Fine-Grained System Identification of Nonlinear Neural Circuits
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.
© 2021 Copyright held by the owner/author(s). This work is licensed under a Creative Commons Attribution International 4.0 License. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1745301. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work was also funded by a cloud computing grant from Amazon Web Services in collaboration with the Information Science and Technology initiative at Caltech. This work was also supported by the Simons Collaboration on the Global Brain (grant 543015 to Markus Meister). Jeremy Bernstein was supported in part by an NVIDIA Fellowship and by NASA TRISH-RFA-BRASH 1901. Yu-Li Ni was supported by Taipei Veterans General Hospital-National Yang-Ming University Excellent Physician Scientists Cultivation Program, No. 103-Y-A-003. The authors thank James Parkin for providing original illustrations of retinal neurons.
Accepted Version - 2106.05400.pdf
Published - 3447548.3467402.pdf