A Disentangled Low-Rank RNN Framework for Uncovering Neural Connectivity and Dynamics

TL;DR

This paper tackles the challenge of uncovering interpretable connectivity and dynamics from high-dimensional neural data by introducing DisRNN, a disentangled low-rank RNN. It reformulates lrRNN within a variational autoencoder framework and adds a partial-correlation penalty to enforce group-wise latent independence, yielding multiple latent groups that drive independent sub-circuits. The authors demonstrate on synthetic data, monkey M1, and mouse voltage imaging that partial disentanglement improves latent structure quality and yields more interpretable low-rank sub-connectivities, with clear links to task variables and cortical regions. The approach provides a principled, extensible framework for inferring modular neural computation and holds potential for deeper mechanistic insights into brain dynamics.

Abstract

Low-rank recurrent neural networks (lrRNNs) are a class of models that uncover low-dimensional latent dynamics underlying neural population activity. Although their functional connectivity is low-rank, it lacks disentanglement interpretations, making it difficult to assign distinct computational roles to different latent dimensions. To address this, we propose the Disentangled Recurrent Neural Network (DisRNN), a generative lrRNN framework that assumes group-wise independence among latent dynamics while allowing flexible within-group entanglement. These independent latent groups allow latent dynamics to evolve separately, but are internally rich for complex computation. We reformulate the lrRNN under a variational autoencoder (VAE) framework, enabling us to introduce a partial correlation penalty that encourages disentanglement between groups of latent dimensions. Experiments on synthetic, monkey M1, and mouse voltage imaging data show that DisRNN consistently improves the disentanglement and interpretability of learned neural latent trajectories in low-dimensional space and low-rank connectivity over baseline lrRNNs that do not encourage partial disentanglement.

Figures (10)

• Figure 1: (a): Schematic of the DisRNN, showing independent latent groups and the corresponding low-rank connectivities. (b): Group-wise independence: $(z_1,z_2)\perp(z_3,z_4)$, while within-groups are highly entangled, and components from different groups are marginally independent.
• Figure 2: (a): The PC and $R^2$ of the estimated latent, and the connectivity correlation. The starbars indicate the pairwise $t$-test significance levels. Arrows indicate the higher or lower the better. (b): Group 2 latent trajectories with the true dynamics in 3D plots; and the 1D trajectories from different methods on selected latent components. All latent dimensions are plotted in Fig. \ref{['fig:synthetic_rnn_latent']} in Appendix \ref{['appendix:synthetic']}. (c): The learned sub-connectivities from different methods and the ground truth.
• Figure 3: (a): Recovered latent trajectories from different methods v.s. the ground-truth trajectories, and their alignment $R^2$ scores. (b): The corresponding low-rank connectivity for $K=2$ DisRNN and $K=4$ DisRNN. For DisRNN, for example, the rank-4 connectivity can be decomposed into two rank-2 sub-connectivities, one responsible for the dynamics of the $x$-movement, and the other for the $y$-movement. (c): The $R^2$ scores of aligning the estimated latent to rotated coordinate systems.
• Figure 4: (a): Experiment setup. (b): Reconstruction performances w.r.t. different numbers of components for DisRNN or different numbers of groups for DisRNN. (c): Cortical map with region abbreviations. (d): 1 rank-12 group, a no disentanglement configuration, i.e., a standard low-rank RNN. Left are brain maps $\bm A_{:, g}$ and the corresponding time series $\bm z_g^{(t)}$. Right is the corresponding rank-12 connectivity corresponding to group 1. Similar for (e) and (f).
• Figure 5: The synthetic latent consists of two independent groups.