Neural Networks and Numerical Analysis

Contents

1. Introduction
   1. A brief historical perspective
   2. Plan
   3. Last words
2. Acknowledgement
3. 1 Objective functions, neural networks, and linear algebra
   1. 1.1 Notations
   2. 1.2 The least squares method
      1. 1.2.1 Recursivity
      2. 1.2.2 Nonlinearity
      3. 1.2.3 Functions and Neural Networks
   3. 1.3 Logistic function, cross-entropy, classification, CNNs
      1. 1.3.1 Logistic function, cross-entropy
      2. 1.3.2 Classification
      3. 1.3.3 Convolutive neural networks
   4. 1.4 Summary of the chapter
4. 2 Approximation properties
   1. 2.1 Functional spaces
   2. 2.2 Cybenko theorem
   3. 2.3 Simple constructive proofs
      1. 2.3.1 Approximation in dimension one
      2. 2.3.2 Approximation in higher dimensions
   4. 2.4 Connection with finite element theory
      1. 2.4.1 1D piecewise affine finite elements
      2. 2.4.2 2D piecewise ...