Coulomb branches in supersymmetric gauge theories

2026年8月28日(金) 15:30 - 17:00

中島 啓 (東京大学 カブリ数物連携宇宙研究機構 (Kavli IPMU) 教授)

Supersymmetric gauge theories in 3 and 4 dimensions have no mathematically rigorous foundation. Coulomb branches of gauge theories originally defined via low energy effective theories by non-rigorous physical argument in 90s. I will explain how I interpret this original argument and make a mathematically rigorous definition of Coulomb branches in my joint work with Braverman and Finkelberg.

会場: 大河内記念ホール (メイン会場) / via Zoom

イベント公式言語: 英語

Mathematical Application Research Team Meeting #18

2026年8月28日(金) 14:00 - 15:15

松尾 信一郎 (名古屋大学 大学院多元数理科学研究科 准教授)

Mathematical Application Research Team is delighted to welcome Prof. Shinichiroh Matsuo from Nagoya University for an upcoming team meeting. We warmly invite everyone to join us to hear his talk. Please note that, exceptionally, this meeting will be held at Okochi Hall. Immediately following Prof. Matsuo’s talk, Prof. Hiraku Nakajima will give a seminar entitled “Coulomb branches in supersymmetric gauge theories.” We encourage participants to join us for both talks. Title: The Index of Wilson--Dirac Operators Revisited: Beyond Regular Lattices on Flat Tori Abstract: This is joint work with Mikio Furuta. Our ultimate goal is to discretise Seiberg--Witten theory. In view of PL = DIFF in dimension four, we would like to construct something like a PL Seiberg--Witten theory. As a first step towards this goal, we have studied the discretisation of the analytic index of Dirac operators. In earlier work, using K-theoretic methods, we showed that the index of the Wilson--Dirac operator associated with a sufficiently fine regular lattice on a flat torus agrees with that of the corresponding continuum Dirac operator. However, this lattice-index construction was confined to regular lattices on flat tori. In this talk, I will introduce “mesoscopic” Wilson--Dirac operators on arbitrary closed Riemannian manifolds. They form a family of bounded integral-difference operators on \(L^2\), parametrised by a mesoscopic length \(a>0\), and they converge, in a suitable sense, to the continuum Dirac operator as \(a \to 0\). The mesoscopic operators are self-adjoint and Fredholm, but not odd, so the usual graded Fredholm index is unavailable. We prove that the “index” of a mesoscopic Wilson--Dirac operator agrees with the index of the corresponding continuum Dirac operator when \(a\) is sufficiently small. Replacing the integrals in our mesoscopic operators by Riemann sums produces finite-dimensional lattice approximations on general closed Riemannian manifolds. The mesoscopic Wilson--Dirac operators thus provide a bridge between the microscopic continuum Dirac operator and the macroscopic lattice Dirac operators.

会場: via Zoom / 大河内記念ホール

イベント公式言語: 英語

Multistability in Biochemical Reaction Systems: Structural Approach

2026年8月27日(木) 16:00 - 17:00

岡田 崇 (広島大学 大学院統合生命科学研究科 数理生命科学プログラム 准教授)

In living cells, biochemical reactions form intricate networks that can exhibit multistability, allowing a single system to maintain multiple stable states under identical conditions. However, determining theoretically whether a given reaction system can exhibit multistability is challenging because detailed kinetic parameters are often unknown. In this presentation, we introduce a structural framework that decomposes biochemical networks into subnetworks based solely on network topology. For each subnetwork, we define a scalar quantity, and an index-theoretic argument shows that the sign of this quantity determines whether the subnetwork can contribute to multistability. Our method identifies indicator species whose concentrations distinguish all steady states without detailed kinetic information, thereby enabling efficient measurement design in large networks.

会場: via Zoom

イベント公式言語: 英語

Scattering amplitude from quantum computing with reduction formula

2026年8月27日(木) 15:00 - 16:00

Wai Kin Lai (Lecturer, The University of Hong Kong, China)

In this talk, I will present a new general framework for computing scattering amplitudes in quantum field theory with quantum computers in a fully nonperturbative way. After giving a motivation for the application of quantum computing to particle physics, I will briefly introduce the basics of quantum computing. After that, I will give the details of the proposed quantum algorithm for calculating scattering amplitudes, which utilizes the Lehmann-Symanzik-Zimmermann (LSZ) reduction formula. In this framework, one only has to construct one-particle states of zero momentum, and no wave packets of incoming particles are needed. The framework is able to incorporate scatterings of bound states, and is ideal for scatterings involving a small number of particles. This framework is expected to have particular advantages when applied to exclusive hadron scatterings. As a proof of concept, by simulations on classical hardware, I demonstrate that in the one-flavor Gross-Neveu model, the fermion propagator, the connected fermion four-point function, and the propagator of a fermion-antifermion bound state obtained from our proposed quantum algorithm have the desired pole structure crucial to the implementation of the LSZ reduction formula. Brief CV: Wai Kin Lai received PhD in physics at the University of Pittsburgh in 2016. He was a postdoctoral reseacher at the Technical University of Munich from 2016 to 2020. From 2020 to 2023, he was a postdoctoral researcher at South China Normal University, and was a visiting assistant researcher at the University of California, Los Angeles from 2022 to 2023. Wai Kin Lai is currently a lecturer at HKU SPACE in Hong Kong. Wai Kin Lai's research interests are applications of effective field theories of QCD to particle phenomenology and studies of nonperturbative physics with quantum computation.

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語

AI for Science Summer School

2026年8月25日(火) - 27日(木)

瀧 雅人 (立教大学 大学院人工知能科学研究科 准教授)
王 凌霄 (理化学研究所 数理創造研究センター (iTHEMS) 数理展開部門 AI展開チーム 副チームディレクター)
Vinicius Massami Mikuni (名古屋大学 素粒子宇宙起源研究所 (KMI) 准教授)
武石 直也 (東京大学 先端科学技術研究センター 講師)
李 葱茏 (Senior Research Scientist, Google DeepMind, UK)
田中 章詞 (理化学研究所 革新知能統合研究センター (AIP) 上級研究員)

Summer school for modern AI methods and their applications in scientific discovery. We want to answer the questions in AI for Science, Why do you need AI for your research? Which AI is most suitable for your needs? How can you use AI properly for your task? The school will cover both lectures and hands-on coding sessions, with topics including machine learning basics, generative models, Bayesian and simulation-based inference, foundation models and LLM agents. The problems include, experiment-to-phenomenology (inference and prediction), computation (generation), theory (auto-workflow and Co-Scientist), etc.

会場: 研究本館 4階 435-437号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Hidden Networks: From Phase Reductions to Effective Network Interactions

2026年8月24日(月) 15:30 - 17:00

Christian Bick (Associate Professor, Department of Mathematics, Vrije Universiteit Amsterdam, Netherlands)

From networks of interconnected neurons in the brain to coupled electrochemical reactions: The collective dynamics of interacting dynamical systems shape the function (or dysfunction) of many systems that are critical for our everyday lives. For coupled oscillatory processes, synchronization is a prime example of emergent collective dynamics. But how oscillators interact is not necessarily obvious from (physical) connections between the oscillators. Here we look at phase reductions as a way to uncover the hidden 'effective' network interactions for coupled oscillators dynamics. On the one hand, these give insight into when oscillators do and do not interact (despite a link). On the other hand, they elucidate when and how nonpairwise higher-order interactions shape synchronization phenomena in coupled oscillator networks.

会場: 大河内記念ホール (メイン会場) / via Zoom

イベント公式言語: 英語

UK-Japan Workshop on Quantum Gravity 2026

2026年8月24日(月) - 28日(金)

The universe at extremely early times is expected to be described by some theory of quantum gravity, although we still do not know precisely what quantum gravity actually is. In modern approaches to quantum gravity, the path integral point of view provides a fundamental framework towards answering this pressing question. However, an evaluation or even just a precise definition of the path-integral for a full-fledged quantum gravity is one of the most important open problems in modern theoretical physics. With the "UK-Japan Workshop on Quantum Gravity 2026" we want to bring together experts working on different aspects of the gravitational path-integral, such as Gravitational Scattering Amplitudes; Complex Geometries and Exact WKB; Quantum Cosmology; Exact Methods and Resurgence Analysis; with the long-term goal of providing innovative ways of tackling modern problems in quantum gravity. This workshop is the second event sponsored by the Royal Society International Collaboration Award Grant "Re-PaInt: A Resurgence Path-Integral approach to quantum gravity" shared between Masazumi Honda at Riken iTHEMS and Daniele Dorigoni at Durham University, and aimed at fostering and developing an international partnership between the two institutes, as well as the greater Japan and UK theoretical physics communities working on quantum gravity, broadly intended. The page for the 2025 meeting held at the RIKEN campus in Kobe can be found in the Related Links section below.

会場: Durham University

イベント公式言語: 英語

RIKEN–IPMU mini-workshop on QCA and K-theory

2026年8月24日(月) - 26日(水)

Three-day lecture series by Bowen Yang, based on joint work with Mattie Ji (arXiv:2602.16572 and arXiv:2606.19657), in which quantum cellular automata are classified by an algebraic K-theory spectrum.

会場: via Zoom / レクチャーホール、Kavli IPMU, 東京大学

イベント公式言語: 英語

The 3rd NCTS-iTHEMS Joint Workshop on Theoretical, Mathematical, and Computational Sciences

2026年8月18日(火) - 21日(金)

The 3rd NCTS-iTHEMS Joint Workshop will be held from August 18 to 21, 2026, at National Taiwan University. Following the previous two editions, which focused mainly on theoretical physics, this year’s workshop marks a new stage in the partnership between RIKEN iTHEMS and NCTS. In particular, the workshop follows the signing of the iTHEMS-NCTS Collaboration Research Agreement in April 2026, which aims to further strengthen researcher exchange, international workshops, and joint research activities. With the participation of both the NCTS Physics and Mathematics Divisions, this year’s workshop broadens its scope from theoretical physics to the wider interface among theoretical, mathematical, and computational sciences. Key topics include high-energy physics and gravity, condensed matter physics, quantum computing and information, geometry and topology, applied mathematics, machine learning, and scientific AI. The program will feature plenary lectures, research talks, and a poster session, providing a platform for interdisciplinary exchange and future collaborations between iTHEMS and NCTS. Registration is open to the public. Feel free to sign up if you're interested! Venue NCTS Physics Lecture Hall, 4th Floor, Cosmology Hall, NTU Speakers Plenary Speakers Tan Bui-Thanh (UT Austin) Etera Livine (ENS Lyon) Tzu-Chieh Wei (SUNY Stony Brook) Invited Speakers Chi-Kang Chang (RIKEN iTHEMS) Chien-Yu Chou (RIKEN iTHEMS) Antoine Diez (RIKEN iTHEMS) Keita Goto (RIKEN iTHEMS) Ryusuke Hamazaki (RIKEN iTHEMS) Masazumi Honda (RIKEN iTHEMS / Saitama U) Muzi Hong (RIKEN iTHEMS) Masaaki Imaizumi (RIKEN AIP / U of Tokyo) Derek Inman (RIKEN iTHEMS) Isao Ishikawa (Kyoto U) Riccardo Muolo (RIKEN iTHEMS) Álvaro Pastor-Gutiérrez (RIKEN iTHEMS) Wei-Hsiang Shao (RIKEN iTHEMS) Chuan-Tsung Chan (Tunghai University) Po-Yao Chang (NTHU) Heng-Yu Chen (NTU) Hao-Chung Cheng (NTU) Hao-Wei Huang (NTHU) Yi-Ping Huang (NTHU) Jer-Lai Kuo (AS) Chia-Hsiang Lin (NCKU) Chin-Hung Lin (NYCU) Yu-Chen Shu (NCKU) Cheng-Fang Su (NYCU) Chiao-Hsuan Wang (NTU) (In alphabetical order of surnames) Organizing Committee Chi-Kang Chang (RIKEN iTHEMS) Che-Yu Chen (RIKEN iTHEMS) Ching-Kai Chiu (RIKEN iTHEMS) (co-chair) Pei-Ming Ho (NTU/NCTS) Masazumi Honda (RIKEN iTHEMS) Chang-Tse Hsieh (NTU/NCTS) (co-chair) Ming-Lun Hsieh (NTU/NCTS) Isao Ishikawa (Kyoto U) Satoshi Iso (RIKEN iTHEMS) Min-Hsiung Lin (NCKU/NCTS) Yuki Yokokura (RIKEN iTHEMS) (In alphabetical order of surnames)

会場: NCTS Physics Lecture Hall, 4th Floor, Cosmology Hall, NTU

イベント公式言語: 英語

Genome Language Models: From DNA Sequences to Biological Foundation Models

2026年8月13日(木) 15:00 - 16:00

Minrui Chen (九州大学 博士課程)

Recent advances in protein language models have greatly transformed protein structure prediction, functional annotation, and biomolecular design. In contrast, genome language models aim to learn directly from DNA sequences, which represent a more upstream layer of biological information encoding genes, regulatory logic, variant effects, and evolutionary signals. In this talk, I will introduce the basic motivation and recent progress of DNA and genome language models, including DNABERT, DNABERT-2, HyenaDNA, Evo, Evo 2, and AlphaGenome. I will discuss how different model architectures and tokenization strategies address the challenges of genomic sequence modeling, such as long-range dependencies, multi-scale biological structure, and genome-scale context.

会場: 研究本館 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語

In Search of The Building Blocks of the Universe

2026年8月7日(金) 15:00 - 16:30

Anamaria Hell (カブリ数物連携宇宙研究機構 (Kavli IPMU) 特任研究員)

We live in an exceptional era of precision cosmology, marked by rapidly advancing observational probes that explore the Universe across many length scales. While these experiments offer clues about the geometry, dynamics, and large-scale structure of the cosmos, they still leave the origin and much of the evolution and structure of the Universe unknown. One of the key steps to answer these questions is to uncover the building blocks of theoretical models in both linear and non-linear regimes. In this talk, I will present methods for uncovering physical degrees of freedom, outlining the standard approaches and presenting an alternative, simple and straightforward way. I will then show how one can naturally connect this approach to machine learning. Finally, I will introduce the framework of constrained gravity, and discuss how such approaches can help address long-standing challenges in fundamental physics and open new directions across disciplines.

会場: セミナー室 (359号室) 3階 359号室とZoomのハイブリッド開催

イベント公式言語: 英語

How Reputation Sustains Cooperation: Mathematical Theories of Indirect Reciprocity

2026年8月6日(木) 15:00 - 16:00

村瀬 洋介 (理化学研究所 数理創造研究センター (iTHEMS) 数理展開部門 数理社会科学チーム チームディレクター)

Cooperation among unrelated individuals is a central puzzle in the evolution of social behavior. Indirect reciprocity offers one influential explanation: people help others not only because they expect direct returns, but also because their actions affect their reputation. In this seminar, I will review mathematical theories of indirect reciprocity, focusing on how reputation and social norms can sustain cooperation. I will begin with the classical framework of public assessment, where everyone shares the same view of each individual’s reputation, including the seminal work of Ohtsuki and Iwasa on the “leading eight” social norms. I will then turn to private assessment, where individuals may disagree about others’ reputations, and discuss why synchronization of opinions becomes essential for cooperation. Overall, the seminar aims to provide an accessible overview of how mathematical models allow us to formalize moral judgments—what counts as good or bad behavior—and to understand the evolution of cooperation through reputation.

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語

Theoretical Approaches for Cell Deaths

2026年8月6日(木) 13:00 - 14:00

姫岡 優介 (東京大学 生物普遍性研究機構 助教)

Understanding the boundary between cell life and death is a fundamental challenge and a highly important theme in biology. In this talk, focusing on microbial cell death, I would like to discuss how "cell death" can be understood from the perspective of mathematical sciences. Research on microbial cell death has progressed by identifying the molecular mechanisms that drive relevant biochemical processes, which are identified based on empirically known cell death markers. However, there has been little discussion on what death actually is in the first place, or how it can be "defined." Furthermore, recent reports have shown that commonly used live/dead assays—such as dead-cell staining and metabolic activity measurements—can yield conflicting results regarding cell viability, highlighting the growing need to discuss what criteria we should use to define "death." In this study, we propose a definition: a cell is "dead" if it cannot return to a predetermined "representative point of the living state," no matter how gene expression levels or external nutrient concentrations are controlled. Plant seeds may appear "dead" at first glance due to their lack of apparent biochemical activity, yet they germinate when watered. Our proposal in this study is to determine the life or death of a cell based on whether an operation equivalent to "watering" exists [1]. Of course, it is experimentally impossible to prove that a cell cannot regain activity under any operation; however, it is theoretically possible using mathematical models. We developed a method called "Stoichiometric Rays" to calculate the controllability of metabolic reaction systems. Using this, we calculated states that cannot be controlled back to the "representative point of the living state" regardless of how enzyme levels and external nutrient concentrations are manipulated. Consequently, we succeeded in quantifying the separating hyperplane between the "living state" and the "dead state" in a mathematical model of metabolism [2], which we call the Separating Alive and Non-life Zone (SANZ) Hypersurface. In this talk, I will outline the theory, the quantification of the SANZ hypersurface, and its biological interpretation. In addition, through our research [3], we have partially identified a class of models that do not exhibit "death" in the sense described above. I would also like to discuss the relationship between the absence of "death" in these models and the autonomy of life.

会場: セミナー室 (359号室) 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Four Fermi Theory in Four Dimensions is Renormalisable

2026年8月3日(月) 15:00 - 16:30

Charlie Cresswell-Hogg (Post-Doctoral fellow, Department of Physics, Sussex University, UK / Post-Doctoral fellow, Dortmund University, Germany)

We demonstrate the renormalisability of quantum field theories in four dimensions with elementary self-interacting Dirac fermions and to leading order in the limit of many fermion flavours Nf. Starting from the underlying divergence structure and using Gross-Neveu-type interactions as a template, we explain why extended four-fermion theories including higher-derivative interactions are well-defined, renormalisable, and predictive with only a few free parameters. We also provide the exact large-Nf leading beta functions of couplings and discuss quantum scaling dimensions, universality, 1/Nf corrections, and extensions to other types of four fermion interactions. Implications for effective theory and model building are indicated.

会場: via Zoom

イベント公式言語: 英語

Quantum Gravity and Emergent Cosmology: A Group Field Theory Perspective

2026年7月31日(金) 14:00 - 16:00

Luca Marchetti (カブリ数物連携宇宙研究機構 (Kavli IPMU) 特任研究員)

This seminar is the second part of a two-part mini-seminar series organized by the Quantum Gravity Gatherings study group. It is intended to have a more lecture-style format, with an extended duration of up to two hours. This will allow the speaker sufficient time to introduce the framework in a clear and pedagogical manner, while also leaving ample room for questions and discussion with the audience. Title: Quantum Gravity and Emergent Cosmology: A Group Field Theory Perspective Abstract: I will introduce the Group Field Theory (GFT) approach to quantum gravity, emphasizing its connections with matrix and tensor models, discrete gravity path integrals, and loop quantum gravity. Through these connections, GFTs emerge naturally as quantum field theories of "spacetime atoms". I will then discuss how semiclassical, macroscopic physics can emerge from GFT, touching upon the challenges of defining locality and coarse-graining in quantum gravity, and on how these can be naturally addressed within relational frameworks. I will present a concrete implementation of this relational strategy in GFT and show how a simple relational coarse-graining scheme can be used to extract cosmological physics. Within the resulting cosmological models, the initial singularity is resolved into a quantum bounce, while cosmological perturbations emerge from the quantum entanglement of the underlying quantum-gravity degrees of freedom, with effective dynamics modified on trans-Planckian scales. Finally, I will show that quantum-gravitational interactions alone can generate cosmic acceleration, leading both to dynamical dark energy and to a slow-roll inflationary phase. I will conclude by showing recent observational constraints on such emergent dynamical dark energy models, and by providing an outlook on future research directions.

会場: 研究本館 3階 359号室とZoomのハイブリッド開催

イベント公式言語: 英語

Loop expansion in polymer field theory: application to phase separation

2026年7月30日(木) 16:00 - 17:00

川名 清晴 (Research Fellow, Korea Institute for Advanced Study (KIAS), Republic of Korea)

Liquid-liquid phase separation underlies phenomena ranging from protein condensate formation to the phase coexistence of synthetic polymers. In this talk, we develop a field theoretic loop expansion in homopolymer systems by identifying the inverse polymer density ρ^{-1} as the Planck constant ℏ in quantum field theory. The 1-loop approximation is known as the random phase approximation (RPA) and has been extensively applied to many (hetero)polymer systems. We calculate the leading-order (2-loop) and next-to-leading-order (3-loop) corrections to the RPA free energy, denoted as RPA+ and RPA++, respectively. Testing the binodal predicted by the RPA+ against molecular dynamics simulations of bead-spring chains with Gaussian pair interactions, we find that the RPA+ qualitatively improves the dilute-phase coexistence density over the RPA, while the critical point error remains comparable to that of the RPA. Our results establish the loop expansion as a systematic route for refining the RPA-based binodal predictions for polymer phase separation. This talk is based on arXiv: 2605.01261.

会場: via Zoom

イベント公式言語: 英語

Quantum Reference Frames for Quantum Gravity

2026年7月30日(木) 14:00 - 16:00

Luca Marchetti (カブリ数物連携宇宙研究機構 (Kavli IPMU) 特任研究員)

This seminar is the first part of a two-part mini-seminar series organized by the Quantum Gravity Gatherings study group. It is intended to have a more lecture-style format, with an extended duration of up to two hours. This will allow the speaker sufficient time to introduce the framework in a clear and pedagogical manner, while also leaving ample room for questions and discussion with the audience. Title: Quantum Reference Frames for Quantum Gravity Abstract: Internal quantum reference frames provide a general framework for handling symmetries in quantum theory, with applications ranging from quantum gravity and gauge theories to quantum information and foundational physics. I will first introduce the formalism in simple mechanical systems, before turning to classical gravity. There, I will motivate the need for internal, dynamical frames in background-independent theories to define relationally local gauge-invariant observables, and show how this framework leads to a relational update of general covariance: frame covariance. I will then move to non-perturbative quantum gravity, showing how quantum reference frames can be used to define a manifestly gauge-invariant relational path integral, which is also invariant under transformations between quantum reference frames. It therefore provides a perspective-neutral description of quantum gravitational physics. I will also discuss the associated relational effective actions. Although effective actions are, in general, not frame-covariant off shell, the on-shell physics they encode is. Finally, I will present several physical consequences of this framework, including the fuzziness of frame-changed local correlators, the non-trivial interplay between quantum-reference-frame transformations and time evolution, and the frame-dependence properties of ground sectors and Hartle-Hawking prescriptions. I will conclude by outlining future directions, with particular emphasis on a relational notion of the renormalization group flow.

会場: 研究本館 3階 359号室とZoomのハイブリッド開催

イベント公式言語: 英語

Current challenges teaching undergraduate first year physics in Canada

2026年7月30日(木) 13:00 - 14:00

カトゥリン・ボシゥメン (理化学研究所 数理創造研究センター (iTHEMS) 副センター長)

I will talk about the challenges of teaching first year physics in 2026 to undergraduate students in computer science and engineering in Canada. Topics will include issues with textbook publishers (online vs physical books), open access textbook/homework systems, teaching, learning and setting evaluations, labs and homework in the era of AI, student attitudes towards learning, academic accommodation for disabilities, etc. This seminar could be interesting to those of you who will face teaching in your future, especially abroad. Although my perspective is based on physics and Canada, a number of issues raised are broadly relevant to other fields and countries.

会場: 研究本館 3階 359号室とZoomのハイブリッド開催

イベント公式言語: 英語

An optimal transport and information geometric framework for infinite-dimensional Gaussian measures and Gaussian processes (II)

2026年7月28日(火) 15:00 - 16:15

Minh Ha Quang (理化学研究所 革新知能統合研究センター (AIP) 不完全情報学習チーム 上級研究員)

Divergences between probability distributions play a crucial role in many areas of probability theory, statistics, machine learning, and their applications. While a large part of the literature is focused on divergences between finite-dimensional distributions, there is a growing body of work on infinite-dimensional distances/divergences, which are motivated by applications in functional data analysis, Bayesian inverse problems, and functional Bayesian neural networks, among others. In this lecture, we present an overview of recent results on some of the most important divergences being studied, including the Kullback-Leibler, Renyi, and Geometric Jensen-Shannon divergences. We discuss the many challenges that arise in the infinite-dimensional setting, e.g. the lack of a natural reference measure such as the Lebesgue measure and the fact that many functions such as determinants and logarithm are only well-defined in specific settings. In particular, in the setting of Gaussian measures on infinite-dimensional Hilbert spaces, the closed form expressions for the above divergences are only generalizable to equivalent Gaussian measures. We present the resolution to the above challenges via the geometrical framework of positive definite unitized (or regularized) trace class and Hilbert-Schmidt operators, including the Alpha and Alpha-Beta Log-Determinant divergences. Using this framework and the methodology of reproducing kernel Hilbert spaces (RKHS), we furthermore obtain consistent finite-dimensional  approximations of the above divergences in the Gaussian process setting, with dimensional-independent sample complexities. The resulting numerical algorithms can be readily employed in practical applications. We shall also discuss the generalization of the above classical divergences above to the quantum setting, namely the Quantum Jensen-Shannon divergence between quantum states, defined in terms of the von Neumann and Tsallis entropies, from finite to infinite-dimensional settings.

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語

An optimal transport and information geometric framework for infinite-dimensional Gaussian measures and Gaussian processes (I)

2026年7月28日(火) 13:30 - 14:45

Minh Ha Quang (理化学研究所 革新知能統合研究センター (AIP) 不完全情報学習チーム 上級研究員)

Optimal transport (OT) and information geometry (IG) have been attracting much research attention in various fields, in particular machine learning and statistics. In this lecture, we present results on the generalization of IG and OT distances for finite-dimensional Gaussian measures to the setting of infinite-dimensional Gaussian measures and Gaussian processes. Our focus is on the Entropic Regularization of the 2-Wasserstein distance and the generalization of the Fisher-Rao Riemannian metric and related quantities. In both settings, regularization leads to many desirable theoretical properties, including in particular dimension-independent convergence and sample complexity. The mathematical formulation involves the interplay of IG and OT with Gaussian processes and the methodology of reproducing kernel Hilbert spaces (RKHS). All of the presented formulations admit closed form expressions that can be efficiently computed and applied practically. The mathematical formulations will be illustrated with numerical experiments on Gaussian processes.

会場: セミナー室 (359号室) (メイン会場) / via Zoom

イベント公式言語: 英語