Estimating receptive fields of simple and complex cells in early visual cortex: A convolutional neural network model with parameterized rectification

Abstract

Neurons in the primary visual cortex respond selectively to simple features of visual stimuli, such as orientation and spatial frequency. Simple cells, which have phase-sensitive responses, can be modeled by a single receptive field filter in a linear-nonlinear model. However, it is challenging to analyze phase-invariant complex cells, which require more elaborate models having a combination of nonlinear subunits. Estimating parameters of these models is made more difficult by cortical neurons' trial-to-trial response variability. We develop a simple convolutional neural network method to estimate receptive field models for both simple and complex visual cortex cells from their responses to natural images. The model consists of a spatiotemporal filter, a parameterized rectifier unit (PReLU), and a two-dimensional Gaussian "map" of the receptive field envelope. A single model parameter determines the simple vs. complex nature of the receptive field, capturing complex cell responses as a summation of homogeneous subunits, and collapsing to a linear-nonlinear model for simple type cells. The convolutional method predicts simple and complex cell responses to natural image stimuli as well as grating tuning curves. The model estimates yield a continuum of values for the PReLU parameter across the sampled neurons, showing that the simple/complex nature of cells can vary in a continuous manner. We demonstrate that complex cells respond less reliably than simple cells - compensation for this unreliability reveals good predictive performance on novel sets of natural images, with predictive performance for complex cells proportionately closer to that for simple cells. Most spatial receptive field structures are well fit by Gabor functions, whose parameters confirm well-known properties of cat A17/18 receptive fields.