arXiv subjects

Hiroshi Yamashita

Publications and source records attributed to Hiroshi Yamashita.

12 recordsLinked to original sources

arXiv2026

Slow-spectrum preshaping for reservoir computing: Attractor reconstruction in attracting submanifolds under partial observation

Data-driven reproduction of chaotic dynamics under partial observation remains a challenge despite its practical importance. Reservoir computing (RC) and other data-driven approaches often succeed in short-term prediction but are sensitive to hyperparameters and frequently fail to reproduce the long-term statistical properties of the system. As recently shown, a major cause of this failure is spurious slow modes induced by training, which render the reconstructed invariant set transversally unstable in the representation space. To address this, a design principle called Attractor Reconstruction in Attracting Submanifolds (ARAS) was proposed, which requires the reconstruction to lie in a low-dimensional, transversally attracting submanifold. Under full observation, ARAS was realized by an input-layer design that limits the number of slow modes perturbed during training and anchors the remaining modes to stay fast, thereby suppressing spurious slow modes. However, under partial observation, this design alone fails because the submanifold designed to be attracting cannot retain the observation history needed to unfold the observed data into a faithful reconstruction. In this study, we propose slow-spectrum preshaping, which introduces a slow spectrum into the reservoir prior to feeding input data. The induced slow modes then retain a memory of past observations within the submanifold, while the input-layer design makes the submanifold transversally attracting, so that ARAS is realized under partial observation. Through numerical experiments on various chaotic systems, we show that our approach enables reliable short-term prediction and long-term reproduction of chaos over a wide range of hyperparameters without a posteriori tuning.

nlin.CD↗

arXiv2026

Inducing fast-slow separation enables robust learning of complex dynamics

Many real-world systems share a fast-slow structure: most degrees of freedom relax quickly, while a few slow modes govern the long-term evolution. Their dynamics often collapse onto low-dimensional complex structures such as chaotic attractors, and a goal of nonlinear science is to predict and faithfully reproduce them from observed time series. Machine-learning models and data-driven approaches can embed a chaotic attractor in high-dimensional spaces, but embedding alone does not guarantee faithful reproduction. Training can create spurious slow modes, excess modes unnecessary for the target dynamics, which destabilize the reconstruction. To prevent this instability, we introduce input-layer designs for reservoir computing, a framework suited to physical implementation. Through restriction of network controllability, the designs limit the number of slow modes available to learning and anchor the remaining modes to stay fast in advance, even for a black-box model. The reconstruction is thereby confined to a transversally attracting subspace, and spurious slow modes are suppressed. Across diverse chaotic systems, the designs robustly reproduce the attractors and their dynamical invariants, extend the horizon of accurate prediction, and withstand perturbations of the internal weights, without extensive tuning. Inducing fast-slow separation and reconstructing attractors in attracting subspaces offers a design principle for reliable data-driven modeling.

nlin.CD↗

arXiv2026

Convolutional Formulation of Large-Scale Quadratic Unconstrained Binary Optimization with Dense Interactions

The spatial photonic Ising machine (SPIM) is a promising optical hardware solver for large-scale combinatorial optimization problems with dense interactions. As the SPIM can represent Ising problems with rank-one coupling matrices, multiplexed versions have been proposed to enhance applicability to higher-rank interactions. However, the multiplexing cost reduces implementation efficiency, and even without multiplexing, the SPIM can represent coupling matrices beyond rank-one. To clarify the intrinsic representation power of the SPIM, we propose spatial quadratic unconstrained binary optimization (spQUBO), a formulation of Ising problems with spatially convolutional structures. We prove that any spQUBO reduces to a two-dimensional spQUBO with the convolutional structure preserved, which can be efficiently implemented on the SPIM without multiplexing. We demonstrate its applicability to distance-based combinatorial optimization, including placement problems and clustering problems. These results advance our understanding of the class of optimization problems where SPIMs exhibit unique advantage in efficiency and scalability. Furthermore, the convolutional structure of spQUBO also enables efficient computation using Fast Fourier Transforms.

cond-mat.dis-nn↗

arXiv2026

Designing Zero-Mean Feature Functions for Multimodal Distributions

To improve the accuracy of Monte Carlo estimation of expectations, a set of zero-mean feature functions, known as control variates, can be used. They can be used as feature functions for linear regression of the target function, and we can obtain an unbiased and variance-reduced estimate using its residual. One known way to construct such functions is a method using an equality called Stein's identity, but these functions are not sufficient for the case where the target distribution is multimodal. We propose a different approach to constructing these zero-mean functions based on distribution approximation and the density ratio. We demonstrate that combining the functions constructed by these two strategies can effectively reduce the estimation variance for a bimodal distribution.

stat.CO↗

arXiv2026

Deterministic Discrete Denoising

We propose a deterministic denoising algorithm for discrete-state diffusion models. The key idea is to derandomize the generative reverse Markov chain by introducing a variant of the herding algorithm, which induces deterministic state transitions driven by weakly chaotic dynamics. It serves as a direct replacement for the stochastic denoising process, without requiring retraining or continuous state embeddings. We demonstrate consistent improvements in both efficiency and sample quality on text and image generation tasks. In addition, the proposed algorithm yields improved solutions for diffusion-based combinatorial optimization. Thus, herding-based denoising is a simple yet promising approach for enhancing the generative process of discrete diffusion models. Furthermore, our results reveal that deterministic reverse processes, well established in continuous diffusion, can also be effective in discrete state spaces.

cs.LG↗

arXiv2025

Formation of a Single Bioconvection Spot in Euglena Suspension Induced by Negative Phototaxis

Microorganisms are known to alter their motility in response to external stimuli. A typical example is the responseknown as taxis, which includes behaviors such as moving toward a light source (positive phototaxis) or away from it(negative phototaxis). In this study, we focused on bioconvection induced by the negative phototaxis of a Euglenasuspension exposed to strong light from the bottom. Recent studies have revealed that Euglena bioconvectioninduced by negative phototaxis exhibits localized structure. In a previous study, we found that a single Euglenabioconvection spot (EBC spot) maintains its structure in a cylindrical container. Such a localized structure is notexclusive to Euglena, but has also reported in red tide algae, suggesting that this is a universal feature ofbioconvection phenomena. In this paper, we investigated the formation conditions of EBC spot phenomena throughexperiments and numerical simulations. In the experiments, we examined the variation in EBC spot formation as afunction of suspension height and average cell density, revealing that the critical average cell density increases withsuspension height. In the numerical simulations, we conducted bioconvection simulations based on a model ofEuglena motility that incorporated three types of behavior: the negative gravitaxis, negative phototaxis, andbehavior of moving toward darker areas. Our model successfully reproduced the localized state of a two-dimensional EBC spot. Furthermore, calculations corresponding to the experimental conditions of suspension heightand average cell density revealed that the critical average cell density for bioconvection decreases as thesuspension height increases.

physics.flu-dyn↗

arXiv2024

Traffic signal optimization in large-scale urban road networks: an adaptive-predictive controller using Ising models

Realizing smooth traffic flow is important for achieving carbon neutrality. Adaptive traffic signal control, which considers traffic conditions, has thus attracted attention. However, it is difficult to ensure optimal vehicle flow throughout a large city using existing control methods because of their heavy computational load. Here, we propose a control method called AMPIC (Adaptive Model Predictive Ising Controller) that guarantees both scalability and optimality. The proposed method employs model predictive control to solve an optimal control problem at each control interval with explicit consideration of a predictive model of vehicle flow. This optimal control problem is transformed into a combinatorial optimization problem with binary variables that is equivalent to the so-called Ising problem. This transformation allows us to use an Ising solver, which has been widely studied and is expected to have fast and efficient optimization performance. We performed numerical experiments using a microscopic traffic simulator for a realistic city road network. The results show that AMPIC enables faster vehicle cruising speed with less waiting time than that achieved by classical control methods, resulting in lower CO2 emissions. The model predictive approach with a long prediction horizon thus effectively improves control performance. Systematic parametric studies on model cities indicate that the proposed method realizes smoother traffic flows for large city road networks. Among Ising solvers, D-Wave's quantum annealing is shown to find near-optimal solutions at a reasonable computational cost.

math.OC↗

arXiv2023

Spatial-photonic Ising machine by space-division multiplexing with physically tunable coefficients of a multi-component model

This paper proposes a space-division multiplexed spatial-photonic Ising machine (SDM-SPIM) that physically calculates the weighted sum of the Ising Hamiltonians for individual components in a multi-component model. Space-division multiplexing enables tuning a set of weight coefficients as an optical parameter and obtaining the desired Ising Hamiltonian at a time. We solved knapsack problems to verify the system's validity, demonstrating that optical parameters impact the search property. We also investigated a new dynamic coefficient search algorithm to enhance search performance. The SDM-SPIM would physically calculate the Hamiltonian and a part of the optimization with an electronics process.

physics.optics↗

arXiv2023

Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machine

The spatial photonic Ising machine (SPIM) [D. Pierangeli et al., Phys. Rev. Lett. 122, 213902 (2019)] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. The primitive version of the SPIM, however, can accommodate Ising problems with only rank-one interaction matrices. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, it acquires the learning ability of Boltzmann machines. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions. Thus, the proposed model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.

cond-mat.dis-nn↗

arXiv2023

Entropic Herding

Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is inspired by the maximum entropy principle of statistical inference. In this paper, we propose an extension of the herding algorithm, called entropic herding, which generates a sequence of distributions instead of points. Entropic herding is derived as the optimization of the target function obtained from the maximum entropy principle. Using the proposed entropic herding algorithm as a framework, we discuss a closer connection between herding and the maximum entropy principle. Specifically, we interpret the original herding algorithm as a tractable version of entropic herding, the ideal output distribution of which is mathematically represented. We further discuss how the complex behavior of the herding algorithm contributes to optimization. We argue that the proposed entropic herding algorithm extends the application of herding to probabilistic modeling. In contrast to original herding, entropic herding can generate a smooth distribution such that both efficient probability density calculation and sample generation become possible. To demonstrate the viability of these arguments in this study, numerical experiments were conducted, including a comparison with other conventional methods, on both synthetic and real data.

stat.ML↗

arXiv2022

Inertial migration of red blood cells under a Newtonian fluid in a circular channel

We present a numerical analysis of the lateral movement and equilibrium radial positions of red blood cells (RBCs) with major diameter of 8 $μ$m under a Newtonian fluid in a circular channel with 50-$μ$m diameter. Each RBC, modelled as a biconcave capsule whose membrane satisfies strain-hardening characteristics, is simulated for different Reynolds numbers $Re$ and capillary numbers $Ca$, the latter of which indicate the ratio of the fluid viscous force to the membrane elastic force. The effects of initial orientation angles and positions on the equilibrium radial position of an RBC centroid are also investigated. The numerical results show that depending on their initial orientations, RBCs have bistable flow modes, so-called rolling and tumbling motions. Most RBCs have a rolling motion. These stable modes are accompanied by different equilibrium radial positions, where tumbling RBCs are further away from the channel axis than rolling ones. The inertial migration of RBCs is achieved by alternating orientation angles, which are primarily affected by the initial orientation angles. Then the RBCs assume the aforementioned bistable modes during the migration, followed by further migration to the equilibrium radial position at much longer time periods. The power (or energy dissipation) associated with membrane deformations is introduced to quantify the state of membrane loads. The energy expenditures rely on stable flow modes, the equilibrium radial position of RBC centroids, and the viscosity ratio between the internal and external fluids.

physics.flu-dyn↗

arXiv2021

Variation of focusing patterns of laterally migrating particles in a square-tube flow due to non-Newtonian elastic force

The elasto-inertial effects on particle focusing in a square-tube flow were investigated experimentally and numerically. Microscale experiments using spherical particles in dilute polymer solutions demonstrated that the particles are focused on the midline and/or the diagonal in a downstream cross-section, depending on the polymer concentration. Numerical computations based on the FENE-P model for the viscoelastic flow reproduced these focusing patterns. It was revealed that the transitions among the patterns are accounted for by the elastic forces due to the first normal stress difference and the polymer elongation, which are the essentials of the viscoelastic fluid.

physics.flu-dyn↗