Does invariant recognition predict tuning of neurons in sensory cortex?
Tuning properties of simple cells in cortical V1 can be described in terms of a "universal shape" characterized by parameter values which hold across different species. This puzzling set of findings begs for a general explanation grounded on an evolutionarily important computational function of the visual cortex. We ask here whether these properties are predicted by the hypothesis that the goal of the ventral stream is to compute for each image a "signature" vector which is invariant to geometric transformations, with the the additional assumption that the mechanism for continuously learning and maintaining invariance consists of the memory storage of a sequence of neural images of a few objects undergoing transformations (such as translation, scale changes and rotation) via Hebbian synapses. For V1 simple cells the simplest version of this hypothesis is the online Oja rule which implies that the tuning of neurons converges to the eigenvectors of the covariance of their input. Starting with a set of dendritic fields spanning a range of sizes, simulations supported by a direct mathematical analysis show that the solution of the associated "cortical equation" provides a set of Gabor-like wavelets with parameter values that are in broad agreement with the physiology data. We show however that the simple version of the Hebbian assumption does not predict all the physiological properties. The same theoretical framework also provides predictions about the tuning of cells in V4 and in the face patch AL which are in qualitative agreement with physiology data.