CORNN: Convex optimization of recurrent neural networks for rapid inference of neural dynamics

Advances in optical and electrophysiological recording technologies have made it possible to record the dynamics of thousands of neurons, opening up new possibilities for interpreting and controlling large neural populations in behaving animals. A promising way to extract computational principles from these large datasets is to train data-constrained recurrent neural networks (dRNNs). Performing this training in real-time could open doors for research techniques and medical applications to model and control interventions at single-cell resolution and drive desired forms of animal behavior. However, existing training algorithms for dRNNs are inefficient and have limited scalability, making it a challenge to analyze large neural recordings even in offline scenarios. To address these issues, we introduce a training method termed Convex Optimization of Recurrent Neural Networks (CORNN). In studies of simulated recordings, CORNN attained training speeds $\sim$100-fold faster than traditional optimization approaches while maintaining or enhancing modeling accuracy. We further validated CORNN on simulations with thousands of cells that performed simple computations such as those of a 3-bit flip-flop or the execution of a timed response. Finally, we showed that CORNN can robustly reproduce network dynamics and underlying attractor structures despite mismatches between generator and inference models, severe subsampling of observed neurons, or mismatches in neural time-scales. Overall, by training dRNNs with millions of parameters in subminute processing times on a standard computer, CORNN constitutes a first step towards real-time network reproduction constrained on large-scale neural recordings and a powerful computational tool for advancing the understanding of neural computation.