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.

In this paper, we revisit the recurrent back-propagation (RBP) algorithm, discuss the conditions under which it applies as well as how to satisfy them in deep neural networks. We show that RBP can be unstable and propose two variants based on conjugate gradient on the normal equations (CG-RBP) and Neumann series (Neumann-RBP). We further investigate the relationship between Neumann-RBP and back propagation through time (BPTT) and its truncated version (TBPTT). Our Neumann-RBP has the same time complexity as TBPTT but only requires constant memory, whereas TBPTT’s memory cost scales linearly with the number of truncation steps. We examine all RBP variants along with BPTT and TBPTT in three different application domains: associative memory with continuous Hopfield networks, document classification in citation networks using graph neural networks and hyperparameter optimization for fully connected networks. All experiments demonstrate that RBPs, especially the Neumann-RBP variant, are efficient and effective for optimizing convergent recurrent neural networks.