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.

翻译：物理储备池计算利用物理系统的内在动力学进行信息处理，同时保持内部动力学固定并仅训练线性读出层；然而输入编码的作用仍不明确。我们证明最优输入编码是一个受系统涨落-响应结构支配的几何问题。通过测量稳态涨落和线性响应，我们推导出在固定功率约束下最大化任务特定线性记忆的输入方向分析准则，称为基于响应的最优记忆编码（ROME）。基于反向传播的编码器优化被证明等价于ROME，揭示了任务依赖特征混合与固有噪声之间的权衡。我们将ROME应用于包括自旋波导和脉冲神经网络在内的多种储备池平台，展示了在物理和神经形态储备池中（即使在不可微系统中）的有效编码器设计。