Selective and invariant features of neural response surfaces measured with principal curvature

Abstract

The responses of most visual cortical neurons are highly nonlinear functions of image stimuli. With the sparse coding network, a recurrent model of V1 computation, we apply techniques from differential geometry to these nonlinear responses and classify them as forms of selectivity or invariance. The selectivity and invariance of responses of individual neurons are quantified by measuring the principal curvatures of neural response surfaces in high-dimensional image space. An extended two-layer version of the network model that captures some properties of higher visual cortical areas is also characterized using this approach. We argue that this geometric view allows for the quantification of feature selectivity and invariance in network models in a way that provides insight into the computations necessary for object recognition.