# Invariant Recognition Predicts Tuning of Neurons in Sensory Cortex

## Abstract

Tuning properties of simple cells in cortical V1 can be described in terms of a “universal shape” characterized quantitatively by parameter values which hold across different species (Jones and Palmer 1987; Ringach 2002; Niell and Stryker 2008). This puzzling set of findings begs for a general explanation grounded on an evolutionarily important computational function of the visual cortex. We show here that these properties are quantitatively 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 (Anselmi et al. 2013b). The mechanism for continuously learning and maintaining invariance may be the memory storage of a sequence of neural images of a few (arbitrary) objects via Hebbian synapses, while undergoing transformations such as translation, scale changes and rotation. For V1 simple cells this hypothesis 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, we show with simulations suggested by a direct analysis, that the solution of the associated “cortical equation” effectively provides a set of Gabor-like shapes with parameter values that quantitatively agree with the physiology data. The same theory provides predictions about the tuning of cells in V4 and in the face patch AL (Leibo et al. 2013a) which are in qualitative agreement with physiology data.

## Notes

### Acknowledgments

This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF 1231216.

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