Network Designs Via Signaling Dynamics On Geometric Dynamic Graphs

Artificial neural networks are treated as black boxes. Generally,only the states of a subset of the network are considered to determine its efficacy, while the relationship between a neural network’s topology and its function remains under-theorized. For my analysis, I use a new class of event-driven recurrent neural networks—a geometric dynamic network modeled on canonical neurobiological signaling principles that allows to directly encode input data into its evolving dynamics—to forward a new type of machine learning approach. I accomplish this by first, mapping causal neuronal signal flows in the C. elegans connectome to show how the dynamic evolution of signal flows results in a unique internal representation of particular input data. Second, I propose two distinct approaches to determine the upper-bound for the amount of network dynamics needed for capturing the signaling evolution of the system. Using the upper-bound values, I construct a mathematical object representing the causal neuronal signaling dynamics, and delineate the interaction of sub-sub structures at various scales/heights of sub-graphs. Finally, based on recent theoretical propositions regarding optimal signaling in a geometric dynamic network, I show that neurons modify their axonal morphology so that the propagation time of an action potential, and the membrane’s refractory period become balanced. Thus, this work not only lays the foundation to construct and analyze a new class of artificial neural networks whose overall behavior and underlying dynamics are transparently coupled, it also provides fertile grounds for future work on biologically inspired artificial intelligence