  Biological neural networks face a formidable task: performing reliable
computations in the face of intrinsic stochasticity in individual neurons,
imprecisely specified synaptic connectivity, and nonnegligible delays in
synaptic transmission. A common approach to combatting such biological
heterogeneity involves averaging over large redundant networks of $N$ neurons
resulting in coding errors that decrease classically as $1/\sqrt{N}$. Recent
work demonstrated a novel mechanism whereby recurrent spiking networks could
efficiently encode dynamic stimuli, achieving a superclassical scaling in which
coding errors decrease as $1/N$. This specific mechanism involved two key
ideas: predictive coding, and a tight balance, or cancellation between strong
feedforward inputs and strong recurrent feedback. However, the theoretical
principles governing the efficacy of balanced predictive coding and its
robustness to noise, synaptic weight heterogeneity and communication delays
remain poorly understood. To discover such principles, we introduce an
analytically tractable model of balanced predictive coding, in which the degree
of balance and the degree of weight disorder can be dissociated unlike in
previous balanced network models, and we develop a mean field theory of coding
accuracy. Overall, our work provides and solves a general theoretical framework
for dissecting the differential contributions neural noise, synaptic disorder,
chaos, synaptic delays, and balance to the fidelity of predictive neural codes,
reveals the fundamental role that balance plays in achieving superclassical
scaling, and unifies previously disparate models in theoretical neuroscience.
