Machine learning techniques have grown rapidly in recent years, and have become indispensable in many fields, including physics. For example, neural networks effectively represent wave functions in many-body quantum systems, where they have been applied to detect phase transitions. Moreover, Monte Carlo sampling and molecular dynamics simulations can be made significantly faster using machine learning.

Conversely, fundamental concepts in physics such as the Langevin equation and symmetries have significantly contributed to the growth of machine learning.

Now, a Special Topics edition of the Journal of the Physical Society of Japan presents 11 review articles exploring the interplay of physics and machine learning. The first part of the issue explores the applications of machine learning in physics.

Nomura and Imada demonstrate how artificial neural networks, such as restricted Boltzmann machines, represent wave functions in many-body quantum systems, shedding light on high-temperature superconductivity and quantum spin liquid.

Bayo, Çivitcioğlu, Webb, Honecker, and Römer review the recent advancements in the application of machine learning techniques like deep neural networks for detecting phase transitions—a fundamental challenge in condensed matter physics.

Mochizuki and Miyajima explore the application of machine learning image recognition techniques for detecting Berezinskii-Kosterlitz-Thouless transitions, which are notoriously difficult using traditional statistical methods.

Nakamura presents a comprehensive review of Gaussian process regression—a probabilistic machine learning technique that does not rely on neural networks, using magnetic properties as a case study.

Yamaji discusses how machine learning techniques can be used for analyzing experimental data, focusing on the application of neural networks in studying self-energy spectroscopy, which is critical for understanding concepts of superconductivity.

Tomiya highlights the potential of neural networks to accelerate quantum chromodynamic Monte Carlo simulations, demonstrating how machine learning can reduce computational costs while improving accuracy.

Transformer models are foundational to the recent advancements in large-language models. Hammad and Nojiri review the application of attention-based Transformer networks in the identification of heavy-boosted particles in high-energy colliders.

Furthermore, the second part of the issue focuses on how physics can advance machine learning.

Hirono presents a review of diffusion models, which are widely used in image, audio, and video generation, investigating their similarities to the diffusion process described by the Langevin equation.

Approximating a given probability distribution with another distribution is a standard technique in physics. Tanaka reviews generative diffusion models, which automate this procedure, from probabilistic and group theoretical perspectives.

Kamata and Fukushima expand on this review by examining the connection between stochastic quantization and diffusion models.

Takahashi demonstrates how the replica method from statistical mechanics can be used to analyze high-dimensional variable selection in machine learning.

This Special Edition thus offers a comprehensive overview of the vibrant intersections between physics and machine learning. As these domains continue to progress together, they hold great potential for addressing some of the most significant scientific challenges of the era.

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