness in the generated iEEG). The system comprises four networks:

1. Scalp encoder $E_s$: maps scalp EEG ${𝒙}_s\in {\mathrm{ℝ}}^{C_s\times T}$ to a posterior $q(𝒛|{𝒙}_s)=\mathrm{Normal}({𝝁}_s,{𝝈}_s^2)$.

2. iEEG decoder $D_i$: decodes $𝒛$ to synthetic iEEG ${\widehat{𝒙}}_i\in {\mathrm{ℝ}}^{C_i\times T}$.

3. iEEG discriminator $D_{\mathrm{adv}}$: a PatchGAN critic that distinguishes real from synthetic iEEG waveforms.

4. IED classifier $C_{\mathrm{IED}}$: a shared-head classifier trained on synthetic iEEG to detect IED events.

The total training objective is: (Objective)$$\begin{array}{ccc}& {ℒ}_{\mathrm{V}\mathrm{A}\mathrm{E}\text{-}\mathrm{c}\mathrm{G}\mathrm{A}\mathrm{N}}={ℒ}_{\mathrm{ELBO}}+{\lambda }_{\mathrm{adv}}{ℒ}_{\mathrm{GAN}}+{\lambda }_{\mathrm{IED}}{ℒ}_{\mathrm{CE}},& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${ℒ}_{\mathrm{CE}}$ is a binary cross-entropy loss on the IED classifier and the weights ${\lambda }_{\mathrm{adv}}=1.0$, ${\lambda }_{\mathrm{IED}}=5.0$ are set by validation.

Results.

Evaluated on a cohort of $34$ patients who had concurrent scalp and intracranial recordings during long-term monitoring, the VAE-cGAN achieves an IED detection accuracy of $\mathrm{𝟕𝟔}\%$ on held-out scalp EEG-an improvement of $\mathrm{𝟏𝟏}$ percentage points over the best purely scalp-based baseline. Qualitative analysis shows that the synthetic iEEG captures the focal spike morphology characteristic of the patients' epileptogenic zones, suggesting that the cross-modal translation has learned a meaningful anatomical mapping.

RCVAE with Bi-LSTM: High-Accuracy Seizure Prediction on CHB-MIT

The Recurrent Conditional VAE (RCVAE) replaces the feedforward encoder and decoder of a standard CVAE with bidirectional LSTM networks, making the latent representation explicitly temporal and enabling the model to capture the slow build-up of pre-ictal changes that precede seizure onset by minutes to hours.

The encoder LSTM reads the EEG sequence ${𝒙}_{1:T}$ and produces a context-aware posterior: (Encoder)$$\begin{array}{ccc}& ({𝝁}_t,{𝝈}_t)={\mathrm{BiLSTM}}_{\varphi }({𝒙}_{1:T}),{𝒛}_t={𝝁}_t+{𝝈}_t\odot {𝝐}_t,{𝝐}_t\sim \mathrm{Normal}(0,𝐈),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\odot$ denotes element-wise multiplication (the reparameterisation trick). The decoder LSTM generates a synthetic continuation ${\widehat{𝒙}}_{T+1:T+H}$ over a prediction horizon $H$, conditioned on the latent trajectory ${𝒛}_{1:T}$ and the class label $y$ (seizure vs. non-seizure): (Decoder)$$\begin{array}{ccc}& {\widehat{𝒙}}_{t+1}={\mathrm{LSTM}}_{\theta }({\widehat{𝒙}}_t,{𝒛}_t,y).& \text{<span class="tml-eqn"></span>}\end{array}$$

On the CHB-MIT dataset evaluated in the pre-ictal vs. inter-ictal discrimination task (30-minute pre-ictal window, leave-one-seizure-out cross-validation), the RCVAE with Bi-LSTM achieves:

• Accuracy: $\mathrm{𝟗𝟓.𝟗𝟒}\%$

• AUC: $\mathrm{𝟗𝟔}\%$

• Sensitivity: $94.8\%$

• Specificity: $97.1\%$

These results represent the state-of-the-art on CHB-MIT for the specific evaluation protocol used, surpassing both convolutional and attention-based competitors. Ablation studies confirm that both the recurrent encoder (+$4.3\%$ accuracy over feedforward CVAE) and the bidirectional reading of context (+$2.1\%$ over unidirectional LSTM) contribute meaningfully to the final performance.

Privacy Preservation through Synthetic EEG

EEG carries identifiable biomarkers. Individual differences in skull thickness, electrode placement, and cortical folding pattern produce subject-specific spectral signatures that are robust enough to identify individuals with $\sim 97\%$ accuracy from a few seconds of resting-state EEG, even months after the original recording. This biometric identifiability creates a profound obstacle to data sharing: a hospital cannot release a patient's EEG recordings without risking re-identification, even if demographic fields are stripped.

Identifiable Biomarkers in EEG.

The principal identifiable features include:

• Alpha peak frequency (APF): the dominant frequency of the occipital alpha rhythm ($8$–$13\mathrm{Hz}$), which varies between $\sim 8.5$ and $\sim 12.5\mathrm{Hz}$ across individuals and is stable within an individual across months.

• Channel-pair coherence fingerprint: the matrix of pairwise coherence values across all electrode pairs at rest constitutes a structural connectivity signature that reflects individual anatomy.

• Mu rhythm lateralisation: the relative amplitude of left vs. right sensorimotor mu rhythm ($8$–$12\mathrm{Hz}$) reflects handedness and motor cortex asymmetry.

• Slow-wave slope during sleep: the travelling slope of sleep slow waves across the scalp encodes individual differences in cortical thickness.

How VAE-Generated EEG Eliminates Identifiable Biomarkers.

The key observation is that a VAE's prior $p(𝒛)=\mathrm{Normal}(0,𝐈)$ is exchangeable: it has no subject identity embedded in it. When the decoder maps a sample from this prior to synthetic EEG, the output reflects the statistical patterns learned from the training population but not the specific anatomical configuration of any single patient. In particular:

1. APF scrambling. The decoded signal's alpha peak frequency reflects the prior distribution over APFs, not the individual's true APF. A study using a CVAE trained on $120$ subjects found that synthetic EEG reduced subject identification accuracy from $97.2\%$ to $51.4\%$-near chance level-while retaining seizure classification accuracy within $2\%$ of the real-data baseline.

2. Coherence anonymisation. The channel-pair coherence fingerprint of synthetic EEG sampled from the prior is drawn from the population-level coherence distribution, not from any individual's fingerprint. Identification attacks based on coherence matching drop below $55\%$ on synthetic data.

3. Clinical utility preservation. A seizure detector trained on synthetic EEG and tested on real EEG achieves $F_1=0.81$, compared to $F_1=0.84$ for the real-data trained baseline-a gap small enough for practical data-sharing purposes.

TikZ Architecture: VAE-cGAN for Cross-Modal EEG Translation

Summary and Outlook

The VAE family-including CVAE, $\beta$-VAE, RCVAE, and the hybrid VAE-cGAN-brings three capabilities that are particularly valuable in the epilepsy domain. First, the structured latent space enables semantically meaningful interpolation: moving along a latent trajectory from an interictal to an ictal code produces a plausible sequence of transitional waveforms, reflecting the pre-ictal build-up that is a key target for seizure prediction. Second, the probabilistic encoder provides uncertainty estimates: the width of the posterior ${\sigma }_{\varphi }(𝒙)$ is a natural measure of how atypical a given EEG segment is, offering an anomaly detection signal without any additional classifier training. Third, and most importantly for clinical deployment, the population-level prior strips identifying biomarkers, enabling synthetic data sharing in a regulatory environment that increasingly restricts the circulation of real patient recordings.

The horizon beyond these models includes diffusion-based EEG synthesis (discussed in later sections), which combines the generative quality of GANs with the theoretical tractability of VAEs, and foundation model approaches in which a single large transformer is pretrained on multi-institutional EEG corpora and fine-tuned for specific tasks. The unifying thread is the replacement of scarce, privacy-sensitive real data with algorithmically generated surrogates that preserve the statistical structure needed for clinical utility while discarding the identifiable content that prevents sharing.

Diffusion Models for EEG Synthesis and Seizure Detection

Generative adversarial networks dominated EEG augmentation for several years, but they brought with them the chronic instabilities that have plagued adversarial training since its inception: mode collapse, training divergence, and the need for careful hyperparameter shepherding. Diffusion models offer a principled alternative. By replacing the adversarial game with a progressive denoising process grounded in stochastic differential equations, they provide stable training dynamics, superior sample diversity, and the ability to incorporate conditioning signals through well-understood mathematical mechanisms. In the context of epilepsy research, where training datasets are small, class imbalances are severe, and inter-subject variability is enormous, these properties translate directly into measurable clinical value.

This section develops the theoretical foundations and concrete architectures of diffusion-based EEG synthesis. We begin with the Diff-EEG framework, which chains continuous wavelet transforms, vector-quantised variational autoencoders, and guided latent diffusion into a system capable of generating subject-specific preictal recordings (Diff-EEG: Guided Latent Diffusion on Spectral Representations). We then examine EEG-DIF, which reframes seizure forecasting as a masked image inpainting problem and leverages denoising diffusion implicit models for early warning (EEG-DIF: Diffusion Forecasting as Image Inpainting). GenEEG extends the paradigm to continual learning, enabling patient-adaptive synthesis without catastrophic forgetting (GenEEG: Patient-Adaptive Latent Diffusion with Continual Learning). Finally, we explore unsupervised anomaly detection through the lens of reconstruction error under a jointly trained DDPM and VQ-VAE (Unsupervised Anomaly Detection via DDPM and VQ-VAE).

Diff-EEG: Guided Latent Diffusion on Spectral Representations

Raw EEG signals are nonstationary: their statistical properties change over time as the brain transitions between vigilance states, responds to stimuli, and, in the case of epilepsy patients, undergoes the cascade of electrophysiological changes that culminates in a seizure. Applying a diffusion model directly to the time-domain signal forces the denoiser to learn these complex nonstationarities from scratch. The Diff-EEG architecture (Ye et al., 2024) sidesteps this difficulty by first converting raw EEG into a two-dimensional time-frequency representation via the continuous wavelet transform, then compressing this representation into a discrete latent space via a vector-quantised variational autoencoder, and finally running guided diffusion entirely within the compact latent space.

Stage 1: Time-Frequency Representation via CWT

For a multichannel EEG recording $𝒙(t)\in {ℝ}^C$, the continuous wavelet transform with respect to a mother wavelet $\psi$ produces a scalogram $𝐖\in {ℝ}^{C\times S\times T}$ where $S$ denotes the number of frequency scales and $T$ the number of time steps. Formally, at channel $c$, scale $s$, and time $\tau$: (CWT)$$\begin{array}{ccc}& W_c(s,\tau )={\int }_{-\infty }^{\infty }{x}_c(t)\frac{1}{\sqrt{s}}\overline{\psi \left(\frac{t-\tau }{s}\right)}\mathrm{d}t.& \text{<span class="tml-eqn"></span>}\end{array}$$ The Morlet wavelet is the canonical choice for EEG analysis because it provides a near-Gaussian envelope in both time and frequency, yielding a scalogram whose ridges correspond intuitively to oscillatory bursts at well-defined instantaneous frequencies.

The scalogram transforms the one-dimensional signal processing problem into a two-dimensional image processing problem. Each channel's time-frequency slice resembles a greyscale image, and the full multichannel scalogram $𝐖$ can be treated as a multi-channel image amenable to convolutional processing. This representation captures the broadband synchrony that characterises preictal and ictal EEG far more faithfully than either the raw time series or a simple short-time Fourier transform, because wavelets adapt their time-frequency resolution to the local oscillatory content through the scale parameter.

Stage 2: VQ-VAE Compression

A vector-quantised variational autoencoder (VQ-VAE) encodes the scalogram $𝐖$ into a discrete latent code $𝐙\in {\{1,\dots ,K\}}^{H\times W}$, where $H\times W\ll S\times T$ is the spatial resolution of the latent grid and $K$ is the codebook size. The encoder $E_{\varphi }$ maps $𝐖$ to a continuous representation $\widehat{𝐙}=E_{\varphi }(𝐖)\in {ℝ}^{H\times W\times d}$, which is then quantised entry-wise to the nearest codebook vector: (Quantize)$$\begin{array}{ccc}& {𝐙}_{ij}={\mathrm{arg\hspace{0.17em}min}}_{k\in \{1,\dots ,K\}}\Vert {\hat{Z}}_{ij}-{𝒆}_k{\Vert }_2,& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${\{{𝒆}_k\}}_{k=1}^K\subset {ℝ}^d$ is the learned codebook. The decoder $D_{\psi }$ reconstructs the scalogram from ${𝐙}_q={({𝒆}_{{𝐙}_{ij}})}_{ij}$, and the VQ-VAE is trained with the commitment loss: (LOSS)$$\begin{array}{ccc}& {ℒ}_{\text{VQ}}=\Vert 𝐖-D_{\psi }({𝐙}_q){\Vert }_2^2+\Vert \mathrm{sg}[\widehat{𝐙}]-{𝐙}_q{\Vert }_2^2+\beta \Vert \widehat{𝐙}-\mathrm{sg}[{𝐙}_q]{\Vert }_2^2,& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\mathrm{sg}[\cdot ]$ denotes the stop-gradient operator and $\beta >0$ is the commitment coefficient. The discrete latent code $𝐙$ captures the essential structure of the EEG spectrogram in a representation that is orders of magnitude smaller than the original scalogram, enabling efficient diffusion in the latent space.

Stage 3: Variance-Preserving SDE Diffusion

The reverse process recovers data from noise by integrating the reverse SDE, which requires the score function ${\nabla }_{{𝐳}_t}\log p_t({𝐳}_t)$. A neural network ${𝒔}_{\theta }({𝐳}_t,t,𝒄)$ is trained to approximate this score conditioned on a context vector $𝒄$: (Score LOSS)$$\begin{array}{ccc}& {ℒ}_{\text{score}}={𝔼}_{t,{𝐳}_0,{𝐳}_t}[\lambda (t)\Vert {𝒔}_{\theta }({𝐳}_t,t,𝒄)-{\nabla }_{{𝐳}_t}\log p_t({𝐳}_t|{𝐳}_0){\Vert }_2^2],& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\lambda (t)$ is an importance weighting and ${\nabla }_{{𝐳}_t}\log p_t({𝐳}_t|{𝐳}_0)=-({𝐳}_t-{\mu }_t{𝐳}_0)/{\sigma }_t^2$.

Classifier-Free Guidance and Conditioning

In Diff-EEG, the conditioning vector $𝒄$ is a concatenation of three embeddings: a subject embedding ${𝒆}_{\text{sub}}\in {ℝ}^{d_s}$ that encodes the patient's identity and baseline EEG characteristics, a session embedding ${𝒆}_{\text{sess}}\in {ℝ}^{d_{se}}$ that encodes recording conditions (electrode placement, amplifier settings, date), and a class embedding ${𝒆}_{\text{cls}}\in {ℝ}^{d_c}$ that indicates whether the target segment is preictal, interictal, or ictal. This triple conditioning structure enables the model to generate not merely realistic EEG, but realistic EEG that belongs to a specific subject, recorded under specific conditions, and representing a specific brain state.

The Diff-EEG model was trained for 900,000 gradient steps on a cluster of EEG datasets anchored by CHB-MIT, using the AdamW optimiser with cosine annealing. The U-Net backbone of the score network uses cross-attention layers to inject the conditioning vector, following the architecture of Rombach et al.'s Latent Diffusion Model but adapted to the two-dimensional latent representation of EEG scalograms. Training stability was substantially better than the GAN baselines: no mode collapse episodes occurred, and the validation loss decreased monotonically after an initial burn-in period.

Results on CHB-MIT

The primary evaluation used the CHB-MIT scalp EEG dataset, which contains 686 hours of recordings from 24 paediatric patients with intractable epilepsy. The class imbalance is severe: preictal segments (the 30 minutes preceding each seizure) constitute only 2–5% of the total recording time per patient. A classifier trained without augmentation achieves sensitivity of 70.68% and specificity of 92.30% on a held-out test partition. Augmenting the preictal training class with Diff-EEG synthetic samples (matching the interical sample count) raises sensitivity to 74.08% and specificity to 95.89%.

Condition	Sensitivity (%)	Specificity (%)
Baseline (no augmentation)	70.68	92.30
Diff-EEG augmentation	74.08	95.89
Improvement	+3.40	+3.59

The simultaneous improvement in both sensitivity and specificity is noteworthy. In binary classification, sensitivity and specificity are ordinarily in tension: a classifier that predicts “seizure” more aggressively gains sensitivity at the cost of specificity. The fact that Diff-EEG augmentation improves both metrics indicates that the synthetic samples help the classifier learn a more accurate decision boundary rather than merely shifting it. The synthetic preictal signals capture the spectral precursors of seizure onset, populated from the true conditional distribution, rather than interpolating between observed examples in a manner that blurs class boundaries.

EEG-DIF: Diffusion Forecasting as Image Inpainting

Early seizure warning is clinically distinct from seizure detection: rather than identifying that a seizure is occurring right now, the goal is to predict that one will occur within the next few minutes, giving patients and caregivers time to respond. This temporal forecasting task has a natural reformulation in the language of image inpainting. Consider a spectrogram computed over a sliding window of EEG: the observed portion is the “context” that has already been revealed, and the future spectrogram is the “masked region” to be imputed. A diffusion model trained to inpaint masked spectrograms thus becomes, ipso facto, a forecaster of future EEG activity.

The EEG-DIF framework (Chen et al., 2024) formalises this insight. EEG segments are converted to Mel-scaled spectrograms, which are then partitioned into a revealed context region (the current epoch) and a masked future region (the prediction horizon, typically 30–60 seconds ahead). The diffusion model is trained with a binary mask $𝐌\in {\{0,1\}}^{H\times W}$ that specifies which spectrogram pixels are observed. The inpainting objective conditions the reverse diffusion on the revealed context:

(Inpaint)$$\begin{array}{ccc}& p({𝐒}_{\text{future}}|{𝐒}_{\text{context}})\approx \int p_{\theta }({𝐒}_{\text{future}},{𝐳}_T,\dots ,{𝐳}_1|{𝐒}_{\text{context}})\mathrm{d}{𝐳}_{1:T},& \text{<span class="tml-eqn"></span>}\end{array}$$

where ${𝐒}_{\text{context}}=(1-𝐌)\odot 𝐒$ are the observed spectrogram pixels and ${𝐒}_{\text{future}}=𝐌\odot 𝐒$ is the masked region. During the reverse pass, the known pixels are resampled at each diffusion step to enforce consistency with the observed context, following the repaint strategy of Lugmayr et al.

DDIM Acceleration

Denoising Diffusion Implicit Models (DDIM; Song et al., 2021) accelerate generation by replacing the stochastic reverse transitions with a deterministic update rule. Given a trained noise predictor ${𝝐}_{\theta }({𝐳}_t,t)$, the DDIM update from step $t$ to step $t-\mathrm{\Delta }t$ is:

(DDIM)$$\begin{array}{ccc}& {𝐳}_{t-\mathrm{\Delta }t}=\sqrt{{\bar{\alpha }}_{t-\mathrm{\Delta }t}}\underset{\text{predicted }{𝐳}_0}{\underbrace{\left(\frac{{𝐳}_t-\sqrt{1-{\bar{\alpha }}_t}{𝝐}_{\theta }({𝐳}_t,t)}{\sqrt{{\bar{\alpha }}_t}}\right)}}+\sqrt{1-{\bar{\alpha }}_{t-\mathrm{\Delta }t}}{𝝐}_{\theta }({𝐳}_t,t),& \text{<span class="tml-eqn"></span>}\end{array}$$

where ${\bar{\alpha }}_t={\prod }_{s=1}^t(1-{\beta }_s)$ is the cumulative noise schedule. Because the update is deterministic, DDIM can skip timesteps: using only 50 steps instead of 1000 yields generation times 20$\times$ faster with negligible quality degradation. In the clinical setting of early seizure warning, where the forecasting system must produce a risk score within a few seconds, this acceleration is not merely convenient but necessary.

The U-Net backbone processes the spectrogram conditioned on a learnable embedding of the mask $𝐌$, so the network is always aware of which regions are observed and which must be imputed. Training used the Siena Scalp EEG dataset (University of Siena), which provides recordings from 14 adult patients with focal epilepsy annotated with seizure onsets. After 200 epochs of training on 30-second spectrogram windows, EEG-DIF achieved an early warning accuracy of 0.89 on the held-out test patients, outperforming both a GRU-based forecasting baseline (0.81) and a standard GAN-augmented classifier (0.84) at the same prediction horizon.

GenEEG: Patient-Adaptive Latent Diffusion with Continual Learning

A fundamental tension in personalised EEG synthesis is that continually adapting a model to new patient data risks overwriting the general knowledge acquired from the broader training population. This is the catastrophic forgetting problem (McCloskey and Cohen, 1989), and it is acutely relevant in the epilepsy domain, where each new patient provides only a handful of seizures but the population distribution is diverse enough that discarding population knowledge would severely hurt individual patient performance.

GenEEG (Liu et al., 2024) addresses this tension through a two-pronged continual learning strategy: elastic weight consolidation (EWC) to penalise changes to parameters that are important for the population model, and experience replay to preserve a small buffer of previously seen exemplars.

Dual Conditioning Architecture

The GenEEG latent diffusion model employs dual conditioning: a population-level stream ${𝒄}_{\text{pop}}$ that encodes the seizure type and EEG montage, and a patient-level stream ${𝒄}_{\text{pat}}$ that encodes the individual patient's morphological signature derived from interictal recordings. At inference, both streams are merged via a cross-attention mechanism:

(DUAL ATTN)$$\begin{array}{ccc}& \mathrm{Attn}(𝐐,𝐊,𝐕)=\mathrm{softmax}\left(\frac{𝐐{𝐊}^{\top }}{\sqrt{d_k}}\right)𝐕,& \text{<span class="tml-eqn"></span>}\end{array}$$

where $𝐐$ is derived from the noisy latent ${𝐳}_t$, $𝐊$ and $𝐕$ are projected from the concatenation $[{𝒄}_{\text{pop}};{𝒄}_{\text{pat}}]$. The dual conditioning allows the model to generate EEG that is simultaneously representative of the patient's population stratum (focal vs. generalised, paediatric vs. adult) and faithful to the individual's specific morphology.

Elastic Weight Consolidation for Diffusion Models

Elastic weight consolidation (EWC; Kirkpatrick et al., 2017) adds a regularisation term to the diffusion training objective that penalises large changes to parameters deemed important for the population model:

(EWC)$$\begin{array}{ccc}& {ℒ}_{\text{GenEEG}}={ℒ}_{\text{diff}}(\theta )+\frac{{\lambda }_{\text{EWC}}}{2}\sum _j{F}_j{({\theta }_j-{\theta }_j^{\ast })}^2,& \text{<span class="tml-eqn"></span>}\end{array}$$

where ${\theta }_j^{\ast }$ are the population model parameters, $F_j$ is the diagonal Fisher information at parameter $j$ (estimated on the population training data), and ${\lambda }_{\text{EWC}}$ controls the rigidity of the consolidation. Parameters with high Fisher information are those whose perturbation most changes the population model's predictions; protecting them preserves the general EEG knowledge while allowing personalisation through the less critical parameters.

In addition to EWC, GenEEG maintains a replay buffer of 200 spectrogram patches drawn from the population training data. At each patient-adaptation step, a minibatch mixes patient-specific segments (70%) with replay exemplars (30%). This combination of constraint-based forgetting prevention (EWC) and rehearsal-based forgetting prevention (replay) is complementary: EWC is most effective for parameters that change continuously, while replay prevents the model from ignoring the structural diversity of the population.

On a five-patient personalisation experiment using the EPILEPSIAE database, GenEEG achieved a macro-F1 score of approximately 0.84 across three classes (interictal, preictal, ictal), compared with 0.76 for a population model without personalisation and 0.79 for a fine-tuned model without continual learning constraints (which suffered measurable forgetting when evaluated on held-out patients from the population). The replay buffer was especially important for maintaining interictal generation quality, which would otherwise drift toward the patient's specific interictal patterns at the expense of population coverage.

Unsupervised Anomaly Detection via DDPM and VQ-VAE

All of the methods discussed so far have required labelled seizure annotations for training. But annotation is expensive, inconsistent across annotators, and impossible to obtain retrospectively for large archival EEG databases. Unsupervised anomaly detection offers an alternative: train a generative model on unlabelled EEG, then flag as anomalous any segment whose reconstruction is poor under the fitted model. The implicit assumption is that the model, trained predominantly on normal interictal EEG, will reconstruct normal segments well but will fail to reconstruct ictal activity, which falls outside the learned distribution.

A natural implementation couples DDPM with a VQ-VAE. The VQ-VAE provides a compact discrete latent space in which interictal EEG occupies a coherent submanifold. The DDPM is then trained in this latent space on the same unlabelled recordings. At test time, a segment $𝒙$ is encoded to latent $𝐙=E_{\varphi }(𝐖(𝒙))$, partially noised to level $\bar{t}$, and reconstructed via the reverse diffusion. The reconstruction error:

(Score)$$\begin{array}{ccc}& 𝒜(𝒙)=\Vert 𝐙-{\widehat{𝐙}}_{\bar{t}}{\Vert }_2^2,& \text{<span class="tml-eqn"></span>}\end{array}$$

serves as the anomaly score, where ${\widehat{𝐙}}_{\bar{t}}$ is the latent reconstructed after denoising from noise level $\bar{t}$. The noise level $\bar{t}$ controls the granularity of the reconstruction: small $\bar{t}$ detects fine-scale anomalies (e.g., high-frequency ripples), while large $\bar{t}$ detects structural anomalies (e.g., spike-wave morphology). In practice, $\bar{t}$ is selected by maximising the receiver operating characteristic area on a small held-out labelled validation set.

Applied to CHB-MIT with only interictal segments used for training, this approach achieves an area under the ROC curve of 0.81 for ictal detection, a competitive result given that no seizure labels are required. The VQ-VAE latent space acts as a bottleneck that discards patient-specific idiosyncrasies while preserving the spectral features that differentiate normal from abnormal activity.

Diffusion Models for Neuroimaging and Lesion Localization

Structural MRI plays an indispensable role in presurgical epilepsy evaluation. For patients with drug-resistant focal epilepsy, surgical resection of the epileptogenic zone can achieve seizure freedom in 60–80% of cases, but only if the zone can be precisely delineated preoperatively. Focal cortical dysplasia (FCD), the most common surgically amenable substrate in paediatric epilepsy, is notoriously difficult to localise: the dysplastic cortex is often only subtly thickened or blurred relative to the surrounding normal tissue, and even experienced neuroradiologists report false-negative rates exceeding 30% on conventional MRI reads.

Diffusion models offer a fundamentally new approach to this localisation problem. Rather than training a discriminative classifier to recognise FCD from labelled examples, which are scarce, inconsistent across centres, and often incomplete, diffusion models can be trained on the much more abundant resource of healthy brain MRI to learn a probabilistic generative model of normal cortical anatomy. Pathology is then defined operationally as divergence from this generative prior: regions where the patient's scan deviates from what the healthy-trained model would reconstruct are candidate lesions. This section develops this “normative diffusion” paradigm in depth.

Pseudo-Healthy Synthesis for FCD Localisation

The pseudo-healthy synthesis pipeline (Baur et al., 2021; extended to FCD by Pinaya et al., 2023) consists of three conceptually simple steps: forward-diffuse the patient scan to an intermediate noise level, reverse-diffuse back to the image domain using the healthy prior, and compute the voxelwise residual between the input and the reconstruction. Each step has important subtleties that determine the quality of the localisation.

Forward Diffusion as Noise Injection

Given a patient MRI volume ${𝒙}_0\in {ℝ}^{H\times W\times D}$, the forward process adds noise to a chosen timestep $t^{\ast }$: (Forward)$$\begin{array}{ccc}& {𝒙}_{t^{\ast }}=\sqrt{{\bar{\alpha }}_{t^{\ast }}}{𝒙}_0+\sqrt{1-{\bar{\alpha }}_{t^{\ast }}}𝝐,𝝐\sim \mathrm{Normal}(0,𝐈).& \text{<span class="tml-eqn"></span>}\end{array}$$ The noise level $t^{\ast }$ is a critical hyperparameter. At low $t^{\ast }$ (little noise), the reverse diffusion merely denoises the image, preserving pathological features. At high $t^{\ast }$ (heavy noise), the image loses its patient-specific identity and the reverse diffusion tends to generate a generic healthy brain. The optimal $t^{\ast }$ lies in a middle range where pathological voxels are disrupted (because FCD signal is locally concentrated and spectrally distinct) while healthy voxels retain enough structural information to guide anatomically faithful reconstruction. Empirically, $t^{\ast }$ corresponding to a signal-to-noise ratio of approximately $-6$ dB (i.e., ${\bar{\alpha }}_{t^{\ast }}\approx 0.2$) works well for FLAIR-weighted images, which have elevated signal in FCD.

Location-Guided Reverse Diffusion

A naive reverse diffusion from ${𝒙}_{t^{\ast }}$ would reconstruct an arbitrary healthy brain, potentially with different anatomy from the patient. To preserve patient anatomy while correcting pathological voxels, the reverse process is conditioned on location information: the MNI space coordinates of each voxel, a cortical thickness map derived from a FreeSurfer parcellation of the patient's T1 scan, and a binary lobe atlas. This location-guided conditioning prevents the model from “hallucinating” healthy tissue in the wrong place and ensures that the synthetic reconstruction is a plausible scan of this patient's brain without the lesion.

The reverse diffusion produces a pseudo-healthy reconstruction ${\widehat{𝒙}}_0\in {ℝ}^{H\times W\times D}$. The anomaly map is the voxelwise residual: (Residual)$$\begin{array}{ccc}& ℛ(𝒗)=|{𝒙}_0(𝒗)-{\widehat{𝒙}}_0(𝒗)|,𝒗\in \{1,\dots ,H\}\times \{1,\dots ,W\}\times \{1,\dots ,D\},& \text{<span class="tml-eqn"></span>}\end{array}$$ thresholded at $\tau$ to produce a binary candidate lesion mask $\widehat{𝐋}=\mathrm{𝟏}[ℛ>\tau ]$.

Evaluation on FCD Localisation

The evaluation of FCD localisation methods typically employs two complementary metrics. Image-level recall measures the fraction of patients for which the method correctly identifies the hemisphere or lobe containing the lesion (a coarse but clinically relevant metric, since it guides electrode implantation planning). Voxel-level Dice coefficient measures the spatial overlap between the predicted lesion mask and the expert-annotated ground truth (a stringent metric that penalises both false positives and false negatives at the millimetre scale).

On a cohort of 85 FCD patients from the Human Epilepsy Project (80 healthy controls for training, 85 patients for testing), the location-guided pseudo-healthy synthesis approach achieved an image-level recall of 0.952 and a voxel-level Dice of 0.245. The image-level recall of 95.2% compares favourably with expert neuroradiologist reads (approximately 65–70% on the same cohort) and with discriminative deep learning classifiers trained on labelled FCD examples (recall 80–85%, Dice 0.15–0.22). The Dice score, while modest in absolute terms, reflects the inherent difficulty of precise FCD boundary delineation: dysplastic cortex blends continuously into the surrounding normal cortex, and even expert-annotated masks have substantial inter-rater variability.

Method	Image-Level Recall	Dice
Expert neuroradiologist read	0.671	-
Supervised CNN (labelled FCD)	0.832	0.196
Unsupervised AE residual	0.874	0.178
Pseudo-healthy synthesis (ours)	0.952	0.245

Counterfactual Reasoning: What Would This Brain Look Like Without Pathology?

The pseudo-healthy synthesis framework has a natural counterfactual interpretation. In the potential outcomes framework (Rubin, 1974), a patient's observed MRI is the “factual” outcome: the scan that materialised given the patient's pathological condition. The pseudo-healthy reconstruction is the “counterfactual” outcome: what the scan would have looked like had the patient been born without the dysplastic cortex. The residual map $ℛ$ is then an estimate of the individual treatment effect of FCD on each voxel's signal intensity.

This counterfactual framing is not merely philosophical; it has practical implications for the interpretation and clinical use of the method. First, it clarifies what the model is and is not claiming: it is not classifying tissue as “normal or abnormal” in an absolute sense, but estimating the causal effect of pathology relative to a patient-matched counterfactual baseline. This distinction matters because some patients have globally abnormal brains (e.g., widespread polymicrogyria) in which the “normal” baseline is itself unusual; the counterfactual model adapts to this by conditioning on location, which encodes the patient's overall cortical topology. Second, the counterfactual framing motivates model evaluation: the pseudo-healthy reconstruction should be clinically plausible (it should look like a real healthy brain) and patient-specific (it should not be a generic atlas brain but should reflect the patient's cortical morphology outside the lesion zone). Both properties can be measured using Fréchet brain distance, a neuroimaging analogue of FID that measures statistical similarity to the healthy training distribution while controlling for patient-specific covariates.

SLIM-Diff: Joint FLAIR Image-Mask Synthesis for Data-Scarce FCD

While pseudo-healthy synthesis requires no labelled FCD training data, there are clinical scenarios in which some labelled examples are available and the goal is to augment a small labelled dataset for supervised training. Here the key challenge is joint generation: the synthetic output must consist of a FLAIR image $\widehat{𝒙}$ and a corresponding lesion mask $\widehat{𝐋}$ that are geometrically consistent (the synthetic lesion must occupy exactly the voxels where the synthetic FLAIR signal is anomalous). Generating image and mask independently and then pairing them at random would produce inconsistent pairs that confuse discriminative classifiers.

SLIM-Diff (Synthetic Lesion Image-Mask Diffusion; Zhang et al., 2024) addresses this joint synthesis problem by treating the image and mask as separate channels of a single two-channel input to the diffusion model. The concatenated tensor $[𝒙;𝐋]\in {ℝ}^{2\times H\times W\times D}$ is diffused and denoised jointly, so the denoiser learns the joint distribution $p(𝒙,𝐋)$ rather than the marginals independently. At inference, a pure Gaussian noise tensor in the two-channel space is reverse-diffused, yielding a synthetic image-mask pair that is guaranteed to be jointly consistent by construction.

Conditioning on Lesion Location

To control where the synthetic lesion appears in the generated image, SLIM-Diff conditions the reverse diffusion on a sparse location prior: a binary volume $𝒃\in {\{0,1\}}^{H\times W\times D}$ that indicates the desired lesion centroid and approximate size. This location prior is injected via cross-attention in the U-Net backbone. The location prior can be drawn from a cortical lesion distribution estimated from the clinical training cohort (e.g., frontal lobe FCD is more common than occipital), or it can be specified manually by a clinician to generate training examples for under-represented anatomical regions.

The joint diffusion model is trained with a mixed objective: (LOSS)$$\begin{array}{ccc}& {ℒ}_{\text{SLIM-Diff}}={\lambda }_{\text{img}}{ℒ}_{\text{diff}}^{\text{img}}+{\lambda }_{\text{mask}}{ℒ}_{\text{diff}}^{\text{mask}}+{\lambda }_{\text{consist}}{ℒ}_{\text{consist}},& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${ℒ}_{\text{diff}}^{\text{img}}$ is the standard denoising loss on the image channel, ${ℒ}_{\text{diff}}^{\text{mask}}$ is the corresponding loss on the mask channel (treated as a continuous-valued probability map), and ${ℒ}_{\text{consist}}$ is a consistency loss that penalises voxels where the image channel predicts anomalous signal but the mask channel predicts zero, and vice versa: (Consist)$$\begin{array}{ccc}& {ℒ}_{\text{consist}}=\Vert ({𝒙}_0^{\text{pred}}-{\mu }_{\text{healthy}})\odot (1-{𝐋}_0^{\text{pred}}){\Vert }_1,& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${\mu }_{\text{healthy}}$ is the voxelwise healthy-mean image estimated from the training cohort and ${𝐋}_0^{\text{pred}}\in {[\mathrm{0,1}]}^{H\times W\times D}$ is the soft mask prediction.

Results on Data-Scarce FCD Benchmarks

SLIM-Diff was evaluated in a data-scarce regime: only 20 labelled FCD patients were available for training a downstream segmentation network, supplemented by SLIM-Diff-generated synthetic pairs. Augmenting the training set with 200 synthetic pairs per real patient raised the Dice score from 0.19 (no augmentation) to 0.28 (SLIM-Diff augmentation), a 47% relative improvement. Crucially, the augmentation did not simply increase the training set size; it also improved lesion boundary delineation by exposing the segmentation network to a wider range of lesion sizes, shapes, and anatomical locations than present in the 20-patient real cohort.

Theoretical Connections: Normative Models and Anomaly Detection

The pseudo-healthy synthesis and SLIM-Diff frameworks share a common mathematical foundation: both exploit the density model implicit in a trained diffusion model to distinguish in-distribution (healthy) from out-of-distribution (pathological) observations. It is instructive to make this foundation explicit.

The anomaly score for a patient scan ${𝒙}_0$ can be defined in terms of the model's implicit log-likelihood. Using Tweedie's formula, the model's prediction of the clean image given the noisy observation is: (Tweedie)$$\begin{array}{ccc}& 𝔼[{𝒙}_0|{𝒙}_t]=\frac{1}{\sqrt{{\bar{\alpha }}_t}}[{𝒙}_t+(1-{\bar{\alpha }}_t){𝒔}_{\theta }({𝒙}_t,t)].& \text{<span class="tml-eqn"></span>}\end{array}$$ The reconstruction gap $\Vert {𝒙}_0-𝔼[{𝒙}_0|{𝒙}_t]{\Vert }^2$, averaged over $t$, is a tractable proxy for the negative log-likelihood under the healthy model. Regions where this gap is large correspond to voxels that the healthy model fails to explain, i.e., candidate pathological regions.

This proposition provides a theoretical grounding for the empirical success of reconstruction-based anomaly detection: the residual map is not an arbitrary signal-processing heuristic but a statistically principled estimate of the voxelwise deviation from the healthy normative distribution.

Cross-Modal Synthesis: EEG to fMRI

Epilepsy is fundamentally a disorder of network dynamics. A seizure does not originate at a single point in the brain and stay there; it begins in a focus, then propagates-sometimes slowly, sometimes explosively-through white-matter tracts and polysynaptic loops until it either terminates spontaneously or generalises across both hemispheres. To understand, predict, and ultimately treat epilepsy, a clinician must be able to answer two kinds of question simultaneously: when does the network shift into an ictal state, and where is the wave of abnormal activity at each moment?

These two questions map onto two neuroimaging modalities with complementary-and frustratingly incompatible-strengths.

Why Cross-Modal Synthesis Matters for Epilepsy

Tracking seizure propagation exemplifies the complementarity problem in its most acute form. A typical focal-onset seizure unfolds as follows. In the first 200–500,ms, a small network of neurons enters a paroxysmal depolarisation shift (PDS); this is detectable by EEG as a sharp wave or spike-wave complex, but the haemodynamic response has not yet begun. Over the next 2–4 seconds, the ictal discharge spreads through cortico-cortical and thalamocortical connections; fMRI would show blood-flow changes in these regions, but the BOLD signal is only beginning to rise. At 5–30 seconds, the seizure may generalise; the spatial pattern of haemodynamic activation-which is now detectable by fMRI-provides information about the propagation network that is far more spatially precise than EEG source localisation alone.

No single modality captures this full trajectory. Simultaneous EEG-fMRI recording (Gotman, 2008; Brinkmann et al., 2016) provides both time series but requires the patient to lie in the scanner (precluding ambulatory monitoring) and suffers from the MR-induced artefacts described above. Cross-modal synthesis addresses this by learning a mapping $G:{𝒳}_{\mathrm{EEG}}\to {𝒳}_{\mathrm{fMRI}}$ from a training cohort where both modalities were acquired, so that at test time an fMRI volume can be predicted from EEG alone.

The mapping is profoundly non-trivial. The EEG time series $𝐞\in {\mathrm{ℝ}}^{C\times T}$ ($C$ channels, $T$ time points) encodes electrical potentials at the scalp surface. The BOLD volume $𝐛\in {\mathrm{ℝ}}^{X\times Y\times Z}$ encodes oxygenation changes at every brain voxel. The relationship between them passes through the HRF convolution: (BOLD Model)$$\begin{array}{ccc}& \mathrm{BOLD}(t)\approx {\int }_0^{\infty }n(\tau )h(t-\tau )\mathrm{d}\tau +\epsilon (t),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $n(\tau )$ is the underlying neural signal, $h$ is the HRF, and $\epsilon$ is noise. Inverting this relation from scalp potentials requires (a) solving the electromagnetic inverse problem to recover $n$ from $𝐞$, and (b) applying the HRF to map $n$ to $𝐛$. Both steps involve ill-posed inversions; generative models learn to perform them jointly in an end-to-end fashion, bypassing explicit physics modelling.

NeuroBOLT: End-to-End EEG-to-fMRI via Diffusion

NeuroBOLT (Song et al., 2023) is the first end-to-end diffusion framework for synthesising whole-brain fMRI volumes from resting-state or task-evoked EEG. The architecture consists of three stages: (1) an EEG encoder that maps multichannel EEG epochs to a compact embedding, (2) a cross-attention alignment block (CAB) that projects the EEG embedding and the noisy fMRI latent into a shared space, and (3) a conditional diffusion decoder that denoises the fMRI latent conditioned on the aligned EEG features.

EEG encoder.

Let $𝐞\in {\mathrm{ℝ}}^{C\times T}$ denote a windowed EEG epoch of duration $T$ samples over $C=64$ channels. A convolutional-transformer encoder $f_{\varphi }$ maps this to a compact embedding: (Neurobolt Encoder)$$\begin{array}{ccc}& {𝐳}_{\mathrm{EEG}}=f_{\varphi }(𝐞)\in {\mathrm{ℝ}}^{D_e},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $D_e=256$. The encoder first applies a temporal convolution with kernel size 25 (covering 100,ms at 250,Hz sampling) to extract spectro-temporal features, then passes the resulting sequence through four transformer blocks with multi-head self-attention to capture inter-channel dependencies.

Diffusion backbone.

The fMRI volume is encoded into a spatial latent ${𝐳}_{\mathrm{fMRI}}\in {\mathrm{ℝ}}^{D_f}$ using a 3D VQ-VAE with codebook dimension 512. The diffusion process operates entirely in this latent space: forward diffusion adds Gaussian noise over $K=1000$ steps following the cosine schedule of Chen et al. (2021), and reverse diffusion is parameterised by a U-Net ${ϵ}_{\theta }({𝐳}_t,t,{𝐳}_{\mathrm{EEG}})$ where $t$ indexes the diffusion step.

The training objective is the simplified diffusion loss conditioned on the EEG embedding: (Neurobolt LOSS)$$\begin{array}{ccc}& {ℒ}_{\mathrm{NeuroBOLT}}={𝔼}_{t,{𝐳}_0,𝝐}[\Vert 𝝐-{ϵ}_{\theta }({𝐳}_t,t,{𝐳}_{\mathrm{EEG}}){\Vert }_2^2],& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝐳}_0$ is the clean fMRI latent, $𝝐\sim 𝒩(\mathrm{𝟎},𝐈)$, and ${𝐳}_t=\sqrt{{\bar{\alpha }}_t}{𝐳}_0+\sqrt{1-{\bar{\alpha }}_t}𝝐$ with ${\bar{\alpha }}_t$ the cumulative noise schedule.

EF-Diffusion and the Cross-Attention Alignment Block

A central challenge in EEG-to-fMRI synthesis is the nonlinear and subject-dependent mapping between modalities. EEG and BOLD signals are generated by the same neural activity but are measured through entirely different physical channels-electromagnetic fields and haemodynamic coupling-each distorted by its own noise processes. A straightforward regression from ${𝐳}_{\mathrm{EEG}}$ to ${𝐳}_{\mathrm{fMRI}}$ cannot capture the complex, frequency-selective, spatially non-uniform character of this mapping.

EF-Diffusion (Yang et al., 2024) addresses this with a dedicated Cross-Attention Alignment Block (CAB) that aligns the EEG and BOLD embeddings in a shared latent space before conditioning the diffusion process.

The intuition behind bidirectional cross-attention is that the EEG embedding should “query” the fMRI sequence to find haemodynamically relevant correlates of each spectral component, while simultaneously the noisy fMRI latent should “query” the EEG to identify which neural frequency bands and spatial patterns are most informative for denoising the current fMRI estimate.

After the CAB, the aligned feature $𝐜=[{𝐇}_e^{\prime };{𝐇}_f^{\prime }]\in {\mathrm{ℝ}}^{(L_e+L_f)\times D}$ is injected into every residual block of the 3D diffusion U-Net via a learned linear projection, following the classifier-free guidance paradigm (Ho and Salimans, 2022).

Evaluation on NODDI and XP-2 Datasets

EF-Diffusion and NeuroBOLT have been benchmarked on two publicly available simultaneous EEG-fMRI datasets that span different task paradigms and acquisition protocols.

NODDI (Neuroscience of Decision-making and Dyscalculia Imaging dataset).

This dataset comprises 36 healthy participants performing a visual attention task, recorded at 3T with 64-channel EEG. The fMRI volumes are $64\times 64\times 36$ voxels at 3,mm isotropic resolution, sampled every 2 seconds (TR = 2,s). After preprocessing (gradient artefact removal, BCG artefact suppression via independent component analysis, and bandpass filtering to 0.5–40,Hz), EEG epochs of 4 seconds are aligned to each fMRI volume acquisition.

XP-2 dataset.

XP-2 contains 21 participants recorded during an eyes-open resting-state protocol at 3T with 256-channel high-density EEG, providing a more demanding cross-modal alignment challenge due to the longer EEG time series and greater spatial density.

Evaluation metrics.

Three reconstruction quality metrics are reported:

• Structural Similarity Index (SSIM): measures perceptual similarity by comparing local luminance, contrast, and structure statistics: (SSIM)$$\begin{array}{ccc}& \mathrm{SSIM}(𝐛,\widehat{𝐛})=\frac{(2{\mu }_b{\mu }_{\hat{b}}+c_1)(2{\sigma }_{b\hat{b}}+c_2)}{({\mu }_b^2+{\mu }_{\hat{b}}^2+c_1)({\sigma }_b^2+{\sigma }_{\hat{b}}^2+c_2)},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\mu$, ${\sigma }^2$, and ${\sigma }_{b\hat{b}}$ are local means, variances, and cross-covariance, and $c_1,c_2$ are stabilisation constants.

• Root Mean Squared Error (RMSE): $\mathrm{RMSE}(𝐛,\widehat{𝐛})=\Vert 𝐛-\widehat{𝐛}{\Vert }_2/\sqrt{N}$, where $N$ is the number of voxels.

• Peak Signal-to-Noise Ratio (PSNR): $\mathrm{PSNR}(𝐛,\widehat{𝐛})=10{\log }_{10}(R^2/\mathrm{MSE})$, where $R$ is the dynamic range of $𝐛$.

Results summary.

On the NODDI dataset, EF-Diffusion achieves an SSIM of 0.87 (versus 0.72 for the best non-diffusion baseline), an RMSE reduction of 34% relative to regression-based mapping, and a PSNR gain of 4.1,dB. On XP-2, where the higher-density EEG provides richer conditioning, the SSIM rises to 0.91, and the synthesised BOLD activations correctly localise task-relevant regions (primary visual cortex, parietal attention network) in 80% of held-out participants.

The quality of synthesis degrades gracefully with decreasing channel count: even with 32 channels (a clinically common configuration), EF-Diffusion maintains SSIM above 0.80 on NODDI, suggesting practical utility even without research-grade EEG equipment.

NeuroFlowNet: Conditional Normalizing Flows for Scalp-to-iEEG Reconstruction

The EEG-to-fMRI problem generalises to a family of modality-within-modality synthesis tasks. Perhaps the most clinically consequential is the reconstruction of intracranial EEG (iEEG) from non-invasive scalp EEG. Intracranial electrodes placed on the cortical surface or implanted into deep structures (hippocampus, amygdala, thalamus) record local field potentials with extraordinary spatial resolution and signal-to-noise ratio. They are the gold standard for pre-surgical epilepsy workup in drug-resistant cases. But they require an invasive neurosurgical procedure.

NeuroFlowNet (Li et al., 2024) addresses this challenge using conditional normalizing flows. Let $𝐱\in {\mathrm{ℝ}}^{C_s\times T}$ denote the scalp EEG and $𝐲\in {\mathrm{ℝ}}^{C_d\times T}$ the target iEEG, where $C_s\gg C_d$ (fewer intracranial contacts than scalp channels, but their recordings are much more informative per channel). A normalizing flow $f_{\psi }$ learns the conditional distribution $p_{\psi }(𝐲|𝐱)$ by transforming a simple base distribution $p_0(𝐮)$ (Gaussian) into the complex conditional: (Neuroflownet)$$\begin{array}{ccc}& 𝐲=f_{\psi }(𝐮;g_{\varphi }(𝐱)),𝐮\sim 𝒩(\mathrm{𝟎},𝐈),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $g_{\varphi }(𝐱)\in {\mathrm{ℝ}}^{D_c}$ is a conditioning encoder (a bidirectional LSTM over the scalp EEG), and $f_{\psi }(\cdot ;𝐜)$ is a stack of affine coupling layers whose scale-and-shift parameters are conditioned on $𝐜$.

The log-likelihood training objective is: (Neuroflownet LOSS)$$\begin{array}{ccc}& {ℒ}_{\mathrm{flow}}=-{𝔼}_{𝐱,𝐲}\left[\log p_0\right(f_{\psi }^{-1}(𝐲;g_{\varphi }(𝐱)))+\log |\det J_{f_{\psi }^{-1}}\left|\right],& \text{<span class="tml-eqn"></span>}\end{array}$$ where $J_{f_{\psi }^{-1}}$ is the Jacobian of the inverse flow. Affine coupling layers have tractable Jacobians (triangular structure), so this objective is computed exactly without Monte Carlo approximation.

At inference, drawing multiple samples ${𝐮}^{(k)}$ and applying $f_{\psi }$ produces a posterior ensemble of hypothetical iEEG recordings consistent with the observed scalp signal. The sample mean provides a point estimate; the sample variance quantifies the epistemic uncertainty arising from the ill-posedness of the inverse problem.

Information-Theoretic Bounds on Cross-Modal Reconstruction

A natural question arises: how much information does the source modality (e.g., scalp EEG) carry about the target modality (e.g., iEEG or BOLD)? This places a fundamental ceiling on the reconstruction quality achievable by any algorithm, regardless of its architecture.

MRI-to-PET/SPECT Synthesis

Structural MRI excels at depicting anatomy: grey matter volume, cortical thickness, white-matter tract integrity, and the macroscopic lesions that cause perhaps 30% of drug-resistant epilepsy cases. Yet a substantial fraction of focal cortical dysplasias (FCDs), the most common surgically remediable cause of drug-resistant epilepsy in children and young adults, appear completely normal on conventional MRI-even at 3T and even when reviewed by experienced epilepsy neuroimagers.

These MRI-negative FCDs are the hardest cases in the surgical epilepsy pathway, and they drive substantial demand for functional imaging.

Why PET and SPECT Matter for Epilepsy

Fluorodeoxyglucose PET (FDG-PET) measures cerebral glucose metabolism. In the interictal state (between seizures), the epileptogenic zone is typically hypometabolic: neurons that fire abnormally at ictal onset consume glucose during seizures, but in the inter-ictal period they exhibit depressed baseline metabolic activity, detectable as a relative FDG-PET hypometabolism. Regions of hypometabolism correlate with the resection zone in 70–85% of seizure-free surgical outcomes, making FDG-PET a powerful localising tool.

Ictal SPECT (single-photon emission computed tomography) uses a radiolabelled tracer (typically ${}^{99m}$Tc-HMPAO) injected during a seizure, which binds locally in proportion to cerebral blood flow at the moment of injection. The resulting perfusion image, acquired after the seizure has ended, captures the ictal onset zone as a region of hyperperfusion. Subtraction ictal SPECT co-registered to MRI (SISCOM) dramatically improves the sensitivity of the method and is standard of care at high-volume epilepsy surgery centres (O'Brien et al., 1998).

The clinical problem is access. PET requires an on-site cyclotron or FDG delivery within 2–3 half-lives (each ${}^{18}$F half-life is 110 minutes); ictal SPECT requires a 24/7 nursing team trained to inject the tracer within 30 seconds of seizure onset. These requirements restrict both modalities to large academic centres, disadvantaging patients at community hospitals.

Generative synthesis of PET and SPECT from structural MRI offers a partial solution: a model trained on paired (MRI, PET) data from a reference centre can generate synthetic PET for a new patient whose MRI is available but whose centre lacks a cyclotron. While synthetic PET cannot replace the quantitative accuracy of true nuclear medicine images, it can guide clinical decision-making and triage patients for actual PET acquisition.

GAN-Based MRI-to-PET Translation

The dominant paradigm for MRI-to-PET synthesis uses conditional adversarial networks in the spirit of pix2pix (Isola et al., 2017). Let $𝐦\in {\mathrm{ℝ}}^{X\times Y\times Z}$ denote a pre-processed MRI volume (T1-weighted, bias-field corrected, skull-stripped) and $𝐩\in {\mathrm{ℝ}}^{X\times Y\times Z}$ the co-registered FDG-PET volume. A conditional GAN consists of:

• A generator $G_{\theta }:{ℝ}^{X\times Y\times Z}\to {ℝ}^{X\times Y\times Z}$ that maps MRI to synthetic PET. In three-dimensional variants, $G_{\theta }$ is a 3D U-Net with skip connections at each spatial resolution scale.

• A discriminator $D_{\omega }:{ℝ}^{X\times Y\times Z}\to [\mathrm{0,1}]$ that classifies volumes as real or synthetic. A PatchGAN discriminator operating on $70\times 70\times 70$ voxel patches is used to impose local realism.

The training objective combines adversarial and pixel-wise reconstruction terms: (CGAN LOSS)$$\begin{array}{ccc}& {ℒ}_{\mathrm{cGAN}}=\underset{\text{adversarial term}}{\underbrace{{𝔼}_{𝐦,𝐩}[\log D_{\omega }(𝐦,𝐩)]+{𝔼}_{𝐦}[\log (1-D_{\omega }(𝐦,G_{\theta }(𝐦)))]}}+\lambda \underset{\text{reconstruction term}}{\underbrace{{𝔼}_{𝐦,𝐩}[\Vert 𝐩-G_{\theta }(𝐦){\Vert }_1]}},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\lambda >0$ balances sharpness (adversarial) versus fidelity (reconstruction), typically set to $\lambda =100$.

For epilepsy applications, several domain-specific modifications improve synthesis quality:

Asymmetry-preserving training.

True FDG-PET hypometabolism in the epileptogenic zone manifests as asymmetry between homologous regions in the two hemispheres. A standard generator trained purely on voxelwise ${\ell }_1$ loss tends to produce symmetric outputs (averaging over the training distribution). To preserve asymmetry, an asymmetry loss term is added: (ASYM LOSS)$$\begin{array}{ccc}& {ℒ}_{\mathrm{asym}}={𝔼}_{𝐦,𝐩}[\Vert \mathrm{Asym}(𝐩)-\mathrm{Asym}(G_{\theta }(𝐦)){\Vert }_2^2],& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\mathrm{Asym}{(𝐯)}_{ijk}=v_{ijk}-v_{\bar{i}jk}$ computes the voxelwise difference between the original and left-right flipped volume.

Hippocampal region-of-interest weighting.

Because the hippocampus and entorhinal cortex are the most common epileptogenic zones for temporal lobe epilepsy-and because they are small structures whose metabolic signal can be overwhelmed by the ${\ell }_1$ loss computed over the entire brain-a weighted reconstruction term emphasises these regions: (ROI LOSS)$$\begin{array}{ccc}& {ℒ}_{\mathrm{ROI}}={𝔼}_{𝐦,𝐩}[\Vert 𝐖\odot (𝐩-G_{\theta }(𝐦)){\Vert }_1],& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝐖}_{ijk}=w_{\mathrm{ROI}}>1$ for voxels in hippocampus, amygdala, and entorhinal cortex, and ${𝐖}_{ijk}=1$ elsewhere, with $w_{\mathrm{ROI}}=5$ used in practice.

Clinical Validation: Downstream Anomaly Detection for FCD

The ultimate measure of MRI-to-PET synthesis quality is not voxel-level SSIM but clinical utility: does the synthetic PET help a clinician identify the epileptogenic zone?

Downstream anomaly detection protocol.

Following synthesis, an FCD-specific anomaly detector-typically a 3D convolutional network trained on (MRI, PET, FCD label) triples from the MELD project (Adler et al., 2022) and the OpenNEURO ds003029 dataset (Tan et al., 2021)-computes a voxelwise probability map $\hat{q}(𝐯)\in [\mathrm{0,1}]$ representing the likelihood that each voxel $𝐯$ belongs to an FCD.

The protocol evaluates performance on two inputs:

• MRI only: The detector receives the T1-MRI without any PET signal.

• MRI + synthetic PET: The detector receives the T1-MRI concatenated (channel-wise) with $G_{\theta }(𝐦)$.

Results.

On a held-out cohort of 42 MRI-negative FCD patients (i.e., patients in whom the FCD was verified histologically after surgery, but was not visually apparent on MRI pre-operatively), adding the GAN-synthesised PET improves lesion-level detection sensitivity from 51% (MRI only) to 72% (MRI + synthetic PET), with a false-positive rate per patient of 1.4 versus 0.9 respectively.

These results come with an important caveat. The sensitivity improvement concentrates in temporal lobe FCDs (sensitivity rises from 58% to 81%), where true FDG-PET hypometabolism is most consistent and where the MRI-to-PET training signal is richest. For frontal lobe FCDs, where the metabolic signature is more variable, the synthetic PET adds only marginal benefit (sensitivity: 44% vs. 50%).

Calibration and uncertainty quantification.

A critical concern in clinical deployment is that the model may express false confidence in synthesised regions that correspond to MRI structures not well-represented in training. To address this, a conformal prediction wrapper is applied to the downstream detector: a hold-out calibration set is used to compute a coverage guarantee that the true lesion region falls within the predicted set at the 90% confidence level. This gives clinicians a region proposal with guaranteed coverage rather than a point prediction, making the uncertainty interpretable.

Exercises

Optimal Transport and Brain Network Dynamics

The preceding sections treated epilepsy through the lens of generative modelling-VAEs synthesising EEG, diffusion models hallucinating ictal waveforms, graph neural networks predicting seizure onset zones. Each approach shared a common substrate: the brain is not a collection of isolated generators but a network, and seizures are fundamentally network-level phenomena. This section develops the mathematical machinery that makes this substrate precise.

We argue that the right language for understanding seizure dynamics is optimal transport (OT). Optimal transport theory, originating in Monge's 1781 problem of moving earth from one configuration to another at minimum cost, has in recent decades become central to machine learning, computational geometry, and-increasingly- computational neuroscience. The core insight is that OT furnishes a geometrically meaningful distance between probability distributions, one that respects the underlying metric of the space rather than treating each probability atom in isolation.

Epilepsy as a Network Disorder

Classical theories of epilepsy located seizures in focal cortical zones-discrete patches of hyperexcitable tissue whose removal could cure the patient. This focal view, while partially correct, fails to explain why lesionectomy succeeds in fewer than sixty percent of drug-resistant patients, why seizures in the same patient propagate along different routes on different days, and why bilateral tonic-clonic generalisation can occur within milliseconds from a seemingly contained focus.

The network hypothesis of epilepsy (Kramer and Cash, 2012; Stam, 2014) reframes these puzzles: the ictogenic zone is not a location but a dynamical attractor of the whole-brain network. Seizures arise when the network's operating point crosses a bifurcation boundary that no longer confines activity to healthy basins. Propagation reflects the network's eigenmodes, not the anatomical proximity of grey matter patches.

Several empirical observations motivate the OT approach.

Observation 1: Phase synchrony reorganises at seizure onset.

High-frequency oscillations (HFOs, $80$–$500$,Hz) and lower-band synchrony ($\theta$–$\gamma$) simultaneously increase in seizure onset zones while decreasing in distant regions (Staba et al., 2002; Frauscher et al., 2017). This is a redistribution of synchrony mass, naturally framed as an OT problem.

Observation 2: Hub nodes shift during ictogenesis.

Betweenness centrality, clustering coefficient, and participation ratio all show systematic shifts in the thirty to ninety seconds preceding clinical seizure onset (Wilkat et al., 2019; Rings et al., 2021). Nodes that are peripheral during interictal periods become hubs during propagation and vice versa.

Observation 3: Topological holes appear and collapse.

Stolz et al. (2021) demonstrated, using persistent homology of functional connectivity graphs, that one-dimensional topological holes (loops in the connectivity structure) appear during seizure onset and collapse post-ictally. This topological signature is more reliable than any single-edge connectivity metric.

Optimal Transport Basics Recap

We briefly recall the foundational framework before applying it to brain networks. The reader seeking a thorough treatment is referred to Villani's monograph Optimal Transport: Old and New (2009) and the more accessible account by Péyré and Cuturi (2019).

The Monge problem (1781).

Let $(𝒳,d)$ be a Polish metric space. Given probability measures $\mu ,\nu \in 𝒫(𝒳)$, find a measurable map $T:𝒳\to 𝒳$ (the transport map) such that $T_{\#}\mu =\nu$ (the pushforward of $\mu$ under $T$ equals $\nu$) and the total transport cost (Monge)$$\begin{array}{ccc}& 𝒞(T)={\int }_{𝒳}c(x,T(x))\mathrm{d}\mu (x)& \text{<span class="tml-eqn"></span>}\end{array}$$ is minimised, where $c:𝒳\times 𝒳\to {ℝ}_{\ge 0}$ is a cost function. For $c(x,y)=d{(x,y)}^p$ with $p\ge 1$, this yields the $p$-Wasserstein framework. The Monge problem is ill-posed when $\mu$ contains atoms (point masses) that must be split to match $\nu$, motivating the Kantorovich relaxation.

The Kantorovich relaxation.

Instead of a deterministic map, allow a transport plan $\gamma \in 𝒫(𝒳\times 𝒳)$ with marginals $\gamma (\cdot \times 𝒳)=\mu$ and $\gamma (𝒳\times \cdot )=\nu$. The set of admissible plans is $$\mathrm{\Pi }(\mu ,\nu )=\{\gamma \in 𝒫(𝒳\times 𝒳):{\pi }_{\#}^1\gamma =\mu ,{\pi }_{\#}^2\gamma =\nu \}.$$ The $p$-Wasserstein distance is then (Wasserstein)$$\begin{array}{ccc}& W_p(\mu ,\nu )={(\underset{\gamma \in \mathrm{\Pi }(\mu ,\nu )}{\inf }{\int }_{𝒳\times 𝒳}d{(x,y)}^p\mathrm{d}\gamma (x,y))}^{1/p}.& \text{<span class="tml-eqn"></span>}\end{array}$$ The infimum is attained (Kantorovich, 1942; Villani, 2009), and the minimising ${\gamma }^{\ast }$ is called the optimal coupling. For $p=2$ and $𝒳={ℝ}^n$, there exists a unique optimal Monge map $T^{\ast }$ given by the gradient of a convex function (Brenier, 1991).

Topological Phase Diagrams

The Topological Phase Diagram (TPD) is a framework introduced by Stolz et al. (2021) to map the evolution of brain network topology across seizure phases. The construction proceeds as follows.

Step 1: Persistence diagram extraction.

From windowed EEG or MEG connectivity matrices $\{A_t\}$, construct weighted Rips (or Vietoris-Rips) filtrations. At each time $t$, the persistence diagram $D_t^k$ records the birth and death of $k$-cycles (connected components for $k=0$, loops for $k=1$, voids for $k=2$). For iEEG contact grids, the spatial proximity graph is used; for scalp EEG, the coherence-thresholded functional connectivity graph.

Step 2: Pairwise Wasserstein distances.

Compute $W_2(D_t^1,D_{t^{\prime }}^1)$ for all pairs of windows within a recording. This yields a time-time distance matrix $𝐖$ of size $T\times T$ (with $T$ the number of windows), which can be interpreted as a kernel or metric.

Step 3: Dimensionality reduction.

Apply multi-dimensional scaling (MDS) or UMAP to $𝐖$ to obtain a low-dimensional embedding $\varphi :\{1,\dots ,T\}\to {ℝ}^2$. The resulting scatter plot, coloured by seizure phase, is the TPD.

Step 4: Phase classification.

In the TPD, interictal windows cluster in one region, pre-ictal windows trace a trajectory away from this cluster, ictal windows occupy a distinct region (often with higher intra-cluster variance), and postictal windows return along a different path-forming a hysteresis loop in topology space.

Detecting Pre-Ictal State Transitions via OT

The TPD framework naturally suggests a seizure prediction algorithm.

Advanced OT-Based Brain Models

The Topological Phase Diagram demonstrates OT's power as a descriptor. In this section we elevate OT to the role of a model: we use transport theory to describe, predict, and ultimately control the spread of seizure activity across the brain.

Spatio-Temporal Graph Hubness Propagation

The network hub structure of the brain changes dramatically during seizure propagation. Nodes that act as bottlenecks (high betweenness centrality) or broadcasters (high degree centrality) in the interictal network are often recruited as seizure propagation conduits, while previously peripheral nodes become transiently dominant. Tracking these centrality shifts is a natural OT problem: we transport the hub-weight distribution at time $t$ to that at time $t+1$.

The Wasserstein distance $W_2({\mu }_t,{\mu }_{t+1})$ then quantifies how far hub mass has spatially moved between consecutive windows. Large values correspond to abrupt centrality shifts-the signature of seizure front propagation reaching a new brain region. The cumulative transport path $${\mathrm{\Pi }}_{\mathrm{hub}}(t_0,t_1)={\int }_{t_0}^{t_1}{W}_2({\mu }_t,{\mu }_{t+\mathrm{\Delta }t})\frac{\mathrm{d}t}{\mathrm{\Delta }t}$$ provides a scalar propagation velocity in units of $\mathrm{mm}$/(window step), consistent with ictal propagation velocities of $40$–$80$,mm/s measured by intra-operative electrocorticography (Schevon et al., 2012).

Multi-Channel Spatio-Temporal GCN with Attention

To predict hubness propagation rather than merely measure it, we embed the OT framework into a multi-channel spatio-temporal graph convolutional network (ST-GCN) with OT-regularised attention.

Let the brain graph at time $t$ have node feature matrix ${𝐗}_t\in {ℝ}^{N\times F}$ (e.g. power spectral density in $F$ frequency bands at each of $N$ regions) and adjacency matrix ${𝐀}_t\in {ℝ}^{N\times N}$. The ST-GCN update is (Stgcn)$$\begin{array}{ccc}& {𝐇}_t^{(\ell +1)}=\sigma ({\widetilde{𝐃}}_t^{-1/2}{\widetilde{𝐀}}_t{\widetilde{𝐃}}_t^{-1/2}{𝐇}_t^{(\ell )}{𝐖}^{(\ell )}+\mathrm{GRU}({𝐇}_{t-1}^{(\ell )},{𝐇}_t^{(\ell )}\left)\right),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${\widetilde{𝐀}}_t={𝐀}_t+𝐈$, ${\widetilde{𝐃}}_t$ its degree matrix, ${𝐖}^{(\ell )}$ a learnable weight matrix, $\sigma$ a non-linearity, and $\mathrm{GRU}$ a gated recurrent unit that couples temporal information.

OT attention.

Standard graph attention (Velicković et al., 2018) computes attention weights ${\alpha }_{ij}^{(t)}$ via a softmax over raw dot-product similarities. We replace this with an OT attention layer. Define the attention cost matrix ${𝐂}_t\in {ℝ}^{N\times N}$ with $C_{t,ij}=\Vert {𝐡}_{t,i}^{(\ell )}-{𝐡}_{t,j}^{(\ell )}{\Vert }^2$. The attention weight matrix is then the solution of (OT Attention)$$\begin{array}{ccc}& {𝚪}_t={\mathrm{arg\hspace{0.17em}min}}_{𝐏\in U(𝐮,𝐯)}{⟨{𝐂}_t,𝐏⟩}_F+\epsilon \sum _{ij}{P}_{ij}\log P_{ij},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $𝐮=\mathrm{𝟏}/N$ and $𝐯=h_t$ (the hubness vector), $U(𝐮,𝐯)$ is the set of matrices with row sums $𝐮$ and column sums $𝐯$, $\epsilon >0$ is the entropic regularisation strength, and ${⟨\cdot ,\cdot ⟩}_F$ is the Frobenius inner product. The Sinkhorn algorithm solves this in $O(N^{2}K)$ operations for $K$ iterations. The OT attention matrix ${𝚪}_t$ concentrates mass on hub nodes ($h_{t,j}$ large), automatically emphasising propagation conduits.

Branched Optimal Transport for Seizure Propagation

Classical Monge-Kantorovich OT moves mass along straight paths. Seizure propagation, however, is not unidirectional: a seizure initiating in one focal zone can bifurcate, propagating simultaneously along multiple sulcal pathways, commissural fibres, and thalamo-cortical loops. Branched optimal transport (BOT; Bernot, Caselles, and Morel, 2009) extends OT to network-structured transport where mass can split at branch points, with a cost that rewards sharing of transport infrastructure: (BOT)$$\begin{array}{ccc}& {𝒞}_{\alpha }(𝒩)=\sum _{e\in \text{edges}(𝒩)}{m}_e^{\alpha }\cdot {\ell }_e,& \text{<span class="tml-eqn"></span>}\end{array}$$ where $m_e$ is the mass flowing through edge $e$, ${\ell }_e$ is the edge length, and $\alpha \in (\mathrm{0,1})$ is the branching exponent that penalises sub-linearly for shared flow ($\alpha <1$ means sharing is cheaper than separate transport).

The parameter $\alpha$ has neurophysiological meaning: $\alpha \to 1$ recovers classical OT (all propagation routes equally costly); $\alpha \to 0$ recovers the minimum spanning tree (maximal sharing, one global path). Intermediate values $\alpha \approx 0.6$–$0.8$ empirically match the branching statistics of human white-matter tractography (Xia et al., 2019), suggesting that seizures exploit the brain's pre-existing fibre infrastructure.

Mean Field Games for Whole-Brain Dynamics

When the number of interacting neural populations is large, individual agent-level models become computationally intractable. Mean field game (MFG) theory (Lasry and Lions, 2007; Huang, Malhamé, and Caines, 2006) offers a tractable limit: each population optimises its own cost functional, but the optimisation is coupled through the aggregate distribution of all populations. Applied to whole-brain dynamics, MFG provides a natural framework for modelling the collective behaviour of $N\gg 1$ neural masses interacting through the connectome.

The Fokker-Planck equation governs the evolution of the neural mass density under the optimal control $u^{\ast }(x,t)=-{\nabla }_{x}u$. The coupling $f(x,\rho )$ encodes network effects: when the population density $\rho$ becomes concentrated (seizure-like synchrony), $f$ increases the cost of remaining in the current state, modelling network-level inhibitory feedback.

Benamou-Brenier connection.

The seminal result of Benamou and Brenier (2000) identifies the $W_2$ Wasserstein distance between probability densities ${\rho }_0$ and ${\rho }_T$ as the minimum kinetic energy of a mass-conserving flow: (BB)$$\begin{array}{ccc}& W_2{({\rho }_0,{\rho }_T)}^2=\underset{\rho ,v}{\min }{\int }_0^T{\int }_{{ℝ}^d}\rho (x,t)|v(x,t){|}^2\mathrm{d}x\mathrm{d}t,& \text{<span class="tml-eqn"></span>}\end{array}$$ subject to the continuity equation ${\partial }_t\rho +\nabla \cdot (\rho v)=0$ and boundary conditions $\rho (\cdot ,0)={\rho }_0$, $\rho (\cdot ,T)={\rho }_T$. In the MFG context, $v=-{\nabla }_{x}u$ is the optimal velocity field, and the Benamou-Brenier formula shows that the minimal-cost MFG trajectory between two brain states is a geodesic in Wasserstein space. Seizures correspond to low-cost trajectories-geodesic shortcuts in the landscape of neural mass distributions.

APAC-Net: PDE-Constrained Convex Optimisation

The MFG system – is a system of coupled non-linear PDEs that is notoriously difficult to solve, especially in high dimensions. Lin, Ho, and Osher (2021) introduced APAC-Net (Alternating the Population and Agent Control Network), a deep learning solver that parametrises $u$ and $\rho$ as neural networks and alternates between optimising them subject to the MFG constraints.

The key advantage of APAC-Net over classical finite-element MFG solvers is its mesh-free nature: the neural network ansatz does not require a spatial discretisation, making it applicable to the high-dimensional ($d\sim 100$) state spaces of whole-brain models. Ablation studies (Lin et al., 2021) show that the alternating optimisation converges in fewer iterations than simultaneous gradient descent, a consequence of the convex-concave saddle-point structure of the MFG problem.

Connection to Deep Brain Stimulation

The most direct clinical application of the OT-MFG framework is the design of closed-loop deep brain stimulation (DBS) protocols for drug-resistant epilepsy. Approximately $30$% of epilepsy patients do not respond adequately to antiseizure medications, and of those who undergo surgery, roughly $40$% achieve seizure freedom. The remaining patients-approximately $15$–$20$ million worldwide-are candidates for neuromodulation.

Standard DBS limitations.

Current clinical DBS for epilepsy (targeting the anterior nucleus of the thalamus, per the SANTE trial; Fisher et al., 2010) delivers fixed-parameter stimulation: fixed frequency ($145$,Hz), pulse width ($90\mu$s), and amplitude ($5$,V). The stimulation is continuous or cycled (1,min on, 5,min off) without regard to the patient's current brain state. This open-loop approach is inefficient: it stimulates during interictal periods when seizure risk is low and may be poorly timed relative to actual pre-ictal states.

OT-guided closed-loop DBS.

The OT alarm ${\delta }_{\mathrm{OT}}(t)$ from Section Detecting Pre-Ictal State Transitions via OT provides a state-dependent trigger. The MFG optimal control $v^{\ast }(x,t)$ then specifies which brain regions to stimulate and with what spatial pattern. The integrated framework operates as follows:

1. Monitoring: Continuous iEEG from DBS electrode contacts; compute ${\delta }_{\mathrm{OT}}(t)$ every $5$,s.

2. Detection: When ${\delta }_{\mathrm{OT}}(t)>{\tau }_{\mathrm{alarm}}$ (pre-ictal alarm), activate closed-loop mode.

3. Targeting: Compute the optimal branched-OT propagation tree (Section Branched Optimal Transport for Seizure Propagation) from the current hub distribution ${\mu }_t$ to the predicted ictal distribution ${\mu }_{\mathrm{ic}}$. Identify network hubs on the propagation tree.

4. Control: Apply the MFG control signal $v^{\ast }$ at the identified hubs via the DBS device, counteracting the pre-ictal drift in the Wasserstein geodesic and redirecting the brain-state trajectory toward the interictal attractor.

5. Verification: Monitor ${\delta }_{\mathrm{OT}}(t)$ after stimulation; if it returns below ${\tau }_{\mathrm{abort}}$ within $30$,s, deactivate closed-loop mode and log the event.

Wasserstein Distance as a Proper Metric on Persistence Diagrams

We now provide the theoretical foundation for the OT-based epilepsy framework: a proof that the Wasserstein distance on persistence diagrams is indeed a metric, justifying its use as a distance in the TPD.

Exercises

Transformer Architectures for Seizure Prediction

The attention mechanism, originally conceived to allow neural machine translation models to align source and target words, has proven unexpectedly well suited to the structure of electroencephalographic (EEG) data. A seizure is not a local event: it arises from the synchronised, pathological recruitment of neural populations that are often spatially distributed across multiple brain regions. Classical convolutional networks excel at extracting local features within a single electrode channel but struggle to capture the long-range, cross-channel dependencies that characterise the pre-ictal state. The transformer's self-attention mechanism is precisely equipped to reason about such global dependencies: every position in the input sequence can attend to every other position in a single operation, without the depth limitation of convolutional receptive fields.

The application of transformers to EEG seizure prediction addresses three interrelated challenges that thwarted earlier approaches:

1. Channel redundancy. Clinical EEG recordings commonly use 18 to 128 electrodes, but seizures in a given patient are typically driven by a small focal zone. Wearable systems and closed-loop stimulators cannot accommodate 18 electrodes; they demand adaptive channel selection.

2. Non-stationarity. The EEG signal is notoriously non-stationary: background rhythms shift with arousal, medication state, and circadian phase. A model trained on morning recordings may fail in the evening. Patient-specific adaptation is therefore essential.

3. Latency constraints. A seizure warning must arrive early enough for the patient to reach safety or for a neuromodulation device to intervene. This imposes strict latency requirements, often measured in tens of milliseconds for the inference step itself.

The transformer architectures described in this section address all three challenges through attention, hybrid recurrent-attentive designs, and self-supervised pretraining strategies.

The Channel-Aware Set Transformer

The canonical EEG montage used in clinical practice and in the Children's Hospital Boston–Massachusetts Institute of Technology (CHB-MIT) scalp EEG dataset consists of 18 channels placed according to the 10–20 international system. Naively treating all 18 channels as equal inputs is suboptimal for two reasons: (a) only a subset participate actively in any given patient's seizure onset zone, and (b) wearable deployment platforms are typically constrained to two to four electrodes by power and comfort considerations. The Channel-Aware Set Transformer (CAST), introduced in a 2023 study evaluated on the CHB-MIT dataset, addresses both issues through a two-stage attention architecture that dynamically selects the most informative channels before performing temporal seizure prediction.

Stage 1: Intra-channel temporal encoding.

Each of the $C=18$ raw EEG channels is treated as an independent time series of length $T$ samples. The signal in channel $c$ is segmented into overlapping windows of length $L$ samples with hop size $H$, yielding a sequence of $N=\lfloor (T-L)/H\rfloor +1$ windows. Each window is passed through a lightweight one-dimensional convolutional encoder that extracts a $d$-dimensional feature vector:

(ENC)$$\begin{array}{ccc}& {𝒉}_c^{(n)}=\mathrm{ConvEnc}({𝒙}_c^{(n)};{𝜽}_{\mathrm{enc}}),c=1,\dots ,C,n=1,\dots ,N,& \text{<span class="tml-eqn"></span>}\end{array}$$

where ${𝒙}_c^{(n)}\in {\mathrm{ℝ}}^L$ is the $n$-th window of channel $c$, ${𝒉}_c^{(n)}\in {\mathrm{ℝ}}^d$, and ${𝜽}_{\mathrm{enc}}$ are shared across all channels and windows. Sharing parameters enforces channel-agnosticism at this stage: the encoder learns generic EEG features regardless of electrode position.

Stage 2: Inter-channel set attention.

Given the set of channel representations ${\mathscr{H}}^{(n)}=\{{𝒉}_1^{(n)},\dots ,{𝒉}_C^{(n)}\}$ at time step $n$, the CAST applies a set attention block (SAB) that computes pairwise attention between all channel pairs. The SAB is defined as follows.

Channel scoring and dynamic selection.

After the SAB, each updated channel representation ${\widetilde{𝒉}}_c^{(n)}={[\mathrm{SAB}({𝐇}^{(n)})]}_c$ is passed through a learned channel scoring head: (Score)$$\begin{array}{ccc}& s_c^{(n)}=\sigma ({𝐖}_{\mathrm{score}}{\widetilde{𝒉}}_c^{(n)}+b_{\mathrm{score}})\in (0,1),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\sigma$ denotes the sigmoid function. The score $s_c^{(n)}$ quantifies the informativeness of channel $c$ at time step $n$. Dynamic channel selection retains only the top-$k$ channels by score, where $k$ is either fixed (e.g., $k=3$ for wearable deployment) or determined adaptively by a threshold $\tau$ (retaining channels with $s_c^{(n)}>\tau$). The selected subset ${𝒮}^{(n)}\subseteq \{1,\dots ,C\}$ with $|{𝒮}^{(n)}|=k^{(n)}$ feeds into the temporal prediction stage.

On the CHB-MIT benchmark, CAST reduces the average number of active channels from the full clinical montage of 18 channels to only 2.8 channels per prediction window while maintaining high seizure detection performance. This three-channel operating point makes the system suitable for a wristband or behind-the-ear form factor.

Stage 3: Temporal seizure classifier.

The selected channel representations ${\{{\widetilde{𝒉}}_c^{(n)}\}}_{c\in {𝒮}^{(n)}}$ are aggregated by sum pooling: (POOL)$$\begin{array}{ccc}& {𝒛}^{(n)}=\sum _{c\in {𝒮}^{(n)}}{\widetilde{𝒉}}_c^{(n)},& \text{<span class="tml-eqn"></span>}\end{array}$$ producing a fixed-size vector ${𝒛}^{(n)}\in {\mathrm{ℝ}}^d$ regardless of $|{𝒮}^{(n)}|$. A temporal transformer encoder processes the sequence $({𝒛}^{(1)},\dots ,{𝒛}^{(N)})$ with positional encodings and outputs a binary classification: pre-ictal (seizure imminent within the prediction horizon) or inter-ictal (baseline). The full model is trained end-to-end with a weighted binary cross-entropy loss to address the severe class imbalance inherent in seizure prediction tasks (seizure windows represent typically less than 1% of recording time).

Performance on CHB-MIT.

Evaluated on the CHB-MIT scalp EEG dataset across 23 paediatric patients, CAST achieves:

• Sensitivity: 80.1% (fraction of pre-ictal windows correctly flagged as pre-ictal).

• False positive rate (FPR): 0.11 false alarms per hour during the inter-ictal period.

• Inference latency: 33.5,ms on a mobile-class processor (ARM Cortex-A55, 2.0,GHz), suitable for closed-loop neuromodulation.

• Mean active channels: 2.8 out of 18.

The combination of high sensitivity, low false alarm rate, and sub-50,ms latency positions CAST as a viable candidate for real-time, wearable seizure warning systems.

Multidimensional Transformer with LSTM-GRU Hybrid

Seizure dynamics unfold simultaneously in time and across the frequency spectrum. The discharge patterns characteristic of different epilepsy syndromes-the 3,Hz spike-and-wave of childhood absence epilepsy, the high-frequency oscillations (HFOs) above 80,Hz that mark the seizure onset zone in focal epilepsy-are spectral signatures as much as temporal ones. A pure temporal transformer processes raw EEG samples and must learn frequency sensitivity implicitly from data. A more principled approach extracts an explicit time-frequency representation first and then applies attention in the joint time-frequency domain.

The Multidimensional Transformer (MDT) with LSTM-GRU recurrent backbone, reported with 98.3% classification accuracy on held-out test sets, processes EEG through three sequential stages:

Stage 1: Time-frequency feature extraction.

For each channel $c$, a short-time Fourier transform (STFT) is applied with window length $W$ samples and hop size $S$ samples: (STFT)$$\begin{array}{ccc}& {𝐗}_c\in {\mathrm{ℝ}}^{F\times T^{\prime }},{[{𝐗}_c]}_{f,t}=|\mathrm{STFT}(x_c;f,t){|}^2,& \text{<span class="tml-eqn"></span>}\end{array}$$ where $F$ is the number of frequency bins and $T^{\prime }=\lfloor (T-W)/S\rfloor +1$ is the number of time frames. The resulting spectrogram is discretised into $B$ frequency bands (delta 0.5–4,Hz, theta 4–8,Hz, alpha 8–12,Hz, beta 12–30,Hz, low-gamma 30–80,Hz, and HFO above 80,Hz) and a band-specific two-dimensional convolutional encoder extracts spatial-frequency features: (BAND CONV)$$\begin{array}{ccc}& {𝐅}_c^{(b)}=\mathrm{Conv2D}({𝐗}_c^{(b)};{𝜽}_b),b=1,\dots ,B,& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝐗}_c^{(b)}$ is the sub-spectrogram for band $b$ and ${𝜽}_b$ are band-specific convolutional kernels. The six band-specific feature maps are concatenated along the channel axis to form a unified time-frequency tensor ${𝐅}_c\in {\mathrm{ℝ}}^{d_F\times T^{\prime }}$.

Stage 2: Global attention across time-frequency positions.

The tensor ${𝐅}_c$ is reshaped into a sequence of $d_F$ tokens, each corresponding to a frequency feature at a given time frame. A standard transformer encoder with $L$ layers and $h$ attention heads processes this sequence, allowing every time-frequency cell to attend to every other: (TF Transformer)$$\begin{array}{ccc}& {𝐆}_c=\mathrm{TransformerEncoder}({𝐅}_c;{𝜽}_{\mathrm{TF}}),{𝐆}_c\in {\mathrm{ℝ}}^{d_G\times T^{\prime }},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $d_G$ is the transformer model dimension. The global self-attention in the time-frequency space captures relations such as the co-occurrence of slow rhythms and high-frequency ripples that characterise pathological coupling in the pre-ictal state.

Stage 3: Recurrent sequence modelling.

The transformer output ${𝐆}_c$ is a sequence of contextualised time-frequency features. A bidirectional LSTM-GRU unit processes this sequence to model the temporal evolution of these features, which is essential because the pre-ictal state is a dynamic trajectory, not a static pattern. The LSTM and GRU units are stacked:

(LSTM)$$\begin{array}{ccc}& {𝒉}_c^{\mathrm{LSTM}}=\mathrm{BiLSTM}({𝐆}_c;{𝜽}_{\mathrm{LSTM}}),& \text{<span class="tml-eqn"></span>}\end{array}$$ (GRU)$$\begin{array}{ccc}& {𝒉}_c^{\mathrm{GRU}}=\mathrm{GRU}({𝒉}_c^{\mathrm{LSTM}};{𝜽}_{\mathrm{GRU}}),& \text{<span class="tml-eqn"></span>}\end{array}$$ (CLS)$$\begin{array}{ccc}& {\hat{y}}_c=\mathrm{Softmax}({𝐖}_{\mathrm{cls}}{𝒉}_c^{\mathrm{GRU}}+{𝒃}_{\mathrm{cls}}).& \text{<span class="tml-eqn"></span>}\end{array}$$

Predictions across channels are aggregated by majority voting or by a learned channel-weighting scheme similar to the CAST scoring head.

The LSTM component excels at maintaining long-range temporal memory (pre-ictal dynamics that evolve over tens of seconds), while the GRU component provides a lighter-weight gating mechanism for short-range transitions. Together, they capture both the slow build-up of synchrony and the abrupt onset of paroxysmal activity.

On a private dataset of 32 patients with drug-resistant focal epilepsy undergoing stereo-EEG evaluation, the MDT-LSTM-GRU system achieves 98.3% seizure classification accuracy (distinguishing pre-ictal from inter-ictal one-minute epochs), with 97.6% sensitivity and 98.9% specificity.

Hybrid CNN-Transformer for Spatial-Temporal Modelling

The CAST and MDT architectures treat channels as a set or process them independently before cross-channel aggregation. An alternative strategy exploits the geometry of the electrode array: adjacent electrodes record correlated signals, and the spatial gradient of electrical potential encodes information about the underlying source distribution. The Hybrid CNN-Transformer architecture combines (a) a spatial feature extractor based on a convolutional or graph convolutional network (GCN) with (b) a temporal self-attention module, processing EEG in a manner analogous to how vision transformers combine patch embeddings with positional attention.

Spatial feature extraction via CNN/GCN.

Let the electrode positions be modelled as nodes in a graph $𝒢=(𝒱,ℰ)$, where $𝒱=\{c:c=1,\dots ,C\}$ is the set of $C$ electrodes and the edge weight between electrodes $c$ and $c^{\prime }$ is: (EDGE Weight)$$\begin{array}{ccc}& w_{c{c}^{\prime }}=\exp (-\frac{\Vert {𝒑}_c-{𝒑}_{c^{\prime }}{\Vert }_2^2}{2{\sigma }^2}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝒑}_c\in {\mathrm{ℝ}}^3$ is the three-dimensional position of electrode $c$ on the scalp surface and $\sigma$ is a bandwidth parameter. A spectral GCN à la Kipf and Welling (2017) operates on the EEG signal matrix $𝐗\in {\mathrm{ℝ}}^{C\times T}$: (GCN)$$\begin{array}{ccc}& {𝐇}^{(\ell +1)}={\sigma }_{\mathrm{relu}}\left(\widetilde{𝐀}{𝐇}^{(\ell )}{𝐖}^{(\ell )}\right),\widetilde{𝐀}={𝐃}^{-1/2}(𝐀+𝐈){𝐃}^{-1/2},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $𝐀$ is the weighted adjacency matrix, $𝐃$ is the degree matrix, and ${𝐖}^{(\ell )}$ are learnable weight matrices. The GCN propagates information between spatially adjacent electrodes, effectively performing spatial smoothing that respects the electrode geometry.

A parallel pathway applies a standard two-dimensional CNN to a stacked multi-channel EEG image $𝐗$ (treating channels as the height dimension and time as the width dimension), extracting spatial filter responses akin to common spatial pattern (CSP) filters: (CNN Feats)$$\begin{array}{ccc}& {𝐅}_{\mathrm{CNN}}=\mathrm{CNN}(𝐗;{𝜽}_{\mathrm{CNN}}),{𝐅}_{\mathrm{CNN}}\in {\mathrm{ℝ}}^{d_{\mathrm{CNN}}\times T^{\prime }},& \text{<span class="tml-eqn"></span>}\end{array}$$ where the convolutional kernels span all channels simultaneously, learning spatial filters that are equivalent to linear mixing of electrode signals. The CNN and GCN feature maps are concatenated: (Concat)$$\begin{array}{ccc}& {𝐅}_{\mathrm{spatial}}=[{𝐅}_{\mathrm{CNN}};{𝐅}_{\mathrm{GCN}}]\in {\mathrm{ℝ}}^{(d_{\mathrm{CNN}}+d_{\mathrm{GCN}})\times T^{\prime }}.& \text{<span class="tml-eqn"></span>}\end{array}$$

Temporal self-attention.

The concatenated spatial features are treated as a sequence of $T^{\prime }$ tokens, each of dimension $d_{\mathrm{CNN}}+d_{\mathrm{GCN}}$. A transformer encoder with causal masking (to avoid look-ahead bias in online prediction) computes temporal self-attention: (Temporal)$$\begin{array}{ccc}& 𝐎=\mathrm{CausalTransformerEncoder}({𝐅}_{\mathrm{spatial}}+{𝐄}_{\mathrm{pos}};{𝜽}_{\mathrm{temp}}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝐄}_{\mathrm{pos}}\in {\mathrm{ℝ}}^{T^{\prime }\times d}$ is a sinusoidal positional encoding that injects temporal ordering into the otherwise permutation-equivariant attention. Causal masking ensures that prediction at time $t$ uses only past information, a critical requirement for prospective seizure prediction.

The final token representation ${𝐎}_{T^{\prime }}\in {\mathrm{ℝ}}^d$ (the last time step) is passed through a classification head to produce the seizure prediction. The hybrid architecture achieves the best of both worlds: the CNN/GCN captures the spatial structure of epileptic activity, while the temporal transformer captures its dynamic evolution.

Patient-Adaptive GPT for EEG

The transformer architectures described in the preceding subsections are trained in a supervised manner on labelled EEG recordings. This is problematic in two respects: (a) seizure recordings are rare and expensive to annotate-the CHB-MIT dataset, one of the most widely used benchmarks, contains only 182 seizures across 23 patients-and (b) the resulting models are often patient-general, failing to capture the idiosyncratic EEG signature of each individual's epilepsy. Patient-adaptive GPT addresses both shortcomings through a self-supervised pretraining followed by patient-specific fine-tuning strategy inspired by the GPT family of language models.

Pretraining on TUH EEG.

The Temple University Hospital (TUH) EEG Corpus is the largest publicly available EEG dataset, comprising over 30,000 recordings from approximately 14,000 patients accumulated over two decades of clinical practice. The majority of these recordings are not annotated for seizures (inter-ictal recordings predominate), making them unsuitable for standard supervised training. However, they are ideal for self-supervised pretraining: the model learns the statistical regularities of normal and abnormal EEG without requiring seizure labels.

The pretraining objective is an autoregressive next-token prediction analogous to language modelling. The EEG signal is tokenised by quantising the raw waveform into a discrete codebook via a vector quantisation layer: (VQ)$$\begin{array}{ccc}& z_t={\mathrm{arg\hspace{0.17em}min}}_{k\in \{1,\dots ,K\}}\Vert {𝒇}_t-{𝒆}_k{\Vert }_2,{𝒇}_t=\mathrm{ConvEnc}(x_{t-L:t}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $K$ is the codebook size (typically $K=512$), ${𝒆}_k\in {\mathrm{ℝ}}^d$ is the $k$-th codebook embedding, and ${𝒇}_t$ is a local convolutional feature at time $t$. The resulting token sequence $(z_1,z_2,\dots ,z_{T^{\prime }})$ is fed to a GPT-style transformer decoder that predicts the next token: (LM)$$\begin{array}{ccc}& p(z_{t+1}|z_1,\dots ,z_t;{𝜽}_{\mathrm{GPT}})=\mathrm{Softmax}({𝐖}_e{𝒉}_t+{𝒃}_e{)}_K,& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝒉}_t$ is the transformer's hidden state at position $t$. The pretraining loss is the standard autoregressive cross-entropy: (Pretrain LOSS)$$\begin{array}{ccc}& {ℒ}_{\mathrm{pre}}=-\sum _{t=1}^{T^{\prime }-1}\log p(z_{t+1}|z_1,\dots ,z_t;{𝜽}_{\mathrm{GPT}}).& \text{<span class="tml-eqn"></span>}\end{array}$$

Trained on the TUH corpus (over 1.5 billion EEG tokens), the pretrained GPT learns a rich generative model of EEG dynamics: it can generate realistic-looking EEG waveforms, complete partial recordings, and-most importantly-detect out-of-distribution patterns that deviate from the learned prior.

Patient-specific fine-tuning.

Given a new patient with $n_s$ seizure recordings (typically $n_s\in \{3,\dots ,15\}$) and $n_i$ hours of inter-ictal recordings, the pretrained GPT is fine-tuned using a supervised classification head: (Finetune CLS)$$\begin{array}{ccc}& \hat{y}=\mathrm{Sigmoid}({𝐖}_{\mathrm{cls}}\overline{𝒉}+b_{\mathrm{cls}}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\overline{𝒉}=T^{\prime -1}{\sum }_t{𝒉}_t$ is the mean-pooled hidden state over the prediction window. Fine-tuning updates all parameters of the GPT (not just the classification head) with a low learning rate ${\eta }_{\mathrm{ft}}={10}^{-5}$, preventing catastrophic forgetting of the general EEG prior while adapting to the patient's specific seizure signature.

An additional component unique to the patient-adaptive GPT is an anomaly detection auxiliary loss that penalises the model for assigning high likelihood to pre-ictal segments: (ANOM LOSS)$$\begin{array}{ccc}& {ℒ}_{\mathrm{anom}}={𝔼}_{(x,y=1)}[\log p(x|{𝜽}_{\mathrm{GPT}})]-{𝔼}_{(x,y=0)}[\log p(x|{𝜽}_{\mathrm{GPT}})],& \text{<span class="tml-eqn"></span>}\end{array}$$ where $y=1$ indicates the pre-ictal class. Minimising ${ℒ}_{\mathrm{anom}}$ encourages the GPT to assign lower likelihood to pre-ictal EEG (since it deviates from the inter-ictal baseline learned during pretraining), making the model's negative log-likelihood a principled seizure risk score.

Comparative Analysis of Transformer Variants

The four transformer-based architectures described in this section occupy different positions in the design space defined by three axes: (a) channel handling (dynamic selection vs. spatial graph vs. full set), (b) temporal modelling (pure attention vs. hybrid attention-recurrence), and (c) supervision (fully supervised vs. self-supervised pretraining with fine-tuning). Table Table 8 summarises the key architectural features and reported performance metrics.

Model	Dataset	Channels	Accuracy	Sensitivity	FPR (h${}^{-1}$)	Latency
CAST	CHB-MIT (23 pt.)	2.8 of 18 (dyn.)	N/A	80.1%	0.11	33.5,ms
MDT-LSTM-GRU	Private (32 pt.)	18 (all)	98.3%	97.6%	N/A	$\sim$120,ms
CNN-Transformer	CHB-MIT + EPILEPSIAE	18 (spatial)	96.1%	92.4%	0.08	55,ms
Patient-Adaptive GPT	TUH + CHB-MIT	Patient-adaptive	94.7%	88.3%	0.14	80,ms
Classical baselines (for reference)
SVM + CSP	CHB-MIT	18	87.2%	73.6%	0.34	$<$1,ms
LSTM-only	CHB-MIT	18	91.4%	80.2%	0.22	15,ms

Several observations emerge from this comparison. First, the MDT-LSTM-GRU achieves the highest accuracy (98.3%) and sensitivity (97.6%), but at the cost of higher latency ($\sim$120,ms) and requiring all 18 channels-infeasible for a wearable. Second, CAST achieves the lowest channel count (2.8) with competitive sensitivity (80.1%), making it the most wearable-compatible option. Third, the CNN-Transformer achieves the lowest FPR (0.08 per hour), which is the clinically most important metric for quality of life: false alarms cause patient anxiety and reduce adherence to the warning device. Fourth, the patient-adaptive GPT provides the most principled framework for low-resource patients (few labelled seizures) through its self-supervised pretraining strategy, though its overall metrics are not state-of-the-art when labelled data is plentiful.

Transformers for Brain Structure and Tractography

Seizure prediction from EEG addresses when a seizure will occur. An equally important clinical question is how it will spread: which brain structures will be recruited, in which order, and with what clinical consequences. The answers lie in the white matter architecture of the brain. Axonal fibre tracts connect cortical regions, and the structural connectivity network they form determines the pathways along which ictal discharges propagate. Mapping these pathways with sufficient precision to guide surgical planning or closed-loop stimulation targeting is a task that requires integrating diffusion-weighted MRI (DWI) tractography with computational models of network synchrony. Transformers have recently entered this domain through two complementary routes: parcellating the complex output of tractography algorithms (RapidParc) and learning to predict seizure propagation from structural connectivity features.

RapidParc: Global Context Transformer for White Matter Tractography Parcellation

Diffusion tensor imaging (DTI) and its generalisations (HARDI, Q-ball, DSI) measure the preferential diffusion of water molecules along axonal fibres, enabling reconstruction of white matter fibre trajectories through probabilistic or deterministic tractography algorithms. A full-brain tractography reconstruction typically produces between 500,000 and 10,000,000 streamlines, each representing a putative axonal pathway. To be clinically useful, these streamlines must be parcellated: assigned to one of the major known white matter bundles (corticospinal tract, arcuate fasciculus, uncinate fasciculus, etc.) or to cortical projection targets.

Parcellation is a difficult classification problem for several reasons:

1. Streamlines vary in length from tens to hundreds of millimetres; no fixed-length representation is natural.

2. Neighbouring streamlines belonging to different bundles may be spatially interleaved due to crossing fibre regions.

3. The spatial context of a streamline (which other streamlines surround it) is highly informative but requires global reasoning across the full tractogram.

Traditional parcellation methods-either atlas-based registration or supervised pointwise classifiers-treat each streamline independently, ignoring the global context. This leads to anatomical incoherence: a single anatomical bundle may be fragmented into disconnected segments because neighbouring streamlines are classified independently and may receive conflicting labels.

RapidParc architecture.

RapidParc addresses the global context problem by treating the entire tractogram as a set of streamlines and processing it with a transformer that attends across the full set. Each streamline ${𝒔}_i=(p_{i,1},p_{i,2},\dots ,p_{i,N_i})\in {\mathrm{ℝ}}^{N_i\times 3}$ (a sequence of 3D Cartesian coordinates) is first encoded by a PointNet-style permutation-invariant encoder: (Pointnet)$$\begin{array}{ccc}& {𝒇}_i=\mathrm{PointNet}({𝒔}_i;{𝜽}_{\mathrm{PN}})\in {\mathrm{ℝ}}^{d_f},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\mathrm{PointNet}$ applies a shared MLP to each point, then max-pools across points, producing a fixed-dimensional streamline feature regardless of streamline length $N_i$.

The streamline features ${\{{𝒇}_i\}}_{i=1}^M$ (where $M$ is the number of streamlines, potentially millions) form a set. RapidParc processes this set in two stages to manage the quadratic cost of full self-attention at million-streamline scale.

Local neighbourhood attention. For each streamline $i$, a $k$-nearest-neighbour graph in the streamline feature space identifies the $k$ most similar streamlines. A local Set Attention Block (SAB) processes the neighbourhood: (Local SAB)$$\begin{array}{ccc}& {\widetilde{𝒇}}_i={[\mathrm{SAB}(\{{𝒇}_j:j\in 𝒩(i)\})]}_i,& \text{<span class="tml-eqn"></span>}\end{array}$$ where $𝒩(i)$ is the neighbourhood of streamline $i$. This local attention step has cost $𝒪(M\cdot k^2)$ rather than $𝒪(M^2)$.

Global inducing-point attention. A small set of $P\ll M$ inducing points $𝐈\in {\mathrm{ℝ}}^{P\times d_f}$ (learnable summary representations of the most important structural features) enables global information propagation via pooling attention: (Global ATTN)$$\begin{array}{ccc}& \widetilde{𝐈}=\mathrm{Attention}(𝐈,\widetilde{𝐅},\widetilde{𝐅}),\widetilde{𝐅}={[{\widetilde{𝒇}}_1,\dots ,{\widetilde{𝒇}}_M]}^{\top },& \text{<span class="tml-eqn"></span>}\end{array}$$ (Unpool)$$\begin{array}{ccc}& {\widehat{𝒇}}_i={\widetilde{𝒇}}_i+\mathrm{Attention}({\widetilde{𝒇}}_i,\widetilde{𝐈},\widetilde{𝐈}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where the second attention operation “unpools” the global context from the inducing points back to each streamline. The inducing points act as a compressed global summary of the tractogram that every streamline can attend to in $𝒪(M\cdot P)$ operations.

The final streamline feature ${\widehat{𝒇}}_i$ integrates both local neighbourhood context and global tractogram structure. A classification head assigns a bundle label from a set of $B$ anatomical bundles (RapidParc supports $B=72$ bundles from the TractSeg atlas): (Classify)$$\begin{array}{ccc}& {\hat{y}}_i={\mathrm{arg\hspace{0.17em}max}}_{b\in \{1,\dots ,B\}}{[\mathrm{Softmax}({𝐖}_{\mathrm{parc}}{\widehat{𝒇}}_i+{𝒃}_{\mathrm{parc}})]}_b.& \text{<span class="tml-eqn"></span>}\end{array}$$

RapidParc achieves 94.7% mean overlap (Dice) with manual expert parcellations on the Human Connectome Project (HCP) dataset, compared to 89.1% for the previous state-of-the-art TractSeg method (Wasserthal et al., 2018), while reducing parcellation time from approximately 5 minutes to 12 seconds per subject-a $25\times$ speedup that makes large-cohort tractography studies tractable.

From Tractography to Seizure Propagation Pathways

The connection between white matter structure and seizure dynamics is both conceptually compelling and practically important. Epileptic networks are defined not by the activity of isolated neurons but by the hypersynchronous entrainment of large populations interconnected by axonal pathways. When a seizure originates in a focal onset zone (say, the left hippocampus in mesial temporal lobe epilepsy), it propagates to secondary zones via the same fibre tracts that support normal cognitive function: the fornix, the cingulum bundle, the uncinate fasciculus. The rate, direction, and extent of this propagation determine the clinical semiology: a seizure that recruits the motor cortex via the corticospinal tract produces convulsions, while one that recruits the limbic system produces automatisms and amnesia.

Micro-to-macro pathway: from cellular pathology to network hypersynchrony.

Understanding seizure propagation requires bridging four levels of organisation, each connected to the next by a mathematical model:

1. Cellular/synaptic level. At the scale of individual neurons, epileptic tissue exhibits characteristic pathological changes: reduced inhibitory interneuron density (GABA-ergic deficiency), enhanced NMDA receptor expression, mossy fibre sprouting in the dentate gyrus (for temporal lobe epilepsy), and dyslamination in focal cortical dysplasias. These microscopic changes alter the balance between excitation ($E$) and inhibition ($I$), quantified by the $E/I$ ratio: (EI Ratio)$$\begin{array}{ccc}& r_{E/I}=\frac{{\sum }_i{g}_{E,i}}{{\sum }_j{g}_{I,j}},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $g_{E,i}$ and $g_{I,j}$ are the conductances of excitatory and inhibitory synapses, respectively. A region with $r_{E/I}>1$ is hyperexcitable and prone to self-sustaining bursting.

2. Local network level. Groups of neurons form local recurrent circuits (cortical columns, hippocampal CA1/CA3 circuits) whose collective dynamics are described by neural mass or neural field models. The Wilson-Cowan model captures the mean firing rates of excitatory ($E$) and inhibitory ($I$) populations: (Wilson Cowan E)$$\begin{array}{cccc}& {\tau }_E\dot{E}& =-E+\sigma (w_{EE}E-w_{IE}I+I_E^{\mathrm{ext}}),& \text{<span class="tml-eqn"></span>}\\ & {\tau }_I\dot{I}& =-I+\sigma (w_{EI}E-w_{II}I+I_I^{\mathrm{ext}}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $w_{EE},w_{EI},w_{IE},w_{II}$ are coupling strengths and $\sigma$ is a sigmoid transfer function. In the epileptic regime (high $w_{EE}$, low $w_{IE}$), the system exhibits bistability: a small perturbation can tip it from a stable fixed point (inter-ictal) to a sustained oscillation (ictal).

3. Large-scale network level. Individual cortical regions (nodes) are coupled by structural white matter connections (edges) whose weights are estimated from DTI tractography. The structural connectome $𝐖\in {\mathrm{ℝ}}^{N\times N}$ (where $N$ is the number of parcellated brain regions) encodes the probability and number of streamlines between each pair of regions. A network-level model of seizure propagation extends the Wilson-Cowan dynamics to the full connectome: (Network EI)$$\begin{array}{ccc}& {\tau }_E{\dot{E}}_i=-E_i+\sigma (w_{EE}{E}_i-w_{IE}{I}_i+I_E^{\mathrm{ext}}+\lambda \sum _{j\ne i}{W}_{ij}{E}_j),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\lambda$ controls the strength of inter-regional coupling via the structural connectome $𝐖$. Seizure propagation in this model corresponds to the recruitment of additional nodes into the synchronised ictal state as the excitatory signal spreads along high-weight edges of $𝐖$.

4. Macroscopic clinical level. The network propagation pattern ${\{E_i(t)\}}_{i=1}^N$ maps directly to observable clinical features: the temporal order in which regions reach ictal state determines the evolution of seizure semiology. A region $i$ becomes ictal at time $t_i^{\ast }=\inf \{t:E_i(t)>{\theta }_{\mathrm{ictal}}\}$, and the propagation sequence $(i_1,i_2,\dots ,i_k)$ ordered by $t_{i_1}^{\ast }<t_{i_2}^{\ast }<\dots <t_{i_k}^{\ast }$ is the seizure propagation pathway. Transformers trained on historical seizure recordings and their associated structural connectomes learn to predict this pathway from DTI data alone, enabling pre-surgical structural connectivity mapping without recording seizures.

Transformer Architecture for Seizure Propagation Prediction

Given the parcellated structural connectome $𝐖\in {\mathrm{ℝ}}^{N\times N}$ and a known (or hypothesised) seizure onset region $i^{\ast }$, the goal is to predict the propagation pathway: the sequence of regions recruited into the ictal state, and the probability that each region will be recruited.

A Seizure Propagation Transformer (SPT) formulates this as a graph-conditioned sequence generation problem. The structural connectome defines a graph ${𝒢}_{\mathrm{conn}}=(𝒱,ℰ,𝐖)$ with $N$ nodes (brain regions) and edge weights from DTI. A graph attention network (GAT) encodes each node's structural context: (GAT)$$\begin{array}{ccc}& {𝒉}_i=\mathrm{GAT}{(𝐖,{𝐅}_{\mathrm{region}};{𝜽}_{\mathrm{GAT}})}_i\in {\mathrm{ℝ}}^{d_h},& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝐅}_{\mathrm{region}}\in {\mathrm{ℝ}}^{N\times d_r}$ contains region-level features including DTI-derived metrics (fractional anisotropy, mean diffusivity, radial diffusivity of incoming and outgoing tracts) and functional MRI resting-state connectivity profiles.

The onset region $i^{\ast }$ is encoded as a special [ONSET] token prepended to the sequence. The SPT then autoregressively generates the propagation pathway: (SPT)$$\begin{array}{ccc}& p(i_{t+1}|i_1,\dots ,i_t,i^{\ast },𝐖)=\mathrm{Softmax}({𝐖}_{\mathrm{spt}}\mathrm{TransformerDecoder}({𝒉}_{i^{\ast }},{𝒉}_{i_1},\dots ,{𝒉}_{i_t};{𝜽}_{\mathrm{SPT}})+{𝒃}_{\mathrm{spt}}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where the transformer decoder attends to both the previously generated propagation sequence and the structural connectome node encodings (via cross-attention to ${\{{𝒉}_j\}}_{j=1}^N$). The model is trained on a dataset of 847 focal epilepsy patients with stereoelectroencephalography (SEEG) recordings that document the actual propagation sequence, with the structural connectome derived from the same patient's preoperative DTI.

Evaluated on held-out patients, the SPT achieves:

• AUC 0.89 for predicting whether each region will be recruited (binary classification per region).

• Kendall's $\tau =0.72$ for predicting the order of regional recruitment (rank correlation of predicted vs. actual propagation sequence).

• 82% concordance between the model's top-ranked surgical resection target and the clinical SEEG-derived target in a retrospective series of 120 operated patients.

Connecting Micro-Cellular Pathology to Macro-Network Hypersynchrony

The multi-level framework introduced in From Tractography to Seizure Propagation Pathways describes the hierarchy from cellular pathology to clinical semiology in conceptual terms. We now describe how generative models and transformers are used to bridge these levels quantitatively, transforming histopathological measurements into predictions of network-level dynamics.

From histopathology to connectome perturbation.

Post-surgical histopathological analysis of resected epileptic tissue provides ground truth measurements of cellular pathology: interneuron density, mossy fibre sprouting index, neuronal loss fraction, and dysmorphic neuron count. A generative model of the form: (Delta W)$$\begin{array}{ccc}& \mathrm{\Delta }{W}_{ij}=f_{𝜽}({\varphi }_i,{\varphi }_j,\Vert r_i-r_j{\Vert }_2),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${\varphi }_i\in {\mathrm{ℝ}}^{d_{\varphi }}$ is the pathology feature vector of region $i$, $r_i$ is its spatial position, and $f_{𝜽}$ is a neural network, predicts the perturbation to the structural connectome caused by the pathology. The perturbed connectome $𝐖+\mathrm{\Delta }𝐖$ is then fed to the network-level Wilson-Cowan model (Equation (Network EI)) to predict the altered network dynamics.

Transformer-based multi-scale fusion.

A cross-scale transformer fuses features from four levels of organisation into a unified representation that supports seizure pathway prediction and treatment response forecasting:

(Cross ATTN FUSE)$$\begin{array}{ccc}& {𝒓}_i=\mathrm{CrossAttn}(\underset{\text{cellular}}{\underbrace{{\varphi }_i}},\underset{\text{local network}}{\underbrace{{\mu }_i}},\underset{\text{connectome}}{\underbrace{{𝒉}_i}},\underset{\text{clinical}}{\underbrace{{𝒔}_i}};{𝜽}_{\mathrm{cross}}),& \text{<span class="tml-eqn"></span>}\end{array}$$

where ${\varphi }_i$ is the histopathology feature, ${\mu }_i$ is the Wilson-Cowan fixed-point characterising local dynamics, ${𝒉}_i$ is the GAT-encoded structural connectivity feature from Equation (GAT), and ${𝒔}_i$ is the clinical feature vector (EEG power spectra, SEEG contact localisation, ictal onset zone label). The cross-attention mechanism learns to weight each scale's contribution differently for each query region, adapting to the clinical scenario (e.g., weighting histopathology more heavily for post-surgical outcome prediction, and connectivity more heavily for propagation pathway prediction).

This multi-scale framework achieves a performance gain of 11.4 percentage points in seizure outcome prediction (Engel class I vs. non-class-I surgical outcome) compared to models using only MRI-based connectivity features, demonstrating that microscopic pathological information adds predictive value beyond what structural imaging alone can provide.

Exercises

LLMs for Clinical Epilepsy Management

The neurologist's clinical note is among the richest and most information-dense documents in medicine. A single outpatient visit for a patient with refractory focal epilepsy may generate several paragraphs of free text documenting seizure semiology, anti-seizure medication side-effects, neuroimaging impressions, prior surgical evaluations, and patient-reported quality-of-life outcomes-all interleaved with subjective commentary, abbreviations, and institution-specific shorthand. This richness is also a liability: the very density of information that makes clinical notes valuable makes them nearly impossible to audit systematically at population scale using rule-based systems.

Large language models have altered this calculus. Their ability to parse long, heterogeneous documents and extract structured facts without hand-crafted rules makes them natural candidates for the quality-assurance gap that has long plagued epilepsy care. In this section we examine how LLMs are being deployed for clinical epilepsy management, with particular attention to the AURA platform developed at West Virginia University Medicine, the generation of structured EEG reports from raw signal transcriptions, and the inherent risks that accompany LLM deployment in high-stakes clinical settings.

The AURA Platform: Autonomous Registry for Epilepsy Care

West Virginia University (WVU) Medicine operates a Comprehensive Epilepsy Program that serves a geographically dispersed rural population with limited access to subspecialty neurology. Patients travel hours for clinic visits, yet a substantial fraction arrive with outdated investigations, missing baseline tests, or care gaps that have accumulated silently across multiple providers. The Autonomous Registry for Epilepsy Care (AURA) was designed to address this problem at the registry level rather than the individual-chart level.

AURA ingests structured and unstructured data from the Epic EHR system and applies a suite of LLM-based parsing modules to identify care gaps across the entire registered epilepsy population. In a study of 820 patient visits over a 90-day monitoring window, AURA revealed systematic deficiencies that had been invisible to periodic manual chart review:

• 54% of patients had outdated MRI studies (most recent brain MRI more than five years old or performed at a facility without 3,T field strength, limiting lesion detectability for focal cortical dysplasia).

• 91% lacked a documented neuropsychological evaluation, despite national guidelines recommending baseline cognitive testing for surgical candidacy assessment.

• 35% had no interpretable EEG on file within the prior three years, or had only routine scalp EEG when a prolonged video-EEG study was clinically indicated.

• 81% of female patients of child-bearing age had undocumented folic acid supplementation despite being on anti-seizure medications with known teratogenic risk profiles.

Most striking was the finding that 11% of the total cohort-88 patients-met documented criteria for drug-resistant epilepsy based on their medication histories and seizure diaries, yet had never received a formal surgical referral. These patients were not overlooked because their epileptologists deemed surgery inappropriate; in many cases the notes contained explicit phrases such as “consider surgical evaluation when scheduling allows” or “patient agrees to proceed with epilepsy monitoring unit admission.” The referral had simply never been placed. This is a logistical failure, not a diagnostic one.

Architecture of the AURA Pipeline

The AURA pipeline consists of four stages that transform raw EHR data into prioritised care-gap notifications. Figure fig:epilepsy:aura-pipeline illustrates the flow.

The LLM parsing module operates in a retrieve-then-generate paradigm. For each patient in the registry, relevant note segments from the prior twelve months are retrieved using BM25 sparse retrieval followed by a dense re-ranking step that uses a neurology-domain fine-tuned encoder. The top-$k$ segments are concatenated into a structured prompt that instructs the LLM to extract a fixed schema: (1) names and daily doses of current anti-seizure medications, (2) dates of the three most recent EEGs and their interpretations, (3) date and field strength of the most recent brain MRI, (4) documentation of any folic acid supplementation order, and (5) any provider language suggesting surgical candidacy.

The schema extraction is followed by a DRE screening module that cross-references the extracted medication list with a curated drug database to determine whether the patient has failed two or more adequate anti-seizure medication trials. Patients who test positive for DRE and who lack a pending EMU (epilepsy monitoring unit) admission or surgical consultation order are flagged in the priority queue.

EEG-to-Text Report Generation

A parallel LLM application in epilepsy care concerns the automated generation of clinical EEG reports from intermediate signal-derived representations. The Temple University Hospital (TUH) EEG corpus-with over 16,000 recordings and more than 26,000 paired clinical reports-has enabled the training of sequence-to-sequence models that map signal-level feature descriptions to natural-language clinical summaries.

The generation pipeline operates in two stages. In the first stage, a classical or deep-learning-based EEG feature extractor produces a structured intermediate description: a list of channel-level annotations specifying dominant frequency, amplitude, continuity, symmetry, reactivity, and the presence of epileptiform discharges or seizure patterns. This structured description is deterministic and explainable-it constitutes the evidence that the report must be faithful to.

In the second stage, a fine-tuned language model (typically a GPT-style decoder or a T5-class encoder-decoder) takes the structured description as a prefix and generates the free-text report. The model is trained with cross-entropy loss on the TUH paired corpus, but inference-time constrained decoding is applied to enforce clinical conventions: reports must include specific sections (“Background”, “Epileptiform activity”, “Impression”), and certain high-risk terms (“status epilepticus”, “seizure”) must not appear unless their corresponding feature codes are present in the input description.

This two-stage structure separates the perception problem (what does the EEG show?) from the communication problem (how should we describe it?), limiting the scope within which the LLM can hallucinate. The signal-level extractor provides a factual anchor; the language model provides linguistic fluency.

Hallucination Risks in Clinical LLM Deployment

Vision-Language Models for Epilepsy Diagnosis

Structural neuroimaging occupies a central role in the presurgical evaluation of drug-resistant focal epilepsy. A high-resolution 3,T MRI of the brain is the cornerstone investigation, with specific sequences targeting focal cortical dysplasia (FCD), cavernous malformations, hippocampal sclerosis, and neoplastic lesions. Yet the sensitivity of visual inspection, even by experienced epileptologists, is limited: FCD lesions are notoriously subtle, and up to 30% of presurgical MRIs are initially read as normal despite the presence of a surgically remediable lesion.

Vision-language models (VLMs) offer a route toward automated lesion detection paired with natural-language diagnostic reports that can serve as a second reader for the radiologist and epileptologist. In this section we examine two architecturally distinct VLM systems that have been applied to epilepsy-related imaging tasks: Hilbert-VLM, which combines 3D MRI processing with Hilbert space-filling curves and state space models, and MedVQA-TREE, which applies retrieval-augmented generation to multimodal clinical question answering.

Hilbert-VLM: Space-Filling Curves and Mamba SSMs for 3D MRI

Three-dimensional MRI volumes present a fundamental challenge for standard transformer architectures: the sequence length grows as $O(H\times W\times D)$, rapidly exceeding the practical context window even for modern long-context models. A $256\times 256\times 180$ volumetric scan produces over 11 million voxels; processing this as a flat sequence with full self-attention is computationally infeasible.

Hilbert-VLM resolves this problem through a principled linearisation strategy: it uses Hilbert space-filling curves to impose a 1D ordering on 3D voxel coordinates that preserves spatial locality-voxels that are close in 3D space remain close in the 1D Hilbert ordering, unlike the conventional raster-scan (row-major) ordering where spatially adjacent voxels in the depth dimension are separated by $H\times W$ positions in the sequence.

The linearised volume is then processed by a Mamba selective state space model (SSM). Mamba processes sequences in $O(L)$ time and memory (where $L$ is sequence length) by replacing the quadratic attention matrix with a parameterised recurrence whose transition matrix is input-dependent-the selectivity mechanism that distinguishes Mamba from classical fixed-coefficient SSMs such as S4. Formally, at sequence position $t$ the Mamba layer maintains a hidden state ${𝐡}_t\in {ℝ}^d$ governed by: (Mamba Recurrence)$$\begin{array}{cccc}& {𝐡}_t& ={\overline{𝐀}}_t{𝐡}_{t-1}+{\overline{𝐁}}_t{𝐱}_t,& \text{<span class="tml-eqn"></span>}\\ & {𝐲}_t& ={𝐂}_t{𝐡}_t,& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${\overline{𝐀}}_t$ and ${\overline{𝐁}}_t$ are the discretised state-transition and input matrices, and all parameter matrices $(𝐀,𝐁,𝐂)$ are functions of the current input ${𝐱}_t$, computed by small linear projections. This selectivity allows the model to gate information flow dynamically: irrelevant voxels (white matter, cerebrospinal fluid) are suppressed while lesion-bearing cortical regions are propagated through the state.

The volumetric feature extraction backbone draws on SAM2 (Segment Anything Model 2), which provides a hierarchical image encoder pretrained on a large corpus of natural and medical images. SAM2 features are extracted at multiple scales and serve as the visual tokens fed into the Hilbert-Mamba processing stack.

Hilbert-Mamba Cross-Attention (HMCA)

Lesion segmentation and textual diagnosis generation are coupled through the Hilbert-Mamba Cross-Attention (HMCA) module. HMCA implements a cross-attention mechanism in which the query stream is the language decoder (a GPT-style autoregressive model generating the diagnostic text) and the key–value stream is the Hilbert-ordered Mamba hidden states from the volumetric encoder. Let ${𝐪}_s\in {ℝ}^{d_q}$ be the query at text position $s$ and ${\{{𝐡}_t\}}_{t=1}^L$ the sequence of Mamba hidden states. The cross-attention output at position $s$ is: (HMCA)$$\begin{array}{ccc}& {𝐨}_s=\sum _{t=1}^L{\alpha }_{st}𝐕{𝐡}_t,{\alpha }_{st}=\frac{\exp \left({𝐪}_s^{\top }𝐊{𝐡}_t/\sqrt{d_k}\right)}{{\sum }_{t^{\prime }}\exp \left({𝐪}_s^{\top }𝐊{𝐡}_{t^{\prime }}/\sqrt{d_k}\right)},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $𝐊$ and $𝐕$ are learned projection matrices. Because the Hilbert ordering preserves spatial locality, the attention weights ${\alpha }_{st}$ at text tokens describing, for example, “right temporal lesion” concentrate on Hilbert indices corresponding to the right temporal lobe-providing an implicit spatial grounding for the generated text.

Performance on BraTS2021

Hilbert-VLM was evaluated on the BraTS2021 benchmark, which provides 1,251 multi-parametric MRI cases (T1, T1ce, T2, FLAIR) with expert-annotated brain tumour sub-region masks. While BraTS is primarily a tumour segmentation benchmark, it serves as a proxy for structural lesion detection relevant to epilepsy (e.g., low-grade gliomas and cavernous malformations are common epileptogenic substrates).

Hilbert-VLM achieved:

• Dice score: 82.35% on the whole-tumour sub-region, representing a significant improvement over standard 3D U-Net baselines that apply raster-scan serialisation.

• Classification accuracy: 78.85% on a companion tumour subtype classification task (distinguishing glioblastoma, low-grade glioma, and meningioma from the imaging and generated diagnostic text), demonstrating that the HMCA coupling of visual and linguistic streams provides discriminative signal for pathology typing.

The Dice improvement over raster-scan baselines was most pronounced for lesions near sulcal boundaries-precisely the regions where FCD and hippocampal sclerosis manifest-consistent with the spatial locality preservation hypothesis underlying the Hilbert ordering.

MedVQA-TREE: RAG-Enhanced Multimodal Reasoning

MedVQA-TREE (Textual Retrieval-Enhanced Evidence) addresses a complementary problem: given an ultrasound image (or other modality) and a natural-language clinical question, generate an accurate, evidence-grounded answer. Medical visual question answering (MedVQA) is challenging because it requires models to integrate low-level perceptual features (lesion echogenicity, boundary definition, posterior acoustic shadowing) with high-level clinical knowledge (differential diagnoses, relevant anatomy, prognostic implications).

MedVQA-TREE enhances a standard VQA architecture with a retrieval-augmented generation (RAG) component. At inference time, the image is encoded by a vision encoder, and the resulting visual embedding is used to retrieve the $k$ most relevant passages from a curated medical knowledge base (textbook passages, clinical guidelines, and de-identified radiology reports). These passages are concatenated with the clinical question and the visual tokens to form the input to a multimodal language model that generates the answer.

The retrieval step is visual-query-driven: the image embedding (not a textual question embedding) is used for retrieval, ensuring that the retrieved passages are semantically grounded in the visual content of the image rather than the surface form of the question. This design addresses a known failure mode of text-only RAG for VQA, where question-driven retrieval may retrieve passages that answer the textual question correctly but are irrelevant to the specific image content.

On a held-out ultrasound VQA benchmark, MedVQA-TREE achieved 99% accuracy, a result that reflects both the constrained answer space (most questions are closed-form: “Is there a lesion present?”, “Is the lesion hyper- or hypo-echoic?”) and the power of visual RAG to ground answers in retrieved clinical evidence. Open-ended generation questions showed lower accuracy, consistent with the general observation that accuracy metrics over-estimate performance on closed-form tasks relative to free-generation tasks.

Exercises

The Emerging Synthesis

The preceding sixteen sections of this chapter have traced a sweeping arc: from classical seizure detection through GAN-based EEG augmentation, from optimal-transport network geometry to transformer-based EEG encoders, from diffusion models that generate pseudo-healthy MRI to large language models that triage patients in the emergency department. Taken individually, each of these methods is a technically impressive achievement. Taken together, they represent something qualitatively different-a paradigm shift in how the medical and engineering communities conceptualise epilepsy itself.

This section identifies three such paradigm shifts, examines how the enabling technologies converge into a unified generative framework, and articulates a near-future vision in which closed-loop brain stimulation is guided by a personalised, continuously updated generative model of the patient's brain.

Paradigm Shift 1 - Pathology Redefined by Generative Divergence

The old definition.

For a century, epileptic pathology was defined by consensus: neurologists agreed on what constituted an abnormal MRI finding, an abnormal EEG discharge, or an abnormal histological specimen. This consensus was inevitably anchored in human perceptual limits-the eye could not detect sub-voxel structural differences, and the qualitative reading of an EEG was bounded by the clinician's experience with thousands rather than millions of recordings.

The generative redefinition.

Pseudo-healthy synthesis, introduced in sec:epilepsy:normative, inverts this logic. A diffusion model or a variational autoencoder is trained on a large cohort of neurologically healthy individuals and learns the distribution $p_{\theta }(𝐱)$ over healthy brain morphologies. Given a new patient scan ${𝐱}^{\ast }$, the model produces the most probable healthy counterpart: (Pseudo Healthy Argmin)$$\begin{array}{ccc}& {\widehat{𝐱}}_{\mathrm{healthy}}={\mathrm{arg\hspace{0.17em}min}}_{𝐱\in \mathrm{supp}(p_{\theta })}d(𝐱,{𝐱}^{\ast }),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $d$ is a perceptual or SSIM-based distance. The pathology map is then the residual (Residual MAP)$$\begin{array}{ccc}& \mathrm{\Delta }({𝐱}^{\ast })={𝐱}^{\ast }-{\widehat{𝐱}}_{\mathrm{healthy}},& \text{<span class="tml-eqn"></span>}\end{array}$$ which highlights every voxel in which the patient's brain deviates from the generative model's expectation of health.

This redefines pathology as generative divergence: a voxel is abnormal not because a human reader said so, but because the generative model cannot explain it under its learned distribution of health. The implications are profound. Focal cortical dysplasias invisible to a neuroradiologist's eye generate residuals of 0.3–0.5 standard deviations in the pseudo-healthy framework (Alaverdyan et al., 2020; Ravi et al., 2022). Hippocampal atrophy that falls within the neuroradiologist's “normal” range for age can still be flagged if the patient's overall morphological profile places them far from the healthy manifold.

Mathematical consequence.

Under this paradigm, the sensitivity of detection scales with the expressiveness of the generative model, not with the neurologist's training. Formally, let $\mathrm{supp}(p_{\theta })$ be the support of the learned healthy distribution. The detection sensitivity at significance level $\alpha$ is (Detection Sensitivity)$$\begin{array}{ccc}& \mathrm{Sens}(\alpha ,p_{\theta })=\mathrm{Pr}(d({𝐱}^{\ast },{\widehat{𝐱}}_{\mathrm{healthy}})>{\tau }_{\alpha }|{𝐱}^{\ast }\sim p_{\mathrm{lesion}}),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${\tau }_{\alpha }$ is the $\alpha$-quantile of the null (healthy) distance distribution. As the capacity of $p_{\theta }$ grows-through deeper networks, larger training sets, or improved diffusion schedules- the support $\mathrm{supp}(p_{\theta })$ tightens around the true healthy manifold, and $\mathrm{Sens}(\alpha ,p_{\theta })$ increases for fixed $\alpha$. In this sense, better generative models are more sensitive detectors-a virtuous cycle that does not exist in consensus-based clinical reading.

Paradigm Shift 2 - From Local Lesion to Network Geometry Breakdown

The focal dogma and its limits.

The resective surgery paradigm-identify the seizure focus, remove it, cure the patient-presupposes that epilepsy is a local phenomenon. This assumption breaks down in at least 30–40,% of surgical candidates, who achieve no meaningful seizure reduction after technically successful resections (Engel et al., 2003; Jehi, 2018).

The failure of the focal dogma is not an accident: it is the consequence of ignoring the network context in which the focus is embedded. A lesion that sits at a connector hub-a node that bridges multiple large-scale networks-will propagate seizure activity far more aggressively than an equally-sized lesion in a peripheral node, because the hub's removal (or disruption) disconnects otherwise segregated systems and creates new aberrant pathways.

Optimal transport as a geometry language.

Optimal transport (Optimal Transport and Brain Network Dynamics) provides a principled language for quantifying the deviation of a patient's connectivity geometry from a reference distribution. Let ${\mu }_i$ and ${\nu }_j$ be the empirical distributions of functional connectivity matrices for patient $i$ and reference subject $j$ respectively. The 2-Wasserstein distance (W2)$$\begin{array}{ccc}& W_2{({\mu }_i,{\nu }_j)}^2=\underset{\gamma \in \mathrm{\Gamma }({\mu }_i,{\nu }_j)}{\inf }\int \Vert 𝐂-{𝐂}^{\prime }{\Vert }_F^2\mathrm{d}\gamma (𝐂,{𝐂}^{\prime })& \text{<span class="tml-eqn"></span>}\end{array}$$ measures the minimum energetic cost of deforming the patient's connectivity geometry into the reference. Unlike correlation-based comparisons, $W_2$ is geometrically aware: it respects the structure of the space of positive definite matrices and penalises both magnitude and direction mismatches in connectivity.

Transformer-based propagation modelling.

Graph transformers (sec:epilepsy:transformer) complement the OT geometry by modelling temporal propagation. Given a connectivity graph $𝒢=(𝒱,ℰ,𝐖)$ where $𝐖$ is the adjacency weighted by OT-derived transport costs, a graph attention transformer predicts the probability that a focal discharge at node $v_0$ will spread to node $v_k$ within $\tau$ seconds: (Spread)$$\begin{array}{ccc}& P(\text{spread to }{v}_k|v_0,𝒢,\tau )={\mathrm{GTransformer}}_{\theta }({𝐡}_{v_0},{𝐀}_{𝒢},\tau ),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝐡}_{v_0}$ is the node embedding and ${𝐀}_{𝒢}$ is the attention matrix derived from $𝐖$. The conjunction of OT geometry with transformer-based spread modelling yields a new clinical question: not “where is the lesion?” but “which node, if disrupted, minimally changes the network geometry while maximally reducing spread probability?”

This is the network surgery question-the search for an optimal therapeutic intervention in geometry space rather than anatomical space.

Paradigm Shift 3 - From Analysis to Logistics via Language Models

The care execution gap.

The term care execution gap describes the discrepancy between what clinical knowledge prescribes and what the healthcare system actually delivers. In epilepsy, this gap is severe. Guidelines recommend that a seizure lasting more than five minutes (status epilepticus) receive benzodiazepine treatment within ten minutes. Yet emergency medicine studies find median treatment times of 30–60 minutes in community settings (Alldredge et al., 2001; Silbergleit et al., 2012).

The cause is not ignorance of the guideline: it is the logistics failure of coordinating multiple concurrent clinical tasks-airway management, IV access, drug preparation, documentation, consultation- under time pressure. This is not a problem that improved seizure detection algorithms can solve. It is a problem of workflow orchestration.

LLMs as logistics engines.

The AURA system (LLMs for Clinical Epilepsy Management), and the class of LLM-based clinical assistants it represents, addresses the care execution gap by operating at the process rather than the diagnosis layer. An LLM that has internalised clinical protocols through instruction tuning can:

1. parse free-text nursing notes to identify seizure onset time;

2. compute elapsed time and flag imminent status epilepticus risk;

3. generate a prioritised task list for the attending nurse;

4. draft a referral message to the neurology on-call service; and

5. update the electronic health record with a structured seizure summary-all within 90 seconds of the nursing note being entered.

Formally, the LLM operates as a workflow policy ${\pi }_{\mathrm{LLM}}:𝒮\to 𝒜$, mapping the current clinical state $s\in 𝒮$ (structured EHR data plus free text) to an action $a\in 𝒜$ (a message, a task list, a referral draft, or a drug dosing calculation). The policy is not learned from trial-and-error interaction with the environment-that would be too dangerous-but from demonstrations encoded in clinical guidelines and curated case reports: (LLM Policy)$$\begin{array}{ccc}& {\pi }_{\mathrm{LLM}}={\mathrm{arg\hspace{0.17em}max}}_{\pi }{𝔼}_{(s,a)\sim {𝒟}_{\mathrm{guide}}}\left[\log \pi (a|s)\right],& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝒟}_{\mathrm{guide}}$ is a corpus of guideline-concordant state–action pairs. The result is a logistics co-pilot that compresses the time from seizure onset to therapeutic action-not by improving the detector, but by eliminating the coordination bottleneck.

Convergence: How the Technologies Interlock

The three paradigm shifts are not independent. They are three facets of a single integrated framework in which diffusion models, optimal transport, graph transformers, and large language models each contribute to a different layer of the epilepsy care pipeline. Figure fig:epilepsy:convergence illustrates this convergence.

The three columns in Figure fig:epilepsy:convergence are not merely parallel pipelines: they are mutually informing. The dashed feedback arrows encode two critical cross-layer dependencies.

Pathology map to network geometry.

A pseudo-healthy residual map localises structural abnormalities but does not reveal their network significance. By propagating the residual to the OT-based network geometry layer, the framework asks: “given that this lesion exists here, how does it distort the patient's connectivity geometry relative to healthy controls?” A lesion in a white-matter tract that is a minimum-cost geodesic between two large-scale networks will register a higher $W_2$-divergence than a morphologically identical lesion in a non-hub location.

Spread probability to LLM triage.

The LLM triage layer is not purely reactive (processing EHR text after the fact). In a prospective deployment, the spread probability map computed by the graph transformer can be serialised as structured text and injected into the LLM's context window. The result is a triage action that is informed by the patient's specific seizure propagation geometry:

“Current EEG telemetry indicates discharge origin at the right posterior temporal lobe with estimated 73% probability of spread to ipsilateral frontal lobe within 8 seconds. Based on your institution's protocol, IV lorazepam 0.1 mg/kg should be prepared immediately. Neurology on-call has been notified (pager 4471). Please confirm airway patency and establish IV access.”

This kind of language is not generated by a lookup table. It is the output of a model that has synthesised structural abnormality, network geometry, spread probability, body weight from the EHR, and institution-specific drug dosing guidelines into a single coherent clinical recommendation.

Future Vision: Closed-Loop Predictive Deep Brain Stimulation

The convergence described above points toward a near-future clinical technology that does not yet exist in full form but is technically within reach: closed-loop predictive deep brain stimulation guided by a continuously updated generative brain model.

Architecture overview.

The system operates in four phases that cycle at different timescales (Figure fig:epilepsy:closed-loop):

1. Slow loop (minutes to hours). A diffusion-based normative model is updated nightly with the patient's most recent structural MRI and the accumulated pseudo-healthy residuals from the past week. This produces an updated estimate of lesion extent and morphological trajectory.

2. Medium loop (seconds to minutes). An OT-based connectivity monitor computes the Wasserstein deviation of the patient's real-time functional connectivity from the healthy reference, updated every 30 seconds. A rising $W_2$ trajectory is a leading indicator of seizure susceptibility.

3. Fast loop (milliseconds to seconds). A graph transformer running on the implanted device processes continuous LFP (local field potential) signals from DBS electrodes, predicts propagation probabilities in real time, and passes them to the stimulation controller.

4. Reactive layer (sub-millisecond). When the fast-loop propagation probability exceeds a threshold ${\tau }_{\mathrm{stim}}$, the stimulation controller delivers a precisely timed current pulse to the target node-not the seizure focus, but the hub node identified by the OT network geometry layer as the bottleneck for propagation.

Why this is not science fiction.

Each component of the proposed system already exists in proof-of-concept form. Responsive neurostimulation devices (RNS; NeuroPace) have been FDA-approved since 2013 and implement a rudimentary fast loop (Bergey et al., 2015). Diffusion-based normative models have been validated on multi-site FCD datasets (Ravi et al., 2022). OT-based connectivity monitoring has been demonstrated in real-time EEG pipelines at latencies below 500 ms (Jiang et al., 2023). Graph transformers for seizure spread prediction achieve AUC above 0.85 on held-out patients (Covert et al., 2022).

What is missing is integration: a unified system architecture that couples these components, handles the communication between loops, and maintains safety guarantees across all timescales. This integration is the next grand challenge of generative epileptology.

Benchmarks, Datasets, and Reproducibility

Every quantitative claim in this chapter rests on a foundation of datasets, evaluation protocols, and performance metrics. That foundation is, in the honest assessment of the field, unstable. Studies report wildly different numbers for apparently similar tasks: seizure detection sensitivities range from 70,% to 99.8,% across published papers that all claim to solve the same problem. Proposed augmentation methods report improvements of 5–20 percentage points over baselines that are rarely identical across studies. LLM-based triage systems are evaluated on proprietary datasets that no external group can access.

This section provides the reader with the tools to navigate this landscape: a comprehensive dataset catalog, a taxonomy of evaluation protocols, a diagnosis of the reproducibility crisis, and a decision framework for choosing appropriate metrics.

Comprehensive Dataset Catalog

Table Table 9 provides a structured overview of the major publicly available datasets used in epilepsy AI research. We organise these by modality and discuss each below.

Dataset	Modality	Annotations	Sub	Hrs	Sz	Access
CHB-MIT	Scalp EEG	Seizure onset/offset	23	983	198	R
TUH EEG Seizure	Scalp EEG	Seizure type, duration	592	1476	4029	R
EPILEPSIAE	iEEG/EEG	Seizure onset, pre-ictal	30	1399	272	C
Siena Scalp EEG	Scalp EEG	Seizure onset/offset	14	128	190	R
Kaggle Seizure	Scalp EEG	1-h segments, binary label	10			O
BraTS 2024	MRI (T1/T2/FLAIR/ADC)	Tumour subregions	2200			R
UHB FCD	MRI (T1)	FCD lesion masks	85			C
HUP iEEG	iEEG	Seizure onset zone, SEEG	102	2400	516	C
Bonn EEG	EEG (5-class)	Normal/interictal/ictal	100			O
PhysioNet CHB	Scalp EEG	Seizure timing	23	983	198	R

CHB-MIT Scalp EEG Database.

The Children's Hospital Boston – MIT dataset (Shoeb, 2009) contains continuous scalp EEG recordings from 23 paediatric patients with intractable seizures. Recordings span an average of 43 hours per patient, with seizure onset and offset times manually annotated by clinical experts. CHB-MIT is the de facto standard benchmark for patient-specific seizure prediction and detection algorithms.

Three properties of CHB-MIT deserve careful attention. First, the dataset is paediatric; models trained on CHB-MIT may not generalise to adult populations. Second, the annotation granularity varies: some seizures have precise second-level onset annotations while others have minute-level precision. Third, the inter-seizure intervals span orders of magnitude across patients, making naive random train/test splitting inappropriate-temporal splits are mandatory.

Temple University Hospital EEG Corpus (TUH).

The TUH EEG Corpus (Obeid & Picone, 2016) is the largest publicly available clinical EEG repository in the world, containing over 25,000 recordings from more than 14,000 patients. The seizure sub-corpus (TUH EEG Seizure, or TUSZ) contains 4,029 annotated seizures across 592 patients, with fine-grained seizure type labels (focal non-specific, generalised tonic-clonic, absence, etc.).

TUH is the benchmark of choice for cross-patient generalisation studies because of its demographic diversity (age range 1–95 years, multiple acquisition sites and hardware configurations) and its rich metadata. However, TUH data requires preprocessing: electrode placement varies across recordings, and a significant fraction of annotations are uncertain (marked with a “?” qualifier).

EPILEPSIAE.

The EPILEPSIAE database (Ihle et al., 2012) focuses on pre-ictal states, providing long-term continuous EEG and intracranial EEG (iEEG) recordings from 30 patients at multiple European epilepsy centres. Total recording time exceeds 1,399 hours, making EPILEPSIAE the primary resource for seizure prediction (as opposed to detection) research. Each recording includes a comprehensive clinical history, enabling patient-stratified analyses.

Access to EPILEPSIAE is controlled and requires a data-use agreement, which limits its use in rapid-iteration research workflows. Researchers should plan for a 4–8 week approval process.

Siena Scalp EEG Dataset.

The Siena dataset (Detti et al., 2020) provides 128 hours of scalp EEG from 14 patients with pharmacoresistant epilepsy recorded at the University of Siena. Despite its modest size, Siena is valuable for its consistent acquisition protocol and detailed metadata including antiepileptic drug regimens, which allows pharmacological covariate analysis.

BraTS (Brain Tumour Segmentation) Dataset.

The BraTS challenge dataset (Menze et al., 2015; Baid et al., 2021) is primarily a tumour segmentation resource, but it is widely used in epilepsy MRI research because tumour-related epilepsy accounts for approximately 30,% of new epilepsy diagnoses. BraTS provides multi-parametric MRI (T1, T1ce, T2, FLAIR) with expert-annotated sub-region labels (whole tumour, tumour core, enhancing tumour). Pseudo-healthy synthesis models that learn from the tumour-free hemisphere of BraTS patients can then be applied to FCD detection.

UHB FCD Dataset.

The University Hospital Bonn Focal Cortical Dysplasia dataset contains T1-weighted MRI from 85 patients with histopathologically confirmed FCD, paired with expert lesion masks. This is the primary benchmark for FCD detection algorithms, including pseudo-healthy synthesis and morphometric mapping approaches. Access is controlled; the dataset is available through collaboration with the Bonn Epileptology group.

Bonn EEG Dataset.

The Bonn dataset (Andrzejak et al., 2001) contains 500 single-channel EEG epochs categorised into five classes: healthy eyes open, healthy eyes closed, interictal from non-epileptogenic zones, interictal from epileptogenic zones, and ictal. Despite its age and small size, Bonn remains one of the most frequently cited benchmarks, particularly in machine learning papers that propose new feature extraction methods. Researchers should note that the 100,% accuracy claims common in Bonn-based papers do not translate to real clinical settings, where continuous long-term recordings present very different statistical challenges.

Evaluation Protocols

Patient-specific vs. cross-patient protocols.

The most fundamental distinction in epilepsy AI evaluation is between patient-specific and cross-patient protocols. A patient-specific protocol trains and evaluates a model on data from the same patient, using temporal splits (typically the first 80,% of seizures for training and the remainder for testing). A cross-patient protocol trains on one cohort of patients and evaluates on a disjoint set, testing generalisation across individuals.

Formally, let $𝒟={\{({𝐗}_p,{𝐲}_p)\}}_{p=1}^P$ be a dataset of $P$ patients. In the patient-specific protocol, the evaluation risk for patient $p$ is (Patient Specific RISK)$$\begin{array}{ccc}& R_{\mathrm{ps}}(f,p)={𝔼}_{(𝐱,y)\sim {𝒟}_p^{\mathrm{test}}}\left[\ell (f_p(𝐱),y)\right],& \text{<span class="tml-eqn"></span>}\end{array}$$ where $f_p$ is trained only on ${𝒟}_p^{\mathrm{train}}$. In the cross-patient protocol, (Cross Patient RISK)$$\begin{array}{ccc}& R_{\mathrm{cp}}(f)=\frac{1}{|{𝒫}_{\mathrm{test}}|}\sum _{p\in {𝒫}_{\mathrm{test}}}{𝔼}_{(𝐱,y)\sim {𝒟}_p}\left[\ell (f(𝐱),y)\right],& \text{<span class="tml-eqn"></span>}\end{array}$$ where $f$ is trained on ${𝒟}_{{𝒫}_{\mathrm{train}}}$ and ${𝒫}_{\mathrm{train}}\cap {𝒫}_{\mathrm{test}}=\varnothing$. Cross-patient evaluation is more clinically relevant but consistently yields 10–25 percentage point lower performance than patient-specific evaluation on the same dataset (Boonyakitanont et al., 2020).

Seizure prediction horizon.

For seizure prediction (as opposed to detection), the evaluation protocol must specify a prediction horizon $h$ and a seizure prediction horizon (SPH)–seizure occurrence period (SOP) protocol. The SOP is the window during which a predicted seizure must occur; the SPH is the buffer between prediction and SOP onset during which the prediction is assumed to be acted upon by the patient. A typical protocol sets SPH = 10 minutes and SOP = 30 minutes.

Crucially, performance on a 30-minute SOP is not comparable to performance on a 60-minute SOP, even on the same dataset, because the base rate of “seizure within the window” changes.

Temporal splits and data leakage.

EEG data has strong temporal autocorrelation: a 10-second epoch recorded immediately before a seizure is more similar to a 10-second epoch recorded immediately after than to one recorded 24 hours earlier. Random train/test splitting of EEG epochs therefore causes temporal data leakage: the model appears to predict seizures because it has seen adjacent epochs during training, not because it has learned a meaningful pre-ictal signature.

The correct approach is to split at the level of recording sessions or seizure events, ensuring that no temporal neighbourhood of any test event appears in the training set. Many published papers, particularly those targeting Bonn or CHB-MIT with random 80/20 splits, do not enforce this constraint.

The Reproducibility Crisis in Epilepsy AI

A 2022 systematic review of 174 seizure detection papers found that only 11,% released code, 23,% reported hyperparameters in sufficient detail for reimplementation, and fewer than 5,% provided pre-trained model weights (Beniczky & Wiebe, 2022, adapted figure). The consequences are severe: independent replication studies typically find 5–15 percentage point gaps between reported and replicated performance (Shoaib & Shah, 2023).

Root causes.

The reproducibility crisis in epilepsy AI has three interacting root causes:

1. Inconsistent metrics. Different papers report different metrics-some report sensitivity alone, some report sensitivity + specificity, some report AUC, some report F1 score. Without a common primary metric, it is impossible to construct a meaningful leaderboard or track field progress.

2. Missing hyperparameters. Deep learning models have hundreds of hyperparameters (learning rate, weight decay, batch size, augmentation strengths, early stopping criteria). Papers routinely report only the architecture and the optimiser, omitting the settings that determined which local minimum the model converged to.

3. No code release. Without executable code, a reader cannot determine whether a reported accuracy was achieved through legitimate generalisation or through subtle implementation choices-data normalisation strategies, overlapping windows, class balancing-that are not described in the paper.

Partial remedies.

Several practices can partially mitigate the reproducibility crisis. First, fixed public splits: dataset curators can release official train/validation/test splits (as was done for BraTS), making results directly comparable. Second, model cards: structured documentation of data preprocessing, hyperparameters, and evaluation protocols attached to every released model. Third, hosted evaluation servers: blind test sets held by a third party, with authors submitting predictions rather than code (the approach used by the PhysioNet Seizure Prediction Challenge). None of these remedies is perfect, but together they substantially reduce the variance in reported results.

The Metrics Zoo: Choosing the Right Measure

Epilepsy AI papers employ at least a dozen distinct evaluation metrics, each encoding a different clinical trade-off. We organise them by domain.

EEG-domain metrics.

Let $\mathrm{TP}$, $\mathrm{FP}$, $\mathrm{TN}$, $\mathrm{FN}$ denote true positives, false positives, true negatives, and false negatives for seizure event detection.

• Sensitivity (recall): $\mathrm{Sens}=\mathrm{TP}/(\mathrm{TP}+\mathrm{FN})$. The fraction of true seizures correctly identified.

• Specificity: $\mathrm{Spec}=\mathrm{TN}/(\mathrm{TN}+\mathrm{FP})$. The fraction of non-seizure epochs correctly identified.

• False positive rate per hour (FPR/hr): $\mathrm{F}\mathrm{P}\mathrm{R}/\mathrm{h}\mathrm{r}=\mathrm{FP}/T_{\mathrm{total}}$, where $T_{\mathrm{total}}$ is the total recording duration in hours. This metric is clinically more meaningful than specificity for home monitoring applications, where a single false alarm at 3am may disrupt the patient's life as much as a missed seizure.

• Area Under the ROC Curve (AUC): $\mathrm{AUC}=\mathrm{Pr}(f({𝐱}^{+})>f({𝐱}^{-}))$, where ${𝐱}^{+}$ and ${𝐱}^{-}$ are positive and negative examples respectively. AUC is threshold-agnostic but insensitive to extreme class imbalance.

MRI-domain metrics.

• Dice coefficient: $\mathrm{Dice}(A,B)=2|A\cap B|/(|A|+|B|)$, where $A$ is the predicted lesion mask and $B$ is the ground truth. Dice is the primary metric for FCD and lesion segmentation tasks.

• Structural Similarity Index Measure (SSIM): For pseudo-healthy synthesis, where the output is an image rather than a mask, SSIM measures perceptual similarity between generated and reference images: (SSIM)$$\begin{array}{ccc}& \mathrm{SSIM}(𝐱,\widehat{𝐱})=\frac{(2{\mu }_x{\mu }_{\hat{x}}+c_1)(2{\sigma }_{x\hat{x}}+c_2)}{({\mu }_x^2+{\mu }_{\hat{x}}^2+c_1)({\sigma }_x^2+{\sigma }_{\hat{x}}^2+c_2)},& \text{<span class="tml-eqn"></span>}\end{array}$$ where $\mu$, ${\sigma }^2$, ${\sigma }_{x\hat{x}}$ are local means, variances, and covariance, and $c_1,c_2$ are stabilisation constants.

• Peak Signal-to-Noise Ratio (PSNR): $\mathrm{PSNR}=10{\log }_{10}(I_{\max }^2/\mathrm{MSE})$, where $I_{\max }$ is the maximum pixel intensity and MSE is mean squared error. PSNR is sensitive to global brightness shifts and is less preferred than SSIM for medical images.

Network-domain metrics.

• Graph Edit Distance (GED): For connectivity graph comparisons, GED counts the minimum number of node and edge operations required to transform one graph into another. (GED)$$\begin{array}{ccc}& \mathrm{GED}({𝒢}_1,{𝒢}_2)=\underset{(e_1,\dots ,e_k)\in 𝒫({𝒢}_1,{𝒢}_2)}{\min }\sum _{i=1}^{k}c(e_i),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $𝒫({𝒢}_1,{𝒢}_2)$ is the set of edit paths between ${𝒢}_1$ and ${𝒢}_2$, and $c(e_i)$ is the cost of edit operation $e_i$.

• RMSE of Wasserstein Distance: For OT-based connectivity models, the standard evaluation reports the root mean squared error between the predicted ${\hat{W}}_2$ trajectory and the true $W_2$ trajectory over a held-out test period: (RMSE W2)$$\begin{array}{ccc}& {\mathrm{RMSE}}_{W_2}=\sqrt{\frac{1}{T}\sum _{t=1}^T{({\hat{W}}_2(t)-W_2(t))}^2}.& \text{<span class="tml-eqn"></span>}\end{array}$$

LLM evaluation metrics.

LLM-based clinical systems are evaluated on a combination of:

• BLEU / ROUGE: $n$-gram overlap between generated and reference text. Low information content for clinical applications because clinically correct statements may use synonymous phrasing.

• BERTScore: Semantic similarity between generated and reference text computed from contextual BERT embeddings. More appropriate than BLEU for clinical language tasks.

• Clinical accuracy: Human expert ratings of whether generated recommendations are concordant with clinical guidelines. Gold standard but expensive.

• Time-to-action: In prospective triage studies, the latency between seizure onset and the first correct clinical action (administering medication, calling neurology). This is the most clinically meaningful metric but requires prospective study designs.

A Decision Framework for Metric Selection

Figure fig:epilepsy:metrics-tree provides a decision tree for choosing evaluation metrics in epilepsy AI research. The tree is organised around three primary questions: (1) what is the output modality of the system, (2) what is the deployment context, and (3) what is the primary clinical trade-off.

A Reproducibility Checklist for Epilepsy AI Papers

The following checklist consolidates the reproducibility requirements discussed in this section. Authors of epilepsy AI papers are encouraged to include a checklist table in supplementary materials; reviewers are encouraged to request it.

1. Dataset: Which dataset(s) were used? Which version or release? Were any subjects excluded, and why?

2. Splits: Are splits temporal or random? Are they at the epoch, session, or patient level? Are splits fixed and released alongside the paper?

3. Protocol: Patient-specific or cross-patient? If cross-patient, which subjects are in train/val/test?

4. Preprocessing: What filtering, normalisation, referencing, and artefact rejection were applied? Are preprocessing scripts released?

5. Architecture: Is the full architecture specified, including all layer sizes, activation functions, and normalisation strategies?

6. Hyperparameters: Are all hyperparameters reported, including learning rate schedule, batch size, dropout rates, augmentation parameters, and early stopping criteria?

7. Metrics: Are all metrics defined precisely, including how ties are broken, how multi-class problems are aggregated, and how the prediction horizon is defined for prediction tasks?

8. Statistical testing: Is performance reported with confidence intervals or standard errors across cross-validation folds or runs? Is a significance test performed?

9. Code: Is executable code released? Is it sufficient to reproduce the reported numbers from the released dataset?

10. Compute: What hardware was used? How long did training take? Are there estimates of energy consumption?

Exercises

Open Problems and Future Directions

The preceding sections have established a comprehensive mathematical framework for generative AI in epilepsy research: GANs and diffusion models for seizure signal synthesis, VAEs for latent seizure manifolds, optimal transport for cross-patient normalisation, and transformers for long-range ictal dynamics. Across each of these domains, the frontier has advanced considerably in the past five years. Yet the gap between what is mathematically possible in controlled laboratory settings and what is clinically deployable at the bedside of a patient with drug-resistant epilepsy remains formidable.

This section identifies seven open problems that, in our assessment, represent the most important barriers to progress. We frame each problem as a precise mathematical question wherever possible, and we close with a conjecture about the structural nature of the solution space. The reader should treat these not as discouraging limitations but as an invitation: the next generation of breakthroughs in epilepsy AI will come from those who engage seriously with the hardest questions.

Open Problem 1: Real-Time Generative Seizure Prediction for Implantable Devices

Approximately one-third of people with epilepsy do not achieve seizure freedom with medication (Brodie et al., 2012). For this population, implantable closed-loop neurostimulation devices offer hope: a device that detects the pre-ictal state and delivers a brief therapeutic stimulus before the seizure generalises. The NeuroPace RNS System and Medtronic Percept represent current-generation implementations. However, these devices use hand-crafted feature extractors and threshold classifiers. Generative models offer a fundamentally different paradigm: instead of classifying the current EEG into “pre-ictal” or “interictal”, a generative model would predict the likely future trajectory of the EEG signal and intervene when the predicted trajectory converges on a seizure attractor.

The key obstacle is latency. Current diffusion-based sequence models require on the order of $T\times N_{\mathrm{step}}$ forward passes, where $T$ is the context window length and $N_{\mathrm{step}}$ is the number of denoising steps. Even with $N_{\mathrm{step}}=10$ (aggressive DDIM acceleration) and $T=1000$ time points at 250,Hz (4 seconds of context), the computational budget on an implant with a 32-bit ARM cortex-M4 running at 64,MHz and a power budget of 50,$\mu$W is exceeded by several orders of magnitude.

Promising directions.

Two lines of work appear most promising. First, neural architecture search (NAS) over quantised (4-bit or 8-bit integer) state-space models such as S4 or Mamba can discover architectures whose parameter footprints fit on-chip while retaining competitive classification performance. Second, amortised variational inference with a low-dimensional latent space $𝒛\in {\mathrm{ℝ}}^d$ (with $d\le 8$) can encode the pre-ictal trajectory in a compact representation that is cheap to update at each new sample. The trade-off between latent dimension and predictive accuracy is governed by the rate-distortion bound: (RATE Distortion)$$\begin{array}{ccc}& 𝔼[\Vert {𝒙}_{t+H}-{\widehat{𝒙}}_{t+H}{\Vert }_2^2]\ge D^{\ast }\left(\frac{R}{{\log }_{2}e}\right),& \text{<span class="tml-eqn"></span>}\end{array}$$ where $D^{\ast }(R)$ is the rate-distortion function of the pre-ictal process and $R$ is the bit-rate of the latent code.

Open Problem 2: Personalized Brain Digital Twins via Generative Models

The epileptic brain is not a generic brain with an extra oscillation. Seizure onset zones differ between patients in location, extent, and connectivity. A generative model trained on population-level EEG will, at best, capture the average seizure phenotype. What is clinically needed is a personalized brain digital twin: a generative model $p_{{𝜽}_i}$ calibrated to the specific neuroanatomy, connectivity, and seizure semiology of patient $i$ from a small number of observed seizures.

The mathematical challenge is few-shot personalisation: each patient typically provides $n_i\in \{3,5,10\}$ recorded seizures, an order of magnitude fewer than the thousands of examples needed to train a model from scratch. Meta-learning approaches such as MAML (Finn et al., 2017) frame personalisation as finding initial parameters ${𝜽}_0$ such that a small number of gradient steps on patient $i$'s data reaches a good personalised model: (MAML)$$\begin{array}{ccc}& {𝜽}_0^{\ast }={\mathrm{arg\hspace{0.17em}min}}_{{𝜽}_0}\sum _{i=1}^N{ℒ}_i({𝜽}_0-\alpha {\nabla }_{{𝜽}_0}{ℒ}_i({𝜽}_0)),& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${ℒ}_i$ is the reconstruction loss on patient $i$'s seizure data. Whether the seizure manifold has the geometry required for meta-learning (i.e., whether patient-specific optima lie close to a common initialisation in parameter space) is an empirically open question.

Open Problem 3: Cross-Patient Generalization Without Catastrophic Forgetting

A seizure detection model deployed in a clinical device must adapt continuously as new seizures are recorded. Each new seizure provides evidence about the patient's evolving ictal pattern (seizure semiology can change with disease progression and medication changes), yet the model must not forget the patterns learned from earlier data. This is the continual learning problem applied to EEG, but with additional cross-patient complexity: we want a model that accumulates knowledge across all patients without suffering from negative transfer.

Formally, let $𝒟=\{({𝒟}_1,\dots ,{𝒟}_N)\}$ be a stream of patient datasets arriving sequentially. After learning on ${𝒟}_1,\dots ,{𝒟}_k$, the model $f_{𝜽}$ should satisfy: (Continual)$$\begin{array}{ccc}& \forall j\le k:\text{AUC}(f_{𝜽};{𝒟}_j)\ge \text{AUC}(f_{{𝜽}_j^{\ast }};{𝒟}_j)-ϵ,& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝜽}_j^{\ast }$ is the oracle model trained exclusively on ${𝒟}_j$ and $ϵ$ is a tolerated forgetting budget. The tension is fundamental: gradient updates on ${𝒟}_{k+1}$ will, in general, increase the loss on all previous ${𝒟}_j$.

The interaction between the generative model's forgetting and the classifier's forgetting creates a coupled dynamical system that has received little theoretical attention. An analysis leveraging the Fisher information matrix of the generative model (elastic weight consolidation applied to generative models, EWC-Gen) may yield tight forgetting bounds.

Open Problem 4: Ethical Synthetic EEG - Deepfake Risks and Regulatory Traceability

Synthetic EEG generation, developed throughout this chapter as a tool for data augmentation and privacy preservation, carries a dual-use risk that has received insufficient attention. A high-fidelity EEG generator trained on seizure data from a specific patient could, in principle, produce traces that: (a) mislead a physician into diagnosing epilepsy in a healthy individual; (b) fabricate forensic evidence of a neurological event; or (c) fool a clinical AI system into prescribing antiseizure medication or authorising a disability claim.

The mathematical foundation for provenance is steganographic watermarking of generated signals. A differentiable watermark embeds a unique identifier $m\in {\{\mathrm{0,1}\}}^k$ into the generated signal $\widehat{𝒙}$ such that the watermark is (i) imperceptible (the spectral distortion $\Vert \widehat{𝒙}-{\widehat{𝒙}}_m{\Vert }_2<\delta$), (ii) robust to clinical signal processing (bandpass filtering, re-referencing, artifact rejection), and (iii) recoverable by an authorised detector $D_{\psi }(m|{\widehat{𝒙}}_m)$ with bit accuracy $>0.99$. The trade-off between imperceptibility $\delta$ and robustness to processing is characterised by a watermarking rate-distortion function analogous to Equation .

Open Problem 5: Unified Multimodal Foundation Model for Epilepsy (EEG + MRI + Clinical Text)

Current epilepsy AI systems operate in modality-specific silos. A scalp EEG classifier is trained on EEG. An MRI-based lesion detector is trained on volumetric scans. A clinical NLP system extracts seizure semiology from clinic notes. Each system reaches independent conclusions that a neurologist must integrate mentally. The vision of a unified multimodal foundation model for epilepsy is a single model $f_{𝜽}:({𝒙}_{\mathrm{EEG}},{𝒙}_{\mathrm{MRI}},{𝒙}_{\mathrm{text}})\to \hat{y}$ that jointly encodes all available modalities and produces a unified clinical assessment.

The generative perspective adds an important dimension. Rather than a discriminative model, we want a generative model $p_{𝜽}({𝒙}_{\mathrm{EEG}},{𝒙}_{\mathrm{MRI}},{𝒙}_{\mathrm{text}}|𝒚)$ over the joint observation space conditional on the clinical label $𝒚$ (e.g., epilepsy syndrome type, seizure onset zone, medication response). Such a model supports not only classification but cross-modal synthesis (generate the expected EEG given an MRI lesion map), imputation (infer missing MRI from EEG and clinic notes), and counterfactual reasoning (what would the EEG look like if the patient underwent a successful resection?).

Open Problem 6: Causal Generative Models for Understanding Seizure Mechanisms

Generative models of seizure activity are currently associative: they learn $p({𝒙}_{\mathrm{seizure}})$ or $p({𝒙}_{\mathrm{seizure}}|{𝒙}_{\mathrm{interictal}})$ but cannot answer interventional or counterfactual questions (Pearl's second and third rungs of the causal hierarchy). A clinician facing a pre-surgical evaluation does not want to know what seizures look like in general; she wants to know: “If I resect electrode contacts 12–15 in this patient, will seizures stop?” This is a counterfactual query that no purely associative generative model can answer.

A causal generative model of seizure dynamics would encode the structural equations governing ictal propagation: (SCM)$$\begin{array}{ccc}& {𝑿}_j=f_j(\mathrm{pa}(j),U_j),j=1,\dots ,C,& \text{<span class="tml-eqn"></span>}\end{array}$$ where ${𝑿}_j\in {\mathrm{ℝ}}^T$ is the EEG signal at electrode $j$, $\mathrm{pa}(j)$ denotes the causal parents of $j$ in the ictal propagation graph $G$, and $U_j$ is an independent exogenous noise variable. Intervening on node $j$ (ablating it) corresponds to replacing $f_j$ with the constant $\text{do}({𝑿}_j=0)$ and simulating the resulting altered dynamics.

The challenge is that the causal graph $G$ of seizure propagation is latent: it must be inferred from observed EEG. Causal discovery algorithms such as PC or FCI are designed for static variables, not for time series with non-linear, non-stationary dynamics.

Open Problem 7: Optimal Transport-Guided Neuromodulation (Closed-Loop DBS)

Deep brain stimulation (DBS) and responsive neurostimulation (RNS) deliver electrical pulses to suppress aberrant oscillations associated with seizures. The current generation of closed-loop devices use threshold-based triggers: stimulation fires when a detector exceeds a predetermined amplitude or power threshold. This reactive paradigm intervenes after the ictal process has begun.

A more principled approach, as yet unrealised, would use the generative model to compute the optimal transport map from the current ictal EEG distribution to the desired interictal EEG distribution and drive the stimulation waveform along the geodesic connecting the two distributions in the Wasserstein space $({𝒫}_2({\mathrm{ℝ}}^C),W_2)$.

The main computational obstacle is that the Brenier map must be computed and updated in real time (at 1,kHz stimulation frequency) from streaming EEG data. Neural OT solvers (Makkuva et al., 2020; Rout et al., 2022) provide amortised approximations but have not been validated in closed-loop neuromodulation settings.

Conjecture: No Single Generative Architecture Will Dominate All Epilepsy Tasks

The history of machine learning is punctuated by epochs of apparent universal dominance: convolutional networks in the 2010s, then transformers from 2017, then diffusion models from 2021. Each transition was followed by a period of evangelism during which practitioners applied the dominant architecture uniformly across all domains. We conjecture that this pattern will not hold for epilepsy AI.

The practical implication is that the field should invest in compositional architectures that combine the strengths of multiple paradigms rather than competing to crown a single successor. The mathematical challenge is to design composition interfaces: latent spaces, message-passing protocols, and objective functions that allow, for example, a VAE brain twin to feed a conditioning signal to an OT-guided stimulator via a diffusion posterior sampler.

Clinical Translation and Ethics

The seven open problems of the preceding section are scientific. But the path from a published algorithm to a tool that changes the life of a patient with drug-resistant epilepsy also traverses a thicket of regulatory, ethical, legal, and societal challenges. This section addresses these challenges directly. We organise them around four themes: the FDA regulatory pathway, privacy and synthetic data, demographic bias in EEG datasets, and explainability of generative latent spaces.

FDA Regulatory Pathway for AI in Neurology

The United States Food and Drug Administration regulates AI-based neurological devices under 21 CFR Part 882 (neurological devices). Three regulatory pathways are relevant:

510(k) Premarket Notification.

Available when the device is substantially equivalent to a legally marketed predicate device. For an AI seizure detector, the predicate might be a cleared ambulatory EEG monitor (e.g., Natus Quantum). The 510(k) pathway requires demonstrating equivalent sensitivity/specificity but does not require randomised controlled trial (RCT) evidence. Turnaround is typically 3–6 months.

De Novo Classification.

For AI devices with no substantially equivalent predicate, the De Novo pathway creates a new regulatory classification with special controls. The FDA's 2021 Artificial Intelligence/ Machine Learning (AI/ML) Action Plan and the subsequent Predetermined Change Control Plan (PCCP) framework are particularly relevant for adaptive AI systems that update their parameters based on post-deployment data.

Premarket Approval (PMA).

Required for high-risk Class III devices, including implantable closed-loop neurostimulators. PMA requires valid scientific evidence including one or more RCTs. For an OT-guided DBS system (Open Problem 7), PMA is the required pathway, typically requiring 5–10 years of clinical development.

Software as a Medical Device.

The FDA's Software as a Medical Device (SaMD) framework, developed in collaboration with the International Medical Device Regulators Forum (IMDRF), classifies AI software by the severity of the condition it addresses and the criticality of the decision it supports. A generative EEG system that informs a physician's diagnosis (rather than making autonomous decisions) falls under lower-risk SaMD classification, significantly easing the regulatory burden. This design choice - keeping the clinician in the loop - has regulatory advantages beyond the ethical ones.

The critical issue for generative models specifically is locked versus adaptive algorithms. The FDA's 2021 guidance distinguishes:

• Locked algorithms: the model does not change after deployment. Standard regulatory controls apply.

• Adaptive algorithms: the model updates based on real-world performance data. A PCCP must be submitted specifying the anticipated modifications, the performance monitoring strategy, and the retraining boundaries.

For a generative brain twin (Open Problem 2) that personalises to a patient's new seizures over time, the adaptive pathway is essential. The PCCP must specify: what triggers a model update (e.g., $N>5$ new seizures recorded), what data is used for retraining, and what performance validation is performed before the updated model is activated.

Privacy: HIPAA, GDPR, and Synthetic Data as a Privacy Solution

Intracranial EEG is Protected Health Information (PHI) under HIPAA and Special Category Personal Data under GDPR Article 9 (data revealing health information). Sharing iEEG datasets across institutions for collaborative model training requires either (a) a Data Use Agreement (DUA) covering de-identification, (b) federated learning that keeps raw data on-site, or (c) synthetic data generation as a privacy-preserving surrogate.

Synthetic EEG offers an attractive third option: train a generative model on real iEEG under institutional approval, then release the synthetic dataset publicly without a DUA. However, this approach is only as strong as the privacy guarantee of the generative model.

In practice, applying DP-SGD to EEG generative models introduces a quality-privacy trade-off. At $\epsilon =1$ (strong privacy), generative model FID typically degrades by 30–50% compared to the non-private baseline. At $\epsilon =10$ (weak privacy, often considered insufficient for medical data), the FID gap reduces to $<10\%$. Determining the appropriate $\epsilon$ budget for synthetic iEEG is an unresolved policy question: existing HIPAA de-identification standards do not map directly onto the $(\epsilon ,\delta )$ framework.

A complementary approach to DP-SGD is membership inference auditing: after training, an adversary attempts to determine whether a specific patient's data was in the training set. The audit provides an empirical privacy bound independent of the theoretical DP analysis. Shokri et al.'s (2017) shadow training attack and the LiRA attack (Carlini et al., 2022) are the standard auditing tools. A synthetic EEG dataset should only be released publicly if the best known membership inference attack achieves AUC $<0.55$ (close to random chance) on the training cohort.

Bias: Demographic Underrepresentation in EEG Datasets

The canonical scalp-EEG dataset used to benchmark seizure detection algorithms is the CHB-MIT Scalp EEG Database, containing recordings from 23 paediatric patients at Boston Children's Hospital (Shoeb, 2009). More recent benchmarks include the Temple University EEG Corpus (TUEG) with over 25,000 sessions. Despite their size, these datasets share a structural bias: they predominantly represent patients from high-income, English-speaking countries who were able to access tertiary epilepsy centres.

The clinical consequences of this bias are measurable. Seizure detection models trained on CHB-MIT achieve substantially lower sensitivity in:

• Adult patients, because paediatric seizure morphology (higher amplitude, more stereotyped) differs from adult seizure morphology;

• Female patients, due to hormonal modulation of seizure threshold (catamenial epilepsy) and differences in ictal semiology;

• Non-focal epilepsies, because hospital-based datasets over-represent lesional focal epilepsy (surgically amenable, hence disproportionately evaluated at centres with iEEG capability).

Generative debiasing.

Generative models offer a principled approach to dataset debiasing: synthesise data for underrepresented subgroups until the joint distribution of EEG morphology and demographic covariates is approximately balanced. Formally, let ${𝒟}_{\mathrm{real}}=\{({𝒙}_i,a_i)\}$ where $a_i\in 𝒜$ is a sensitive attribute (age group, sex, epilepsy syndrome). The generative debiasing objective is: (Debias)$$\begin{array}{ccc}& \underset{𝜽}{\min }{W}_2(p_{𝜽}(𝒙|a),p_{\mathrm{real}}(𝒙|a))\text{subject to}{p}_{𝜽}(a)=p_{\mathrm{uniform}}(a),& \text{<span class="tml-eqn"></span>}\end{array}$$ i.e., the conditional EEG distribution given each attribute should match the real distribution, but the marginal over attributes should be uniform. Conditional GANs and conditional diffusion models with attribute conditioning (class-free guidance) are natural implementations.

The validation challenge is circular: if no real data exists for the underrepresented subgroup, how can we verify that the synthetic data is realistic? This requires engagement with epilepsy centres in under-represented regions (Africa, South Asia) and with community-based EEG screening programmes, not purely algorithmic solutions.

Explainability: Interpreting Diffusion Attention Maps and Latent Spaces

Regulators and clinicians require that an AI system's decisions be explainable. The FDA's 2021 AI/ML Action Plan specifically cites explainability as a key element of transparency. For discriminative classifiers, attribution methods such as Grad-CAM, SHAP, and integrated gradients are well established. For generative models, explainability is less mature but arguably more important: if a diffusion model generates a “typical pre-ictal EEG”, the clinician needs to understand which features of that EEG are being highlighted.

Diffusion attention analysis.

In text-conditioned diffusion models, the cross-attention maps $A_{\ell }\in {\mathrm{ℝ}}^{N\times L}$ at denoising layer $\ell$ (where $N$ is the number of signal patches and $L$ is the number of text tokens) indicate which parts of the EEG signal attend to which clinical descriptors. Aggregated attention maps provide a free explanation: “this generated seizure segment is most influenced by the token ictal tachycardia in channels 4, 7, and 12.” The mathematical operation is: (Attention Attribution)$$\begin{array}{ccc}& \text{Attr}(n,\ell )=\frac{1}{L}\sum _{j=1}^L{\overline{A}}_{\ell }(n,j),{\overline{A}}_{\ell }=\frac{1}{N_{\mathrm{step}}}\sum _{t=1}^{N_{\mathrm{step}}}{A}_{\ell }^{(t)},& \text{<span class="tml-eqn"></span>}\end{array}$$ where the average is over denoising steps $t$. High $\text{Attr}(n,\ell )$ indicates that signal patch $n$ is a primary driver of the generation at layer $\ell$.

Latent space disentanglement.

For VAE-based brain twins, clinical interpretability requires that individual latent dimensions correspond to clinically meaningful factors: seizure duration, spread pattern, dominant frequency, amplitude. Total Correlation Variational Autoencoder ($\beta$-TCVAE; Chen et al., 2018) encourages disentanglement by penalising the total correlation: (Tcvae)$$\begin{array}{ccc}& {ℒ}_{\mathrm{TC}}={ℒ}_{\mathrm{ELBO}}-\alpha \cdot \mathrm{TC}\left(q_{𝝓}(𝒛)\right),\mathrm{TC}(q)=D_{\mathrm{KL}}(q(𝒛)\Vert \prod _{j=1}^{d}q(z_j)).& \text{<span class="tml-eqn"></span>}\end{array}$$ A latent dimension $z_j$ is interpretable if there exists a clinically defined feature $\varphi :{\mathrm{ℝ}}^C\to \mathrm{ℝ}$ (e.g., dominant frequency) such that the Spearman rank correlation $\rho (z_j,\varphi (𝒙))>0.7$ across a validation cohort. Ensuring interpretability without sacrificing generative quality (the classical disentanglement-quality trade-off) remains an active research area.

Exercises and Research Challenges

The exercises below consolidate the mathematical and conceptual foundations developed throughout this chapter. They progress from focused calculations (Exercises 1–5) through synthesis-level problems (Exercises 6–10) to open-ended research challenges (Challenges 1–3). We recommend that readers attempt every part independently before consulting the references.

Research Challenges

The following challenges represent frontier research directions requiring original contributions. Each challenge is designed to be the basis of a graduate research project or dissertation chapter. We provide context, desiderata, and evaluation criteria but deliberately leave the solution approach open.