Methods for Building Network Models of Neural Circuits

Abstract

Artificial recurrent neural networks (RNNs) are powerful models for understanding and modeling dynamic computation in neural circuits. As such, RNNs that have been constructed to perform tasks analogous to typical behaviors studied in systems neuroscience are useful tools for understanding the biophysical mechanisms that mediate those behaviors. There has been significant progress in recent years developing gradient-based learning methods to construct RNNs. However, the majority of this progress has been restricted to network models that transmit information through continuous state variables since these methods require the input-output function of individual neuronal units to be differentiable. Overwhelmingly, biological neurons transmit information by discrete action potentials. Spiking model neurons are not differentiable and thus gradient-based methods for training neural networks cannot be applied to them. This work focuses on the development of supervised learning methods for RNNs that do not require the computation of derivatives. Because the methods we develop do not rely on the differentiability of the neural units, we can use them to construct realistic RNNs of spiking model neurons that perform a variety of benchmark tasks, and also to build networks trained directly from experimental data. Surprisingly, spiking networks trained with these non-gradient methods do not require significantly more neural units to perform tasks than their continuous-variable model counterparts. The crux of the method draws a direct correspondence between the dynamical variables of more abstract continuous-variable RNNs and spiking network models. The relationship between these two commonly used model classes has historically been unclear and, by resolving many of these issues, we offer a perspective on the appropriate use and interpretation of continuous-variable models as they relate to understanding network computation in biological neural circuits. Although the main advantage of these methods is their ability to construct realistic spiking network models, they can equally well be applied to continuous-variable network models. An example is the construction of continuous-variable RNNs that perform tasks for which they provide performance and computational cost competitive with those of traditional methods that compute derivatives and outperform previous non-gradient-based network training approaches. Collectively, this thesis presents efficient methods for constructing realistic neural network models that can be used to understand computation in biological neural networks and provides a unified perspective on how the dynamic quantities in these models relate to each other and to quantities that can be observed and extracted from experimental recordings of neurons