Understanding Deep Neural Networks - From Generalization to Interpretability

Explore a seminar on theoretical machine learning that delves into the understanding of deep neural networks, focusing on generalization and interpretability. Gain insights from Gitta Kutyniok of Technische Universität Berlin as she discusses the dawn of deep learning, its impact on mathematical problems, and numerical results. Examine graph convolutional neural networks, including two approaches to convolution on graphs and spectral graph convolution. Investigate spectral filtering using functional calculus and compare the repercussion of filters on different graphs. Analyze the transferability of functional calculus filters and rethink transferability concepts. Address fundamental questions concerning deep neural networks, exploring the general problem setting, relevance mapping, and rate-distortion viewpoint. Conclude with observations from an MNIST experiment, providing a comprehensive overview of current research in deep learning theory and applications.

Intro
The Dawn of Deep Learning
Impact of Deep Learning on Mathematical Problems
Numerical Results
Graph Convolutional Neural Networks Graph convolutional neural networks
Two Approaches to Convolution on Graphs
Spectral Graph Convolution
Spectral Filtering using Functional Calculus
Graphs Modeling the Same Phenomenon
Comparing the Repercussion of a Filter on Two Graphs
Transferability of Functional Calculus Filters
Rethinking Transferability
Fundamental Questions concerning Deep Neural Networks
General Problem Setting
What is Relevance?
The Relevance Mapping Problem
Rate-Distortion Viewpoint
Problem Relaxation
Observations
MNIST Experiment