# Identifying Connectivity Distributions from Neural Dynamics Using Flows

arXiv: https://arxiv.org/abs/2603.26506 · HTML: https://mlsanity.com/paper/2603.26506/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 62 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Linking connectivity, dynamics and computations in low-rank recurrent neural networks](https://mlsanity.com/paper/1711.09672/) (2017)
- [Representation learning for neural population activity with Neural Data Transformers](https://mlsanity.com/paper/2108.01210/) (2021)
- [Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains](https://mlsanity.com/paper/1604.03053/) (2016)
- [Recurrent Network Models Of Sequence Generation And Memory](https://mlsanity.com/paper/1603.04687/) (2016)
- [Inferring stochastic low-rank recurrent neural networks from neural data](https://mlsanity.com/paper/2406.16749/) (2024)
- [Low Tensor Rank Learning of Neural Dynamics](https://mlsanity.com/paper/2308.11567/) (2023)
- [Shaping dynamics with multiple populations in low-rank recurrent networks](https://mlsanity.com/paper/2007.02062/) (2020)
- [Transition to chaos in random networks with cell-type-specific connectivity](https://mlsanity.com/paper/1407.2297/) (2014)
- [Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks](https://mlsanity.com/paper/1707.08337/) (2017)
- [Trial matching: capturing variability with data-constrained spiking neural networks](https://mlsanity.com/paper/2306.03603/) (2023)
- [Maximum Entropy Flow Networks](https://mlsanity.com/paper/1701.03504/) (2017)
- [Extended mean-field theories for networks of real neurons](https://mlsanity.com/paper/2504.15197/) (2025)
- [A Factorized Low-Rank RNN Framework for Uncovering Independent Neural Latent Dynamics and Connectivity](https://mlsanity.com/paper/2511.13899/) (2025)

## Abstract (arXiv)

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 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. 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 a distribution over connection weights that is maximally unbiased over unidentifiable components while matching the 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.