Overview
Syllabus
Intro
The Dawn of Artificial Intelligence in Public Life
Spectacular Success in Science
Impact on Mathematical Problem Settings
Artificial Intelligence = Alchemy?
Problem with Reliability
Role of Mathematics Two Key Challenges for Mathematics
First Appearance of Neural Networks
Artificial Neurons
Affine Linear Maps and Weights
Definition of a Deep Neural Network
Training of Deep Neural Networks
Mathematics for Artificial Intelligence
Glimpse into Generalization
Graph Neural Networks
A Special Form of Generalization Capability
Generalization Result
Glimpse into Explainability
Artificial Intelligence for Mathematics
Anisotropic Structures as Model for Images
(Cone-adapted) Discrete Shearlet Systems
Optimally Sparse Approximation Theorem (K. Lin, 2011)
Solving Inverse Problems
(Limited Angle) Computed Tomography
Zooming in on the Limited-Angle CT Problem
Numerical Results
Deep Network Shearlet Edge Extractor (DeNSE)
Numerical Deep Learning Approaches to PDES
What can Deep Neural Networks do?
Theoretical Results
A Serious Problem Computability on Digital Machines (informal)
Some Thoughts on the Result
Conclusions
Taught by
International Mathematical Union