Harnessing omnipresent oscillator networks as computational resource

Nature is pervaded with oscillatory behavior. 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 reservoir 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. Secondly, the learning capabilities of the oscillator network can be explained using Kuramoto model's order parameter. This work provides the foundation for utilizing nature's oscillator networks as a new class of information processing systems.

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.

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.

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.

A Jellyfish Cyborg: Exploiting Natural Embodied Intelligence as Soft Robots

In the advanced field of bio-inspired robotics, the emergence of cyborgs represents the successful integration of engineering and biological systems. Building on previous research that showed how electrical stimuli could initiate and speed up a jellyfish's movement, this study presents a groundbreaking approach that explores how the natural embodied intelligence of the animal can be harnessed to address pivotal challenges such as spontaneous exploration, navigation in various environments, control of whole-body motion, and real-time predictions of behavior. We have developed a comprehensive data acquisition system and a unique setup for stimulating jellyfish, allowing for a detailed study of their movements. Through careful analysis of both spontaneous behaviors and behaviors induced by targeted stimulation, we have identified subtle differences between natural and induced motion patterns. By using a machine learning method called physical reservoir computing, we have successfully shown that future behaviors can be accurately predicted by directly measuring the jellyfish's body shape when the stimuli align with the animal's natural dynamics. Our findings also reveal significant advancements in motion control and real-time prediction capabilities of jellyfish cyborgs. In summary, this research provides a comprehensive roadmap for optimizing the capabilities of jellyfish cyborgs, with potential implications in marine reconnaissance and sustainable ecological interventions.

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.

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? We consider learning period three with random neural networks and report the universal property associated with it. We first show that the trained networks have a thermodynamic limit that depends on the choice of target data and network settings. Our analysis reveals that almost all learned periods are unstable and each network has its characteristic attractors (which can even be untrained ones). Here, we propose the concept of characteristic bifurcation expressing embeddable attractors intrinsic to the network, in which the target data points and the scale of the network weights function as bifurcation parameters. In conclusion, learning period three generates various attractors through characteristic bifurcation due to the stability change in latently existing numerous unstable periods of the system.

Hierarchy of the echo state property in 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.

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.

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.