Inhibitory budget matching constrains homeostatic plasticity in competitive spiking networks

Competitive spiking networks can form sensory representations through local synaptic plasticity and lateral inhibition. A canonical example is the Diehl-Cook architecture, in which Poisson-encoded sensory inputs drive excitatory neurons through spike-timing-dependent plasticity (STDP), while a separate inhibitory population imposes competition between excitatory units. In most implementations this competitive circuit is fixed, although inhibitory synapses are plastic in cortical circuits and contribute to excitation-inhibition balance. It therefore remains unclear under which conditions biologically motivated inhibitory plasticity can replace fixed lateral competition without disrupting representation learning. Here we study this question in a competitive STDP network trained on MNIST. We compare fixed inhibition with a Vogels-style inhibitory STDP rule, slow homeostatic inhibition, and a budget-constrained slow homeostatic rule that conserves the total inhibitory input received by each excitatory neuron. A fixed-inhibition operating-point map showed that stability depends on the dynamical regime: 56% of tested fixed-inhibition runs completed training, whereas stronger inhibition at higher input gain produced runaway activity. The reference regime g = 2.0, wIE = 10.0, selected for subsequent comparisons, combined complete stability across replicate initializations with high classification performance (84.3 {+/-} 0.6% after 30,000 training examples). In this regime, the budget-constrained rule was stable in all replicate runs when its inhibitory budget matched the fixed-inhibition reference (BI = 3990), reaching 83.5 {+/-} 0.6% accuracy with firing-rate and inhibitory-conductance statistics close to fixed inhibition, whereas a mismatched budget (BI = 7980) produced runaway activity in every replicate. Parameter maps showed that Vogels-derived iSTDP was broadly but not uniformly stable (90% runs completed), while slow homeostatic inhibition was even more broadly stable (96%). Budget-constrained stability depended strongly on the conserved budget, i.e., low and matched budgets were stable or nearly stable, intermediate budgets were mixed, and BI = 7980 failed in all tested runs. These results show that inhibitory plasticity in competitive STDP networks is not governed by a local homeostatic update alone. Stable plastic competition depends jointly on the operating regime and on an inhibitory budget that fixes the total strength of competition while allowing local inhibitory weights to adapt. Mechanistically, budget matching separates local redistribution of inhibitory weights from changes in total inhibitory drive, preventing plasticity from shifting the network away from a stable competitive state. This identifies inhibitory budget matching as a practical design principle for replacing fixed inhibition with plastic, homeostatically regulated competition in STDP-based spiking networks.