Organization of computation in reservoir computing

2026-07-20

AI Summary

Traditional metrics struggle to characterize the geometric organization of task-relevant information in the high-dimensional state space of reservoir computing. This work proposes an analysis framework based on spectral decomposition, establishing—for the first time—a quantitative link between state-space modes and information processing capacity. By integrating spectral decomposition, information capacity analysis, and nonlinear dynamical system modeling, the study quantifies the representational energy of distinct modes and reveals that low-energy modes, despite their susceptibility to noise, may nonetheless encode critical computational functions. These findings challenge the conventional design paradigm that relies solely on high-dimensional expansion and offer a new theoretical foundation for optimizing physical reservoirs.

Abstract

Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations. Although reservoir performance is often characterized through memory, nonlinearity, and their tradeoff, such aggregate measures do not reveal how task-relevant information is organized within the state space. Here, we introduce an eigen-spectral decomposition framework linking the degree-wise information processing capacity to the corresponding state space modes. As a result, we are able to quantify the degree-wise representation energy, and show that in some cases, substantial amounts of information processing capacity may reside in low-energy modes that are vulnerable to experimental noise. These results suggest that useful reservoir computation depends not only on dimensionality expansion, but also on the geometric organization of task-relevant information, with direct implications on physical reservoir computers.

Problem

• reservoir computing
• state space
• information organization
• representation energy
• task-relevant information

Innovation

• reservoir computing
• eigen-spectral decomposition
• information processing capacity
• state space organization
• low-energy modes