Physical computing systems provide a promising route toward hardware-native machine learning, but their computational capabilities remain difficult to characterize in a principled, task-independent, and data-efficient way. We extend the Information Processing Capacity (IPC) framework to stationary physical computing systems and establish several fundamental results: individual capacities are bounded between zero and one, their sum over a complete basis is bounded by the number of readouts, and noise strictly reduces this bound. We address the finite-sample estimation of IPC and derive the asymptotic form of the systematic positive bias affecting naive estimators. Building on these results, we introduce data-efficient estimation methods based on Richardson extrapolation and Sobol quasi-random sampling. We validate the framework experimentally using a photonic computing system based on picosecond laser pulses propagating through a nonlinear optical fibre. By varying the laser power and fibre length, we observe systematic shifts of the IPC distribution toward higher-order nonlinear capacities induced by the Kerr effect. Finally, we demonstrate that the total IPC strongly correlates with performance on benchmark machine-learning tasks and provides a reliable estimate of the effective dimensionality of the system. These results establish IPC as a practical bridge between the intrinsic dynamics of physical computing systems and their machine-learning performance.

Understanding Neural networks ingeneral, and howtotrain Recurrent Neural Networks (RNNs) in particular,remains acentral question in modern machine learning.

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep connection with kernel methods. Our contributions are threefold: a) We rigorously establish the recurrent kernel limit of Reservoir Computing and prove its convergence.

Developmental Graph Cellular Automata (DGCA) are a novel model for morphogenesis, capable of growing directed graphs from single-node seeds. In this paper, we show that DGCAs can be trained to grow reservoirs. Reservoirs are grown with two types of targets: task-driven (using the NARMA family of tasks) and task-independent (using reservoir metrics). Results show that DGCAs are able to grow into a variety of specialized, life-like structures capable of effectively solving benchmark tasks, statistically outperforming `typical' reservoirs on the same task. Overall, these lay the foundation for the development of DGCA systems that produce plastic reservoirs and for modeling functional, adaptive morphogenesis.

We present a novel approach to EEG decoding for non-invasive brain-machine interfaces (BMIs), with a focus on motor-behavior classification. While conventional con-volutional architectures such as EEGNet and DeepConvNet are effective in capturing local spatial patterns, they are markedly less suited for modeling long-range temporal dependencies and nonlinear dynamics [1, 2]. To address this limitation, we integrate an Echo State Network (ESN), a prominent paradigm in reservoir computing into the decoding pipeline [3, 4, 5]. ESNs construct a high-dimensional, sparsely connected recurrent reservoir that excels at tracking temporal dynamics, thereby complementing the spatial representational power of CNNs. Evaluated on a skateboard-trick EEG dataset preprocessed via the PREP pipeline and implemented in MNE-Python, our ESNNet achieves 83.2% within-subject and 51.3% LOSO accuracies, surpassing widely used CNN-based baselines [6, 7].

Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 8166 Messina, Italy Complex and even chaotic dynamics, though prevalent in many natural and engineered systems, has been largely avoided in the design of electromechanical systems due to concerns about wear and controlability. Here, we demonstrate that complex dynamics might be particularly advantageous in soft robotics, offering new functionalities beyond motion not easily achievable with traditional actuation methods. We designed and realized resilient magnetic soft actuators capable of operating in a tunable dynamic regime for tens of thousands cycles without fatigue. We experimentally demonstrated the application of these actuators for true random number generation and stochastic computing. These findings show that exploring the complex dynamics in soft robotics would extend the application scenarios in soft computing, human-robot interaction and collaborative robots as we demonstrate with biomimetic blinking and randomized voice modulation. A large number of mechanical systems, including simple ones such as the double pendulum, exhibit dynamics characterized by deterministic periodic and chaotic responses depending on the excitation frequency f and amplitude A of the applied force [1]. Mechanical systems with a tendency to chaotisation demonstrate multiple resonances and various transitions to chaos [2]. Today, the concept of complexity and, especially, deterministic chaos that refers to systems without stochastic fluctuations jet losing stability of phase space trajectories is explored for a variety of directions [3] even including biological systems [4] or optics [5]. In particular, chaos is a fundamental aspect of electromechanical systems and is broadly explored in motion planning for mobile rigid robots, fluid mixing, and improving energy harvesting, as well as in mechanisms used in washing machines, dishwashers, and air conditioners [6]. Although the analysis of traditional robotics and mechanisms has revealed inherent chaotic dynamics [7], chaos can also be intentionally generated through nonlinear feedback [6] to achieve specific functionalities. In contrast to rigid mechanisms, soft actuators can facilitate transition into complex dynamics without the need for dedicated feedback algorithms. Mechanically soft actuators do not possess any rigid components in their embodiment rendering them ideally suited to explore complex and even chaotic dynamics which is typically observed at higher frequencies (Supplementary Tables 1 and 2). The inherent nonlinear oscillations emerging in soft actuators for specific parameter values [8, 9] can be applied for secure, biomimetic, and soft computing applications.

In this study, we design a reservoir computing (RC) network by exploiting short- and long-term memory dynamics in Au/Ti/MoS$_2$/Au memristive devices. The temporal dynamics is engineered by controlling the thickness of the Chemical Vapor Deposited (CVD) MoS$_2$ films. Devices with a monolayer (1L)-MoS$_2$ film exhibit volatile (short-term memory) switching dynamics. We also report non-volatile resistance switching with excellent uniformity and analog behavior in conductance tuning for the multilayer (ML) MoS$_2$ memristive devices. We correlate this performance with trap-assisted space-charge limited conduction (SCLC) mechanism, leading to a bulk-limited resistance switching behavior. Four-bit reservoir states are generated using volatile memristors. The readout layer is implemented with an array of nonvolatile synapses. This small RC network achieves 89.56\% precision in a spoken-digit recognition task and is also used to analyze a nonlinear time series equation.

Forecasting nonlinear time series with multi-scale temporal structures remains a central challenge in complex systems modeling. We present a novel reservoir computing framework that combines delay embedding with random Fourier feature (RFF) mappings to capture such dynamics. Two formulations are investigated: a single-scale RFF reservoir, which employs a fixed kernel bandwidth, and a multi-scale RFF reservoir, which integrates multiple bandwidths to represent both fast and slow temporal dependencies. The framework is applied to a diverse set of canonical systems: neuronal models such as the Rulkov map, Izhikevich model, Hindmarsh-Rose model, and Morris-Lecar model, which exhibit spiking, bursting, and chaotic behaviors arising from fast-slow interactions; and ecological models including the predator-prey dynamics and Ricker map with seasonal forcing, which display multi-scale oscillations and intermittency. Across all cases, the multi-scale RFF reservoir consistently outperforms its single-scale counterpart, achieving lower normalized root mean square error (NRMSE) and more robust long-horizon predictions. These results highlight the effectiveness of explicitly incorporating multi-scale feature mappings into reservoir computing architectures for modeling complex dynamical systems with intrinsic fast-slow interactions.