Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 The Modern Mathematics of Deep Learning
- 2 Generalization in Deep Learning
- 3 Expressivity of Deep Neural Networks
- 4 Optimization Landscape of Neural Networks
- 5 Explaining the Decisions of Convolutional and Recurrent Neural Networks
- 6 Stochastic Feedforward Neural Networks: Universal Approximation
- 7 Deep Learning as Sparsity-Enforcing Algorithms
- 8 The Scattering Transform
- 9 Deep Generative Models and Inverse Problems
- 10 Dynamical Systems andOptimal Control Approach to Deep Learning
- 11 Bridging Many-Body Quantum Physics and Deep Learning via Tensor Networks
2 - Generalization in Deep Learning
Published online by Cambridge University Press: 29 November 2022
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 The Modern Mathematics of Deep Learning
- 2 Generalization in Deep Learning
- 3 Expressivity of Deep Neural Networks
- 4 Optimization Landscape of Neural Networks
- 5 Explaining the Decisions of Convolutional and Recurrent Neural Networks
- 6 Stochastic Feedforward Neural Networks: Universal Approximation
- 7 Deep Learning as Sparsity-Enforcing Algorithms
- 8 The Scattering Transform
- 9 Deep Generative Models and Inverse Problems
- 10 Dynamical Systems andOptimal Control Approach to Deep Learning
- 11 Bridging Many-Body Quantum Physics and Deep Learning via Tensor Networks
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Summary
This chapter provides theoreticalinsights into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, non-robustness, and sharp minima, responding to an open question in the literature. We also discuss approaches to provide non-vacuousgeneralization guarantees for deep learning. On the basis of the theoreticalobservations, wepropose new open problems.
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- Mathematical Aspects of Deep Learning , pp. 112 - 148Publisher: Cambridge University PressPrint publication year: 2022
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