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oberwolfach_workshop

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Material for 'Mathematics of Deep Learning Workshop' (Invited Talk)

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# 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](slides/Grohs/Bedlewo_MathematicalLearning.pdf)                         | [Approximation Theory and Expressivity I](slides/Kutyniok/Talk_BanachCenter2_2019.pdf)                                  | [Approximation Theory](slides/Grohs/Bedlewo_ApproximationTheory.pdf)                | [Deep Neural Networks for PDEs](slides/Grohs/Bedlewo_PDEs.pdf)                                              | [Interpretability](slides/Kutyniok/Talk_BanachCenter5_2019.pdf)                                           |
| [Introduction to Neural Networks](slides/Kutyniok/Talk_BanachCenter1_2019.pdf)                          | [Neural Network Approximation in TensorFlow](https://colab.research.google.com/github/juliusberner/oberwolfach_workshop/blob/master/NN_Approximation.ipynb) | [Deep Learning meets Inverse Problems](slides/Kutyniok/Talk_BanachCenter3_2019.pdf) | [Deep Learning meets Parametric Partial Differential Equation](slides/Kutyniok/Talk_BanachCenter4_2019.pdf) | [Generalization for Deep Learning](slides/Grohs/Bedlewo_Generalization.pdf)                               |
| [Introduction to TensorFlow](https://colab.research.google.com/github/juliusberner/oberwolfach_workshop/blob/master/Fashion_MNIST.ipynb) | [Deep Learning for Kolmogorov PDEs](https://colab.research.google.com/github/juliusberner/oberwolfach_workshop/blob/master/DL_Kolmogorov.ipynb)          |                                                                                     | [NN Training in the Overparametrized Setting](slides/Berner/overparametrized_training.pdf)                  | [Linear Regression with LASSO](https://colab.research.google.com/github/juliusberner/oberwolfach_workshop/blob/master/Linear_Regression_with_LASSO.ipynb) |

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### Talks

1. Gitta Kutyniok 
   - [Introduction to Neural Networks](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Kutyniok/Talk_BanachCenter1_2019.pdf)
   - [Approximation Theory and Expressivity I](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Kutyniok/Talk_BanachCenter2_2019.pdf)
   - [Deep Learning meets Inverse Problems](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Kutyniok/Talk_BanachCenter3_2019.pdf)
   - [Deep Learning meets Parametric Partial Differential Equation](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Kutyniok/Talk_BanachCenter4_2019.pdf)
   - [Interpretability](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Kutyniok/Talk_BanachCenter5_2019.pdf)

2. Philipp Grohs
   - [Mathematical Foundations of ML](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Grohs/Bedlewo_MathematicalLearning.pdf)
   - [Approximation Theory](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Grohs/Bedlewo_ApproximationTheory.pdf)
   - [Deep Neural Networks for PDEs](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Grohs/Bedlewo_PDEs.pdf)
   - [Generalization for Deep Learning](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Grohs/Bedlewo_Generalization.pdf)

3. Julius Berner
   - [NN Training in the Overparametrized Setting](https://github.com/juliusberner/oberwolfach_workshop/raw/master/slides/Berner/overparametrized_training.pdf)

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### Notebooks

#### Google Colaboratory

1. Philipp Grohs
   - Linear Regression with LASSO: [Linear_Regression_with_LASSO](https://colab.research.google.com/github/juliusberner/oberwolfach_workshop/blob/master/Linear_Regression_with_LASSO.ipynb)

2. Julius Berner
   - A simple approach to the Fashion-MNIST dataset: [Fashion_MNIST](https://colab.research.google.com/github/juliusberner/oberwolfach_workshop/blob/master/Fashion_MNIST.ipynb)

- Framework for constructing deep neural networks to efficiently approximate various functions: [NN_Approximation](https://colab.research.google.com/github/juliusberner/oberwolfach_workshop/blob/master/NN_Approximation.ipynb)

- Deep learning based method for solving high-dimensional Kolmogorov PDEs: [DL_Kolmogorov](https://colab.research.google.com/github/juliusberner/oberwolfach_workshop/blob/master/DL_Kolmogorov.ipynb)

#### Local Environment

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

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

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