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
10 - Dynamical Systems andOptimal Control Approach to 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
Summary
We give a short and concise review about the dynamical system and the control theory approach to deep learning. From the viewpoint of the dynamical systems, the back-propagation algorithm in deep learning becomes a simple consequence of the variational equations in ODEs. From the viewpoint of control theory, deep learning is a case of mean-field control in that all the agents share the same control. As an application, we discuss a new class of algorithms for deep learning based on Pontryagin’s maximum principle in control theory.
- Type
- Chapter
- Information
- Mathematical Aspects of Deep Learning , pp. 422 - 438Publisher: Cambridge University PressPrint publication year: 2022
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