Metabolic Cost Asymmetry as a Structural Regulariser for Recurrent Spiking Neural Networks

Abstract

Cortical energy expenditure is heavily dominated by synaptic transmission, with excitatory (glutamatergic) signalling demanding substantially more ATP than inhibitory (GABAergic) signalling. Yet existing trainable spiking neural networks treat energy as a generic, synapse-type-agnostic penalty. Here, we embed this fundamental glutamate/GABA cost asymmetry as a Lagrangian penalty within a surrogate-gradient learning framework, and use it to train a Dale's-law-compliant recurrent microcircuit on the Spiking Heidelberg Digits (SHD) benchmark. Because glutamatergic synapses are metabolically more expensive, a single scalar penalty applied uniformly to all weights automatically exerts stronger gradient pressure on excitatory pathways. We demonstrate that this differential pressure alone is sufficient to produce three major effects. First, it moves the network out of the suboptimal, inhibition-dominated regime of the unpenalised network, simultaneously improving accuracy and reducing total energy several-fold. Second, it induces an emergent pruning hierarchy in which excitatory connections are eliminated first, while inhibitory connections exhibit graded resistance. Third, it actively expands the dimensionality of the population code at moderate penalty strengths. These structural motifs remain robust across a two-dimensional sweep of five cost ratios and fifteen structural densities (75 distinct conditions). Ultimately, our results demonstrate that a single biophysical cost asymmetry, operating without auxiliary regularisers or architectural priors, is sufficient to organise sparse, pathway-specific circuit structure in recurrent spiking networks.