Neural latching dynamics: a percolation phase transition to sustained cognition
Complex systems and Biological physics seminar
Tuesday 20 July 2010
Alessandro Treves (SISSA)
A Potts associative memory, a simplified model of an extended cortical network, can retrieve up to p_c ~ C S^2/[a ln S] randomly assigned memory patterns, if C is the number of tensor connections per unit, S the number of Potts active states, and "a" the pattern sparseness (Kropff and Treves, 2005). That is, if memories are stored on the connections by a model Hebbian rule, analogous to the Hopfield model, attractor dynamics lead to the full cortical activity distribution from a partial, e.g. sensory cue. If patterns are correlated with each other and neural dynamics is endowed with plain fatigue, the network after retrieving the first pattern can hop to a second, to a third and so on – what we have dubbed latching dynamics (Treves, 2005). While with a few stored patterns latching dies out after a while, we find that it extends indefinitely in time above a critical value pl, which in a mean-field regime is independent of C and scales up with S. I shall discuss the critical issue of the values of C and S for which p_l < p_c, allowing a cortical network to function as a memory when cued and then to sustain infinite spontaneous transitions. It may be that humans crossed pl from below some hundred thousand years ago, through a kind of percolation phase transition. Work done in collaboration with Eleonora Russo.