arXiv subjects

Kohei Nakajima

Publications and source records attributed to Kohei Nakajima.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2024

Informational Embodiment: Computational role of information structure in codes and robots

The body morphology plays an important role in the way information is perceived and processed by an agent. We address an information theory (IT) account on how the precision of sensors, the accuracy of motors, their placement, the body geometry, shape the information structure in robots and computational codes. As an original idea, we envision the robot's body as a physical communication channel through which information is conveyed, in and out, despite intrinsic noise and material limitations. Following this, entropy, a measure of information and uncertainty, can be used to maximize the efficiency of robot design and of algorithmic codes per se. This is known as the principle of Entropy Maximization (PEM) introduced in biology by Barlow in 1969. The Shannon's source coding theorem provides then a framework to compare different types of bodies in terms of sensorimotor information. In line with PME, we introduce a special class of efficient codes used in IT that reached the Shannon limits in terms of information capacity for error correction and robustness against noise, and parsimony. These efficient codes, which exploit insightfully quantization and randomness, permit to deal with uncertainty, redundancy and compacity. These features can be used for perception and control in intelligent systems. In various examples and closing discussions, we reflect on the broader implications of our framework that we called Informational Embodiment to motor theory and bio-inspired robotics, touching upon concepts like motor synergies, reservoir computing, and morphological computation. These insights can contribute to a deeper understanding of how information theory intersects with the embodiment of intelligence in both natural and artificial systems.

cs.RO↗

arXiv2024

Self-Organized Criticality Explains Readiness Potential

Readiness potential is a widely observed brain activity in several species including crayfish before the spontaneous behavioral initiation. However, it is poorly understood how this spontaneous activity is generated. The hypothesis that some specific, dedicated site is responsible for the spontaneity has been questioned. Here, by using intracellular recording and staining of the brain neurons in crayfish and modeling using the sandpile, which is the original model of self-organized criticality (SOC), we show that readiness potential can emerge everywhere in the brain because it is a SOC system. Despite the diversity in neurons and their morphology, brain neurons showed signatures of criticality and readiness potential. We find that the previously known readiness potential in a neuron is a consequence of the critical behavior of the entire network. Indeed, seemingly unrelated membrane potential activity in neurons in different animals can shape readiness potential when its time series are averaged after their alignment with respect to the spontaneous behavioral initiation. We show that the sandpile model not made for the potential, can form the premovement buildup activity similar to readiness potential. Scaling properties of the synaptic avalanches are in line with those of vertebrate species; thus, not only is the critical brain hypothesis supported in crayfish, but our findings might also provide a unified view of the basis of spontaneity in animal behavior.

q-bio.NC↗

arXiv2024

Extending echo state property for quantum reservoir computing

The echo state property (ESP) represents a fundamental concept in the reservoir computing (RC) framework that ensures output-only training of reservoir networks by being agnostic to the initial states and far past inputs. However, the traditional definition of ESP does not describe possible non-stationary systems in which statistical properties evolve. To address this issue, we introduce two new categories of ESP: $\textit{non-stationary ESP}$, designed for potentially non-stationary systems, and $\textit{subspace/subset ESP}$, designed for systems whose subsystems have ESP. Following the definitions, we numerically demonstrate the correspondence between non-stationary ESP in the quantum reservoir computer (QRC) framework with typical Hamiltonian dynamics and input encoding methods using non-linear autoregressive moving-average (NARMA) tasks. We also confirm the correspondence by computing linear/non-linear memory capacities that quantify input-dependent components within reservoir states. Our study presents a new understanding of the practical design of QRC and other possibly non-stationary RC systems in which non-stationary systems and subsystems are exploited.

quant-ph↗

arXiv2024

Designing Chaotic Attractors: A Semi-supervised Approach

Chaotic dynamics are ubiquitous in nature and useful in engineering, but their geometric design can be challenging. Here, we propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as a template, called a skeleton. We exploit a bifurcation of the reservoir to intentionally induce unsuccessful training of the skeleton, revealing inherent chaos. The emergence of this untrained attractor, resulting from the interaction between the skeleton and the reservoir's intrinsic dynamics, offers a novel semi-supervised framework for designing chaos.

cs.NE↗

arXiv2024

Exploiting Chaotic Dynamics as Deep Neural Networks

Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However, strategies to effectively exploit chaotic dynamics for information processing have largely remained elusive. In this study, we reveal that the essence of chaos can be found in various state-of-the-art deep neural networks. Drawing inspiration from this revelation, we propose a novel method that directly leverages chaotic dynamics for deep learning architectures. Our approach is systematically evaluated across distinct chaotic systems. In all instances, our framework presents superior results to conventional deep neural networks in terms of accuracy, convergence speed, and efficiency. Furthermore, we found an active role of transient chaos formation in our scheme. Collectively, this study offers a new path for the integration of chaos, which has long been overlooked in information processing, and provides insights into the prospective fusion of chaotic dynamics within the domains of machine learning and neuromorphic computation.

cs.NE↗

arXiv2023

Virtual reservoir acceleration for CPU and GPU: Case study for coupled spin-torque oscillator reservoir

We provide high-speed implementations for simulating reservoirs described by $N$-coupled spin-torque oscillators. Here $N$ also corresponds to the number of reservoir nodes. We benchmark a variety of implementations based on CPU and GPU. Our new methods are at least 2.6 times quicker than the baseline for $N$ in range $1$ to $10^4$. More specifically, over all implementations the best factor is 78.9 for $N=1$ which decreases to 2.6 for $N=10^3$ and finally increases to 23.8 for $N=10^4$. GPU outperforms CPU significantly at $N=2500$. Our results show that GPU implementations should be tested for reservoir simulations. The implementations considered here can be used for any reservoir with evolution that can be approximated using an explicit method.

cs.DC↗

arXiv2023

Input-driven chaotic dynamics in vortex spin-torque oscillator

A new research topic in spintronics relating to the operation principles of brain-inspired computing is input-driven magnetization dynamics in nanomagnet. In this paper, the magnetization dynamics in a vortex spin-torque oscillator (STO) driven by a series of random magnetic field are studied through a numerical simulation of the Thiele equation. It is found that input-driven synchronization occurs in the weak perturbation limit, as found recently. As well, chaotic behavior is newly found to occur in the vortex core dynamics for a wide range of parameters, where synchronized behavior is disrupted by an intermittency. Ordered and chaotic dynamical phases are examined by evaluating the Lyapunov exponent. The relation between the dynamical phase and the computational capability of physical reservoir computing is also studied.

cond-mat.mes-hall↗

arXiv2023

Embedding bifurcations into pneumatic artificial muscle

Harnessing complex body dynamics has been a long-standing challenge in robotics. Soft body dynamics is a typical example of high complexity in interacting with the environment. An increasing number of studies have reported that these dynamics can be used as a computational resource. This includes the McKibben pneumatic artificial muscle, which is a typical soft actuator. This study demonstrated that various dynamics, including periodic and chaotic dynamics, could be embedded into the pneumatic artificial muscle, with the entire bifurcation structure using the framework of physical reservoir computing. These results suggest that dynamics that are not presented in training data could be embedded by using this capability of bifurcation embeddment. This implies that it is possible to embed various qualitatively different patterns into pneumatic artificial muscle by learning specific patterns, without the need to design and learn all patterns required for the purpose. Thus, this study sheds new light on a novel pathway to simplify the robotic devices and training of the control by reducing the external pattern generators and the amount and types of training data for the control.

cs.RO↗

arXiv2023

Computational capability for physical reservoir computing using a spin-torque oscillator with two free layers

A numerical analysis on the computational capability of physical reservoir computing utilizing a spin-torque oscillator with two free layers is reported. Conventional spintronics devices usually consist of two ferromagnets, where the direction of magnetization in one layer, called the free layer, can move while that of the other, the reference layer, is fixed. Recently, however, devices with two free layers, where the reference layer is replaced by another free layer, have been developed for various practical applications. Adding another free layer drastically changes the dynamical response of the device through the couplings via the spin-transfer effect and the dipole magnetic field. A numerical simulation of the Landau-Lifshitz-Gilbert equation and a statistical analyses of the Lyapunov exponent and the synchronization index reveal the appearance of an amplitude-modulated oscillation and chaos in the oscillators with two free layers. Such complex dynamics qualitatively change the computational capability of physical reservoir computing because the computational resource is dynamics of the physical system. An evaluation of the short-term memory capacity clarifies that oscillators with two free layers have a larger capacity than those of conventional oscillators. An enhancement in capacity near the edge of echo state property, i.e., the boundary between zero and finite synchronization index, is also found.

cond-mat.mes-hall↗

arXiv2022

Quantum-Classical Hybrid Information Processing via a Single Quantum System

Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task, which limits their flexibility in near-term applications. We propose a quantum reservoir processor to harness quantum dynamics in computational tasks requiring both classical and quantum inputs. This analog processor comprises a network of quantum dots in which quantum data is incident to the network and classical data is encoded via a coherent field exciting the network. We perform a multitasking application of quantum tomography and nonlinear equalization of classical channels. Interestingly, the tomography can be performed in a closed-loop manner via the feedback control of classical data. Therefore, if the classical input comes from a dynamical system, embedding this system in a closed loop enables hybrid processing even if access to the external classical input is interrupted. Finally, we demonstrate preparing quantum depolarizing channels as a novel quantum machine learning technique for quantum data processing.

quant-ph↗

arXiv2022

Quantum Noise-Induced Reservoir Computing

Quantum computing has been moving from a theoretical phase to practical one, presenting daunting challenges in implementing physical qubits, which are subjected to noises from the surrounding environment. These quantum noises are ubiquitous in quantum devices and generate adverse effects in the quantum computational model, leading to extensive research on their correction and mitigation techniques. But do these quantum noises always provide disadvantages? We tackle this issue by proposing a framework called quantum noise-induced reservoir computing and show that some abstract quantum noise models can induce useful information processing capabilities for temporal input data. We demonstrate this ability in several typical benchmarks and investigate the information processing capacity to clarify the framework's processing mechanism and memory profile. We verified our perspective by implementing the framework in a number of IBM quantum processors and obtained similar characteristic memory profiles with model analyses. As a surprising result, information processing capacity increased with quantum devices' higher noise levels and error rates. Our study opens up a novel path for diverting useful information from quantum computer noises into a more sophisticated information processor.

quant-ph↗

arXiv2022

Composite FORCE learning of chaotic echo state networks for time-series prediction

Echo state network (ESN), a kind of recurrent neural networks, consists of a fixed reservoir in which neurons are connected randomly and recursively and obtains the desired output only by training output connection weights. First-order reduced and controlled error (FORCE) learning is an online supervised training approach that can change the chaotic activity of ESNs into specified activity patterns. This paper proposes a composite FORCE learning method based on recursive least squares to train ESNs whose initial activity is spontaneously chaotic, where a composite learning technique featured by dynamic regressor extension and memory data exploitation is applied to enhance parameter convergence. The proposed method is applied to a benchmark problem about predicting chaotic time series generated by the Mackey-Glass system, and numerical results have shown that it significantly improves learning and prediction performances compared with existing methods.

cs.LG↗

arXiv2022

Physical Deep Learning with Biologically Plausible Training Method

The ever-growing demand for further advances in artificial intelligence motivated research on unconventional computation based on analog physical devices. While such computation devices mimic brain-inspired analog information processing, learning procedures still relies on methods optimized for digital processing such as backpropagation. Here, we present physical deep learning by extending a biologically plausible training algorithm called direct feedback alignment. As the proposed method is based on random projection with arbitrary nonlinear activation, we can train a physical neural network without knowledge about the physical system. In addition, we can emulate and accelerate the computation for this training on a simple and scalable physical system. We demonstrate the proof-of-concept using a hierarchically connected optoelectronic recurrent neural network called deep reservoir computer. By constructing an FPGA-assisted optoelectronic benchtop, we confirmed the potential for accelerated computation with competitive performance on benchmarks. Our results provide practical solutions for the training and acceleration of neuromorphic computation.

cs.NE↗

arXiv2021

Learning Temporal Quantum Tomography

Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which requires a vast number of resources. Furthermore, the tomography for a quantum device with temporal processing, which is fundamentally different from the standard tomography, has not been formulated. We develop a practical and approximate tomography method using a recurrent machine learning framework for this intriguing situation. The method is based on repeated quantum interactions between a system called quantum reservoir with a stream of quantum states. Measurement data from the reservoir are connected to a linear readout to train a recurrent relation between quantum channels applied to the input stream. We demonstrate our algorithms for quantum learning tasks followed by the proposal of a quantum short-term memory capacity to evaluate the temporal processing ability of near-term quantum devices.

quant-ph↗

arXiv2021

Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces

Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms to be performed on near-term intermediate-scale quantum computers. The crucial idea is using the quantum Hilbert space as a quantum-enhanced feature space in machine learning models. While the quantum feature map has demonstrated its capability when combined with linear classification models in some specific applications, its expressive power from the theoretical perspective remains unknown. We prove that the machine learning models induced from the quantum-enhanced feature space are universal approximators of continuous functions under typical quantum feature maps. We also study the capability of quantum feature maps in the classification of disjoint regions. Our work enables an important theoretical analysis to ensure that machine learning algorithms based on quantum feature maps can handle a broad class of machine learning tasks. In light of this, one can design a quantum machine learning model with more powerful expressivity.

quant-ph↗

arXiv2021

Transient Chaos in BERT

Language is an outcome of our complex and dynamic human-interactions and the technique of natural language processing (NLP) is hence built on human linguistic activities. Bidirectional Encoder Representations from Transformers (BERT) has recently gained its popularity by establishing the state-of-the-art scores in several NLP benchmarks. A Lite BERT (ALBERT) is literally characterized as a lightweight version of BERT, in which the number of BERT parameters is reduced by repeatedly applying the same neural network called Transformer's encoder layer. By pre-training the parameters with a massive amount of natural language data, ALBERT can convert input sentences into versatile high-dimensional vectors potentially capable of solving multiple NLP tasks. In that sense, ALBERT can be regarded as a well-designed high-dimensional dynamical system whose operator is the Transformer's encoder, and essential structures of human language are thus expected to be encapsulated in its dynamics. In this study, we investigated the embedded properties of ALBERT to reveal how NLP tasks are effectively solved by exploiting its dynamics. We thereby aimed to explore the nature of human language from the dynamical expressions of the NLP model. Our short-term analysis clarified that the pre-trained model stably yields trajectories with higher dimensionality, which would enhance the expressive capacity required for NLP tasks. Also, our long-term analysis revealed that ALBERT intrinsically shows transient chaos, a typical nonlinear phenomenon showing chaotic dynamics only in its transient, and the pre-trained ALBERT model tends to produce the chaotic trajectory for a significantly longer time period compared to a randomly-initialized one. Our results imply that local chaoticity would contribute to improving NLP performance, uncovering a novel aspect in the role of chaotic dynamics in human language behaviors.

cs.CL↗

arXiv2021

A Unifying Framework for Information Processing in Stochastically Driven Dynamical Systems

A dynamical system can be regarded as an information processing apparatus that encodes input streams from the external environment to its state and processes them through state transitions. The information processing capacity (IPC) is an excellent tool that comprehensively evaluates these processed inputs, providing details of unknown information processing in black box systems; however, this measure can be applied to only time-invariant systems. This paper extends the applicable range to time-variant systems and further reveals that the IPC is equivalent to coefficients of polynomial chaos (PC) expansion in more general dynamical systems. To achieve this objective, we tackle three issues. First, we establish a connection between the IPC for time-invariant systems and PC expansion, which is a type of polynomial expansion using orthogonal functions of input history as bases. We prove that the IPC corresponds to the squared norm of the coefficient vector of the basis in the PC expansion. Second, we show that an input following an arbitrary distribution can be used for the IPC, removing previous restrictions to specific input distributions. Third, we extend the conventional orthogonal bases to functions of both time and input history and propose the IPC for time-variant systems. To show the significance of our approach, we demonstrate that our measure can reveal information representations in not only machine learning networks but also a real, cultured neural network. Our generalized measure paves the way for unveiling the information processing capabilities of a wide variety of physical dynamics which has been left behind in nature.

cs.LG↗