Deep Learning and Physics

Preface
Acknowledgments
Contents
1 Forewords: Machine Learning and Physics
	1.1 Introduction to Information Theory
	1.2 Physics and Information Theory
	1.3 Machine Learning and Information Theory
	1.4 Machine Learning and Physics
Part I Physical View of Deep Learning
	2 Introduction to Machine Learning
		2.1 The Purpose of Machine Learning
			2.1.1 Mathematical Formulation of Data
		2.2 Machine Learning and Occam's Razor
			2.2.1 Generalization
		2.3 Stochastic Gradient Descent Method
		Column: Probability Theory and Information Theory
		Column: Probability Theory and Information Theory
		Joint and Conditional Probabilities
		Relative Entropy
	3 Basics of Neural Networks
		3.1 Error Function from Statistical Mechanics
			3.1.1 From Hamiltonian to Neural Network
			3.1.2 Deep Neural Network
		3.2 Derivation of Backpropagation Method Using Bracket Notation
		3.3 Universal Approximation Theorem of Neural Network
		Column: Statistical Mechanics and Quantum Mechanics
		Column: Statistical Mechanics and Quantum Mechanics
		Canonical Distribution in Statistical Mechanics
		Bracket Notation in Quantum Mechanics
	4 Advanced Neural Networks
		4.1 Convolutional Neural Network
			4.1.1 Convolution
			4.1.2 Transposed Convolution
		4.2 Recurrent Neural Network and Backpropagation
		4.3 LSTM
		Column: Edge of Chaos and Emergence of Computability
		Column: Edge of Chaos and Emergence of Computability
		Sorting Algorithm
		Implementation Using Recurrent Neural Network
		KdV Equation and Box-Ball System
		Critical State and Turing Completeness of One-Dimensional Cellular Automata
	5 Sampling
		5.1 Central Limit Theorem and Its Role in Machine Learning
		5.2 Various Sampling Methods
			5.2.1 Inverse Transform Sampling
			5.2.2 Rejection Sampling
			5.2.3 Markov Chain
			5.2.4 Master Equation and the Principle of Detailed Balance
			5.2.5 Expectation Value Calculation Using Markov chains, and Importance Sampling
		5.3 Sampling Method with the Detailed Balance
			5.3.1 Metropolis Method
			5.3.2 Heatbath Method
		Column: From Ising Model to Hopfield Model
		Column: From Ising Model to Hopfield Model
	6 Unsupervised Deep Learning
		6.1 Unsupervised Learning
		6.2 Boltzmann Machine
			6.2.1 Restricted Boltzmann Machine
		6.3 Generative Adversarial Network
			6.3.1 Energy-Based GAN
			6.3.2 Wasserstein GAN
		6.4 Generalization in Generative Models
		Column: Self-learning Monte Carlo method
		Column: Self-Learning Monte Carlo Method
Part II Applications to Physics
	7 Inverse Problems in Physics
		7.1 Inverse Problems and Learning
		7.2 Regularization in Inverse Problems
		7.3 Inverse Problems and Physical Machine Learning
		Column: Sparse Modeling
		Column: Sparse Modeling
	8 Detection of Phase Transition by Machines
		8.1 What is Phase Transition?
		8.2 Detecting Phase Transition by a Neural Network
		8.3 What the Neural Network Sees
	9 Dynamical Systems and Neural Networks
		9.1 Differential Equations and Neural Networks
		9.2 Representation of Hamiltonian Dynamical System
	10 Spinglass and Neural Networks
		10.1 Hopfield Model and Spinglass
		10.2 Memory and Attractor
		10.3 Synchronization and Layering
	11 Quantum Manybody Systems, Tensor Networks and Neural Networks
		11.1 Neural Network Wave Function
		11.2 Tensor Networks and Neural Networks
			11.2.1 Tensor Network
			11.2.2 Tensor Network Representation of Restricted Boltzmann Machines
	12 Application to Superstring Theory
		12.1 Inverse Problems in String Theory
			12.1.1 Compactification as an Inverse Problem
			12.1.2 The Holographic Principle as an Inverse Problem
		12.2 Curved Spacetime Is a Neural Network
			12.2.1 Neural Network Representation of Field Theory in Curved Spacetime
			12.2.2 How to Choose Input/Output Data
		12.3 Emergent Spacetime on Neural Networks
			12.3.1 Is AdS Black Hole Spacetime Learned?
			12.3.2 Emergent Spacetime from Material Data
		12.4 Spacetime Emerging from QCD
		Column: Black Holes and Information
		Column: Black Holes and Information
	13 Epilogue
		13.1 Neural Network, Physics and Technological Innovation (Akio Tomiya)
		13.2 Why Does Intelligence Exist? (Akinori Tanaka)
		13.3 Why do Physical Laws Exist? (Koji Hashimoto)
Bibliography
Index