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Scientific Lectures //

A Virtual Spiking Neuron Model Using Traveling Waves: Theory and Preliminary Simulation Results

Thomas P. Caudell, Ph.D. - Professor in the Departments of ECE, CS, and Psychology at the University of New Mexico

Presented: October 23, 2014

ABSTRACT: Categorical Neural Semantics Theory (CNST) applies category theory to help understand the structure-function relationship in neural systems. Category theory, also called conceptual mathematics; it is the study of mathematical structures and relationships between them. CNST formalizes the relationship between the structure of knowledge in the world and the structure of neural processing. In the near future, our CNST research will be exploring neural networks with extensive feedback connections. This will require integrating dynamical systems concepts into our neural semantic representations. Dynamical systems study how the state of a system evolves in time, and this evolution can depend strongly on how signals propagate around in the system. Neural networks are frequently studied within a dynamical systems framework, but they often lack some of the finer grained temporal properties of biological neural systems. We are interested in ways to efficiently incorporate some of these finer grained dynamics into our neural network models and to evaluate how they reflect neural semantic representations. This talk will present a hybrid neural model based of traveling waves that has the potential to bridge the canonical McCulloch-Pitts model with the more biologically plausible leaky integrate and fire model. A basic review of artificial neural models will be followed by a detailed description of the traveling wave neuron. Simulations will be shown that compare its functionality to the canonical biological models. Future work will be discussed as well.

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