Entropy, Inhibition and Memory in Balanced Spiking Reservoirs

Recurrent neural networks are studied along two largely parallel tracks: as machine-learning models evaluated by task performance and as computational-neuroscience models of cortical circuits evaluated by dynamical realism. Reservoir computing offers a meeting point, yet the link between dynamical regime and computational performance has not been systematically mapped in biologically constrained spiking architectures. We treat the Brunel balanced excitatory-inhibitory network as a reservoir and characterize separation capacity (kernel quality) and transient memory (corrected linear memory capacity, validated by non-parametric mutual information) across the full phase diagram. The analysis uses a four-state Markov source whose Shannon entropy rate is set in closed form by a single parameter at fixed marginal entropy. Both capabilities increase monotonically with the inhibitory ratio g, remaining jointly highest in the asynchronous irregular regime, with diminishing increments consistent with eventual saturation; the synchronous irregular regime, despite a network timescale three orders of magnitude longer, supports neither. Memory further requires sparse input coupling: dense coupling collapses the driven timescale and erases memory in every regime. Inhibitory balance thus emerges as a unified architectural control parameter, providing a quantitative design criterion for cortical-circuit modeling and reservoir computing applications.