Bridging Theory and Practice in Crafting Robust Spiking Reservoirs

The edge-of-chaos heuristic has long served as a guiding principle for designing reservoir computers, yet its relevance to machine performance remains elusive. Here, taking the spectral radius of the reservoir network as the control parameter, we show that the radius yielding the best forecasting performance does not coincide with the Lyapunov edge of the isolated, teacher-forced, or closed-loop generative reservoir. By analyzing the collective dynamics of the teacher-forced reservoir, we find that the target dynamics are represented mainly by stable Lyapunov modes whose finite-time stability is strongly modulated by the input. This finding motivates a stability-expressivity transfer index, which balances the stability of these modes against their expressivity in representing the target. Across chaotic and quasiperiodic targets, and for both asymmetric and symmetric reservoirs, this index accurately identifies the optimal spectral radius for autonomous forecasting.

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 shifts the focus from training a system's internal dynamics to designing dynamics that expose useful computational capabilities via linear projection. We study random Boolean networks as reservoirs: cellular automata with random recurrent wiring and a random rule at each node. Their main parameter is the connectivity, the mean number of edges into a node. Without input, these networks pass from ordered to chaotic dynamics at a connectivity of 2, where their dynamics are expected to facilitate computation. How the input is connected is itself a design factor: if the input shares the network's edges, the connectivity sets both the dynamics and how many nodes receive the input, the input fan-out. We set the input fan-out separately and compare 7,560 reservoir designs, all combinations of six design factors, each built as many random reservoirs, on recalling the majority or the parity of a few input bits seen several steps earlier. The optimal connectivity falls from 2.5 to 1.75-2 as more nodes receive the input, but hardly depends on the task or on the other design factors, except self-loops, which connect a node to itself and raise the optimal connectivity. A measure computed from the reservoir states without a trained readout peaks at a connectivity that also falls with the fan-out and rises with self-loops, but does not replace training a readout. Reservoirs of one design vary widely, so a design should be judged by its typical reservoir.