Optimal Memory Encoding Through Fluctuation-Response Structure
This work addresses a key bottleneck in physical reservoir computing for researchers and engineers by providing a principled method to design input encoders, even in non-differentiable systems, though it is incremental as it builds on existing reservoir computing frameworks.
The paper tackled the problem of optimal input encoding in physical reservoir computing by showing it is governed by the system's fluctuation-response structure, deriving an analytical criterion (ROME) that maximizes task-specific linear memory under a fixed power constraint and demonstrating its effectiveness across various reservoir platforms.
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.