Banach Center – Oberwolfach Graduate Seminar: Mathematics of Deep Learning

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

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Overview

Monday	Tuesday	Wednesday	Thursday	Friday
Mathematical Foundations of ML	Approximation Theory and Expressivity I	Approximation Theory	Deep Learning meets Parametric Partial Differential Equation	Interpretability
Introduction to Neural Networks	Neural Network Approximation in TensorFlow	Deep Learning meets Inverse Problems	Deep Neural Networks for PDEs
Introduction to TensorFlow	Deep Learning for Kolmogorov PDEs

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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

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Notebooks

Google Colaboratory

• 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)