Analyzing the Dynamics of WSBM-based Echo State Networks using InputDSA

Echo State Networks (ESNs) offer an efficient framework for temporal prediction, but their randomly initialized reservoirs are often over-parameterized and dynamically redundant. Existing pruning methods largely rely on static connectivity or activation statistics, which may overlook neurons that shape input-driven state transitions. We propose Dynamical Mode Pruning (DMP), a reservoir pruning method that ranks neurons by their contribution to dominant transition modes obtained from a trajectory-averaged Jacobian Gramian. DMP removes low-impact units and retrains only the readout. Experiments on chaotic and real-world time-series benchmarks show that DMP improves or preserves forecasting accuracy while reducing redundant reservoir components. Our results suggest that dynamical influence is a useful criterion for reservoir refinement beyond static structural importance alone.

Biological systems maintain function in fluctuating environments by transforming past stimulation into internal dynamical states that support future-oriented responses. Reservoir computing provides a computational analogue, but standard formulations often treat the recurrent substrate as a fixed random network and train only the readout. Here we ask how the substrate itself changes when reservoir architecture is placed under evolutionary selection for prediction. Using the Kuramoto--Sivashinsky equation as a testbed for spatiotemporal chaos, we evolved reservoirs over five construction hyperparameters: size, connectivity degree, spectral radius, input scaling, and readout regularization. Evolution reduced prediction error at the population level, extended the low-error forecast horizon, and organized the design space along a diminishing-return size--efficiency frontier. Structural analyses showed that evolved reservoirs remained within a conserved stochastic-block-model-like spectral envelope while refining low-eigenvalue modes, locking modularity to an intermediate band, and pruning connection cost within that band. Pareto analysis showed that elite reservoirs occupied a horizontal floor in the cost--modularity plane, indicating that accuracy and efficiency were achieved jointly rather than through a simple trade-off. These findings show that evolutionary optimization does not merely improve prediction, but exposes interpretable structural constraints on the recurrent substrate: it stabilizes a task-suitable dynamical class and refines the architectural degrees of freedom most relevant for prediction. Evolutionary reservoir computing therefore provides a bio-inspired framework for studying how predictive demands shape adaptive dynamical networks.

Reservoir computing exploits the fixed dynamics of a recurrent network for temporal processing, requiring only a trained linear readout. Biological neural connectomes, shaped by millions of years of evolution, may encode computational structure beyond what random reservoirs provide, yet whether that structure can be further enhanced by principled optimisation remains an open question. We address it by applying four gradient-free, bio-inspired optimisers (Particle Swarm Optimisation, Differential Evolution, Grey Wolf Optimiser, and Whale Optimisation Algorithm) to the edge weights of connectome-based echo-state networks across six species spanning six orders of magnitude in neural complexity: C. elegans (279 neurons), Drosophila (49 nodes), mouse (112), rat (73), macaque (29 regions, continuous FLNe synaptic strengths), and human structural MRI connectivity (83 parcels). Each connectome is evaluated on four canonical reservoir computing benchmarks: Memory Capacity (MC), Lorenz attractor prediction, NARMA-10 system identification, and Mackey-Glass chaotic time-series prediction. All four optimisers consistently outperform unoptimised biological baselines across every task and species when initialised from biological weights. WOA achieves the largest gains on every task: up to a 17x MC improvement (C. elegans: 1.39 to 23.91) and up to 89% NRMSE reduction (Mackey-Glass, human), corresponding to an average 214% improvement across all species and tasks. Crucially, random initialisation on the same topology reliably underperforms biology, establishing biological weight values as an essential inductive bias that topology alone cannot recover. These results position bio-inspired, biologically-initialised optimisation as a principled and broadly effective strategy for connectome reservoir computing across the animal kingdom.