Identifying Connectivity Distributions from Neural Dynamics Using Flows

TL;DR

This paper introduces a novel inference framework using maximum entropy and continuous normalizing flows to identify the distribution of neural connectivity structures from observed dynamics, addressing degeneracy issues.

Contribution

It characterizes the conditions for unique connectivity structure inference in lrRNNs and develops a flow-based method to learn unbiased connectivity distributions from neural data.

Findings

The method captures complex connectivity distributions like heavy-tailed structures.

Validated on synthetic data with multistable and cyclic attractors.

Applied to rat cortex data during decision-making tasks.

Abstract

Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurrent neural networks (lrRNNs) to infer low-dimensional latent dynamics and connectivity structure from observed activity, enabling a mechanistic interpretation of the dynamics. However, standard approaches for training lrRNNs can recover spurious structures irrelevant to the underlying dynamics. We first characterize the identifiability of connectivity structures in lrRNNs and determine conditions under which a unique solution exists. Then, to find such solutions, we develop an inference framework based on maximum entropy and continuous normalizing flows (CNFs), trained via flow matching. Instead of estimating a single connectivity matrix, our method learns the maximally unbiased distribution over connection weights consistent with observed dynamics. This approach captures complex yet necessary distributions such as heavy-tailed connectivity found in empirical data. We validate our method on synthetic datasets with connectivity structures that generate multistable attractors, limit cycles, and ring attractors, and demonstrate its applicability in recordings from rat frontal cortex during decision-making. Our framework shifts circuit inference from recovering connectivity to identifying which connectivity structures are computationally required, and which are artifacts of underconstrained inference.