README.md

Banach Center – Oberwolfach Graduate Seminar: Mathematics of Deep Learning

Teaching material for 'Mathematics of Deep Learning Workshop' (https://www.mfo.de/occasion/1947a)

---

Overview

Monday	Tuesday	Wednesday	Thursday	Friday
Mathematical Foundations of ML	Approximation Theory and Expressivity I	Approximation Theory	Deep Neural Networks for PDEs	Interpretability
Introduction to Neural Networks	Neural Network Approximation in TensorFlow	Deep Learning meets Inverse Problems	Deep Learning meets Parametric Partial Differential Equation	Generalization for Deep Learning
Introduction to TensorFlow	Deep Learning for Kolmogorov PDEs		NN Training in the Overparametrized Setting	Linear Regression with LASSO

---

Talks

1. Gitta Kutyniok

   • Introduction to Neural Networks
   • Approximation Theory and Expressivity I
   • Deep Learning meets Inverse Problems
   • Deep Learning meets Parametric Partial Differential Equation
   • Interpretability

2. Philipp Grohs

   • Mathematical Foundations of ML
   • Approximation Theory
   • Deep Neural Networks for PDEs
   • Generalization for Deep Learning

3. Julius Berner

   • NN Training in the Overparametrized Setting

---

Notebooks

Google Colaboratory

1. Philipp Grohs

   • Linear Regression with LASSO: Linear_Regression_with_LASSO

2. Julius Berner

   • A simple approach to the Fashion-MNIST dataset: Fashion_MNIST

   • Framework for constructing deep neural networks to efficiently approximate various functions: NN_Approximation

   • Deep learning based method for solving high-dimensional Kolmogorov PDEs: DL_Kolmogorov

Local Environment

1. Install the Python development environment
2. Create a virtual environment
3. Install requirements.txt

(see https://www.tensorflow.org/install/pip)