Symmetry breaking in soft clustering decoding of neural codes
Alexander G. Dimitrov, Albert E. Parker, Tomáš Gedeon · BMC Neuroscience · 2009
The first step toward discovering general principles of sensory processing is to determine the correspondence between neural activity patterns and sensory stimuli. We refer to this correspondence as a "neural code." The Information Bottleneck and the Information Distortion methods [ 1 , 3 ] approach the neural coding problem by finding an optimal clustering of paired stimulus/response observation ( X ; Y ) by solving a constrained optimization problem, with both equality and inequality constraints, in hundreds to thousands of dimensions. The method of annealing has been used to solve this optimization problem: starting at an uninformative solution, one tracks this solution as an annealing parameter varies. The solutions undergo a series of rapid changes with the increase of the annealing parameter (Figure 1 ). We relate the changes to bifurcations or phase transitions in a dynamical system. The form of the bifurcations is dictated by the subgroup structure of S N [ 2 ]. As a consequence of this symmetry, generically only pitchfork-like and saddle node bifurcations are possible. The purpose of this contribution is to describe these bifurcations in detail, and to indicate some of the consequences of the bifurcation structure. The results are then applied to the neural coding problem.