Optimal Memory Encoding Through Fluctuation-Response Structure

2026-03-23

AI Summary

This work addresses the unclear mechanism by which input encoding affects linear memory performance in physical reservoir computing and the absence of theory-guided optimal design strategies. The authors formulate optimal input encoding as a geometric optimization problem governed by the system’s fluctuation–response structure and introduce the ROME (Response-Optimized Memory Encoding) criterion: under a fixed power constraint, the input direction that maximizes task-relevant linear memory is identified through measurements of steady-state fluctuations and linear response. Integrating the fluctuation–dissipation theorem and linear response theory from nonequilibrium statistical physics within the reservoir computing framework, ROME applies universally to both differentiable and non-differentiable systems. It reveals that optimal encoding fundamentally exploits the system’s intrinsic response structure to balance task-feature mixing against inherent noise. Experiments on platforms including spin-wave waveguides and spiking neural networks demonstrate ROME’s generality and efficiency.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• reservoir computing
• input encoding
• memory capacity
• fluctuation-response
• optimal encoding

Innovation

• reservoir computing
• optimal input encoding
• fluctuation-response
• linear memory
• neuromorphic systems