Recurrent neural networks (RNNs) have emerged as a prominent tool for modeling cortical function, and yet their conventional architecture is lacking in physiological and anatomical fidelity. In particular, these models often fail to incorporate two crucial biological constraints: i) Dale's law, i.e., sign constraints that preserve the "type" of projections from individual neurons, and ii) Structured connectivity motifs, i.e., highly sparse yet defined connections amongst various neuronal populations. Both constraints are known to impair learning performance in artificial neural networks, especially when trained to perform complicated tasks
but as modern experimental methodologies allow us to record from diverse neuronal populations spanning multiple brain regions, using RNN models to study neuronal interactions without incorporating these fundamental biological properties raises questions regarding the validity of the insights gleaned from them. To address these concerns, our work develops methods that let us train RNNs which respect Dale's law whilst simultaneously maintaining a specific sparse connectivity pattern across the entire network. We provide mathematical grounding and guarantees for our approaches incorporating both types of constraints, and show empirically that our models match the performance of RNNs trained without any constraints. Finally, we demonstrate the utility of our methods for inferring multi-regional interactions by training RNN models of the cortical network to reconstruct 2-photon calcium imaging data during visual behaviour in mice, whilst enforcing data-driven, cell-type specific connectivity constraints between various neuronal populations spread across multiple cortical layers and brain areas. In doing so, we find that the interactions inferred by our model corroborate experimental findings in agreement with the theory of predictive coding, thus validating the applicability of our methods.