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.

翻译：我们研究高维构成功能的非线性模型很少恢复的问题。我们的研究的动机是神经科学中新出现的利用收集的测量数据恢复精细测的生物神经电路模型的机会。根据神经科学中现有的领域知识,我们探索在哪些条件下可以恢复产生培训数据的基本生物电路。我们的结果表明对理论和实践两方面的兴趣都有洞察力。最值得注意的是,我们发现对重量的标志限制是系统恢复的必要条件,我们从理论上以可识别性保证和模拟生物电路的经验来建立该系统。我们最后通过利用从老鼠视网膜收集的数据,对视网膜电路进行案例研究,展示了这一方法的实际潜力。