The book "The Elements of Differentiable Programming" by Mathieu Blondel and Vincent Roulet from Google DeepMind provides a comprehensive introduction to the field of differentiable programming, which is a programming paradigm that enables end-to-end differentiation of complex computer programs, including those with control flows and data structures. The book is divided into five parts: 1. **Fundamentals**: This part covers the basics of differentiation and probabilistic learning, including univariate and multivariate functions, directional derivatives, gradients, Jacobians, and higher-order derivatives. It also discusses differential geometry and generalized derivatives. 2. **Differentiable Programs**: This part reviews differentiable programs, such as neural networks, sequence networks, and control flows. It explains how to represent computer programs using computation chains, directed acyclic graphs (DAGs), and arithmetic circuits. The book also covers activation functions, residual neural networks, and recurrent neural networks. 3. **Differentiating through Programs**: This part focuses on how to differentiate through programs, including automatic differentiation, differentiating through optimization and integration. It covers finite differences, automatic differentiation methods like forward and reverse modes, and techniques for checkpointing and reversible layers. 4. **Smoothing Programs**: This part discusses techniques for smoothing programs, such as infimal convolution and convolution. It explores the connections between these techniques and their applications in optimization and integration. 5. **Optimizing Differentiable Programs**: This part covers optimization concepts, including basic optimization algorithms, first-order and second-order optimization methods, and duality. It provides an overview of the fundamental techniques useful for differentiable programming. The book aims to provide a solid foundation for graduate students and researchers in machine learning, with a focus on core mathematical tools and practical applications. It emphasizes the importance of designing principled differentiable operations and inducing probability distributions over program execution to quantify uncertainty.The book "The Elements of Differentiable Programming" by Mathieu Blondel and Vincent Roulet from Google DeepMind provides a comprehensive introduction to the field of differentiable programming, which is a programming paradigm that enables end-to-end differentiation of complex computer programs, including those with control flows and data structures. The book is divided into five parts: 1. **Fundamentals**: This part covers the basics of differentiation and probabilistic learning, including univariate and multivariate functions, directional derivatives, gradients, Jacobians, and higher-order derivatives. It also discusses differential geometry and generalized derivatives. 2. **Differentiable Programs**: This part reviews differentiable programs, such as neural networks, sequence networks, and control flows. It explains how to represent computer programs using computation chains, directed acyclic graphs (DAGs), and arithmetic circuits. The book also covers activation functions, residual neural networks, and recurrent neural networks. 3. **Differentiating through Programs**: This part focuses on how to differentiate through programs, including automatic differentiation, differentiating through optimization and integration. It covers finite differences, automatic differentiation methods like forward and reverse modes, and techniques for checkpointing and reversible layers. 4. **Smoothing Programs**: This part discusses techniques for smoothing programs, such as infimal convolution and convolution. It explores the connections between these techniques and their applications in optimization and integration. 5. **Optimizing Differentiable Programs**: This part covers optimization concepts, including basic optimization algorithms, first-order and second-order optimization methods, and duality. It provides an overview of the fundamental techniques useful for differentiable programming. The book aims to provide a solid foundation for graduate students and researchers in machine learning, with a focus on core mathematical tools and practical applications. It emphasizes the importance of designing principled differentiable operations and inducing probability distributions over program execution to quantify uncertainty.