The mathematics of artificial intelligence

DOI10.4171/icm2022/141arXiv2203.08890OpenAlexW4389775319MaRDI QIDQ6200206

Gitta Kutyniok

Publication date: 22 March 2024

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

Full work available at URL: https://arxiv.org/abs/2203.08890

zbMATH Keywords

inverse problemsapproximation theoryapplied harmonic analysisdeep learningpartial different equations

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Asymptotic expansions of solutions to PDEs (35C20) General harmonic expansions, frames (42C15) Rate of convergence, degree of approximation (41A25)

Related Items (1)

Why should mathematicians ask politicians to avoid the ancient dilemma of pure and applied mathematics?

Cites Work

• The Little Engine that Could: Regularization by Denoising (RED)
• Compactly supported shearlets are optimally sparse
• Multilayer feedforward networks are universal approximators
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• Numerical solution of the parametric diffusion equation by deep neural networks
• A theoretical analysis of deep neural networks and parametric PDEs
• Deep microlocal reconstruction for limited-angle tomography
• 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
• Introduction to Shearlets
• Solving ill-posed inverse problems using iterative deep neural networks
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• Solving high-dimensional partial differential equations using deep learning
• Optimal Approximation with Sparsely Connected Deep Neural Networks
• Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks
• Reconciling modern machine-learning practice and the classical bias–variance trade-off
• Learning representations by back-propagating errors
• A Stochastic Approximation Method
• The Computational Complexity of Understanding Binary Classifier Decisions
• The Modern Mathematics of Deep Learning
• Approximation by superpositions of a sigmoidal function
• Sparse components of images and optimal atomic decompositions

This page was built for publication: The mathematics of artificial intelligence