Fine-Grained System Identification of Nonlinear Neural Circuits

TL;DR

This paper develops a method for recovering detailed nonlinear neural circuit models from data, revealing key conditions like sign constraints for successful system identification, with practical applications demonstrated on retinal circuits.

Contribution

It introduces a novel approach for sparse nonlinear model recovery of neural circuits, including theoretical guarantees and empirical validation with biological data.

Findings

Sign constraints are necessary for system recovery.

Theoretical identifiability guarantees are established.

Successful application to mouse retina data.

Abstract

We study the problem of sparse nonlinear model recovery of high dimensional compositional functions. Our study is motivated by emerging opportunities in neuroscience to recover fine-grained models of biological neural circuits using collected measurement data. Guided by available domain knowledge in neuroscience, we explore conditions under which one can recover the underlying biological circuit that generated the training data. Our results suggest insights of both theoretical and practical interests. Most notably, we find that a sign constraint on the weights is a necessary condition for system recovery, which we establish both theoretically with an identifiability guarantee and empirically on simulated biological circuits. We conclude with a case study on retinal ganglion cell circuits using data collected from mouse retina, showcasing the practical potential of this approach.