arXiv subjects

Kohei Nakajima

Publications and source records attributed to Kohei Nakajima.

At least 19 recordsLinked to original sources

arXiv2026

Programming Spintronic Reservoir Computing

We present a programming framework for a spintronic reservoir computer (RC) that maps prescribed input-output relationships directly onto the readout layer, bypassing conventional data-driven black-box approaches. Our spintronic RC is based on magnetoresistive random-access memory and exploits magnetization dynamics for computation. We introduce a general metric that quantifies the system's programmability and reveals how the governing equations and system parameters constrain the class of realizable functions. We then construct externally controllable readout layers by exploiting the explicit parameter dependence of the prescribed equations. This metric and construction enable programming explicit functions on the spintronic RC, indicating a potential route to in-memory computing. Our demonstrations include neural-network emulation, bifurcation embedding, and a Newton solver for fifth-order algebraic equations. In addition, we prove the universal approximation property of the spintronic RC in the limit of infinite system size and input duration, and show its consistency with programmability.

cs.ET↗

arXiv2026

One-shot prediction of noise-induced bifurcations with reservoir computing

Dynamical systems can exhibit complex responses when noise is injected. In particular, dynamics can be qualitatively altered by dynamic noise, a phenomenon known as noise-induced bifurcation. Predicting noise-induced bifurcations is a critical challenge in nonlinear physics. Recently, it has been reported that reservoir computing, a machine learning framework, can reconstruct the unseen global structure of a dynamical system, including bifurcations, from limited time series data. However, learning global structures in random dynamical systems has not yet been systematically addressed. In this study, we report that a simple reservoir computing framework can predict the noise-induced bifurcation structure from the time series at a single noise condition. We demonstrate dynamic noise cancellation and the reconstruction of entire noise-induced bifurcation structures, including noise-induced chaos and noise-induced order, in representative dynamical systems. Additionally, we provide a theoretical explanation for noise cancellation and demonstrate noise cancellation of a neuromorphic spintronics device. Our results provide significant insights into understanding and harnessing real-world noisy complex dynamics.

nlin.CD↗

arXiv2026

Memory Uncertainty Relation and Harmonic Memory in Random Recurrent Networks

We present an inequality that bounds the short-term memory capability of dynamical systems from below. It can be interpreted as an uncertainty relation between a measure of short-term memory and that of the size of state fluctuations induced by input signals. The lower bound can be achieved by a readout weight and thus represents a suboptimal memory called harmonic memory. We examine analytically and numerically the inequality in a number of reservoir systems subject to input noise. We illustrate cases in which equality is achieved exactly, equality holds asymptotically, and the inequality is strict. We also study the effect of a state-space regularization to elucidate the inequality in terms of the fluctuation structure of the state-space. We find that a certain strength of input noise induces extra memory under the regularization, and we refer to this phenomenon as noise-induced memory. We observe that the memory uncertainty relation does not hold in general for the regularized memory and harmonic memory. This fact is explained in terms of the mechanism of noise-induced memory.

nlin.AO↗

arXiv2026

Optimal Memory Encoding Through Fluctuation-Response Structure

Physical reservoir computing exploits the intrinsic dynamics of physical systems for information processing, while keeping the internal dynamics fixed and training only linear readouts; yet the role of input encoding remains poorly understood. We show that optimal input encoding is a geometric problem governed by the system's fluctuation-response structure. By measuring steady-state fluctuations and linear response, we derive an analytical criterion for the input direction that maximizes task-specific linear memory under a fixed power constraint, termed Response-based Optimal Memory Encoding (ROME). Backpropagation-based encoder optimization is shown to be equivalent to ROME, revealing a trade-off between task-dependent feature mixing and intrinsic noise. We apply ROME to various reservoir platforms, including spin-wave waveguides and spiking neural networks, demonstrating effective encoder design across physical and neuromorphic reservoirs, even in non-differentiable systems.

cs.NE↗

arXiv2026

Ensemble Reservoir Computing for Physical Systems

Physical computing exploits unconventional physical substrates to overcome limitations such as the high energy consumption inherent in digital computation. However, intrinsic noise and temporal fluctuations (e.g., oscillations) generally deteriorate computational performance. Here, we propose ensemble reservoir computing (ERC), a novel framework that employs ensemble averaging of spatially multiplexed systems to achieve robust information processing despite noise and temporal fluctuations. First, we prove that ensemble averaging in ERC eliminates temporal fluctuations and noise from dynamical states under certain conditions, thereby restoring computational performance to its noise-free level. Next, we show that ERC not only removes the noise and fluctuations but also actively exploits the computational capabilities that conventional reservoir computing (RC) leaves unutilized. This computational enhancement is demonstrated across diverse dynamical systems (e.g., periodic, chaotic, and strange-nonchaotic systems), in which ERC outperforms conventional RC. Finally, using energy-efficient spin-torque oscillators (STOs), we demonstrate that ERC maintains high performance even under realistic conditions, in which noise and temporal fluctuations coexist: STOs with ERC achieved 99\% accuracy on an error detection test, where conventional STO reservoir with linear regression only shows a chance level performance, highlighting ERC's robustness and performance gains for physical systems.

math.DS↗

arXiv2025

Memory Determines Learning Direction: A Theory of Gradient-Based Optimization in State Space Models

State space models (SSMs) have gained attention by showing potential to outperform Transformers. However, previous studies have not sufficiently addressed the mechanisms underlying their high performance owing to a lack of theoretical explanation of SSMs' learning dynamics. In this study, we provide such an explanation and propose an improved training strategy. The memory capacity of SSMs can be evaluated by examining how input time series are stored in their current state. Such an examination reveals a tradeoff between memory accuracy and length, as well as the theoretical equivalence between the structured state space sequence model (S4) and a simplified S4 with diagonal recurrent weights. This theoretical foundation allows us to elucidate the learning dynamics, proving the importance of initial parameters. Our analytical results suggest that successful learning requires the initial memory structure to be the longest possible even if memory accuracy may deteriorate or the gradient lose the teacher information. Experiments on tasks requiring long memory confirmed that extending memory is difficult, emphasizing the importance of initialization. Furthermore, we found that fixing recurrent weights can be more advantageous than adapting them because it achieves comparable or even higher performance with faster convergence. Our results provide a new theoretical foundation for SSMs and potentially offer a novel optimization strategy.

cs.LG↗

arXiv2025

Multifunctional physical reservoir computing in soft tensegrity robots

Recent studies have demonstrated that the dynamics of physical systems can be utilized for the desired information processing under the framework of physical reservoir computing (PRC). Robots with soft bodies are examples of such physical systems, and their nonlinear body-environment dynamics can be used to compute and generate the motor signals necessary for the control of their own behavior. In this simulation study, we extend this approach to control and embed not only one but also multiple behaviors into a type of soft robot called a tensegrity robot. The resulting system, consisting of the robot and the environment, is a multistable dynamical system that converges to different attractors from varying initial conditions. Furthermore, attractor analysis reveals that there exist "untrained attractors" in the state space of the system outside the training data. These untrained attractors reflect the intrinsic properties and structures of the tensegrity robot and its interactions with the environment. The impacts of these recent findings in PRC remain unexplored in embodied AI research. We here illustrate their potential to understand various features of embodied cognition that have not been fully addressed to date.

cs.RO↗

arXiv2025

Harnessing omnipresent oscillator networks as computational resource

Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal framework for harnessing oscillator networks as computational resource. This computing framework is introduced by the ubiquitous model for phase-locking, the Kuramoto model. We force the Kuramoto model by a nonlinear target-system, then after substituting the target-system with a trained feedback-loop it emulates the target-system. Our results are two-fold. Firstly, the trained network inherits performance properties of the Kuramoto model, where all-to-all coupling is performed in linear time with respect to the number of nodes and parameters for synchronization are abundant. The latter implies that the network is generically successful since the system learns via sychronization. Secondly, the learning capabilities of the oscillator network, which describe a type of collective intelligence, can be explained using Kuramoto model's order parameter. In summary, this work provides the foundation for utilizing nature's oscillator networks as a new class of information processing systems.

cs.LG↗

arXiv2025

Haptic Perception via the Dynamics of Flexible Body Inspired by an Ostrich's Neck

In biological systems, both skin sensitivity and body flexibility play crucial roles in haptic perception. Fully soft robots often suffer from structural fragility and delayed sensory processing, limiting their practical functionality. The musculoskeletal system combines the adaptability of soft materials with the durability of rigid-body robots. It also leverages morphological computation, where the morphological structures contribute to information processing, for dynamic and adaptive behaviors. This study focuses on the pecking behaviors of birds, which enables precise haptic perception through the musculoskeletal system of their flexible neck. Physical reservoir computing is applied to flexible structures inspired by an ostrich neck to analyze the relationship between haptic perception and physical characteristics. Experiments with both a physical robot and simulations reveal that, with appropriate viscoelasticity, the flexible structure can discriminate object softness and retain that information through behavior. Drawing on these findings and anatomical insights from the ostrich neck, a haptic perception system is proposed that exhibits both separability and behavioral memory in flexible structures, enabling rapid learning and real-time inference. The results demonstrate that through the dynamics of flexible structures, diverse functions can emerge beyond their original design as manipulators.

cs.RO↗

arXiv2025

Attractor-merging Crises and Intermittency in Reservoir Computing

Reservoir computing can embed attractors into random neural networks (RNNs), generating a ``mirror'' of a target attractor because of its inherent symmetrical constraints. In these RNNs, we report that an attractor-merging crisis accompanied by intermittency emerges simply by adjusting the global parameter. We further reveal its underlying mechanism through a detailed analysis of the phase-space structure and demonstrate that this bifurcation scenario is intrinsic to a general class of RNNs, independent of training data.

nlin.CD↗

arXiv2025

Thermodynamic limit in learning period three

A continuous one-dimensional map with period three includes all periods. This raises the following question: Can we obtain any types of periodic orbits solely by learning three data points? In this paper, we report the answer to be yes. Considering a random neural network in its thermodynamic limit, we first show that almost all learned periods are unstable, and each network has its own characteristic attractors (which can even be untrained ones). The latently acquired dynamics, which are unstable within the trained network, serve as a foundation for the diversity of characteristic attractors and may even lead to the emergence of attractors of all periods after learning. When the neural network interpolation is quadratic, a universal post-learning bifurcation scenario appears, which is consistent with a topological conjugacy between the trained network and the classical logistic map. In addition to universality, we explore specific properties of certain networks, including the singular behavior of the scale of weight at the infinite limit, the finite-size effects, and the symmetry in learning period three.

stat.ML↗

arXiv2025

Backpropagation through Soft Body: Investigating Information Processing in Brain-Body Coupling Systems

Animals achieve sophisticated behavioral control through dynamic coupling of the brain, body, and environment. Accordingly, the co-design approach, in which both the controllers and the physical properties are optimized simultaneously, has been suggested for generating refined agents without designing each component separately. In this study, we aim to reveal how the function of the information processing is distributed between brains and bodies while applying the co-design approach. Using a framework called ``backpropagation through soft body," we developed agents to perform specified tasks and analyzed their mechanisms. The tasks included classification and corresponding behavioral association, nonlinear dynamical system emulation, and autonomous behavioral generation. In each case, our analyses revealed reciprocal relationships between the brains and bodies. In addition, we show that optimized brain functionalities can be embedded into bodies using physical reservoir computing techniques. Our results pave the way for efficient designs of brain--body coupling systems.

cs.NE↗

arXiv2024

Reservoir Computing Generalized

A physical neural network (PNN) has both the strong potential to solve machine learning tasks and intrinsic physical properties, such as high-speed computation and energy efficiency. Reservoir computing (RC) is an excellent framework for implementing an information processing system with a dynamical system by attaching a trained readout, thus accelerating the wide use of unconventional materials for a PNN. However, RC requires the dynamics to reproducibly respond to input sequence, which limits the type of substance available for building information processors. Here we propose a novel framework called generalized reservoir computing (GRC) by turning this requirement on its head, making conventional RC a special case. Using substances that do not respond the same to identical inputs (e.g., a real spin-torque oscillator), we propose mechanisms aimed at obtaining a reliable output and show that processed inputs in the unconventional substance are retrievable. Finally, we demonstrate that, based on our framework, spatiotemporal chaos, which is thought to be unusable as a computational resource, can be used to emulate complex nonlinear dynamics, including large scale spatiotemporal chaos. Overall, our framework removes the limitation to building an information processing device and opens a path to constructing a computational system using a wider variety of physical dynamics.

nlin.CD↗

arXiv2024

A Jellyfish Cyborg: Exploiting Natural Embodied Intelligence as Soft Robots

Jellyfish cyborgs present a promising avenue for soft robotic systems, leveraging the natural energy-efficiency and adaptability of biological systems. Here we demonstrate a novel approach to predicting and controlling jellyfish locomotion by harnessing the natural embodied intelligence of these animals. We developed an integrated muscle electrostimulation and 3D motion capture system to quantify both spontaneous and stimulus-induced behaviors in Aurelia coerulea jellyfish. Using Reservoir Computing, a machine learning framework, we successfully predicted future movements based on the current body shape and natural dynamic patterns of the jellyfish. Our key findings include the first investigation of self-organized criticality in jellyfish swimming motions and the identification of optimal stimulus periods (1.5 and 2.0 seconds) for eliciting coherent and predictable swimming behaviors. These results suggest that the jellyfish body motion, combined with targeted electrostimulation, can serve as a computational resource for predictive control. Our findings pave the way for developing jellyfish cyborgs capable of autonomous navigation and environmental exploration, with potential applications in ocean monitoring and pollution management.

cs.RO↗

arXiv2024

Coherence influx is indispensable for quantum reservoir computing

Echo state property (ESP) is a fundamental property that allows an input-driven dynamical system to perform information processing tasks. Recently, extensions of ESP to potentially nonstationary systems and subsystems, that is, nonstationary ESP and subset/subspace ESP, have been proposed. In this paper, we theoretically and numerically analyze the sufficient and necessary conditions for a quantum system to satisfy nonstationary ESP and subset/subspace nonstationary ESP. Based on extensive usage of the Pauli transfer matrix (PTM) form, we find that (1) the interaction with a quantum-coherent environment, termed $\textit{coherence influx}$, is indispensable in realizing nonstationary ESP, and (2) the spectral radius of PTM can characterize the fading memory property of quantum reservoir computing (QRC). Our numerical experiment, involving a system with a Hamiltonian that entails a spin-glass/many-body localization phase, reveals that the spectral radius of PTM can describe the dynamical phase transition intrinsic to such a system. To comprehensively understand the mechanisms under ESP of QRC, we propose a simplified model, multiplicative reservoir computing (mRC), which is a reservoir computing (RC) system with a one-dimensional multiplicative input. Theoretically and numerically, we show that the parameters corresponding to the spectral radius and coherence influx in mRC directly correlates with its linear memory capacity (MC). Our findings about QRC and mRC will provide a theoretical aspect of PTM and the input multiplicativity of QRC. The results will lead to a better understanding of QRC and information processing in open quantum systems.

quant-ph↗

arXiv2024

Gradient-based optimization of spintronic devices

The optimization of physical parameters serves various purposes, such as system identification and efficiency in developing devices. Spin-torque oscillators have been applied to neuromorphic computing experimentally and theoretically, but the optimization of their physical parameters has usually been done by grid search. In this paper, we propose a scheme to optimize the parameters of the dynamics of macrospin-type spin-torque oscillators using the gradient descent method with automatic differentiation. First, we prepared numerically created dynamics as teacher data and successfully tuned the parameters to reproduce the dynamics. This can be applied to obtain the correspondence between the simulation and experiment of the spin-torque oscillators. Next, we successfully solved the image recognition task with high accuracy by connecting the coupled system of spin-torque oscillators to the input and output layers and training all of them through gradient descent. This approach allowed us to estimate how to control the experimental setup and design the physical systems so that the task could be solved with a high accuracy using spin-torque oscillators.

cond-mat.mes-hall↗

arXiv2024

Training Spiking Neural Networks via Augmented Direct Feedback Alignment

Spiking neural networks (SNNs), the models inspired by the mechanisms of real neurons in the brain, transmit and represent information by employing discrete action potentials or spikes. The sparse, asynchronous properties of information processing make SNNs highly energy efficient, leading to SNNs being promising solutions for implementing neural networks in neuromorphic devices. However, the nondifferentiable nature of SNN neurons makes it a challenge to train them. The current training methods of SNNs that are based on error backpropagation (BP) and precisely designing surrogate gradient are difficult to implement and biologically implausible, hindering the implementation of SNNs on neuromorphic devices. Thus, it is important to train SNNs with a method that is both physically implementatable and biologically plausible. In this paper, we propose using augmented direct feedback alignment (aDFA), a gradient-free approach based on random projection, to train SNNs. This method requires only partial information of the forward process during training, so it is easy to implement and biologically plausible. We systematically demonstrate the feasibility of the proposed aDFA-SNNs scheme, propose its effective working range, and analyze its well-performing settings by employing genetic algorithm. We also analyze the impact of crucial features of SNNs on the scheme, thus demonstrating its superiority and stability over BP and conventional direct feedback alignment. Our scheme can achieve competitive performance without accurate prior knowledge about the utilized system, thus providing a valuable reference for physically training SNNs.

cs.NE↗

arXiv2024

How noise affects memory in linear recurrent networks

The effects of noise on memory in a linear recurrent network are theoretically investigated. Memory is characterized by its ability to store previous inputs in its instantaneous state of network, which receives a correlated or uncorrelated noise. Two major properties are revealed: First, the memory reduced by noise is uniquely determined by the noise's power spectral density (PSD). Second, the memory will not decrease regardless of noise intensity if the PSD is in a certain class of distribution (including power law). The results are verified using the human brain signals, showing good agreement.

cs.NE↗