On Invariance and Selectivity in Representation Learning

Fabio Anselmi, Lorenzo Rosasco, Tomaso A. Poggio

Abstract: We discuss data representation which can be learned automatically from data, are invariant to transformations, and at the same time selective, in the sense that two points have the same representation only if they are one the transformation of the other. The mathematical results here sharpen some of the key claims of i-theory -- a recent theory of feedforward processing in sensory cortex.