A Liquid-Crystal Model for Neural Networks

In this pap er , t he interaction between molecular free-point dipoles is prop osed as an analog of t he dynamics of randomly interconnected neurons. Typically, neural interaction has been described as being ana logous to the stochastic aspects of the magnetic Ising spin model. For example, Hopfield 's attractor neural network follows t he zero-field spin-glass analogy and warrants the neur al interconnections to have bilateral symmetric weights across the inte racting neurons. But t he act ua l neur al intercon nect ions may not pose such a symmet ry, because the stochastic aspects of excitatory and inhi bitory synapt ic responses are not the same; and, in general, ra ndom asymmetry in synaptic couplings more closely approximates physiological reality. The int erconnecting weights that decide the collect ive response across a neur al arrangement are asymmet ric bot h temporally as well as spatially. Lack of spatial symmet ry effects in the specificat ion of anisot ropic proli feration of neur al state-t ransit ions has motivat ed t he present work; the consiste nt requirement of symmetric weight s in neural assembly modeling (analogous to the Ising spin-glass model) is thereby obviated. In th e relevant considerat ions, neur al interactions are depicted as being similar to t hose of molecular free-point dipol esspecifically, those of a liquid crystal in the nematic phase having a long-range orient ati onal order. This partial anisot ropy in spatial orientation incorporates an asymmetry in synapt ic coupling act ivity, and is addressed via Langevin 's theory of dipole orientation . A stoc hast ically justifiable sigmoidal act ivatio n function is derived therefrom to represent the squas hing action in the input-output relation of t he complex dynamics pertinent to the cellular automata. 44 D. De GraH, P. S. Neelakanta, R. Sudhakar, and F. Medina