Abstract In recent years, the number of neurons that we can record simultaneously has seen an exponential increase, presenting a daunting challenge: how do we analyze these complex and high-dimensional datasets to gain insight into how neural circuits perform computation? Tools from dynamical systems theory have successfully unraveled the computational machinery of artificial recurrent neural networks (RNNs) trained to perform goal-directed tasks. If we could apply these tools to biological neural circuits, it would provide unparalleled access to the inner workings of the brain and potentially allow us to connect theories of neural computation to real biological data. However, for these tools to be useful, we need to create in silico replicas whose dynamics faithfully represent the dynamics of the underlying biological system. To date, the best in silico replicas of biological networks are RNNs trained to produce output that matches recorded patterns of neuronal firing. While this approach is rapidly growing in popularity, it has critical flaws. Current training methodologies are not constrained to produce accurate representations of the underlying dynamics; in fact, RNNs are actually rewarded for inventing superfluous dynamics, so long as those dynamics help to reproduce recorded neural data. Additionally, these models often assume that the relationship (“embedding”) between latent activity and neural firing rates is linear; when this assumption proves false, the dynamical accuracy suffers. The problems of superfluous dynamics and non-linear embedding are especially severe when attempting to model a system of interacting neural circuits. The objective of this proposal is to develop a novel artificial neural network architecture that addresses the above challenges and allows our in-silico models to capture accurate dynamics that are built both within and across-circuits. My approach combines two key components: 1) neural ordinary differential equations (NODEs), a computational architecture that we have demonstrated learns dynamics more accurately and compactly than RNNs and 2) invertible neural network (INN) readouts, which eliminate superfluous dynamics and allow the model to approximate nonlinear embeddings. I will validate the ability of this model, called an Ordinary Differential equation auto-encoder with Invertible readout (ODIN), to find accurate within- and across-circuit dynamics using synthetic neural data and previously-collected multi-electrode recordings from monkeys. This tool will help to build a bridge between neural data and both local and distributed neural computations.

Recent advances in dynamical systems theory suggests that the best way to understand the mechanism of neural computation may not lie at the level of individual neurons, but instead through the dynamics of neural populations. To leverage this new perspective, we need tools that can model the dynamics of neural circuits, but the best models currently available have significant limitations that make their dynamical estimates inaccurate, and therefore poorly suited to give interpretable insight into neural computation. I propose a novel neural network architecture that could solve this problem, allowing computational models to learn accurate dynamics from neural data arising from single or multiple interacting neural circuits and helping us infer how neural computations are built by populations of neurons in the brain.