Unlocking Automatic Differentiation

Explore the World of Automatic Differentiation

Automatic differentiation is revolutionizing the way derivatives are computed in applied mathematics and machine learning. This book serves as a comprehensive guide to understanding and mastering this crucial sub-field. By unraveling the complexities of forward and reverse modes, this book promises to transform your understanding of how AD works, ensuring you stay at the cutting edge of mathematical computation.

Custom Derivatives for Higher-Order Functions

Dive into the core of automatic differentiation by composing custom derivatives for higher-order functions. Learn to navigate libraries like ForwardDiff.jl and Enzyme.jl, and see how TaylorSeries.jl can elevate your understanding of higher-order derivatives. Whether you choose to implement AD from scratch or leverage existing libraries, this book will guide you in achieving efficiency and accuracy, crucial for handling complex functions.

Balancing Efficiency with Theoretical Accuracy

The book provides a nuanced exploration of efficiency considerations, particularly for GPU-based applications. Discover emerging tools like Diffractor.jl that promise enhanced efficiency, even as you tackle the intricacies of theoretical accuracy in complex computations. The blend of theory and practice is key to mastering this domain.

Integrate Automatic Differentiation into Machine Learning

Real-world applications are at the heart of this book. Understand how frameworks like JAX, TensorFlow, and PyTorch integrate AD for efficient gradient computation in machine learning tasks. With practical examples and detailed exploration of forward-on-reverse differentiation, this book equips you with strategies to optimize performance and accuracy.

The Latest Developments in AD

Stay updated with the latest advancements in automatic differentiation through research papers, tutorials, and emerging libraries. The book not only provides comprehensive coverage of theoretical advancements but also dives into practical implementations and discussions, utilizing resources from Julia Discourse and GitHub repositories, ensuring your knowledge remains current and applicable.

AI Book Review

"⭐⭐⭐⭐⭐ A profound exploration into the world of automatic differentiation, this book expertly bridges the gap between theoretical foundations and practical applications. The author's deep understanding of composing custom derivatives for higher-order functions shines through, making intricate concepts accessible. With a focus on both forward and reverse modes, the book provides invaluable insights for machine learning and computational mathematics enthusiasts. It stands out for its thorough research, clarity, and relevance in today's rapidly evolving tech landscape, making it an essential read for anyone in the field."

Target Audience

This book is ideal for machine learning practitioners, computational mathematicians, and students seeking a deep understanding of automatic differentiation with custom derivatives.

Key Takeaways

• Comprehensive understanding of automatic differentiation and its significance.
• Insights into both forward and reverse modes, tailored for machine learning applications.
• Step-by-step guidance on composing custom derivatives for higher-order functions.
• Exploration of AD libraries like ForwardDiff.jl and emerging tools like Diffractor.jl.
• Integration techniques for AD in modern machine learning frameworks such as JAX, TensorFlow, and PyTorch.
• Theoretical advancements and practical implementations in AD.
• Efficiency considerations for GPU-based applications, merging theory with practice.
• Case studies and strategies for optimizing AD performance.
• Future trends in automatic differentiation research and technology.