Track 04 · Problems
Open problems, organized by chapter.
Every technical chapter of our reference text closes with its own “Open Problems and Future Directions” section: named conjectures, unresolved bounds, and concrete engineering targets, stated by the people who just finished deriving everything currently known about the subject. This page collects all of them, organized hierarchically by book part and chapter, as a starting point for thesis topics, research proposals, or a weekend of genuine thinking. Some are near-term engineering targets; some are Millennium-Prize-adjacent; a few are explicit conjectures awaiting proof or refutation.
II · Probabilistic Generative Models
8 · Variational Inference
- Tighter ELBO-style bounds (à la importance-weighted autoencoders) that tighten with sample count without degrading encoder gradient signal-to-noise.
- Identifying structured variational families beyond mean-field and normalizing flows that balance expressiveness, cost, and optimization difficulty.
- Extending reparameterization-based variational inference to discrete latent variables beyond the Gumbel-Softmax relaxation.
- Scaling variational inference, and genuine posterior uncertainty, to trillion-parameter models without doubling parameter count.
- Replacing KL-based variational objectives with optimal-transport or Wasserstein-style discrepancies for better multimodal-posterior behaviour.
For more detail, see the Open Problems section of 8 · Variational Inference in the book →
VI · Diffusion Models
20 · Video Diffusion Models
- Real-time video generation: reaching sub-second, interactive latency at current visual quality.
- Minute-scale temporal consistency: coherent objects and identity far beyond today's short context windows.
- Physical grounding: enforcing rigid-body, fluid, and contact dynamics that are physically plausible, not merely visually plausible.
- Compositional generation: reliably composing several independent objects and actions within one generated video.
- Unified multimodal generation: a single model producing synchronized video, audio, speech, and text together.
- Conjecture: a specific distillation-plus-caching architectural path is sufficient to reach real-time video diffusion.
For more detail, see the Open Problems section of 20 · Video Diffusion Models in the book →
21 · Audio and Music Generation
- Real-time audio generation at sub-200ms (speech), sub-50ms (interactive music), and sub-20ms (sound effects) latency.
- Song-length musical coherence: structural, thematic, harmonic, and dynamic coherence over 3 to 5 minutes.
- Codec Bottleneck Conjecture: once neural codec quality crosses a threshold, the perceptual quality bottleneck shifts entirely to the generative model.
- Unified audio generation: one model and weight set for speech, music, and sound effects with compositional mixing.
- Robust, unforgeable audio watermarking: imperceptible, robust, cryptographically unforgeable, and real-time.
For more detail, see the Open Problems section of 21 · Audio and Music Generation in the book →
22 · Diffusion Language Models
- Closing the remaining quality gap with top autoregressive LLMs on the hardest reasoning and coding benchmarks.
- Extending DPO-style alignment to full RLHF for diffusion language models, and how reward models should interact with iterative denoising.
- Adaptive output length without sacrificing the parallel generation advantage.
- Attention mechanisms compatible with both bidirectionality and KV-cache-style incremental computation.
- A single diffusion model unifying language and vision generation.
- Whether diffusion has a genuine information-theoretic, not just computational, advantage over autoregressive generation for some distribution classes.
For more detail, see the Open Problems section of 22 · Diffusion Language Models in the book →
VII · Reasoning and Recursive Computation
23 · Recurrence, Recursion, and Reasoning
- A principled, information-theoretic criterion for optimal reasoning-depth allocation, beyond heuristics like adaptive computation time.
- Verifying that a chain-of-thought is logically sound, not merely that it reaches the correct final answer.
- Whether recursive models can compose learned subroutines into genuinely novel reasoning chains.
- The exact computational complexity class of a Tiny Recursive Model run for polynomially many iterations.
- Whether a recursive reasoning model can improve its own update operator at inference time.
- Latent Reasoning Hypothesis: for any problem in P, a polynomial-size network run for polynomially many latent-space recursive iterations can solve it.
X · Continual Learning
26 · Continual Learning
- Whether continual-learning methods validated at 7B–13B scale behave differently, better or with new failure modes, at 100B+ scale.
- A formal account of "reasoning-chain fragility": how one forgotten fact cascades through multi-step reasoning.
- The theoretical limits of LoRA-based continual learning: the maximum number of tasks representable by a rank-r adapter before interference dominates.
- Continual RLHF: aligning to drifting human preferences without forgetting prior safety constraints.
- Scaling multimodal continual learning beyond two modalities, where cross-modal interference becomes combinatorial.
- CL Scaling Law conjecture: loss follows a power law with a separate "continual-learning tax" term, whose exponent determines whether arbitrarily many tasks can be absorbed at large enough scale.
- No Fixed Architecture Achieves All Five Properties: no fixed architecture or learning rule can simultaneously achieve bounded forgetting, positive forward transfer, sublinear parameter growth, constant-time inference, and single-pass online learning.
For more detail, see the Open Problems section of 26 · Continual Learning in the book →
XI · Agentic AI and Multi-Agent Systems
27 · Agentic AI and Multi-Agent Systems
- Provable multi-agent alignment: does a communication protocol or orchestrator exist that guarantees system-level alignment from individually-aligned agents?
- The information-theoretically optimal communication protocol minimizing inter-agent communication for a target performance level.
- Whether the multi-agent synergy exponent is task-dependent, zero for embarrassingly parallel tasks and positive above a critical task complexity.
- Whether collective forgetting can vanish as agent count grows, even though each individual agent forgets.
- Efficient verification of agent safety: PSPACE-hard in agent count generally, but polynomial for bounded-treewidth agent topologies.
- Alignment Composability conjecture: individually-aligned agents can still compose into a collectively misaligned multi-agent system.
XIII · Privacy and Security
29 · Membership Inference Attacks and Model Privacy
- Privacy-Utility-Fairness Trilemma: high generation quality, strong differential privacy, and demographic equity may not be simultaneously achievable.
- Characterizing the exact achievable Pareto frontier for quality, privacy budget, and fairness gap as a function of group sizes and model capacity.
- Extending binary membership inference to continuous influence regression, generation attribution, and distribution-level inference.
- Influence Subsumes Binary MIA conjecture: influence-function magnitude is asymptotically proportional to the LiRA likelihood ratio.
- Reducing influence-function estimation cost from quadratic to linear in dataset size, or proving a matching lower bound.
- Standardized, legally defensible membership-inference benchmarks suitable for regulatory compliance.
- Whether paired multimodal training creates stronger, cross-modal membership signals, and how to allocate a differential-privacy budget across modalities.
XIV · Neural Architecture Search and Adaptive Networks
30 · Neural Architecture Search and Adaptive Networks
- Whether polynomial, rather than exponential, sample-complexity bounds exist for neural architecture search over structured search spaces.
- Global convergence of differentiable NAS: whether a discretized stationary point matches the true global optimum.
- No Free Lunch for Architectures conjecture: no single architecture is optimal across all generative data distributions and tasks.
- The smoothness and local-minima structure of the architecture-performance landscape at realistic, greater-than-10^15-architecture scale.
- NAS scaling laws: whether architecture-optimized models have a steeper scaling exponent than fixed-architecture models as they grow.
- A practical, computable measure of architecture-dependent expressiveness beyond raw parameter count.
- NAS methods with formal, provable improvement-over-random-search certificates, addressing the field's reproducibility crisis.
- Whether NAS-discovered architectures transfer across tasks and modalities, and a formal task-distance/architecture-distance relationship.
- Making NAS computationally feasible at genuine foundation-model scale, hundreds of billions of parameters.
- Recursive self-improvement via NAS: whether the fixed-point iteration of an architecture searching for its own successor converges, diverges, or oscillates, and the associated safety implications.
XV · Evolutionary AI
31 · Evolutionary AI: Coevolution, Open-Ended Search, and Autonomous Discovery
- Open-Endedness Criterion: a formal three-part definition (unbounded novelty, unbounded complexity, ecological non-collapse) of genuinely open-ended evolution.
- Verification at scale: how to trust or verify evolved artifacts too complex for humans to check directly.
- The Motivation Problem: what intrinsic objective, novelty, curiosity, aesthetics, or empowerment, can drive evolution absent an external fitness function.
- Evolutionary alignment: whether self-modifying evolution eventually drifts misaligned unless human utility is perfectly correlated with evolving fitness.
- Characterizing which fitness-landscape structures make evolutionary search provably sample-efficient versus no-free-lunch-bound.
- Cross-domain transfer in evolution: whether evolved building blocks transfer across problem domains, and whether large language models mediate this transfer.
- Whether physical embodiment fundamentally changes what evolution can discover, at massively parallel modern-simulator scale.
- Evolutionary Sufficiency for Science: whether a coevolving theory-and-experiment system can rediscover, or even surpass, humanity's empirically testable scientific theories.
XVI · Applications of Generative Models in Retrieval
32 · Generative Models in Retrieval: From Memory to Meaning
- Universal retrieval: a single model retrieving across any pair of modalities at human-level competence.
- Real-time updating: closing the temporal gap between a document's creation and its retrievability.
- Compositional retrieval: handling multi-concept, include/exclude/modify queries beyond single-vector similarity.
- Causal retrieval: retrieving documents that causally improve a downstream outcome, not merely topically relevant ones.
- Retrieval with reasoning: multi-hop retrieval that can plan and backtrack, not just decompose and iterate.
- Practical privacy-preserving retrieval and similarity search over encrypted indices at web scale.
- Generation-Retrieval Duality: sufficiently powerful retrieval and generation converge to the same conditional distribution.
- The Universality Conjecture: sufficiently large contrastively-trained multimodal embeddings converge to a modality-independent universal retrieval geometry.
- No Fixed-Dimensional Embedding Suffices for a Growing Corpus: precision decays to zero for any fixed-dimension embedding as corpus size grows without bound.
XVII · Generative Models for Structured Data
Generative Models for Structured Data
- The minimax-optimal generator risk for mixed continuous and discrete tabular data, as a function of column counts and cardinality.
- A conjectured sample-complexity formula for tabular generation combining continuous, categorical, and dependency-graph terms.
- The minimax total-variation distance achievable under differential privacy for full joint tabular distributions.
- No Single Dominant Model: for any tabular generator and fidelity metric, a competing generator outperforms it on some distribution.
- A genuine foundation model for tables: zero- or few-shot generation from schema alone.
- Standardized evaluation protocols for tabular generation, addressing the field's own reproducibility gap.
XVIII · Generative Models for Mathematics
Generative Models for Mathematics
- Whether Transformers can genuinely "learn to prove," and the computational complexity of Transformer-based proof search.
- Whether there is a provable ceiling on autoformalization accuracy.
- Scaling formal mathematical libraries beyond Mathlib to the whole of research mathematics.
- A universal, cross-domain autoformalizer, and the cost-optimal balance of model size, search budget, and verification overhead.
- Grand challenges: an AI-assisted Millennium Prize solution, consistent autonomous IMO gold-medal performance, and a self-improving system that discovers new subfields.
- The AI Taste Conjecture: AI will develop genuine mathematical taste, distinguishing important from trivial problems, within a decade.
For more detail, see the Open Problems section of Generative Models for Mathematics in the book →
XIX · Generative Models for PDE-Based Simulation
Generative Models for PDE-Based Simulation
- The Navier-Stokes existence-and-smoothness problem revisited through diffusion-model rare-event sampling and learned Lyapunov functionals.
- Discretisation-agnostic generation: function-space diffusion models with convergence guarantees, independent of grid resolution.
- Real-time turbulence and interactive simulation: a thousand-fold speedup target for neural PDE surrogates at industrially relevant Reynolds numbers.
- A generative PDE foundation model spanning every major PDE family, with a conjectured scaling law and explicit physical guarantees.
- Enforcing exact conservation laws and certified error bounds in neural PDE surrogates, plus reliable out-of-distribution detection.
- A twenty-question research agenda spanning function-space convergence, neural-operator approximation theory, equivariant diffusion, and a unified cross-physics foundation model, several rated at Millennium Prize difficulty.
XX · Generative Models for Medical Image Segmentation
33 · Generative Models for Medical Image Segmentation
- Calibrated uncertainty in 4D medical volumes, spatiotemporally coupled across cardiac or respiratory cine sequences.
- Diffusion Speed-Quality Tradeoff conjecture: a logarithmic lower bound on function evaluations needed for a target segmentation accuracy.
- No Universal Dominance conjecture: any universal medical segmentation model pays a "generality tax" and loses to some smaller specialized model.
- A differentiable, efficient, stable Navier-Stokes solver embeddable directly in segmentation training for physics-informed regularization.
- Whether concept-bottleneck or neuro-symbolic approaches can break the observed interpretability-versus-accuracy tradeoff.
- Optimal stopping criteria for active-learning-plus-generative-augmentation annotation loops.
34 · Generative AI in Epilepsy Research
- Real-time generative seizure prediction feasible on an implantable device's power and memory budget.
- Personalized brain digital twins from as few as three to ten recorded seizures per patient.
- Cross-patient generalization across a thousand or more patients without catastrophic forgetting or storing raw EEG.
- Provenance watermarking to prevent EEG deepfakes, forensic fabrication, or medical fraud.
- A unified multimodal foundation model spanning EEG, MRI, and clinical text for seizure-onset localization.
- Moving from associative to genuinely causal and counterfactual models of seizure propagation mechanisms.
- No Single Generative Architecture Will Dominate: GANs, diffusion, VAEs, optimal transport, and Transformers each dominate a different epilepsy sub-task.
XXI · Interpretability and Explainability of Generative Models
35 · Interpretability and Explainability of Generative Models
- Scaling interpretability to trillion-parameter models, and whether an "interpretability wall" exists beyond which human-legible descriptions may not.
- A permutation-invariant, efficiently computable "same computation" distance for comparing circuits across different architectures.
- An architecture whose every computation step has a provably faithful, human-legible interpretation, at no cost to model quality.
- Discovering and characterizing cross-modal circuits, text-to-image, temporal video consistency, and audio, essentially uncharacterized today.
- Formally verifying, or refuting, that a discovered circuit implements a claimed semantic specification, beyond toy models.
- The Pareto frontier between capability loss and interpretability constraints, and how it scales with model size.
- Plurality of Interpretability Frameworks conjecture: no single interpretability framework can be simultaneously faithful, complete, and tractable across all architectures and tasks.
XXII · Generative Models for Weather Prediction
36 · Generative Models for Weather Prediction
- Calibrated extreme-event prediction beyond ten days, into the classical "predictability desert."
- Architecturally, not just softly, enforcing mass, energy, and potential-vorticity conservation at every inference step.
- Kilometer-scale, fifty-member global ensemble generation within an operational few-minute window.
- Online learning that assimilates real-time observations without catastrophic forgetting of learned dynamics.
- One model family seamlessly spanning six-hour convection forecasts through century-scale climate projection.
- Reliable tail-risk probabilities for centuries-return-period events from an 85-year observational record.
- The Dominance Conjecture: no single fixed architecture will simultaneously excel at nowcasting, medium-range, subseasonal, and climate-scale prediction.
XXIII · Federated Learning for Generative Models
37 · Federated Learning for Generative Models
- Communication-efficient, convergent federated training of billion-parameter diffusion models across tens of thousands of heterogeneous clients.
- A compositional privacy notion strictly weaker than differential privacy that still meaningfully bounds inference from synthetic samples.
- Federated non-stationary generative learning across a stream of joining and departing clients, without storing past raw data.
- Training a cross-modal generative model when no single client holds paired multimodal data.
- Scalable, complete, and third-party-verifiable federated unlearning for generative models.
- A federated fidelity score that proxies centralized FID without any client sharing raw data.
- Federated Generative Trilemma: a fundamental three-way tension among differential privacy, utility, and communication efficiency.
XXIV · Generative AI for Accessibility and Disabilities
38 · Generative AI for Accessibility and Disabilities
- Real-time, sub-150ms description of dynamically moving physical infrastructure for blind navigation.
- Culturally and linguistically authentic sign-language synthesis across roughly three hundred distinct sign languages.
- Proactive voice preservation: identity-preserving voice banking from thirty minutes of pre-symptomatic speech through disease progression.
- A complete offline accessibility hardware and software stack under a one-hundred-dollar bill of materials.
- Auditing and reweighting large image-text corpora for disability under- and mis-representation.
- A sub-50ms, high-precision detector for dangerous vision-language-model fabrications in navigation descriptions.
- One model adapting content to any, including co-occurring, disability need without per-disability fine-tuning.
- Evaluative Paradigm Shift conjecture: some quality-of-life metric is never monotonically related to any combination of lab task-accuracy metrics.
XXV · Distributed Generative AI
39 · Distributed Generative AI
- Communication-optimal joint search over data, tensor, pipeline, and sequence parallelism under a memory constraint, likely NP-hard.
- Sub-linear-communication approximate distributed attention mechanisms.
- Online topology reconfiguration mid-training with provable convergence and minimal pause.
- The minimum bit-width at which distributed low-precision training still matches full-precision convergence.
- A wide-area-network-tolerant score-composition protocol for cross-datacenter diffusion training.
- A carbon-optimal training protocol minimizing carbon-weighted energy under a wall-clock deadline.
- Minimum-communication, bit-exact scheduling for distributed reverse-mode automatic differentiation, an NP-hard cut/recompute problem.
- Checkpoint-free, non-halting fault recovery tolerating up to a third of devices failing.
- Provable-guarantee load balancing across heterogeneous GPU, TPU, and ASIC clusters.
- Communication Lower Bound conjecture: an information-theoretic floor on bits-per-step for gradient-based training, which, if true, would show existing compression methods are already near-optimal.
For more detail, see the Open Problems section of 39 · Distributed Generative AI in the book →
Not sure where to start?
Read the chapter behind any problem above in full, or open the built-in AI tutor on that chapter and ask it to help you scope a specific problem down to a tractable first project.