Gravity Dual for a Model of Perception

Abstract

One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek-Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based on a vector condensation model coupled with the Euclidean Einstein-Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution.Comment: 21 pages, v2: condition on conformal invariance of a free vector model correcte