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
8 - The Scattering Transform
Published online by Cambridge University Press: 29 November 2022
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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
In this chapter we describe scattering representations, a signal representation built using wavelet multiscale decompositions with a deep convolutional architecture. Its construction highlights the fundamental role of geometric stability in deep learning representations, and provides a mathematical basis to study CNNs. We describe its main mathematical properties, its applications to computer vision, speech recognition and physical sciences, as well as its extensions to Lie Groups and non-Euclidean domains. Finally, we discuss recent applications to modeling high-dimensional probability densities.
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- Mathematical Aspects of Deep Learning , pp. 338 - 399Publisher: Cambridge University PressPrint publication year: 2022
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