A mathematical perspective of machine learning

DOI10.4171/icm2022/155OpenAlexW4389775620MaRDI QIDQ6118171

E. Weinan

Publication date: 20 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/icm2022/155

zbMATH Keywords

neural networkserror analysisapproximation theorycurse of dimensionalitymachine learningscientific computingcontinuous formulationintegral differential equations

Mathematics Subject Classification ID

Computational learning theory (68Q32) Learning and adaptive systems in artificial intelligence (68T05) Proceedings, conferences, collections, etc. pertaining to computer science (68-06)

Cites Work

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• Adapted solution of a backward stochastic differential equation
• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• The heterogeneous multiscale methods
• Machine learning from a continuous viewpoint. I
• A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training
• Approximation and estimation bounds for artificial neural networks
• A convexity principle for interacting gases
• Approximation rates for neural networks with general activation functions
• DGM: a deep learning algorithm for solving partial differential equations
• Rademacher complexity and the generalization error of residual networks
• Solving many-electron Schrödinger equation using deep neural networks
• A priori estimates of the population risk for two-layer neural networks
• Error bounds for approximations with deep ReLU networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A proposal on machine learning via dynamical systems
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
• Universal approximation bounds for superpositions of a sigmoidal function
• Hinging hyperplanes for regression, classification, and function approximation
• Stable architectures for deep neural networks
• Solving the quantum many-body problem with artificial neural networks
• A mean field view of the landscape of two-layer neural networks
• Solving high-dimensional partial differential equations using deep learning
• Adaptive Deep Learning for High-Dimensional Hamilton--Jacobi--Bellman Equations
• The Dawning of a New Era in Applied Mathematics
• Solving parametric PDE problems with artificial neural networks
• Deep Network Approximation for Smooth Functions
• Deep Potential: A General Representation of a Many-Body Potential Energy Surface
• Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
• The Vanishing Gradient Problem During Learning Recurrent Neural Nets and Problem Solutions
• Breaking the Curse of Dimensionality with Convex Neural Networks
• High-dimensional integration: The quasi-Monte Carlo way
• Understanding Machine Learning
• Theory of Reproducing Kernels
• Approximation by superpositions of a sigmoidal function

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