We recorded the activity of single V2 neurons in macaque monkeys. We presented a sequence of binocular images, refreshed every 100 ms, for 20-30 minutes to an area encompassing both the classical center and surround of the receptive fields. Each frame contained locally oriented structure designed to drive V1 cells; local structures were uncorrelated across both space and time. This design was intended to evoke uncorrelated responses in the V1 cells providing input to V2, while robustly driving the V2 cells.

To estimate V2 receptive fields, we first simulate responses of a V1 population using a field of local directional-derivative filters that densely cover the stimulus. Filter responses are squared or half-squared to generate model complex and simple cell responses, respectively. We then sought the best fitting linear model to explain the observed V2 spike rate as a function of model V1 responses. Given the size of the V1 population and the number of spikes in our recordings, a direct least squares solution tended to overfit the data. We therefore used an objective function that penalizes both the squared error of the fit to the data, as well as the sum of absolute values of the linear weights (an L1-norm regularization term). This objective function favors sparse solutions, and has been recently applied to a broad array of optimization and learning problems. We used the LARS/Lasso algorithm (Efron et. al. 2002) in our search.

The model performed well at predicting the responses of a holdout set of firing rates, accounting for more response variance than decorrelated spike-triggered average (average R2: dSTA - 0.055, LARS/Lasso - 0.067). V2 cells were much more likely to pool over complex cells than simple cells, and assigned larger weights to such units for all recorded neurons. For many cells, the selection capabilities of the sparse objective function allowed us to overcome the limitations of data dimensionality, producing receptive fields that depended on the covariance of a small number of afferent units. Together, these results indicate that estimating receptive field structures based on an explicit input model is a promising approach for investigating neural response properties in extrastriate cortex.