AI has undergone remarkable development in recent years. We focuses on two complementary research directions: analyzing AI systems through physics-based approaches and leveraging AI to uncover new scientific insights from experimental data.
Diffusion models for image generation have shown remarkable effectiveness and have become widely adopted. In the work presented in ICML, we proposed a new approach to understanding diffusion models through Feynman's path integral developed in quantum physics. This approach allows us to describe various aspects of score-based diffusion models, facilitating the derivation of backward stochastic differential equations and loss functions. One can introduce a parameter that interpolates stochastic and deterministic sampling, and this parameter plays an analogous role to Planck's constant in quantum mechanics. Leveraging this analogy, we employ the Wentzel-Kramers-Brillouin (WKB) method from quantum physics to analyze the negative log-likelihood, shedding light on the performance disparity between stochastic and deterministic sampling strategies.
Understanding the behavior of complex physical systems is a major challenge in physics. Many physical systems exhibit self-similarity and scale transformation symmetry, and identifying these properties helps in understanding system behavior. Traditionally, detecting self-similarity required assuming a model beforehand, which could introduce bias. In the paper [Phys. Rev. E 111, 024301 (2025)], we developed a new method using neural networks to discover self-similarity in physical systems based on experimental data. This paper was selected as a Physical Review E Editors' Suggestion.
In [arXiv:2403.11420], we provide a novel map with which a wide class of quantum mechanical systems can be cast into the form of a neural network with a statistical summation over network parameters. The basic idea is to approximate the paths of a particle in Feynman's path integral via a neural network. The map can be applied to interacting quantum systems / field theories, even away from the Gaussian limit. Our findings bring machine learning closer to the quantum world.
Biological systems implement various regulatory mechanisms to maintain homeostasis. However, due to the complex interplay of numerous degrees of freedom within these systems, discovering these regulatory mechanisms presents significant challenges. We analyze robust control mechanisms implemented in biological systems using methods of algebraic topology.
Maintaining stability in an uncertain environment is essential for proper functioning of living systems. Robust perfect adaptation (RPA) is a property of a system that generates an output at a fixed level even after fluctuations in input stimulus without fine-tuning parameters. Although there have been a number of biological implementation of RPA in living systems, identifying RPA and its associated control actions in generic high-dimensional biochemical networks has been considered a formidable task due to the complexity of the system.
In [PRX Life 3, 013017], we developed a method to characterize and enumerate all the RPA properties in general chemical reaction networks. We also provide an open-source code RPAFinder that performs the enumeration of RPA for a given reaction network. We also gave a recipe of constructing the corresponding controller for each RPA property. The method would be useful for uncovering control mechanisms operating within biochemical networks for maintaining homeostasis.
In biological systems, chemical reactions form complex networks. Even if ample computational resources were available, faithful modeling of such a system is challenging, because our knowledge about the reaction kinetics and parameters is limited. It is thus desirable to obtain a network that is simpler, has fewer parameters, and yet captures the essential feature of the original network.
We examine this problem through the lens of topology [Phys. Rev. Research 3, 043123 (2021)]. In a collaboration among physicists, a mathematician and a biologist, we developed a topological method of simplifying a complex chemical reaction network. In particular, we proved that, if a subnetwork satisfies certain topological conditions, it can be eliminated while preserving the original steady state exactly. Therefore, the details of such a subnetwork are irrelevant, as far as the remaining part of the network is concerned, and the system can be studied efficiently with a simpler network. In deriving the results, the methods of algebraic topology play an essential role.
The method sheds new light on the analysis of biochemical systems from an algebraic-topological perspective. The tools developed here will be useful for studying complex network systems efficiently and identifying relevant network components for biological functionalities.
Symmetries play a crucial role in understanding the nature of physical systems. Recently, the concept of symmetry has been generalized, allowing us to capture the characteristics of more diverse quantum phases. We utilizes the generalized symmetries to explore universal laws underlying various physical systems.
In recent years, the notion of symmetry has been generalized in several direction. One such generalization is the so-called higher-form symmetries. The defining feature of higher-form symmetries is that the corresponding charged objects are extended: for a p-form symmetry, charged objects are p-dimensional. From this point of view, an ordinary symmetry can be regarded as a 0-form symmetry, whose charged objects are point-like. Many concepts discussed for ordinary symmetries are also generalized to higher-form symmetries. For example, higher-form symmetries can be spontaneously broken: Indeed, photons can be regarded as Nambu-Goldstone modes associated with the breaking of a U(1) 1-form symmetry.
In [Phys. Rev. Lett. 126, 071601 (2021)], we derived effective field theories for broken higher-form symmetries by extending the coset construction. Based on the effective theories, we derived a formula for counting the number of physical gapless Nambu-Goldstone modes for spontaneously broken higher-form symmetries in systems without Lorentz invariance. This is a universal result determined solely by symmetry breaking patterns. In the special case when the system has only 0-form symmetries, it reduces to the counting formula for ordinary symmetries in non-relativistic systems. The number of physical gapless modes is a model-independent result based only on the symmetry breaking patterns.
Fracton phases are new quantum phases of matter that host excitations with restricted mobility. We showed that gapless fracton phases are realized as a result of spontaneously broken higher-form symmetries, whose charges do not commute with spatial translations [SciPost Phys. 16, 050 (2024)]. Based on this understanding, we developed a method to engineer gapless fracton phases with desired mobility restrictions.
Phases of matter has been conventionally classified by Ginzburg-Landau (GL) theory based on the symmetry breaking patterns, which are diagnosed by local order parameters. It is known by now that the GL description is not sufficient to classify quantum phases; there are orders that can only be detected using non-local order parameters, and they are called topological orders. Some of topologically ordered phases appear as a result of spontaneously broken higher-form symmetries, which are a generalization of the conventional symmetries. Indeed, the topological order of the toric code can be understood as a consequence of a spontaneously broken Z2 1-form symmetry.
We gave a constraint on the phase structure of dense QCD using higher-form symmetries（Phys. Rev. Lett. 122, 212001(2019); JHEP 2019, 62). There is a proposal on the phase diagram of dense QCD called quark-hadron continuity scenario, which states that the color superconducting phase can be continuously connected with the superfluid phase of nucleons without phase transitions. Recently, there appeared a proposal that those two states are different, based on the fractional statistics of vortices and colored particles in a color superconductor. We examined this proposal from the view point of generalized symmetries. We found that those two phases have the same symmetries including higher-form ones, and consequently, we showed that the continuity scenario extends as a continuity of quantum phases.