mlsanityData to 14 Oct 2026

Mathematical theory of deep learning

arXiv 2407.18384 ↗First posted 25 Jul 2024cs.LG math.HOcited by 23

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Abstract (arXiv)

This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural network theory. Serving as a guide for students and researchers in mathematics and related fields, the book aims to equip readers with foundational knowledge on the topic. It prioritizes simplicity over generality, and presents rigorous yet accessible results to help build an understanding of the essential mathematical concepts underpinning deep learning.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 Jul 2024.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 8; 2026: 15.

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  1. 2025Online Learning of Neural Networkscited by 5
  2. 2025On Universality Classes of Equivariant Networkscited by 4
  3. 2026Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexitycited by 3
  4. 2025Causal pieces: analysing and improving spiking neural networks piece by piececited by 2
  5. 2025Minimum Width of Deep Narrow Networks for Universal Approximationcited by 2
  6. 2025Feature Attribution from First Principlescited by 1
  7. 2025Autonomous-Flow-Based Generationcited by 1
  8. 2026Equivalence of approximation by networks of single- and multi-spike neuronscited by 1
  9. 2026Adaptivity Under Realizability Constraints: Comparing In-Context and Agentic Learningcited by 1
  10. 2026Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracycited by 1
  11. 2026Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximationcited by 1
  12. 2025Reconstruction of frequency-localized functions from pointwise samples via least squares and deep learningcited by 0
11 more
  1. 2025New Approximation Results and Optimal Estimation for Fully Connected Deep Neural Networkscited by 0
  2. 2026Classification Fields: Arbitrarily Fine Recursive Hierarchical Clustering From Few Examplescited by 0
  3. 2026Structure-Preserving Reconstruction of Convex Lipschitz Functionals on Hilbert Spaces from Finite Samplescited by 0
  4. 2026Fast approximation and learning of binary classification tasks in o-minimal structures using ReLU neural networkscited by 0
  5. 2026Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width Onecited by 0
  6. 2026Local large deviations for linear-region growth in random piecewise-linear networkscited by 0
  7. 2026Mathematics of Data Sciencecited by 0
  8. 2026NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processescited by 0
  9. 2026Learning piecewise-smooth dynamical systemscited by 0
  10. 2026Neural operators approximate strongly continuous convex monotone semigroupscited by 0
  11. 2026Neural Approximation by Function Composition: Rigidity and Doubly Exponential Convergencecited by 0