Speaker

Prof. Tom Taylor

Title

"Hebbian Markov Chains"

Abstract

Encouraged by successes of Killeen and Taylor in modeling certain biological neural processes, I consider the consequences of describing, or caricaturing, the interaction of neurons by Markov chains. A simple, and simple minded, model is presented.

I present simulations of nonhomogeneous Markov chains which "learn" according to Hebb's rule: transition probabilities which are "reinforced" are increased. Surprisingly(?), my results are: such chains do learn. Concretely, they converge to homogeneous Markov chains with increased determinism. In many cases the limiting chain is deterministic: each neuron communicates to only one neuron. The mathematical framework is sufficiently general that they may be applicable to emergent pattern formation in a variety of other contexts.

I also investigate the consequences of the hypothesis that the "unconditioned brain" is composed of neurons which are randomly interconnected. The behavior of such chains becomes independent of initial states with an astonishing rapidity, which increases as the number of neurons increases. By a leap of poetic interpretation, I consider this as evidence that the unconditioned brain computes and communicates poorly.