Spiking neural network initialization for scale-invariant maximization of entropy

Parameter initialization shapes training dynamics, convergence, and performance in neural networks. In spiking neural networks (SNNs), analytical initialization is complicated by three additional mechanisms—binary spike outputs, temporal recurrence (leak), and reset-induced drops in membrane potential—which together suppress activity propagation: (1) over time, where recurrence and reset reduce individual neurons' firing rate, and (2) across depth, where deficits in upstream activity compromise downstream layers, known as spike-rate collapse. Prior initialization methods address only subsets of these challenges. We derive closed-form weight and bias distributions for initialization that jointly account for temporal recurrence, refractory reset, and signal propagation across depth. The method is data-agnostic: it requires only the architecture and neuron hyperparameters. Our derivation centers around a bias correction that yields stationary firing rates and membrane variance, with a principled default spike probability of $p=0.5$ that maximizes per-neuron Bernoulli entropy—counteracting dead neurons ($p\approx 0$) and saturated neurons ($p\approx 1$) at initialization. In controlled simulations across 30 layers, it maintains target firing rates and membrane variance at the individual-neuron level, unlike alternatives tested. Across UEA multivariate time-series classification, neuromorphic classification, and continuous-control reinforcement learning, our SNNs rank first in every paradigm without per-paradigm tuning.