arXiv subjects

Yuki Sughiyama

Publications and source records attributed to Yuki Sughiyama.

At least 19 recordsLinked to original sources

arXiv2026

Simulation-free and finite-time diffusion model

The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.

cs.LG↗

arXiv2025

Information geometry of chemical reaction networks: Cramer-Rao bound and absolute sensitivity revisited

Information geometry is based on classical Legendre duality but allows to incorporate additional structure such as algebraic constraints and Bregman divergence functions. It is naturally suited, and has been successfully used, to describe the thermodynamics of chemical reaction networks (CRNs) based on the Legendre duality between concentration and potential spaces, where algebraic constraints are enforced by the stoichiometry. In this article, the Riemannian geometrical aspects of the theory are explored. It is shown that duality between concentration and potential spaces and the natural parametrizations of equilibrium subspace are isometries, which leads to a multivariate Cramer-Rao bound through the comparison of two Riemannian metric tensors. In the subsequent part, the theory is applied to the recently introduced concept of absolute sensitivity. Using the Riemannian geometric tools, it is proven that the absolute sensitivity is a projection operator onto the tangent bundle of the equilibrium manifold. A linear algebraic characterization and explicit results on first order corrections to the thermodynamics of ideal solutions are provided. Finally, the theory is applied to the IDHKP-IDH glyoxylate bypass regulation system. The novelty of the theory is that it is applicable to CRNs with non-ideal thermodynamical behavior, which are prevalent in highly crowded cellular environments due to various interactions between the chemicals. Indeed, the analyzed example shows remarkable behavior ranging from hypersensitivity to negative-self regulations. These are effects which usually require strongly nonlinear reaction kinetics. However, here, they are obtained by tuning thermodynamical interactions providing a complementary, and physically well-founded, viewpoint on such phenomena.

q-bio.MN↗

arXiv2025

Cramer-Rao bound and absolute sensitivity in chemical reaction networks

Chemical reaction networks (CRN) comprise an important class of models to understand biological functions such as cellular information processing, the robustness and control of metabolic pathways, circadian rhythms, and many more. However, any CRN describing a certain function does not act in isolation but is a part of a much larger network and as such is constantly subject to external changes. In [Shinar, Alon, and Feinberg. "Sensitivity and robustness in chemical reaction networks." SIAM J App Math (2009): 977-998.], the responses of CRN to changes in the linear conserved quantities, called sensitivities, were studied in and the question of how to construct absolute, i.e., basis-independent, sensitivities was raised. In this article, by applying information geometric methods, such a construction is provided. The idea is to track how concentration changes in a particular chemical propagate to changes of all concentrations within a steady state. This is encoded in the matrix of absolute sensitivities. As the main technical tool, a multivariate Cramer-Rao bound for CRN is proven, which is based on the the analogy between quasi-thermostatic steady states and the exponential family of probability distributions. This leads to a linear algebraic characterization of the matrix of absolute sensitivities for quasi-thermostatic CRN. As an example, the core module of the IDHKP-IDH glyoxylate bypass regulation system is analyzed analytically and numerically by extensive random sampling of the concentration space. The experimentally known findings for the robustness of the IDH enzyme are confirmed and a hidden symmetry at the level of distributions is revealed, providing a blueprint for the analysis of the robustness properties of CRNs.

q-bio.MN↗

arXiv2024

Schödinger Bridge Type Diffusion Models as an Extension of Variational Autoencoders

Generative diffusion models use time-forward and backward stochastic differential equations to connect the data and prior distributions. While conventional diffusion models (e.g., score-based models) only learn the backward process, more flexible frameworks have been proposed to also learn the forward process by employing the Schrödinger bridge (SB). However, due to the complexity of the mathematical structure behind SB-type models, we can not easily give an intuitive understanding of their objective function. In this work, we propose a unified framework to construct diffusion models by reinterpreting the SB-type models as an extension of variational autoencoders. In this context, the data processing inequality plays a crucial role. As a result, we find that the objective function consists of the prior loss and drift matching parts.

cs.LG↗

arXiv2024

Thermodynamic and Stoichiometric Laws Ruling the Fates of Growing Systems

We delve into growing open chemical reaction systems (CRSs) characterized by autocatalytic reactions within a variable volume, which changes in response to these reactions. Understanding the thermodynamics of such systems is crucial for comprehending biological cells and constructing protocells, as it sheds light on the physical conditions necessary for their self-replication. Building on our recent work, where we developed a thermodynamic theory for growing CRSs featuring basic autocatalytic motifs with regular stoichiometric matrices, we now expand this theory to include scenarios where the stoichiometric matrix has a nontrivial left kernel space. This extension introduces conservation laws, which limit the variations in chemical species due to reactions, thereby confining the system's possible states to those compatible with its initial conditions. By considering both thermodynamic and stoichiometric constraints, we clarify the environmental and initial conditions that dictate the CRSs' fate-whether they grow, shrink, or reach equilibrium. We also find that the conserved quantities significantly influence the equilibrium state achieved by a growing CRS. These results are derived independently of specific thermodynamic potentials or reaction kinetics, therefore underscoring the fundamental impact of conservation laws on the growth of the system.

cond-mat.stat-mech↗

arXiv2023

The Geometry of Thermodynamic Uncertainty Relations in Chemical Reaction Networks

Recently, Hessian geometry - an extension of information geometry - has emerged as a framework to naturally connect the geometries appearing in the theory of chemical reaction networks (CRN) to their inherent thermodynamical and kinetic properties. This framework is used in this letter to derive multivariate thermodynamic uncertainty relations (TUR) for CRN. The matrices featured in the TUR are shown to be representations of Riemmanian metric tensors, whereby one tensor characterizes the pseudo entropy production rate and the other the current fluctuations. It is shown that the latter tensor is a restriction of the former one to a linear subspace in the flux tangent space. Therefore, in addition to clarifying the geometric origin of TUR in CRN, the Hessian geometric setup yields a characterization of the error term in the TUR as the norm of a linear subspace component of the flux vector and thus characterizes the fluxes where TUR become equalities.

cond-mat.stat-mech↗

arXiv2023

Information Geometry of Dynamics on Graphs and Hypergraphs

We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces, respectively. The former is the conventional duality between density and potential, e.g., the probability density and its logarithmic form induced by a convex thermodynamic function. The latter is the duality between flux and force induced by a convex and symmetric dissipation function, which drives the dynamics of the density. These two are connected topologically by the homological algebraic relation induced by the underlying discrete objects. The generalized gradient flow in this doubly dual flat structure is an extension of the gradient flows on Riemannian manifolds, which include Markov jump processes and nonlinear chemical reaction dynamics as well as the natural gradient and mirror descent. The information-geometric projections on this doubly dual flat structure lead to information-geometric extensions of the Helmholtz-Hodge decomposition and the Otto structure in $L^{2}$ Wasserstein geometry. The structure can be extended to non-gradient nonequilibrium flows, from which we also obtain the induced dually flat structure on cycle spaces. This abstract but general framework can extend the applicability of information geometry to various problems of linear and nonlinear dynamics.

cs.IT↗

arXiv2022

A Hessian Geometric Structure of Chemical Thermodynamic Systems with Stoichiometric Constraints

We establish a Hessian geometric structure in chemical thermodynamics which describes chemical reaction networks (CRNs) with equilibrium states. In our setup, the ideal gas assumption and mass action kinetics are not required. The existence and uniqueness condition of the equilibrium state is derived by using the Legendre duality inherent to the Hessian structure. The entropy production during a relaxation to the equilibrium state can be evaluated by the Bregman divergence. Furthermore, the equilibrium state is characterized by four distinct minimization problems of the divergence, which are obtained from the generalized Pythagorean theorem originating in the dual flatness. For the ideal gas case, we confirm that our existence and uniqueness condition implies Birch's theorem, and that the entropy production represented by the divergence coincides with the generalized Kullback-Leibler divergence. In addition, under mass action kinetics, our general framework reproduces the local detailed balance condition.

cond-mat.stat-mech↗

arXiv2022

Chemical Thermodynamics for Growing Systems

We consider growing open chemical reaction systems (CRSs), in which autocatalytic chemical reactions are encapsulated in a finite volume and its size can change in conjunction with the reactions. The thermodynamics of growing CRSs is indispensable for understanding biological cells and designing protocells by clarifying the physical conditions and costs for their growing states. In this work, we establish a thermodynamic theory of growing CRSs by extending the Hessian geometric structure of non-growing CRSs. The theory provides the environmental conditions to determine the fate of the growing CRSs; growth, shrinking or equilibration. We also identify thermodynamic constraints; one to restrict the possible states of the growing CRSs and the other to further limit the region where a nonequilibrium steady growing state can exist. Moreover, we evaluate the entropy production rate in the steady growing state. The growing nonequilibrium state has its origin in the extensivity of thermodynamics, which is different from the conventional nonequilibrium states with constant volume. These results are derived from general thermodynamic considerations without assuming any specific thermodynamic potentials or reaction kinetics; i.e., they are obtained based solely on the second law of thermodynamics.

cond-mat.stat-mech↗

arXiv2022

Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions

We derive the Hessian geometric structure of nonequilibrium chemical reaction networks (CRN) on the flux and force spaces induced by the Legendre duality of convex dissipation functions and characterize their dynamics as a generalized flow. With this structure, we can extend theories of nonequilibrium systems with quadratic dissipation functions to more general ones with nonquadratic ones, which are pivotal for studying chemical reaction networks. By applying generalized notions of orthogonality in Hessian geometry to chemical reaction networks, we obtain two generalized decompositions of the entropy production rate, each of which captures gradient-flow and minimum-dissipation aspects in nonequilibrium dynamics.

physics.chem-ph↗

arXiv2022

Riemannian Geometry of Optimal Driving and Thermodynamic Length and its Application to Chemical Reaction Networks

It is known that the trajectory of an endoreversibly driven system with minimal dissipation is a geodesic on the equilibrium state space. Thereby, the state space is equipped with the Riemannian metric given by the Hessian of the free energy function, known as Fisher information metric. However, the derivations given until now require both the system and the driving reservoir to be in local equilibrium. In the present work, we rederive the framework for chemical reaction networks and thereby enhance its scope of applicability to the nonequilibrium situation. Moreover, because our results are derived without restrictive assumptions, we are able to discuss phenomena that could not been seen previously. We introduce a suitable weighted Fisher information metric on the space of chemical concentrations and show that it characterizes the dissipation caused by diffusive driving, with arbitrary diffusion rate constants. This allows us to consider driving far from equilibrium. As the main result, we show that the isometric embedding of a steady state manifold into the concentration space yields a lower bound for the dissipation when the system is driven along the manifold. We give an analytic expression for this bound and for the corresponding geodesic, and thereby are able to dissect the contributions from the driving kinetics and from thermodynamics. Finally, we discuss in detail the application to quasi-thermostatic steady states.

cond-mat.stat-mech↗

arXiv2021

Kinetic Derivation of the Hessian Geometric Structure in Chemical Reaction Systems

The theory of chemical kinetics form the basis to describe the dynamics of chemical systems. Owing to physical and thermodynamic constraints, chemical reaction systems possess various structures, which can be utilized to characterize important physical properties of the systems. In this work, we reveal the Hessian geometry which underlies chemical reaction systems and demonstrate how it originates from the interplay of stoichiometric and thermodynamic constraints. Our derivation is based on kinetics, we assume the law of mass action and characterize the equilibrium states by the detailed balance condition. The obtained geometric structure is then related to thermodynamics via the Hessian geometry appearing in a pure thermodynamic derivation. We demonstrate, based on the fact that both equilibrium and complex balanced states form toric varieties, how the Hessian geometric framework can be extended to nonequilibrium complex balanced steady states. We conclude that Hessian geometry provides a natural framework to capture the thermodynamic aspects of chemical reaction kinetics.

physics.bio-ph↗

arXiv2019

Lineage EM Algorithm for Inferring Latent States from Cellular Lineage Trees

Phenotypic variability in a population of cells can work as the bet-hedging of the cells under an unpredictably changing environment, the typical example of which is the bacterial persistence. To understand the strategy to control such phenomena, it is indispensable to identify the phenotype of each cell and its inheritance. Although recent advancements in microfluidic technology offer us useful lineage data, they are insufficient to directly identify the phenotypes of the cells. An alternative approach is to infer the phenotype from the lineage data by latent-variable estimation. To this end, however, we must resolve the bias problem in the inference from lineage called survivorship bias. In this work, we clarify how the survivor bias distorts statistical estimations. We then propose a latent-variable estimation algorithm without the survivorship bias from lineage trees based on an expectation-maximization (EM) algorithm, which we call Lineage EM algorithm (LEM). LEM provides a statistical method to identify the traits of the cells applicable to various kinds of lineage data.

q-bio.PE↗

arXiv2018

Fitness response relation of a multi-type age-structured population dynamics

We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a trade-off relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the response coefficients. These results contribute to predicting and controlling growing populations based on experimentally observed cell-lineage information.

cond-mat.stat-mech↗

arXiv2017

Individual Sensing can Gain more Fitness than its Information

Mutual information and its causal variant, directed information, have been widely used to quantitatively characterize the performance of biological sensing and information transduction. However, once coupled with selection in response to decision-making, the sensing signal could have more or less evolutionary value than its mutual or directed information. In this work, we show that an individually sensed signal always has a better fitness value, on average, than its mutual or directed information. The fitness gain, which satisfies fluctuation relations (FRs), is attributed to the selection of organisms in a population that obtain a better sensing signal by chance. A new quantity, similar to the coarse-grained entropy production in information thermodynamics, is introduced to quantify the total fitness gain from individual sensing, which also satisfies FRs. Using this quantity, the optimizing fitness gain from individual sensing is shown to be related to fidelity allocations for individual environmental histories. Our results are supplemented by numerical verifications of FRs, and a discussion on how this problem is linked to information encoding and decoding.

q-bio.PE↗

arXiv2017

A Quantum Extension of Variational Bayes Inference

Variational Bayes (VB) inference is one of the most important algorithms in machine learning and widely used in engineering and industry. However, VB is known to suffer from the problem of local optima. In this Letter, we generalize VB by using quantum mechanics, and propose a new algorithm, which we call quantum annealing variational Bayes (QAVB) inference. We then show that QAVB drastically improve the performance of VB by applying them to a clustering problem described by a Gaussian mixture model. Finally, we discuss an intuitive understanding on how QAVB works well.

stat.ML↗

arXiv2017

The explicit form of the rate function for semi-Markov processes and its contractions

We derive the explicit form of the rate function for semi-Markov processes. Here, the "random time change trick" plays an essential role. Also, by exploiting the contraction principle of the large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen Symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the Level 2.5 rate function for Markov processes to semi-Markov cases.

cond-mat.stat-mech↗

arXiv2017

Stochastic and Information-thermodynamic Structures of Population Dynamics in Fluctuating Environment

Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness. Living systems have gradually developed strategies for adaptation from random and passive diversification of the phenotype to more proactive decision making, in which environmental information is sensed and exploited more actively and effectively. Understanding the fundamental relation between fitness and information is therefore crucial to clarify the limits and universal properties of adaptation. In this work, we elucidate the underlying stochastic and information-thermodynamic structure in this process, by deriving causal fluctuation relations (FRs) of fitness and information. Combined with a duality between phenotypic and environmental dynamics, the FRs reveal the limit of fitness gain, the relation of time reversibility with the achievability of the limit, and the possibility and condition for gaining excess fitness due to environmental fluctuation. The loss of fitness due to causal constraints and the limited capacity of real organisms is shown to be the difference between time-forward and time-backward path probabilities of phenotypic and environmental dynamics. Furthermore, the FRs generalize the concept of evolutionary stable state (ESS) for fluctuating environment by giving the probability that the optimal strategy on average can be invaded by a suboptimal one owing to rare environmental fluctuation. These results clarify the information thermodynamic structures in adaptation and evolution.

q-bio.PE↗