Phase transitions of the information distortion

Albert Parker, Department of Mathematics, Montana State University

We analyze the phase transitions of a class of annealing problems which originate from Rate Distortion Theory and the Deterministic Annealing approach to clustering. Solutions of these problems have been used to approximate neural coding schemes in simple sensory systems. The phase transitions or bifurcations that the solutions undergo in the annealing process can be analyzed by capitalizing on the symmetries of the solutions. Theoretical and numerical results are presented for the Information Distortion problem.