Our model consists of simple-like linear-nonlinear (LN) subunits, linearly pooled to generate neural responses. A complex cell would have many subunits distributed over space to yield phase invariance, while a simple cell would have only one. When fitting the three stages of this LN-L model (filter, output nonlinearity, spatial pooling), we assume that subunits differ from one another only in location. This constraint reduces the problem of model estimation to a simple well-behaved coordinate descent procedure. This basic method can be extended to create multiple subunit "channels" that add at the final linear stage, for example one excitatory and one suppressive.

We recorded from 38 cells in anesthetized macaque V1 and characterize their receptive fields with dense ternary white pixel noise. The model performs well: across V1 neurons, we measured an average cross-validated correlation coefficient between the actual and predicted firing rate of 0.52 +/- 0.04 (SEM). The model performed equally well for cells distributed along the simple-complex spectrum. Moreover, the subunit model provides a concise and interpretable depiction of the receptive field; the LN subunits describe the tuning parameters and selectivity, while the final linear pooling describes the spatial extent and phase invariance of the cell. The simplicity of the model also allows it to avoid overfitting, outperforming STC for an equivalent amount of data.