Akinori Tanaka - Deep Learning and Physics

The series publishes original research monographs on contemporary mathematical physics. The focus is on important recent developments at the interface of Mathematics, and Mathematical and Theoretical Physics. These will include, but are not restricted to: application of algebraic geometry, D-modules and symplectic geometry, category theory, number theory, low-dimensional topology, mirror symmetry, string theory, quantum field theory, noncommutative geometry, operator algebras, functional analysis, spectral theory, and probability theory.

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What is deep learning for those who want to study physics? Is it completely different from physics? Or is it really similar?

In recent years, machine learning, including deep learning, has begun to be used in various physics studies. Why is that? Is knowing physics useful in machine learning? Conversely, is knowing machine learning useful in physics?

This book is devoted to answers of these questions. Starting with basic ideas of physics, neural networks are derived naturally. And you can learn the concepts of deep learning through the words of physics.

In fact, the foundation of machine learning can be attributed to physical concepts. Hamiltonians that determine physical systems characterize various machine learning structures. Statistical physics given by Hamiltonians defines machine learning by neural networks. Furthermore, solving inverse problems in physics through machine learning and generalization essentially provides progress and even revolutions in physics. For these reasons, in recent years, interdisciplinary research in machine learning and physics has been expanding dramatically.

This book is written for anyone who wants to know, learn, and apply the relationship between deep learning/machine learning and physics. The concepts of statistical mechanics and the bracket notation of quantum mechanics, which are introduced in columns, are used to explain deep learning frameworks.

This book is divided into two parts. The first part concerns understanding the machine learning method from the perspective of physics, and the second part explores the relationship between various problems in physics and the method of machine learning. That is, the first part is written as a textbook, but the second part is not a text book, it is a collection of recent advanced topics (and so, the chapters in the second part can be read almost independently). Please refer to the readers guide at the beginning of each section.

A renowned physicist, Ryoyu Uchiyama, said in the preface to his book, Theory of Relativity [1], If you read this book and do not understand it, you should give up learning the theory of relativity. On the other hand, the field of machine learning physics, which is the subject of this book, is not a discipline established over a long history like the theory of relativity, but a field of research that is still undergoing great progress. So, rather, our message is this: If you read this book and do not understand it, it will be a seed for development in the future.

One of our favorites is the words by S. Weinberg, a particle physicist [2]:

My advice is to go for the messes thats where the action is.

It is up to the readers to make their own way. We hope this book helps the readers learn and study.

The authors