SynapsNet: Enhancing Neuronal Population Dynamics Modeling via Learning Functional Connectivity

TL;DR

This work introduces SynapsNet, a novel deep-learning framework that effectively models population dynamics and functional interactions between neurons and demonstrates that SynapsNet consistently outperforms existing models in forecasting population activity.

Abstract

The availability of large-scale neuronal population datasets necessitates new methods to model population dynamics and extract interpretable, scientifically translatable insights. Existing deep learning methods often overlook the biological mechanisms underlying population activity and thus exhibit suboptimal performance with neuronal data and provide little to no interpretable information about neurons and their interactions. In response, we introduce SynapsNet, a novel deep-learning framework that effectively models population dynamics and functional interactions between neurons. Within this biologically realistic framework, each neuron, characterized by a latent embedding, sends and receives currents through directed connections. A shared decoder uses the input current, previous neuronal activity, neuron embedding, and behavioral data to predict the population activity in the next time step. Unlike common sequential models that treat population activity as a multichannel time series, SynapsNet applies its decoder to each neuron (channel) individually, with the learnable functional connectivity serving as the sole pathway for information flow between neurons. Our experiments, conducted on mouse cortical activity from publicly available datasets and recorded using the two most common population recording modalities (Ca imaging and Neuropixels) across three distinct tasks, demonstrate that SynapsNet consistently outperforms existing models in forecasting population activity. Additionally, our experiments on both real and synthetic data showed that SynapsNet accurately learns functional connectivity that reveals predictive interactions between neurons.

Figures (7)

• Figure 1: SynapsNet overview. (a) The functional connectivity defined between neurons on the model and how input current is inferred based on functional connectivity and population activity (b) An example input frame to the dynamical model which includes past activity over the context window, past input current, past behavioral data, and the unique embedding of the target neuron. (c) The three sets of parameters in SynapsNet: adjacency matrix $A$ for each session, embedding vector $E$ for each neuron, and dynamical model.
• Figure 2: Performance on neural data forecasting. (a) The first three principal components (PCs) of the true and predicted population activity sampled from an example session. (b) Correlation between the first three PCs of the true and predicted activity for the all-time points in the test set of an example session. (c) Comparison between prediction correlations achieved by SynapsNet and NeurPRINT across the test portion of all sessions. **** indicates $p\text{-value} \leq .0001$ achieved by paired-$t$-test.
• Figure 3: Illustration of the learned functional connectivity. (a) The connectivity matrix learned by SynapsNet compared with that of achieved by pair-wise Pearson's correlation. The top and bottom matrices correspond to a sample session from Ca imaging and Neuropixels modalities respectively. (b) 3D visualization of the learned functional connectivity by SynapsNet on a sample Ca imaging session. Dots represent neurons and lines show the type and strength of the connections. Coordinates are in $\mu m$.
• Figure 4: Input currents achieved by functional connectivity. (a) An example calculation of the input current to each neuron based on the population activity and the learned functional connectivity. (b) Average cross-correlations between each neuron's input currents and their activity. The input currents are calculated based on connectivity matrices achieved by three different methods: SynapsNet, pair-wise correlation, and shuffling the SynapsNet's connectivity matrix. The dots and color-shaded areas represent the mean and standard deviation of the correlations. The x-axis shows delays in time steps and the gray-shaded area marks the unavailable time points during the neuron activity forecasting task.
• Figure 5: Synthetic data experiment. (a) Simulation process. (b) Functional connectivity matrices inferred using SynapsNet and other baselines compared with the ground-truth in a single simulation run. (c) Functional connectivity reconstruction accuracies achieved by each method over 50 runs of simulation with random initializations.