Optimal Memory Encoding Through Fluctuation-Response Structure

TL;DR

This paper introduces ROME, a geometric framework for optimal input encoding in physical reservoir computing, leveraging fluctuation-response analysis to enhance memory performance across diverse physical systems.

Contribution

It formulates a novel analytical criterion for input encoding based on the system's fluctuation-response structure, applicable to non-differentiable reservoirs.

Findings

ROME outperforms traditional encoding methods in reservoir tasks.

Effective encoder design is achievable in non-differentiable systems.

Trade-off identified between feature mixing and noise in encoder optimization.

Abstract

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.