Self-Supervised Discovery of Neural Circuits in Spatially Patterned Neural Responses with Graph Neural Networks

TL;DR

This study tackles the challenge of inferring latent neural connectivity from partially observed population activity by introducing a self-supervised graph neural network with separate structure-learning and spike-prediction modules. The approach learns a latent weight matrix $\boldsymbol{W}$ and uses a graph-based predictor to model spiking via a Poisson process, while accommodating unobserved neurons with auxiliary nodes. Across synthetic ring-attractor networks and real head-direction cell data, the method consistently reduces spurious connectivity inferences and yields weight profiles aligning with continuous attractor models, outperforming traditional baselines in both connectivity inference and spike prediction. The framework is robust to external inputs and varying observation completeness, offering a versatile tool for uncovering latent circuitry in large-scale neural recordings with potential extensions to time-varying connectivity and more complex topologies.

Abstract

Inferring synaptic connectivity from neural population activity is a fundamental challenge in computational neuroscience, complicated by partial observability and mismatches between inference models and true circuit dynamics. In this study, we propose a graph-based neural inference model that simultaneously predicts neural activity and infers latent connectivity by modeling neurons as interacting nodes in a graph. The architecture features two distinct modules: one for learning structural connectivity and another for predicting future spiking activity via a graph neural network (GNN). Our model accommodates unobserved neurons through auxiliary nodes, allowing for inference in partially observed circuits. We evaluate this approach using synthetic data generated from ring attractor network models and real spike recordings from head direction cells in mice. Across a wide range of conditions, including varying recurrent connectivity, external inputs, and incomplete observations, our model reliably resolves spurious correlations and recovers accurate weight profiles. When applied to real data, the inferred connectivity aligns with theoretical predictions of continuous attractor models. These results highlight the potential of GNN-based models to infer latent neural circuitry through self-supervised structure learning, while leveraging the spike prediction task to flexibly link connectivity and dynamics across both simulated and biological neural systems.

Figures (6)

• Figure 1: Overview of the generative and inference network model. (a) A ring network with a Mexican-hat connectivity profile, where each neuron is connected to others with the same weight pattern. The full weight matrix is shown below. (b) Simulated network activity, including synaptic activation (top) and spike raster plot across neurons over time (bottom). (c) Structure learning module that estimates synaptic connection strengths based on pairwise spike activity. (d) Spike prediction module that leverages the inferred connectivity to predict future spike times from past neural activity.
• Figure 2: Quality of connectivity inference from spike train data generated by a fully observed network of 100 neurons. (a) Comparison of the ground-truth (orange) and inferred (blue) weight profiles obtained by the GNN-based inference model. The solid blue line represents the average inferred weights across three trials, each initialized with a different random seed, with the shaded blue region indicating $\pm 1$ standard deviation. The inset at the bottom right shows the full inferred weight matrix $\hat{\mathbf{W}}$. Each row corresponds to inference results from spike data simulated using the threshold-crossing model (top) and the LNP model (bottom). (b-d) Subsequent columns present the inference quality of baseline methods: (b) GLM, (c) seqNMF, and (d) TCA.
• Figure 3: Evaluating connectivity inference. Top: bump dynamics in a ring attractor network driven by external input. Bottom: dynamics under a modified recurrent connectivity profile. (a) Transition from a local Mexican-hat profile (top) to a new configuration with local excitation and broadly tuned inhibition (bottom). (b) Spike raster plot showing rotating activity bumps induced by sinusoidal external inputs. (c) Comparison of ground-truth (orange) and inferred (blue) weight profiles estimated using GNN, GLM, seqNMF, and TCA, following the same order as the corresponding sub-figures.
• Figure 4: Evaluation of inference performance in a partially observed network as a function of the total number of neurons used for inference. (a) Ground-truth synaptic weight matrix with a smooth, spatially structured profile on a ring. (b) Synthetic weight matrix among observed neurons only ($N_o = 80$). The matrix is not inferred from spike train data but constructed by masking unobserved rows and columns of the ground-truth matrix in (a), followed by the addition of small uniform noise to mimic inference uncertainty. (c) Full weight matrix after two-dimensional interpolation, showing partial recovery of spatial structure. (d) Control: shuffled version of the inferred matrix, where either rows or columns are randomly permuted to disrupt spatial organization while preserving marginal distributions. (e) Interpolated version of the shuffled matrix exhibits degraded structure and higher error ($\Delta = 0.53$) compared to the unshuffled case ($\Delta = 0.27$). (f) Spike prediction accuracy ($\mathcal{L}_{\text{bps}}$) improves as more neurons are incorporated, with colored curves representing different numbers of observed neurons ($N_o = 60, 80, 100$). Error bars denote one standard deviation. (g) Circuit inference error ($\Delta$) plotted against the total number of neurons used for inference. Small insets show interpolated weight profiles for selected configurations, revealing how the structure quality varies with observed-to-hidden neuron ratios.
• Figure 5: Inferred weight profiles derived from 19 real HD cells in the anterodorsal thalamic nucleus (ADn) of mice, with the number of observed neurons fixed at $N_o=19$ and the number of hidden neurons ($N_h$) increasing from 0 to 20. The weights are obtained through linear interpolation under the assumption that the total number of neurons is set to 100.