Phase transitions in neural networks

Littlewort, G C

Phase transitions in neural networks

Master Thesis

1986

Publisher

University of Cape Town

Department

Department of Physics

Faculty

Faculty of Science

Abstract

The behaviour of computer simulations of networks of neuron-like binary decision elements is studied. The models are discrete in time and deterministic , but the sequence of states of neurons in a net is not generally reversible in time because of the threshold nature of neurons. Self-organisation, or activity-dependent modification of interneuronal connection strengths, is used. Cyclic modes of activity which emerge spontaneously, underlie possible mechanisms of short term memory and associative thinking. The transition from seemingly random activity patterns to cyclic activity is examined in isolated networks with pseudorandomly chosen connection matrices; and the transition is related to the gross properties of the network. Nets with inherent structure (from pseudorandom nature) and imposed structure are studied, when cycles of length greater than, say, 12 time units are considered separately from the less complex, shorter cycles; the aforementioned transitions appear to be consistently rapid, compared to the cycle length, unless architecture is imposed such that nearly independent groups of neurons exist in the same net.

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