# Fine-Grained System Identification of Nonlinear Neural Circuits

arXiv: https://arxiv.org/abs/2106.05400 · HTML: https://mlsanity.com/paper/2106.05400/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 65 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Deep Learning Models of the Retinal Response to Natural Scenes](https://mlsanity.com/paper/1702.01825/) (2017)
- [Neural system identification for large populations separating "what" and "where"](https://mlsanity.com/paper/1711.02653/) (2017)
- [Causal Structure Discovery from Distributions Arising from Mixtures of DAGs](https://mlsanity.com/paper/2001.11940/) (2020)
- [Neural network identifiability for a family of sigmoidal nonlinearities](https://mlsanity.com/paper/1906.06994/) (2019)
- [From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction](https://mlsanity.com/paper/1912.06207/) (2019)

## Abstract (arXiv)

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.