# Optimal Memory Encoding Through Fluctuation-Response Structure

arXiv: https://arxiv.org/abs/2603.21666 · HTML: https://mlsanity.com/paper/2603.21666/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [Finite-Horizon Fisher Memory in Two-Sided Power-Bounded Recurrent Systems](https://mlsanity.com/paper/2609.39800/) (2026)

## Abstract (arXiv)

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.