Identifying Connectivity Distributions from Neural Dynamics Using Flows
This work addresses the challenge of underconstrained circuit inference in neuroscience, shifting focus from recovering specific connectivity to identifying computationally required structures, though it is incremental as it builds on existing low-rank recurrent neural network methods.
The paper tackles the problem of inferring neural connectivity from population recordings, which is degenerate because multiple connectivity structures can produce identical dynamics, by developing an inference framework that learns the maximally unbiased distribution over connection weights consistent with observed dynamics, validated on synthetic datasets and rat frontal cortex recordings.
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.