mlsanityData to 7 Oct 2026

The Mathematics of Artificial Intelligence

arXiv 2203.08890 ↗First posted 16 Mar 2022cs.LG math.HO stat.MLcited by 0

Not on the map. Why?

Abstract (arXiv)

We currently witness the spectacular success of artificial intelligence in both science and public life. However, the development of a rigorous mathematical foundation is still at an early stage. In this survey article, which is based on an invited lecture at the International Congress of Mathematicians 2022, we will in particular focus on the current "workhorse" of artificial intelligence, namely deep neural networks. We will present the main theoretical directions along with several exemplary results and discuss key open problems.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 21 of its 36 references that are in the map. First posted on arXiv 16 Mar 2022.

Builds on

21 of 36 references.

References · 21

  1. 2017A Unified Approach to Interpreting Model Predictionscited by 6,488
  2. 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,040
  3. 2017SmoothGrad: removing noise by adding noisecited by 1,097
  4. 2017Deep Image Priorcited by 1,097
  5. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 919
  6. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  7. 2016Error bounds for approximations with deep ReLU networkscited by 567
  8. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  9. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 431
  10. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  11. 2016On the Expressive Power of Deep Neural Networkscited by 302
  12. 2017Solving ill-posed inverse problems using iterative deep neural networkscited by 145
9 more
  1. 2018Adversarial Regularizers in Inverse Problemscited by 102
  2. 2017Optimal Approximation with Sparsely Connected Deep Neural Networkscited by 90
  3. 2019A Theoretical Analysis of Deep Neural Networks and Parametric PDEscited by 74
  4. 2021The Modern Mathematics of Deep Learningcited by 63
  5. 2020Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networkscited by 27
  6. 2021A Rate-Distortion Framework for Explaining Black-box Model Decisionscited by 11
  7. 2019Extraction of digital wavefront sets using applied harmonic analysis and deep neural networkscited by 4
  8. 2021Deep Microlocal Reconstruction for Limited-Angle Tomographycited by 4
  9. 2015Shearlet-Based Detection of Flame Frontscited by 2

Built on by

Not cited yet.