We review and apply a computational theory of the feedforward path of the ventral stream in visual cortex based on the hypothesis that its main function is the encoding of invariant representations of images. A key justification of the theory is provided by a theorem linking invariant representations to small sample complexity for recognition – that is, invariant representations allows learning from very few labeled examples. The theory characterizes how an algorithm that can be implemented by a set of ”simple” and ”complex” cells – a ”HW module” – provides invariant and selective representations. The invariance can be learned in an unsupervised way from observed transformations. Theorems show that invariance implies several properties of the ventral stream organization, including the eccentricity dependent lattice of units in the retina and in V1, and the tuning of its neurons. The theory requires two stages of processing: the first, consisting of retinotopic visual areas such as V1, V2 and V4 with generic neuronal tuning, leads to representations that are invariant to translation and scaling; the second, consisting of modules in IT, with class- and object-specific tuning, provides a representation for recognition with approximate invariance to class specific transformations, such as pose (of a body, of a face) and expression. In the theory the ventral stream main function is the unsupervised learning of ”good”
representations that reduce the sample complexity of the final supervised learning stage.