Optimal Memory Encoding Through Fluctuation-Response Structure

• URL: http://arxiv.org/abs/2603.21666v1
• Date: Mon, 23 Mar 2026 07:44:35 GMT
• Title: Optimal Memory Encoding Through Fluctuation-Response Structure
• Abstract summary: We show that optimal input encoding is a problem governed by the system's fluctuation-response structure.<n>Backpropagation-based encoder optimization is shown to be equivalent to ROME, revealing a trade-off between task-dependent feature mixing and intrinsic noise.
• Score: 0.688204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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