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Physical reservoir computing -- An introductory perspective

Kohei Nakajima

arXiv:2005.00992v1nlin.AOcs.LGphysics.app-phquant-ph

TL;DR

Physical reservoir computing addresses how physical dynamics can serve as computational resources, a question relevant to decentralized edge processing. The paper introduces the framework through motivations and examples, including soft robotics, and concludes that successful reservoirs require reproducible input–output behavior while physical substrates can add properties beyond abstract mathematical descriptions.

Abstract

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Understanding the fundamental relationships between physics and its information-processing capability has been an active research topic for many years. Physical reservoir computing is a recently introduced framework that allows one to exploit the complex dynamics of physical systems as information-processing devices. This framework is particularly suited for edge computing devices, in which information processing is incorporated at the edge (e.g., into sensors) in a decentralized manner to reduce the adaptation delay caused by data transmission overhead. This paper aims to illustrate the potentials of the framework using examples from soft robotics and to provide a concise overview focusing on the basic motivations for introducing it, which stem from a number of fields, including machine learning, nonlinear dynamical systems, biological science, materials science, and physics.

I. INTRODUCTION

Reservoir computing simplifies recurrent-network training by tuning mainly a readout, while retaining expressive power and enabling multitasking. Physical reservoir computing extends this framework by using physical dynamics as the reservoir.

RC framework

  • RC trains mainly the readout of a nonlinear reservoir rather than tuning all recurrent-network weights.With linear static readout weights, training can use linear or ridge regression and batch learning.Source: §I · p. 1

Advantages

  • Training fewer parameters makes RC learning faster, simpler, and more stable than conventional full-network optimization.The paper contrasts readout-focused training with the time and instability associated with tuning all weights using BPTT.Source: §I · p. 1

Expressive power

  • RC’s simple learning procedure does not imply weaker expressive power than conventional machine-learning techniques.The ESN is described as having a universal approximation property, while comparative studies report merits and demerits across approaches.Source: §I · p. 2

Advantages

  • RC can safely support multitasking in principle because separately learned tasks do not interfere during the learning procedures.The example considers learning tasks T_A and T_B from the same input with separate outputs.Source: §I · p. 2

Physical reservoir computing

  • PRC exploits physical dynamics as a reservoir, extending RC’s reservoir choice beyond simulated recurrent-neural-network dynamics.The framework is presented as relevant to machine learning, dynamical systems, physics, materials science, and biological science.Source: §I · pp. 1–2

II. PREREQUISITE FOR A SUCCESSFUL RESERVOIR

A successful reservoir must reproducibly map identical input sequences to identical responses, but this requirement is difficult for physical dynamical systems. Under the echo-state property, reservoir states depend on input history, allowing a trained readout to approximate temporal tasks.

Prerequisite

  • A successful reservoir must produce the same response whenever the same input sequence is injected.Without reproducibility, the device responds differently on each use and becomes operationally troublesome and unreliable.Source: §II · p. 2
  • Physical reservoirs make reproducibility difficult because dynamical-system behavior generally depends on initial conditions that are hard to infer or control.Precisely selecting the initial condition and controlling input timing can restore repeatability, but these constraints restrict usability.Source: §II · pp. 2–3

Echo-state property

  • When the reservoir fulfills the ESP, its state is determined by the history of prior inputs through an intrinsic input echo function.The reservoir dynamics are written as x(t + 1) = f(x(t), u(t)), while the state is used by a readout to approximate the target output.Source: §II · p. 3

Evaluation

  • Reservoir information-processing capability can be evaluated through properties of the input echo function, including memory capacity.Memory capacity measures how well a reservoir can output previous input sequences.Source: §II · p. 3

Scope

  • Although RC outsources learning to the readout, the reservoir remains a large hyperparameter that is difficult to harness without nonlinear-dynamical-systems knowledge.The framework therefore combines simple training with substantial reservoir-selection and dynamical-analysis demands.Source: §II · p. 3

III. DIVERSE VARIATIONS OF RESERVOIR: TOWARD EXPLOITING PHYSICAL DYNAMICS

Reservoir computing separates the reservoir’s intrinsic dynamics from readout training, allowing diverse physical systems to serve as computational resources. The paper surveys physical, structured, and chaotic reservoirs while noting reproducibility and training considerations.

  • Physical reservoir computing uses natural physical dynamics as computational resources instead of simulated reservoir dynamics.The framework exploits physical dynamics directly, with application scenarios varying according to the physical properties involved.Source: §III · pp. 3, 6
  • Reservoir computing does not require random reservoir weights; brain-inspired, neighboring, and cyclic connection structures are also studied.The reservoir structure itself can be examined as part of the computational account.Source: §III · pp. 3–4
  • Chaotic reservoirs can remain usable when input-driven dynamics suppress chaos and produce generalized synchronization associated with the echo state property.Noise can suppress chaos in large sigmoidal echo state networks, and FORCE learning exploits this property.Source: §III · p. 4
  • Physical reservoirs span liquid-state, quantum, spintronic, nanomaterial, and other dynamical systems, illustrating the framework’s broad material diversity.Examples include Faraday waves, disordered quantum dynamics, magnetic systems, and complex nanowire networks.Source: §III · p. 3, Figure 3 · p. 5
  • Innate training pretrains chaotic reservoirs with their own dynamics so those dynamics can be reproduced and used in machine-learning and robot-control tasks.The approach collects the reservoir’s chaotic dynamics as training data and trains internal weights with FORCE learning.Source: §III · p. 5

A. “Wetware” and its implication

The “Wetware” perspective emphasizes that computation implemented in a physical substrate is shaped by both the substrate’s properties and its environment. This motivates examining physical systems as more than neutral hardware for abstract computation.

  • Physical implementation makes substrate properties and execution conditions affect the computation and add novel system functionality.The paper illustrates this with different robustness to water in conventional PCs and brains.Source: A. “Wetware” and its implication · p. 6
  • Conventional computers are designed top-down for computation, whereas nervous systems operate in physical conditions not fully designed for information processing.The nervous system can function in a somewhat salty aqueous solution, unlike the deliberately specialized PC hardware described here.Source: A. “Wetware” and its implication · p. 6
  • The LSM background characterizes brain information processing through its surrounding liquid physical substrate rather than only through interacting neurons.This perspective treats the physical medium as central to the model rather than as a metaphor alone.Source: A. “Wetware” and its implication · p. 6

B. Liquid computer and the liquid brain

Liquid computing uses perturbations of a liquid surface to transform input histories into distinguishable transient states that a readout can process. Liquid-state-machine formalization and experiments with real water connect this idea to neural information processing and concrete tasks.

  • A liquid computer maps input perturbations into time-varying liquid states observed by a video camera and processed by a readout.The liquid filter is expressed as x(t) = (Lu)(t), with the camera image defining the liquid state.Source: B. Liquid computer and the liquid brain · pp. 6–7
  • Different perturbations and their temporal orderings produce different spatiotemporal liquid-surface patterns.Examples include spoon perturbations and dropping sugar cubes into the liquid.Source: B. Liquid computer and the liquid brain · p. 6, Figure 4 · p. 7
  • A memory-less readout requires the current liquid state to distinguish relevant prior inputs, such as sugar cubes added during the last two seconds.This requirement motivates the liquid system’s ability to encode recent input history in its present state.Source: B. Liquid computer and the liquid brain · p. 7
  • The liquid computer is formalized as a liquid state machine for understanding information processing in neural circuits.The LSM framework connects the physical liquid-computer concept with neural-circuit information processing.Source: B. Liquid computer and the liquid brain · p. 7
  • The liquid brain applied the liquid-computer metaphor to real water as an LSM.The authors described real water as usable for solving the XOR problem.Source: B. Liquid computer and the liquid brain · pp. 7–8
  • Water in a bucket was shown to implement both an XOR task and a speech-recognition task.These demonstrations treat ordinary water as a physical medium exploitable for computation.Source: B. Liquid computer and the liquid brain · p. 8

V. SOFT ROBOTICS

Liquid computers and liquid brains take a bottom-up approach: they begin with the physical properties of liquids and determine how those properties can be exploited for computation.

  • Liquid computers and liquid brains begin from liquid physics and develop computation by exploiting those properties, rather than designing matter around a predefined computation.This contrasts with the conventional computer’s top-down design of hardware structure for computation.Source: §V · p. 8

A. Embodiment and morphological computation

Embodiment describes how a physical body's intrinsic properties contribute to computation, behavior control, or abstract operations. Morphological computation investigates how system shape or morphology affects global behavior, including quantitative analyses of compliant bodies.

Embodiment

Morphological computation

Quantifying physical computation

B. Physical reservoir computing using a soft robotic arm

Soft robots combine complex, high-dimensional dynamics with control challenges, but physical reservoir computing treats those dynamics as computational resources. Examples use soft-body states for computation and control, including an octopus-inspired arm with sensory readings as reservoir states.

Examples

  • Figure 6 presents compliant-body reservoirs including a mass-spring network, SUPERball, Kitty, and an octopus-inspired silicone arm with ten bending sensors sampled every 0.03 [s].Source: Figure 6 · p. 9

Soft-robotic dynamics

Soft-body reservoirs

Soft robotic arm

VI. EXPLOITING PHYSICAL DYNAMICS FOR COMPUTATIONAL PURPOSES

The paper presents three phases of physical reservoir computing: inferring natural dynamics, exploiting physics-specific properties, and using physical substrates already serving other purposes as computational resources.

Phase 0

  • Phase 0 uses PRC to infer the information-processing capability of natural physical dynamics.This includes investigating which physical systems suit particular computations and analyzing their computational capabilities.Source: §VI · p. 10

Phase 2

  • Phase 2 uses a physical substrate that was not prepared for computation, including a robot body whose dynamics support both behavior generation and information processing.This phase extends PRC beyond reproducing a mathematically described physical function.Source: §VI · p. 10

Phase 1

  • Phase 1 adds physical properties to reservoirs, producing capabilities that depend on the exploited type of physics.Examples include spintronic durability in radioactive environments and quantum reservoirs supporting quantum tasks and many computational nodes.Source: Phase 1: Physical properties of a… · pp. 10–11
  • Spintronic reservoirs show high durability in radioactive environments, supporting computation where conventional electronics may break down.The paper presents this as an additional property of the physical substrate.Source: Phase 1: Physical properties of a… · p. 11

Open limitation

  • Current physical-reservoir technologies still require conventional electronics and external devices, including readouts and temperature-maintenance equipment.The paper identifies this dependence as a weakness requiring future improvement.Source: Phase 1: Physical properties of a… · p. 11

Phase 2: Exploiting a physical substrate that is not

Phase 2 exploits the dynamics of a physical system that already performs another function, so behavior generation and information processing occur together within the same substrate.

Phase 2

  • A robot body can serve simultaneously as the source of behavior and as a computational resource.Its dynamics can be used to calculate motor commands that control its own behavior.Source: Phase 2: Exploiting a physical… · p. 11

Closed-loop control

  • In phase 2 closed-loop control, information processing accompanies system behavior rather than being prepared outside the controlled system.The required processing can be bypassed from the digital processor and embedded in the system itself.Source: Figure 8 · p. 12

Phase 2

  • The transition to phase 2 does not require a physical substrate designed specifically for the target computation.PRC can exploit natural physical dynamics without precisely designing the substrate for computation in many cases.Source: Phase 2: Exploiting a physical… · p. 12

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