Artificial intelligence and machine learning
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-223 Polynomial-Time Distribution-Free PAC Learning of DNF Formulas
- Math-297 Sample Compression Conjecture (Linear Size in VC Dimension)
- Math-3789 10 Lectures and 42 Open Problems — Boolean classification and annulus conjecture
- Math-3790 10 Lectures and 42 Open Problems — Tightness of the Multireference Alignment SDP
- Math-4378 10 Lectures and 42 Open Problems — Consistency and sample complexity of Multireference Alignment
- Math-4522 Accurate Answers to Adaptively Chosen Statistical Queries
- Math-4537 Global Optimization of Overparameterized Shallow Networks
- Math-4538 Extrapolating Clusterings from Semidefinite Subsamples
- Math-4583 Optimal Neural-Network Depth for Sparse Recovery
- Math-4599 Universal Approximation by One-Lipschitz Spline Networks
- Math-4600 Global Margin Maximization beyond the Neural Tangent Regime
- Math-4601 Cancellation-Sensitive Norms for Two-Layer Networks
- Math-4603 Geometric Criteria for Benign Overfitting
- Math-4604 Benign, Tempered, and Catastrophic Overfitting Regimes
- Math-4615 Semi-Supervised Sparse Gaussian Classification
- Math-4636 Cross-Entropy Dynamics Beyond Hadamard Initialization
- Math-4637 Hidden-Layer Depth Complexity of Piecewise-Linear Functions
- Math-5191 Learning Capacity of Totally Geodesic Map Families
- Math-5213 Machine-Learning Algorithms Results Report
- Math-5216 Robust Spectral Tensor Methods for Latent-Variable Learning
- Math-5245 Provable Advantages of Convolutional Arithmetic Circuits
- Math-5261 Robustness-Driven Overparameterization in Two-Layer Neural Networks
- Math-5263 Comparative Advantages of Physics-Based and Machine-Learned Models
- Math-5264 High-Dimensional Regression and PDE Learning Without Dimensional Curse
- Math-5275 Computable Neural-Network Approximation from Noisy Samples
- Math-5276 Computable Ground Truths for Learning Problems
- Math-5277 Stochasticity and Sample Complexity in Neural Networks
- Math-5286 Neural Network Robustness under Adversarial and Distribution Shifts
- Math-5292 Mathematical Conjecture Generation with Machine Intelligence
- Math-5294 Training-Loss Implications for Shallow Neural Networks
- Math-5295 Convergence to Implicit Geometry under Class Imbalance
- Math-5296 Neural Approximation of Strongly Convex Drifts with Linear Error
- Math-5303 Expressivity and Training Theory for Deep Material Networks
- Math-5306 Learning Data Manifolds for Augmentation and Nonlinear Components
- Math-5310 Autoencoder Optimization Perspectives
- Math-5311 Optimal Noiseless Rates for Max-Average-Margin Classifiers
- Math-5314 Neural Networks for High-Dimensional Optimal Feedback Control
- Math-5324 Generalization Guarantees for Self-Supervised Representations
- Math-5325 Adam Optimization Performance
- Math-5326 Definition of a Causal Representation
- Math-5327 Criteria for a Good Representation
- Math-5342 Efficient Optimization of Neural-Network Weights
- Math-5346 Formal Verification of AI-Generated Mathematical Proofs
- Math-5348 Agentic and Neuro-Symbolic AI for Mathematical Research
- Math-5350 Causal-Attention Retrieval Motivation
- Math-5352 Complexity and Generalization in Overparameterized Learning
- Math-5353 Unified Mathematical Theory of Modern Learning
- Math-5354 Curricula for Algorithmic Reasoning in Sequence Models
- Math-5355 Inference and Training Effects of the Softmax Bottleneck
- Math-5356 Extremal Top-$m$ Representability of Output Projection Matrices