  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.
