Reliable AI: From Applied Harmonic Analysis to Quantum Computing

Explore a comprehensive lecture on the reliability challenges of artificial intelligence, focusing on generalization and explainability in deep neural networks. Delve into a complete generalization result for graph neural networks and discover a novel explainability approach rooted in applied harmonic analysis. Examine the limitations of digital hardware for AI reliability and uncover surprising connections to quantum computing. Learn about key concepts such as graph convolutional neural networks, spectral graph convolution, and transferability of functional calculus filters. Investigate the rate-distortion viewpoint for explainability and its application in detecting reasons for adversarial examples. Gain insights into the future directions of AI research and the potential role of mathematics in addressing current challenges.

Intro
The Dawn of Artificial Intelligence in Public Life
Artificial Intelligence = Alchemy?
Problem with Reliability
Strong Requirements for Reliability
Main Research Directions
Some Facts about Graph Convolutional Neural Networks
A Special Form of Generalization Capability
Graph Laplacian: Oscillations on Graphs
Spectral Graph Convolution
Spectral Filtering using Functional Calculus
Graphs Modeling the Same Phenomenon
Comparing the Repercussion of a Filter on Two Graphs
DSP Framework akin to the Nyquist-Shannon Approach
What is Transferability precisely?
Transferability of Functional Calculus Filters
Transferability of Functional Calculus CNNs
Explainability
Rate-Distortion Viewpoint
Rate-Distortion Explanation
STL-10 Experiment
Desiderata
Cartoon X (Kolek, Nguyen, Levie, Bruna, K; ECCV 2022)
Telecommunication
Detecting Reason for Adversarial Examples
A Serious Problem
What now?... Mathematics Tells Us the Answer!
Conclusions