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Yoshinobu Kawahara

Publications and source records attributed to Yoshinobu Kawahara.

At least 19 recordsLinked to original sources
arXiv2026

Understanding Latent-Dimension Scaling in Dynamical-System Learning through Spectral Reliability

In deep learning, approximation theory motivates increasing representation size. We ask whether this benefit extends to dynamics learning through autoregressive prediction. We analyze the learned time evolution through the eigenstructure of Koopman operators, using relative residuals to detect spurious eigenpairs arising even as one-step error falls. For bounded Koopman operators, we show that minimal residuals over learned dictionary spaces converge pointwise to their full-space counterparts as these spaces approximate the observable space in $L^2$. Our hypothesis is that Koopman spectral reliability helps explain how consistently rollout error decreases with increasing dimension. We compare two models of a shared Koopman autoencoder trained alternately for reconstruction and latent evolution, using latent-prediction loss (one-step prediction errors in latent coordinates) or spectral-residual loss (relative residuals of candidate eigenpairs). Across six chaotic systems, both models reduced median windowed rollout error from smallest to largest dimension. The spectral-residual model achieved lower medians than the latent-prediction model for all systems and dimensions, and its median fell by a larger factor in every system. Its median decreased monotonically with dimension in four systems, against one for latent prediction. Against four baseline families, its mean valid prediction times were nearly always longer. At the largest dimension under two-stage training, we compared eigenvalue positions with each learned dictionary's residual contours. Spectral-residual eigenvalues concentrated in low-residual regions, whereas latent-prediction eigenvalues also appeared in high-residual regions, consistent with the hypothesis.

cs.LG↗
arXiv2026

Invariant-Measure Reasoners: Stable Representations for Latent Reasoning

Latent reasoning models repeatedly update a latent state using the same recurrent block. As the recurrent depth increases, the sequence of latent states may converge to a compact subset of the state space without necessarily converging to a fixed point. Existing models typically predict by applying a prediction head to a single latent state. However, the latent state can continue to change even after many updates, potentially making predictions unstable across recurrent depths. To address this instability, we introduce invariant-measure reasoners (ImR), a framework that uses an invariant measure as a stable representation. This measure describes the long-run distribution of latent states on the compact subset and is invariant under updates by the recurrent block. ImR predicts from the expectation of the prediction head's output under this measure. We use ImR in two ways: fine-tuning only the prediction head of existing models and training models from scratch. Both approaches reduce prediction instability and improve accuracy in many settings on maze and Sudoku tasks. In some settings, models trained with ImR exhibit non-fixed-point behavior more frequently than existing models yet achieve high accuracy even with such behavior, unlike existing models. These results suggest that ImR can leverage otherwise destabilizing dynamics for latent reasoning.

cs.LG↗
arXiv2026

Priority Coordination Games: Hodge Decomposition and a Sharp Design Limit

In decentralised priority coordination, agents announce priority levels and a shared resource serves them in decreasing order, as at an unsignalised intersection; the levels form the decision layer of a hierarchical controller. Such interactions are routinely replaced by a potential game, i.e.\ by a common objective, for analysis and design. This paper determines what that surrogate misses, using the Hodge decomposition of the incentives into a potential component, which a common objective can represent, and a harmonic component, which it cannot. For the linear payoff, both components are obtained in closed form on every conflict graph and for every deterministic tie-breaking protocol: in common units, the harmonic energy is the number of conflicts and the potential energy adds the number of adjacent pairs of conflicts. Consequently, for every rationality parameter, the best common-objective model of the agents' choice log-odds, weighted uniformly over unilateral moves, has a relative squared error of at least $1/(d_{\max}+1)$, where $d_{\max}$ is the largest number of conflicts of one agent; for an eight-vehicle intersection it is exactly one fifth, for any number of priority levels. Invisible to strict-improvement dynamics, the missed component is, under low-rationality log-linear learning with uniform revision and to leading order, the stationary probability current, and its energy sets the entropy-production rate. Payoff design cannot remove it: on the complete conflict graph of $N$ agents, under a total-order protocol and with at least three priority levels, every nonconstant rank-based payoff leaves a relative error of at least $1/N$, with equality exactly for affine payoffs.

cs.GT↗
arXiv2026

Causal Representation Learning with Instantaneous and Lagged Relations via Nonstationarity

Causal representation learning for time-series data aims to identify latent states and their causal relations from observations. In this setting, an important challenge is to model both lagged causal relations across observation intervals and faster causal effects that appear as instantaneous relations within an interval, while accounting for nonstationarity in time-series data. However, methods that jointly handle these causal relations and nonstationarity remain limited. To address this gap, we establish sufficient conditions for identifying latent states up to component permutation and component-wise invertible transformations, and their instantaneous and lagged causal structures up to the same permutation, using an observed auxiliary variable, such as time or a condition label, associated with changes in transition-noise distributions. Based on these results, we propose iCReN, a framework that uses contrastive learning with discrete or continuous auxiliary variables to learn latent representations and estimate their instantaneous and lagged causal structures. Experiments demonstrate accurate recovery of latent states and both instantaneous and lagged causal structures on synthetic data and the utility of the learned representations for downstream forecasting on real-world data.

cs.LG↗
arXiv2026

Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection

Fractional partial differential equations describe nonlocal dynamics, but discovering them from noisy data is difficult because fractional differentiation amplifies high-frequency measurement noise and the derivative orders are unknown. We propose Weak-Pareto, which combines an adjoint-consistent weak formulation of fractional terms with Pareto-based subset selection over discrete term types and continuous fractional orders. For linear right-hand-side terms, the adjoint transfers fractional operators from measured fields to smooth test functions, replacing noise-sensitive pointwise differentiation with smoothing integration; for nonlinear terms, the noise-suppression effect is partial yet useful. Coefficients are fitted by ridge regression within a branch-aware differential-evolution search over the orders. The support size is then selected at the validation-error-complexity elbow. We show that the variance of fixed linear right-hand-side weak features vanishes under grid refinement, whereas noise amplification in pointwise fractional features increases with derivative order. Across fractional advection-diffusion, reaction-diffusion, and Burgers benchmarks, Weak-Pareto recovers parsimonious structures from clean and noisy measurements. In controlled advection-diffusion and Burgers comparisons, it retains the correct support at every tested multiplicative-noise level, whereas the unregularised strong-form counterpart largely fails once noise is introduced; this advantage persists under additive Gaussian noise. Ablations show that the weak library drives noise robustness and that continuous-order Pareto search avoids the support-selection failure of a dense fixed dictionary. On the advection-diffusion benchmark, Weak-Pareto yields more consistent operator recovery and substantially lower measured runtime than a contemporary neural baseline.

cs.LG↗
arXiv2026

Dynamics-aware identification of governing equations from sparse and noisy data

Sparse identification of nonlinear dynamics (SINDy) and PDE functional identification (PDE-FIND) recover parsimonious ordinary and partial differential equations (ODEs and PDEs) from data. However, sparse and noisy temporal measurements can make derivative estimates unreliable. To address this problem, we evaluate Koopman-based upsampling techniques implemented with dynamic mode decomposition (DMD), extended DMD (EDMD), and optimized DMD. These methods learn finite-dimensional approximations of Koopman evolution on selected observables and are used to interpolate and denoise snapshots inside the observed time window before derivative estimation and sparse regression. The empirical benchmark comprises two ODE systems, Lorenz-63 and Van der Pol, and three periodic PDE systems, Burgers, Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP), and linear advection-diffusion, over sparse and noisy sampling regimes. Polynomial EDMD gives the strongest ODE results, especially in coefficient accuracy. The PDE results are system-dependent: low-rank DMD-assisted reconstructions improve Burgers and advection-diffusion discovery, while the raw baseline (without upsampling) remains competitive for the Fisher-KPP data. A comparison against linear and smoothing-spline interpolation techniques shows that the selected Koopman-based preprocessors provide overall performance gains over these non-dynamical alternatives. We also demonstrate that DMD-assisted upsampling can stabilize Pareto-based non-oracle support-size selection. Overall, Koopman-based upsampling is best viewed as a dynamics-aware preprocessing step that can reduce derivative-estimation error when its observable representation and low-rank structure are appropriate for the data.

cs.LG↗
arXiv2026

Timesteps of Mamba Align with Human Reading Times

This study demonstrates an alignment of per-word processing time in a popular state-space language model Mamba and human readers. In Mamba, the recurrent state transition at each layer conceptually takes some duration of time, the discretization timestep $Δ_t$, determined dynamically in response to the input. Using a naturalistic reading dataset, we show that the per-word timestep from Mamba is a significant predictor of human reading times, and remains significant even when known predictors such as GPT-2 surprisal are controlled for. We further suggest, through formal analysis of Mamba's architecture and internal dynamics, that Mamba can serve as a new, valuable lens to look at human real-time language processing with ever-updated memory, because it allows us to look at how each module (layer) weighs short- and long-term information retention, and how noise may interact with dynamic, continuous memory representation. Code is available online.

cs.CL↗
arXiv2026

Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offs

We propose KO-PDE-IDENT, a data-driven framework for identifying parsimonious partial differential equations (PDEs) with false discovery rate (FDR) control. PDE discovery from noisy observations is often hindered by extreme multicollinearity among candidate terms, which causes typical sparse-regression methods to select spurious terms. To address this problem, KO-PDE-IDENT initially mines a support set of potential candidate terms via model-X knockoff filters with finite-sample FDR control, then refines and ranks the surviving PDE alternatives. The framework integrates three components. First, knockoff feature statistics are constructed by coupling $\ell_{0}$-constrained adaptive best-subset selection with SHapley Additive exPlanations (SHAP), yielding an effective and computationally efficient difference statistic. Second, a recursive feature elimination (RFE) procedure removes terms whose marginal contributions are dispensable and assesses statistical necessity through knockoff-perturbed hypothesis testing. Third, the final model selection is formulated as a multi-criteria decision-making (MCDM) problem, where the optimal governing equation is the alternative that best balances a wide range of criteria such as predictive accuracy, model complexity and coefficient uncertainty. We evaluate KO-PDE-IDENT on five canonical PDEs under severe noise corruption. Empirical results show that our framework can exactly recover the true PDE structure, eliminating false discoveries while retaining all true underlying terms, with low coefficient estimation error.

stat.AP↗
arXiv2026

Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems

We propose a spectral learning method for stochastic nonlinear dynamical systems represented with embedded latent transfer operators in deep feature spaces. We instantiate the method as Deep Spectral Encoder (DSE), an operator-based latent state-space model in which a time-invariant neural encoder implements learnable nonlinear feature maps from observations, and these features define Markovian latent states whose temporal evolution and observation mapping are described by the transfer and observation operators, respectively. Functional canonical correlation analysis in a learnable Galerkin-projected feature space provides state coordinates from past and future observations, and the two linear operators are estimated on the state coordinates as ridge-regularized closed-form solutions that coincide with Galerkin projections of the associated covariance operators. On this representation, we generalize sequential Bayesian filtering and Koopman spectral mode decomposition in feature space. Experiments on several scenarios show stable and superior performance with sequential Bayesian filtering and dynamic mode decomposition baselines even under noise and partial observability.

cs.LG↗
arXiv2026

Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operators

Kalman filters based on the Embedded Latent Transfer Operators (ELTO) emerge as novel statistical tools for sequential state estimation. However, a critical limitation stems from their use of simplified noise models, which fail to dynamically adapt to non-stationary processes. To address this limitation, we introduce an ELTO-based Bayesian filtering approach with a new structured parameterization for the filter's noise model. This parameterization enables structured noise adaptation, which couples the data-driven learning of an optimal time-invariant noise model with dynamic parameter adaptation that responds to changes in dynamics within non-stationary processes. Empirical results show that our structured noise adaptation improves the filter's dynamic state estimation performance in noisy, time-varying environments.

cs.LG↗
arXiv2026

Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics

We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics' topological structure from its metric structure. Imposing minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality), we prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port-Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whereas metric effects enter only through constitutive relations and dissipation. This reduction clarifies what must be fixed and what should be learned, directly informing MeshFT-Net's design. Across evaluations on analytic and realistic datasets, physics-consistency tests, and out-of-distribution validation, MeshFT-Net achieves near-zero energy drift and strong physical fidelity (correct dispersion and momentum conservation) along with robust extrapolation and high data efficiency. By eliminating non-physical degrees of freedom and learning only metric-dependent structure, MeshFT provides a principled inductive bias for stable, faithful, and data-efficient learning-based physical simulation.

cs.LG↗
arXiv2026

Physics-inspired transformer quantum states via latent imaginary-time evolution

Neural quantum states (NQS) are powerful ansätze in the variational Monte Carlo framework, yet their architectures are often treated as black boxes. We propose a physically transparent framework in which NQS are treated as neural approximations to latent imaginary-time evolution. This viewpoint suggests that standard Transformer-based NQS (TQS) architectures correspond to physically unmotivated effective Hamiltonians dependent on imaginary time in a latent space. Building on this interpretation, we introduce physics-inspired transformer quantum states (PITQS), which enforce a static effective Hamiltonian by sharing weights across layers and improve propagation accuracy via Trotter-Suzuki decompositions without increasing the number of variational parameters. For the frustrated $J_1$-$J_2$ Heisenberg model, our ansätze achieve accuracies comparable to or exceeding state-of-the-art TQS while using substantially fewer variational parameters. This study demonstrates that reinterpreting the deep network structure as a latent cooling process enables a more physically grounded, systematic, and compact design, thereby bridging the gap between black-box expressivity and physically transparent construction.

cond-mat.dis-nn↗
arXiv2026

Dualformer: Time-Frequency Dual Domain Learning for Long-term Time Series Forecasting

Transformer-based models, despite their promise for long-term time series forecasting (LTSF), suffer from an inherent low-pass filtering effect that limits their effectiveness. This issue arises due to undifferentiated propagation of frequency components across layers, causing a progressive attenuation of high-frequency information crucial for capturing fine-grained temporal variations. To address this limitation, we propose Dualformer, a principled dual-domain framework that rethinks frequency modeling from a layer-wise perspective. Dualformer introduces three key components: (1) a dual-branch architecture that concurrently models complementary temporal patterns in both time and frequency domains; (2) a hierarchical frequency sampling module that allocates distinct frequency bands to different layers, preserving high-frequency details in lower layers while modeling low-frequency trends in deeper layers; and (3) a periodicity-aware weighting mechanism that dynamically balances contributions from the dual branches based on the harmonic energy ratio of inputs, supported theoretically by a derived lower bound. This design enables structured frequency modeling and adaptive integration of time-frequency features, effectively preserving high-frequency information and enhancing generalization. Extensive experiments conducted on eight widely used benchmarks demonstrate Dualformer's robustness and superior performance, particularly on heterogeneous or weakly periodic data. Our code is publicly available at https://github.com/Akira-221/Dualformer.

cs.LG↗
arXiv2025

Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces

This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method, what we call Jet Extended Dynamic Mode Decomposition (JetEDMD), leveraging the intrinsic structure of RKHS and the geometric notion known as jets to enhance the estimation of the Koopman operator. This method refines the traditional Extended Dynamic Mode Decomposition (EDMD) in accuracy, especially in the numerical estimation of eigenvalues. This paper proves JetEDMD's superiority through explicit error bounds and convergence rate for special positive definite kernels, offering a solid theoretical foundation for its performance. We also investigate the spectral analysis of the Koopman operator, proposing the notion of an extended Koopman operator within a framework of a rigged Hilbert space. This notion leads to a deeper understanding of estimated Koopman eigenfunctions and capturing them outside the original function space. Through the theory of rigged Hilbert space, our study provides a principled methodology to analyze the estimated spectrum and eigenfunctions of Koopman operators, and enables eigendecomposition within a rigged RKHS. We also propose a new effective method for reconstructing the dynamical system from temporally-sampled trajectory data of the dynamical system with solid theoretical guarantee. We conduct several numerical simulations using the van der Pol oscillator, the Duffing oscillator, the Hénon map, and the Lorenz attractor, and illustrate the performance of JetEDMD with clear numerical computations of eigenvalues and accurate predictions of the dynamical systems.

math.DS↗
arXiv2025

Generalized Stochastic Resilience for Early Warning Signals Based on Koopman Operator

Developing methods for detecting tipping phenomena at an early stage is an important problem in various fields such as ecology, medicine, and economics. A tipping phenomenon is characterized by a rapid transition resulting from the accumulation of small parameter changes and is known to be related to bifurcations of dynamical systems. However, few studies have examined how nonlinear properties near bifurcation points affect early warning signal (EWS) performance. In this study, we apply the Koopman operator, which describes the time evolution of dynamical systems in an infinite-dimensional function space, to generalize stochastic resilience the theoretical basis of EWSs such as variance-based ones. As a result, we develop a novel signal capable of more accurately predicting tipping events by separately isolating stochastic fluctuations induced by noise and contributions from a continuous spectrum emerging immediately above tipping points. Our experimental results demonstrate that the proposed approach detects early signs of tipping phenomena more robustly than conventional methods.

math.DS↗
arXiv2025

Wavy Transformer

Transformers have achieved remarkable success across natural language processing (NLP) and computer vision (CV). However, deep transformer models often suffer from an over-smoothing issue, in which token representations converge to similar values as they pass through successive transformer blocks. In this paper, we establish an equivalence between the hidden-state dynamics induced by stacked attention layers and graph neural diffusion on a complete graph. From this perspective, over-smoothing can be interpreted as a consequence of the dissipative nature of the underlying diffusion dynamics. Motivated by this physical interpretation, we propose Wavy Transformer, which consists of a novel attention layer based on second-order wavy dynamics. We also introduce a feed-forward network and a normalization layer designed to preserve the physical state-velocity relationship under the chain rule, thereby extending the transformer architecture. We further validate our proposed techniques on various transformer models for NLP and CV tasks. The results consistently demonstrate that Wavy Transformer improves performance with minimal additional parameters and no extra hyperparameter tuning.

cs.LG↗
arXiv2025

Data-driven simulator of multi-animal behavior with unknown dynamics via offline and online reinforcement learning

Simulators of animal movements play a valuable role in studying behavior. Advances in imitation learning for robotics have expanded possibilities for reproducing human and animal movements. A key challenge for realistic multi-animal simulation in biology is bridging the gap between unknown real-world transition models and their simulated counterparts. Because locomotion dynamics are seldom known, relying solely on mathematical models is insufficient; constructing a simulator that both reproduces real trajectories and supports reward-driven optimization remains an open problem. We introduce a data-driven simulator for multi-animal behavior based on deep reinforcement learning and counterfactual simulation. We address the ill-posed nature of the problem caused by high degrees of freedom in locomotion by estimating movement variables of an incomplete transition model as actions within an RL framework. We also employ a distance-based pseudo-reward to align and compare states between cyber and physical spaces. Validated on artificial agents, flies, newts, and silkmoth, our approach achieves higher reproducibility of species-specific behaviors and improved reward acquisition compared with standard imitation and RL methods. Moreover, it enables counterfactual behavior prediction in novel experimental settings and supports multi-individual modeling for flexible what-if trajectory generation, suggesting its potential to simulate and elucidate complex multi-animal behaviors.

cs.LG↗
arXiv2025

Intrinsic frequency distribution characterises neural dynamics

Decomposing multivariate time series with certain basic dynamics is crucial for understanding, predicting and controlling nonlinear spatiotemporally dynamic systems such as the brain. Dynamic mode decomposition (DMD) is a method for decomposing nonlinear spatiotemporal dynamics into several basic dynamics (dynamic modes; DMs) with intrinsic frequencies and decay rates. In particular, unlike Fourier transform-based methods, which are used to decompose a single-channel signal into the amplitudes of sinusoidal waves with discrete frequencies at a regular interval, DMD can derive the intrinsic frequencies of a multichannel signal on the basis of the available data; furthermore, it can capture nonstationary components such as alternations between states with different intrinsic frequencies. Here, we propose the use of the distribution of intrinsic frequencies derived from DMDs (DM frequencies) to characterise neural activities. The distributions of DM frequencies in the electroencephalograms of healthy subjects and patients with dementia or Parkinson's disease in a resting state were evaluated. By using the distributions, these patients were distinguished from healthy subjects with significantly greater accuracy than when using amplitude spectra derived by discrete Fourier transform. This finding suggests that the distribution of DM frequencies exhibits distinct behaviour from amplitude spectra, and therefore, the distribution may serve as a new biomarker by characterising the nonlinear spatiotemporal dynamics of electrophysiological signals.

eess.SP↗