Synaptic Classification via Spike-Triggered Extrapolation

Abstract

This work introduces a statistical procedure to infer the interaction graph of neuronal networks modeled by Galves-L\"ocherbach dynamics. The methodology performs bivariate inference, identifying synaptic links from the spike trains of pairs of neurons without observing the rest of the network. We propose a Macro-Micro Extrapolation algorithm to address data sparsity by inferring interactions in the limit $\Delta \to 0^+$. The core component is a Spike-Triggered Estimator that leverages the local reset property to decouple synaptic jumps from background noise. By employing an adaptive logic that switches between sample averaging and Pyramid Extrapolation, the framework categorizes connections as excitatory, inhibitory, or null. Numerical simulations demonstrate that the classifier identifies synapses without error across varying noise regimes and complex network topologies, even for observation windows broader than those predicted by the current theoretical bounds.