Gouhei Tanaka

Ziqiang Li, Kantaro Fujiwara, Gouhei Tanaka

The Dissemination Process Classification (DPC) is a popular application of temporal graph classification. The aim of DPC is to classify different spreading patterns of information or pestilence within a community represented by discrete-time temporal graphs. Recently, a reservoir computing-based model named Dynamical Graph Echo State Network (DynGESN) has been proposed for processing temporal graphs with relatively high effectiveness and low computational costs. In this study, we propose a novel model which combines a novel data augmentation strategy called snapshot merging with the DynGESN for dealing with DPC tasks. In our model, the snapshot merging strategy is designed for forming new snapshots by merging neighboring snapshots over time, and then multiple reservoir encoders are set for capturing spatiotemporal features from merged snapshots. After those, the logistic regression is adopted for decoding the sum-pooled embeddings into the classification results. Experimental results on six benchmark DPC datasets show that our proposed model has better classification performances than the DynGESN and several kernel-based models.

Robert Simon Fong, Gouhei Tanaka, Kazuyuki Aihara

Modern learning systems act on internal representations of data, yet how these representations encode underlying physical or statistical structure is often left implicit. In physics, conservation laws of Hamiltonian systems such as symplecticity guarantee long-term stability, and recent work has begun to hard-wire such constraints into learning models at the loss or output level. Here we ask a different question: what would it mean for the representation itself to obey a symplectic conservation law in the sense of Hamiltonian mechanics? We express this symplectic constraint through Legendre duality: the pairing between primal and dual parameters, which becomes the structure that the representation must preserve. We formalize Legendre dynamics as stochastic processes whose trajectories remain on Legendre graphs, so that the evolving primal-dual parameters stay Legendre dual. We show that this class includes linear time-invariant Gaussian process regression and Ornstein-Uhlenbeck dynamics. Geometrically, we prove that the maps that preserve all Legendre graphs are exactly symplectomorphisms of cotangent bundles of the form "cotangent lift of a base diffeomorphism followed by an exact fibre translation". Dynamically, this characterization leads to the design of a Symplectic Reservoir (SR), a reservoir-computing architecture that is a special case of recurrent neural network and whose recurrent core is generated by Hamiltonian systems that are at most linear in the momentum. Our main theorem shows that every SR update has this normal form and therefore transports Legendre graphs to Legendre graphs, preserving Legendre duality at each time step. Overall, SR implements a geometrically constrained, Legendre-preserving representation map, injecting symplectic geometry and Hamiltonian mechanics directly at the representational level.

Aoi Yoshimura, Gouhei Tanaka

Reinforcement learning (RL) policies trained in simulation often suffer from severe performance degradation when deployed in real-world environments due to non-stationary dynamics. While Domain Randomization (DR) and meta-RL have been proposed to address this issue, they typically rely on extensive pretraining, privileged information, or high computational cost, limiting their applicability to real-time and edge systems. In this paper, we propose a lightweight online adaptation framework for RL based on Reservoir Computing. Specifically, we integrate an Echo State Networks (ESNs) as an adaptation module that encodes recent observation histories into a latent context representation, and update its readout weights online using Recursive Least Squares (RLS). This design enables rapid adaptation without backpropagation, pretraining, or access to privileged information. We evaluate the proposed method on CartPole and HalfCheetah tasks with severe and abrupt environment changes, including periodic external disturbances and extreme friction variations. Experimental results demonstrate that the proposed approach significantly outperforms DR and representative adaptive baselines under out-of-distribution dynamics, achieving stable adaptation within a few control steps. Notably, the method successfully handles intra-episode environment changes without resetting the policy. Due to its computational efficiency and stability, the proposed framework provides a practical solution for online adaptation in non-stationary environments and is well suited for real-world robotic control and edge deployment.

Shuhan Zheng, Ziqiang Li, Kantaro Fujiwara et al.

Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of uncovering interaction relations in such systems using observable dynamics is called relational inference. In this study, we propose a Diffusion model for Relational Inference (DiffRI), inspired by a self-supervised method for probabilistic time series imputation. DiffRI learns to infer the probability of the presence of connections between components through conditional diffusion modeling.

Towa Sano, Gouhei Tanaka

Hand gesture recognition (HGR) is a fundamental technology in human computer interaction (HCI).In particular, HGR based on Doppler radar signals is suited for in-vehicle interfaces and robotic systems, necessitating lightweight and computationally efficient recognition techniques. However, conventional deep learning-based methods still suffer from high computational costs. To address this issue, we propose an Echo State Network (ESN) approach for radar-based HGR, using frequency-modulated-continuous-wave (FMCW) radar signals. Raw radar data is first converted into feature maps, such as range-time and Doppler-time maps, which are then fed into one or more recurrent neural network-based reservoirs. The obtained reservoir states are processed by readout classifiers, including ridge regression, support vector machines, and random forests. Comparative experiments demonstrate that our method outperforms existing approaches on an 11-class HGR task using the Soli dataset and surpasses existing deep learning models on a 4-class HGR task using the Dop-NET dataset. The results indicate that parallel processing using multi-reservoir ESNs are effective for recognizing temporal patterns from the multiple different feature maps in the time-space and time-frequency domains. Our ESN approaches achieve high recognition performance with low computational cost in HGR, showing great potential for more advanced HCI technologies, especially in resource-constrained environments.

Daisuke Inoue, Tadayoshi Matsumori, Gouhei Tanaka et al.

Neural networks capable of approximating complex nonlinearities have found extensive application in data-driven control of nonlinear dynamical systems. However, fast online identification and control of unknown dynamics remain central challenges. This paper integrates echo-state networks (ESNs) -- reservoir computing models implemented with recurrent neural networks -- and model predictive path integral (MPPI) control -- sampling-based variants of model predictive control -- to meet these challenges. The proposed reservoir predictive path integral (RPPI) enables fast learning of nonlinear dynamics with ESN and exploits the learned nonlinearities directly in parallelized MPPI control computation without linearization approximations. The framework is further extended to uncertainty-aware RPPI (URPPI), which leverages ESN uncertainty to balance exploration and exploitation: exploratory inputs dominate during early learning, while exploitative inputs prevail as model confidence grows. Experiments on controlling the Duffing oscillator and four-tank systems demonstrate that URPPI improves control performance, reducing control costs by up to 60% compared to traditional quadratic programming-based model predictive control methods.

Gunjan Auti, Hirofumi Daiguji, Gouhei Tanaka

Traditional machine learning approaches in physics rely on global optimization, limiting interpretability and enforcing physical constraints externally. We introduce the Hebbian Physics Network (HPN), a self-organizing computational framework in which learning emerges from local Hebbian updates driven by violations of conservation laws. Grounded in non-equilibrium thermodynamics and inspired by Prigogine/'s theory of dissipative structures, HPNs eliminate the need for global loss functions by encoding physical laws directly into the system/'s local dynamics. Residuals - quantified imbalances in continuity, momentum, or energy - serve as thermodynamic signals that drive weight adaptation through generalized Hebbian plasticity. We demonstrate this approach on incompressible fluid flow and continuum diffusion, where physically consistent structures emerge from random initial conditions without supervision. HPNs reframe computation as a residual-driven thermodynamic process, offering an interpretable, scalable, and physically grounded alternative for modeling complex dynamical systems.

Ziqiang Li, Robert Simon Fong, Kantaro Fujiwara et al.

Reservoir Computing (RC) is a time-efficient computational paradigm derived from Recurrent Neural Networks (RNNs). The Simple Cycle Reservoir (SCR) is an RC model that stands out for its minimalistic design, offering extremely low construction complexity and proven capability of universally approximating time-invariant causal fading memory filters, even in the linear dynamics regime. This paper introduces Multiple Simple Cycle Reservoirs (MSCRs), a multi-reservoir framework that extends Echo State Networks (ESNs) by replacing a single large reservoir with multiple interconnected SCRs. We demonstrate that optimizing MSCR using Particle Swarm Optimization (PSO) outperforms existing multi-reservoir models, achieving competitive predictive performance with a lower-dimensional state space. By modeling interconnections as a weighted Directed Acyclic Graph (DAG), our approach enables flexible, task-specific network topology adaptation. Numerical simulations on three benchmark time-series prediction tasks confirm these advantages over rival algorithms. These findings highlight the potential of MSCR-PSO as a promising framework for optimizing multi-reservoir systems, providing a foundation for further advancements and applications of interconnected SCRs for developing efficient AI devices.

Keigo Nogami, Hiroto Tamura, Gouhei Tanaka

With a growing data privacy concern, federated learning has emerged as a promising framework to train machine learning models without sharing locally distributed data. In federated learning, local model training by multiple clients and model integration by a server are repeated only through model parameter sharing. Most existing federated learning methods assume training deep learning models, which are often computationally demanding. To deal with this issue, we propose federated learning methods with reservoir state analysis to seek computational efficiency and data privacy protection simultaneously. Specifically, our method relies on Mahalanobis Distance of Reservoir States (MD-RS) method targeting time series anomaly detection, which learns a distribution of reservoir states for normal inputs and detects anomalies based on a deviation from the learned distribution. Iterative updating of statistical parameters in the MD-RS enables incremental federated learning (IncFed MD-RS). We evaluate the performance of IncFed MD-RS using benchmark datasets for time series anomaly detection. The results show that IncFed MD-RS outperforms other federated learning methods with deep learning and reservoir computing models particularly when clients' data are relatively short and heterogeneous. We demonstrate that IncFed MD-RS is robust against reduced sample data compared to other methods. We also show that the computational cost of IncFed MD-RS can be reduced by subsampling from the reservoir states without performance degradation. The proposed method is beneficial especially in anomaly detection applications where computational efficiency, algorithm simplicity, and low communication cost are required.

Takumu Fujioka, Gouhei Tanaka

Modern fonts adopt vector-based formats, which ensure scalability without loss of quality. While many deep learning studies on fonts focus on bitmap formats, deep learning for vector fonts remains underexplored. In studies involving deep learning for vector fonts, the choice of font representation has often been made conventionally. However, the font representation format is one of the factors that can influence the computational performance of machine learning models in font-related tasks. Here we show that font representations based on PostScript outlines outperform those based on TrueType outlines in Transformer-based vector font classification. TrueType outlines represent character shapes as sequences of points and their associated flags, whereas PostScript outlines represent them as sequences of commands. In previous research, PostScript outlines have been predominantly used when fonts are treated as part of vector graphics, while TrueType outlines are mainly employed when focusing on fonts alone. Whether to use PostScript or TrueType outlines has been mainly determined by file format specifications and precedent settings in previous studies, rather than performance considerations. To date, few studies have compared which outline format provides better embedding representations. Our findings suggest that information aggregation is crucial in Transformer-based deep learning for vector graphics, as in tokenization in language models and patch division in bitmap-based image recognition models. This insight provides valuable guidance for selecting outline formats in future research on vector graphics.

Shihori Koyama, Daisuke Inoue, Hiroaki Yoshida et al.

Collecting time series data spatially distributed in many locations is often important for analyzing climate change and its impacts on ecosystems. However, comprehensive spatial data collection is not always feasible, requiring us to predict climate variables at some locations. This study focuses on a prediction of climatic elements, specifically near-surface temperature and pressure, at a target location apart from a data observation point. Our approach uses two prediction methods: reservoir computing (RC), known as a machine learning framework with low computational requirements, and vector autoregression models (VAR), recognized as a statistical method for analyzing time series data. Our results show that the accuracy of the predictions degrades with the distance between the observation and target locations. We quantitatively estimate the distance in which effective predictions are possible. We also find that in the context of climate data, a geographical distance is associated with data correlation, and a strong data correlation significantly improves the prediction accuracy with RC. In particular, RC outperforms VAR in predicting highly correlated data within the predictive range. These findings suggest that machine learning-based methods can be used more effectively to predict climatic elements in remote locations by assessing the distance to them from the data observation point in advance. Our study on low-cost and accurate prediction of climate variables has significant value for climate change strategies.

Gouhei Tanaka, Ryosho Nakane

Memristive systems and devices are potentially available for implementing reservoir computing (RC) systems applied to pattern recognition. However, the computational ability of memristive RC systems depends on intertwined factors such as system architectures and physical properties of memristive elements, which complicates identifying the key factor for system performance. Here we develop a simulation platform for RC with memristor device networks, which enables testing different system designs for performance improvement. Numerical simulations show that the memristor-network-based RC systems can yield high computational performance comparable to that of state-of-the-art methods in three time series classification tasks. We demonstrate that the excellent and robust computation under device-to-device variability can be achieved by appropriately setting network structures, nonlinearity of memristors, and pre/post-processing, which increases the potential for reliable computation with unreliable component devices. Our results contribute to an establishment of a design guide for memristive reservoirs toward a realization of energy-efficient machine learning hardware.

Gouhei Tanaka, Tadayoshi Matsumori, Hiroaki Yoshida et al.

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of multiscale dynamics, we propose a reservoir computing (RC) model with diverse timescales by using a recurrent network of heterogeneous leaky integrator (LI) neurons. We evaluate computational performance of the proposed model in two time series prediction tasks related to four chaotic fast-slow dynamical systems. In a one-step-ahead prediction task where input data are provided only from the fast subsystem, we show that the proposed model yields better performance than the standard RC model with identical LI neurons. Our analysis reveals that the timescale required for producing each component of target multiscale dynamics is appropriately and flexibly selected from the reservoir dynamics by model training. In a long-term prediction task, we demonstrate that a closed-loop version of the proposed model can achieve longer-term predictions compared to the counterpart with identical LI neurons depending on the hyperparameter setting.