Driven criticality links universal computation and optimal representations

Abstract

Near-critical dynamics are often linked to enhanced computation, but the underlying mechanism remains unclear. We address this question in reservoir computing, where a fixed recurrent network maps input sequences into high-dimensional states and only a simple readout is trained. We extend fixed-reservoir universality results to discrete-time input-driven reservoirs and connect their key geometric condition, neighborhood separation, to dynamics. To this end, we introduce a finite-resolution neighborhood separability index and an input-conditioned maximal Lyapunov exponent. We find that neighborhood separability, chaotic time-series prediction, and smooth high-dimensional representation geometry are optimized in the same narrow window of marginal driven stability. In this regime, the covariance spectrum approaches the power-law scaling expected for near-optimal smooth representations. Our results link edge-of-instability computation, universality, readout performance, and optimal representation geometry within a common dynamical framework.