Order-Sensitive Fast-Synapse Limits in Sparse Excitatory-Inhibitory Threshold-Reset Networks

What the math gives to ML

The paper identifies a concrete failure mode of collapsing signed fast inputs into their weak limit: threshold-reset dynamics can retain the microscopic order of excitatory and inhibitory arrivals even when both synaptic kernels converge to the same impulse at zero. The key transferable asset is the exact firing interval x+a-b<theta<=x+a, which characterizes states where excitatory-first and inhibitory-first processing produce different outputs, together with persistence under strict perturbation margins and sparse random aggregation. This suggests neural modules that preserve causal E/I event order inside a nominal timestep rather than summing all signed inputs, as well as a training regularizer that controls sensitivity to unresolved event ordering. The most direct targets are event-driven or discretized spiking recurrent networks.