Online Adaptive Reinforcement Learning with Echo State Networks for Non-Stationary Dynamics

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.

Misophonia Trigger Sound Detection on Synthetic Soundscapes Using a Hybrid Model with a Frozen Pre-Trained CNN and a Time-Series Module

Misophonia is a disorder characterized by a decreased tolerance to specific everyday sounds (trigger sounds) that can evoke intense negative emotional responses such as anger, panic, or anxiety. These reactions can substantially impair daily functioning and quality of life. Assistive technologies that selectively detect trigger sounds could help reduce distress and improve well-being. In this study, we investigate sound event detection (SED) to localize intervals of trigger sounds in continuous environmental audio as a foundational step toward such assistive support. Motivated by the scarcity of real-world misophonia data, we generate synthetic soundscapes tailored to misophonia trigger sound detection using audio synthesis techniques. Then, we perform trigger sound detection tasks using hybrid CNN-based models. The models combine feature extraction using a frozen pre-trained CNN backbone with a trainable time-series module such as gated recurrent units (GRUs), long short-term memories (LSTMs), echo state networks (ESNs), and their bidirectional variants. The detection performance is evaluated using common SED metrics, including Polyphonic Sound Detection Score 1 (PSDS1). On the multi-class trigger SED task, bidirectional temporal modeling consistently improves detection performance, with Bidirectional GRU (BiGRU) achieving the best overall accuracy. Notably, the Bidirectional ESN (BiESN) attains competitive performance while requiring orders of magnitude fewer trainable parameters by optimizing only the readout. We further simulate user personalization via a few-shot "eating sound" detection task with at most five support clips, in which BiGRU and BiESN are compared. In this strict adaptation setting, BiESN shows robust and stable performance, suggesting that lightweight temporal modules are promising for personalized misophonia trigger SED.

Hand Gesture Recognition from Doppler Radar Signals Using Echo State Networks

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.

Symplectic Reservoir Representation of Legendre Dynamics

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.

Reservoir Predictive Path Integral Control for Unknown Nonlinear Dynamics

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.

Structuring Multiple Simple Cycle Reservoirs with Particle Swarm Optimization

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.

Federated Learning with Reservoir State Analysis for Time Series Anomaly Detection

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.

Predicting unobserved climate time series data at distant areas via spatial correlation using reservoir computing

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.

Diffusion model for relational inference

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. Experiments on both simulated and quasi-real datasets show that DiffRI is highly competent compared with other state-of-the-art models in discovering ground truth interactions in an unsupervised manner. Our code will be made public soon.

Backbone-based Dynamic Graph Spatio-Temporal Network for Epidemic Forecasting

Accurate epidemic forecasting is a critical task in controlling disease transmission. Many deep learning-based models focus only on static or dynamic graphs when constructing spatial information, ignoring their relationship. Additionally, these models often rely on recurrent structures, which can lead to error accumulation and computational time consumption. To address the aforementioned problems, we propose a novel model called Backbone-based Dynamic Graph Spatio-Temporal Network (BDGSTN). Intuitively, the continuous and smooth changes in graph structure, make adjacent graph structures share a basic pattern. To capture this property, we use adaptive methods to generate static backbone graphs containing the primary information and temporal models to generate dynamic temporal graphs of epidemic data, fusing them to generate a backbone-based dynamic graph. To overcome potential limitations associated with recurrent structures, we introduce a linear model DLinear to handle temporal dependencies and combine it with dynamic graph convolution for epidemic forecasting. Extensive experiments on two datasets demonstrate that BDGSTN outperforms baseline models and ablation comparison further verifies the effectiveness of model components. Furthermore, we analyze and measure the significance of backbone and temporal graphs by using information metrics from different aspects. Finally, we compare model parameter volume and training time to confirm the superior complexity and efficiency of BDGSTN.