Complex Systems

A Liquid-Crystal Model for Neural Networks Download PDF

D. De Groff
P. S. Neelakanta
R. Sudhakar
Department of Electrical Engineering,
Florida Atlantic University, Boca Raton, FL 33431, USA

F. Medina
Department of Physics,
Florida Atlantic University, Boca Raton, FL 33431, USA


In this paper, the interaction between molecular free-point dipoles is proposed as an analog of the dynamics of randomly interconnected neurons. Typically, neural interaction has been described as being analogous to the stochastic aspects of the magnetic Ising spin model. For example, Hopfield's attractor neural network follows the zero-field spin-glass analogy and warrants the neural interconnections to have bilateral symmetric weights across the interacting neurons. But the actual neural interconnections may not pose such a symmetry, because the stochastic aspects of excitatory and inhibitory synaptic responses are not the same; and, in general, random asymmetry in synaptic couplings more closely approximates physiological reality. The interconnecting weights that decide the collective response across a neural arrangement are asymmetric both temporally as well as spatially. Lack of spatial symmetry effects in the specification of anisotropic proliferation of neural state-transitions has motivated the present work; the consistent requirement of symmetric weights in neural assembly modeling (analogous to the Ising spin-glass model) is thereby obviated. In the relevant considerations, neural interactions are depicted as being similar to those of molecular free-point dipoles---specifically, those of a liquid crystal in the nematic phase having a long-range orientational order. This partial anisotropy in spatial orientation incorporates an asymmetry in synaptic coupling activity, and is addressed via Langevin's theory of dipole orientation. A stochastically justifiable sigmoidal activation function is derived therefrom to represent the squashing action in the input-output relation of the complex dynamics pertinent to the cellular automata.