DNN-Assisted Statistical Analysis of a Model of Local Cortical Circuits

Abstract

This paper is about the use of Deep Neural Networks (DNN) to assist in the statistical analysis of a network of a few hundred integrate-and-fire neurons intended to model local circuits in the cerebral cortex. Using training data produced by direct numerical simulations, our first task was to discover, with the aid of a DNN, the mapping that yields model response for each set of parameters and input values. After evaluating the performance of the DNN surrogate both in the accuracy of its outputs and in its performance in parameter tuning, we analyzed the outputs of the well-trained DNN to gain insight into local circuits as basic cortical computational units. Because the DNN surrogate computed with vastly higher speeds than actual simulations of the neuronal network, we were able to sample large sets of parameters and input values to produce a broad statistical picture of input-output relations. One of the aims of this paper is to demonstrate that statistical analyses of this kind can provide general theoretical information on model behavior as well as suggest cortical mechanisms. Among our results are the following: Through a derivative analysis of model responses we identified a certain dichotomy in the behavior of I-neurons, leading to a characterization of high gain states which in turn offered insight into mechanisms for surround suppression. A second-derivative analysis revealed limitations of models of integrate-and-fire neurons, namely their inability to replicate the nonlinearities in gain curves observed in real neurons. Author summaryLocal circuits are basic computational units of the cerebral cortex, and statistical analysis of detailed models of such circuits will shed light on cortical computation. Because analytical tools are either overly simplistic or not applicable, systematic numerical exploration of high-dimensional parameter space is not feasible and simulation-based arguments are seldom more than heuristic, we propose in this paper a data-driven DNN-assisted approach that falls into the general framework of surrogate-based modeling. We consider as a test case a network of integrate-and-fire neurons intended to model local circuits in cortex. With the help of an accurate yet extremely efficient DNN surrogate, we reveal the statistics of model response, providing a detailed picture of model behavior. The information obtained is both general and of a fundamental nature, with direct application to neuroscience. Our results suggest that the methodology proposed can be scaled up to larger and more complex neuronal models.