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Training of Deep Neural Networks
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Classroom Contents
The Mathematics of Artificial Intelligence
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- 1 Intro
- 2 The Dawn of Artificial Intelligence in Public Life
- 3 Spectacular Success in Science
- 4 Impact on Mathematical Problem Settings
- 5 Artificial Intelligence = Alchemy?
- 6 Problem with Reliability
- 7 Role of Mathematics Two Key Challenges for Mathematics
- 8 First Appearance of Neural Networks
- 9 Artificial Neurons
- 10 Affine Linear Maps and Weights
- 11 Definition of a Deep Neural Network
- 12 Training of Deep Neural Networks
- 13 Mathematics for Artificial Intelligence
- 14 Glimpse into Generalization
- 15 Graph Neural Networks
- 16 A Special Form of Generalization Capability
- 17 Generalization Result
- 18 Glimpse into Explainability
- 19 Artificial Intelligence for Mathematics
- 20 Anisotropic Structures as Model for Images
- 21 (Cone-adapted) Discrete Shearlet Systems
- 22 Optimally Sparse Approximation Theorem (K. Lin, 2011)
- 23 Solving Inverse Problems
- 24 (Limited Angle) Computed Tomography
- 25 Zooming in on the Limited-Angle CT Problem
- 26 Numerical Results
- 27 Deep Network Shearlet Edge Extractor (DeNSE)
- 28 Numerical Deep Learning Approaches to PDES
- 29 What can Deep Neural Networks do?
- 30 Theoretical Results
- 31 A Serious Problem Computability on Digital Machines (informal)
- 32 Some Thoughts on the Result
- 33 Conclusions
