AI for Mathematics & Formal Proof
Lean and Mathlib, autoformalization, neural theorem proving, olympiad-level systems and AI-assisted discovery in mathematics.
Most influential
- Self-Normalizing Neural Networks
Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot exploit many levels of abstract represen…
Preprint2,031 citationsarXiv:1706.02515 - Solving olympiad geometry without human demonstrations
Abstract Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning 1–4 , owing to their reputed difficulty among the world’s best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating…
Abstract excerpt by Trieu H. Trinh et al., CC-BY, https://doi.org/10.1038/s41586-023-06747-5; truncated.
Article311 citationsdoi:10.1038/s41586-023-06747-5 - The expressive power of neural networks: a view from the widthArticle516 citations
- Direct Adaptive Neural Control for a Class of Uncertain Nonaffine Nonlinear Systems Based on Disturbance ObserverArticle396 citationsdoi:10.1109/tsmcb.2012.2226577
- Convergence Analysis of Two-layer Neural Networks with ReLU Activation
In recent years, stochastic gradient descent (SGD) based techniques has become the standard tools for training neural networks. However, formal theoretical understanding of why SGD can train neural networks in practice is largely missing. In this paper, we make progress on understanding this mystery by providing a convergence analysis for SGD on a rich subse…
Preprint304 citationsarXiv:1705.09886 - Theory of deep convolutional neural networks: DownsamplingArticle263 citationsdoi:10.1016/j.neunet.2020.01.018
- Neural Operator: Learning Maps Between Function Spaces
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integ…
Preprint217 citationsarXiv:2108.08481doi:10.5555/3648699.3648788 - Global stability analysis of fractional-order Hopfield neural networks with time delayArticle258 citationsdoi:10.1016/j.neucom.2014.12.031
- Adaptive Neural Backstepping Control Design for A Class of Nonsmooth Nonlinear SystemsArticle208 citationsdoi:10.1109/tsmc.2018.2875947
- Recurrent Neural Network for Non-Smooth Convex Optimization Problems With Application to the Identification of Genetic Regulatory NetworksArticle213 citationsdoi:10.1109/tnn.2011.2109735
- Neuro-symbolic approaches in artificial intelligence
Neuro-symbolic artificial intelligence refers to a field of research and applications that combines machine learning methods based on artificial neural networks, such as deep learning, with symbolic approaches to computing and artificial intelligence (AI), as can be found for example in the AI subfield of knowledge representation and reasoning. Neuro-symboli…
Abstract excerpt by Pascal Hitzler et al., CC-BY, https://doi.org/10.1093/nsr/nwac035; truncated.
Article167 citationsdoi:10.1093/nsr/nwac035 - Adaptive Neural Network Output Feedback Control for Stochastic Nonlinear Systems With Unknown Dead-Zone and Unmodeled DynamicsArticle204 citationsdoi:10.1109/tcyb.2013.2276043
- Convergence Analysis of Two-layer Neural Networks with ReLU ActivationArticle192 citations
- Neural Network Learning Adaptive Robust Control of an Industrial Linear Motor-Driven Stage With Disturbance Rejection AbilityArticle177 citationsdoi:10.1109/tii.2017.2684820
- Universal Approximations of Invariant Maps by Neural Networks
We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups. Our goal is to establish network-like computational models that are both invariant/equivariant and provably complete in the sense of their ability to approximate any continuous invariant/equ…
Article139 citationsarXiv:1804.10306doi:10.1007/s00365-021-09546-1
Newest work
- Counting by the Book: Verifying Alaska's Ranked-Choice ElectionsPreprintarXiv:2610.36494
- Resolvent Components of Completely Normal Elements and the Morgan-Mullen ConjecturePreprintarXiv:2610.36534
- The Batch Size Can Be One: Test-Time Adaptation from Classifier GeometryPreprintarXiv:2610.36628
- Can LLMs Reliably Grade Olympiad Proofs? A Study of Mathematical Verification with LLMsPreprintarXiv:2610.36767
- Guided-RLVR: Guided Exploration in Reinforcement Learning with Verifiable RewardsPreprintarXiv:2610.37041
- Watermark Basins: Black-Box Detection of Distilled LLMsPreprintarXiv:2610.37266
- Global Choice without Excluded Middle in Dependent Type TheoryPreprintarXiv:2610.37498
- GTFormer: A Syntax-Free Graph Network Alternative to Transformers for 8192$\times$ Length Extrapolation in Linear TimePreprintarXiv:2610.37524
- Connecting Quantum Proof Systems and Hoare LogicPreprintarXiv:2610.34723
- Improving Reasoning with Rollout Agreement for Group-Based Policy OptimizationPreprintarXiv:2610.34951