Inferring Synaptic Structure in presence of Neural Interaction Time Scales

TL;DR

This paper introduces a new two-step inference method for reconstructing synaptic structures in neural networks, addressing limitations of existing methods that assume a single interaction time scale, and analyzes how binarization time affects inference accuracy.

Contribution

The authors develop a two-step inference approach that accurately recovers delay-structure and synaptic matrices without assuming a fixed interaction time scale.

Findings

The new method successfully reconstructs synaptic matrices across various network topologies.

Inference accuracy depends critically on the binarization time bin $dt$ for excitatory synapses.

The relationship between inferred couplings and actual synaptic efficacies is quadratic but sensitive to $dt$ for excitatory synapses.

Abstract

Biological networks display a variety of activity patterns reflecting a web of interactions that is complex both in space and time. Yet inference methods have mainly focused on reconstructing, from the network's activity, the spatial structure, by assuming equilibrium conditions or, more recently, a probabilistic dynamics with a single arbitrary time-step. Here we show that, under this latter assumption, the inference procedure fails to reconstruct the synaptic matrix of a network of integrate-and-fire neurons when the chosen time scale of interaction does not closely match the synaptic delay or when no single time scale for the interaction can be identified; such failure, moreover, exposes a distinctive bias of the inference method that can lead to infer as inhibitory the excitatory synapses with interaction time scales longer than the model's time-step. We therefore introduce a new two-step method, that first infers through cross-correlation profiles the delay-structure of the network and then reconstructs the synaptic matrix, and successfully test it on networks with different topologies and in different activity regimes. Although step one is able to accurately recover the delay-structure of the network, thus getting rid of any \textit{a priori} guess about the time scales of the interaction, the inference method introduces nonetheless an arbitrary time scale, the time-bin $dt$ used to binarize the spike trains. We therefore analytically and numerically study how the choice of $dt$ affects the inference in our network model, finding that the relationship between the inferred couplings and the real synaptic efficacies, albeit being quadratic in both cases, depends critically on $dt$ for the excitatory synapses only, whilst being basically independent of it for the inhibitory ones.