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AIM Problem Lists3470 Aaronson — Quantum Query Complexity12 Alessandro Carlotto — The general relativistic constraint equations3 AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner59 Andrii Mironchenko — Input-to-state stability of infinite-dimensional systems: recent results and open questions2 Anton Petrunin — A Gallery of Geometry Problems15 Armin Schikorra — Invitation to H-systems in higher dimensions: known results, new facts, and related open problems2 Axial Algebras — Questions and Conjectures2 Bertrand Clarke — A Cheat Sheet for Bayesian Prediction5 COLT Open Problems — supplied archive30 Clay Mathematics Institute — Millennium Prize Problems6 Community consensus34 Dagstuhl 25041 — Graph Classes and Algorithmic Complexity8 Dagstuhl 25081 — Semirings in Database Theory4 Dagstuhl — Quantum Error Correction Meets ZX-Calculus3 Epoch AI — FrontierMath: Open Problems49 Erdős Problems (Thomas Bloom)634 Ewin Tang — Quantum Learning Questions2 FDIG 2025 — Open Problems in Information Geometry3 FOCS 2024 — Quantum Learning10 Formal Conjectures459 ICM Conjectures2898 JMLR — Fast Rates in PAC-Bayes Meta-Learning1 JMLR — Pre-trained Gaussian Processes for Bayesian Optimization4 Jacobs — Twenty Open Problems in Quantum Control20 João Araújo — A survey on varieties generated by small semigroups and a companion website8 Kirby's problem list in low-dimensional topology1 Liouville Quantum Gravity — Holden & Sun3 Nathan Segerlind — The complexity of propositional proofs1 Oberwolfach 2025 — Analytic Number Theory Problem Session11 Open Problem Garden2 Open Problems in Mathematical Biology — Vittadello & Stumpf4 Open Quantum Problems114 Optimization Constants in Mathematics — Davis, Ivanisvili & Tao115 Oğuz Şavk — A survey of the homology cobordism group4 Queueing, Predictions, and LLMs — Mitzenmacher & Shahout42 Randomstrasse101 — Open Problems of 202515 Robert Benedetto — Current trends and open problems in arithmetic dynamics3 SIAM Optimization — Open Problems in Optimization2 Simons Institute — Lattices '22 problems10 Simons Workshop — Linear Systems and Eigenvalue Problems2 Smale's problems for the 21st century2 Tableaux — A notebook of open problems48 The Open Problems Project (computational geometry)38 TheoremDB3909 Tianyuan Workshop — Open Problems in Mathematical Logic22 Universality in Computable Dynamical Systems — Old and New3 Wikipedia — Astronomy5 Wikipedia — Biology5 Wikipedia — Chemistry3 Wikipedia — Computer science7 Wikipedia — Economics2 Wikipedia — Fair division2 Wikipedia — Geoscience4 Wikipedia — Information theory4 Wikipedia — Loop theory and quasigroup theory6 Wikipedia — Mathematics5 Wikipedia — Neuroscience4 Wikipedia — Physics5 Wikipedia — Statistics2 Xavier Blanc — The crystallization conjecture: a review1 arXiv preprints2

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OP-0049Deep learning theoryOpen

Depth separation for functions learnable by gradient descent

Depth-3 networks can express functions depth-2 cannot. Whether training can find them is a different question, and it is open.

Community consensus· 2016

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