Organization of computation in reservoir computing
2026-07-20 • Neural and Evolutionary Computing
Neural and Evolutionary ComputingMachine Learning
AI summaryⓘ
The authors study how reservoir computing systems process information by looking inside their high-dimensional state spaces. They propose a new method using eigen-spectral decomposition to understand how different parts of the system represent information of varying complexity. Their findings show that important information can sometimes be hidden in parts of the system with low signal strength, which are easily disturbed by noise. This means that how information is organized geometrically in the system matters as much as the system's size for good performance. Their work has practical implications for designing physical reservoir computers.
Reservoir ComputingNonlinear Dynamical SystemsState SpaceEigen-spectral DecompositionInformation Processing CapacityDimensionality ExpansionRepresentation EnergyExperimental NoisePhysical Reservoir ComputersMemory-Nonlinearity Tradeoff
Authors
Mohab Abdalla, Damien Rontani
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.