Temporal Modeling of Neural Net Input/Output Behaviors: The Case of XOR

In the context of modeling and simulation of neural nets, we formulate definitions for behavioral realization of memoryless functions. The definitions of realization are substantively different for deterministic and stochastic systems constructed of neuron-inspired components. In contrast to Artificial Neural Nets (ANN), and their myriad-layered deep forms, our definitions of realization fundamentally include temporal and probabilistic characteristics of their inputs, state, and outputs. The realizations that we construct, in particular for the XOR logic gate, provide insight into the temporal and probabilistic characteristics that real neural systems might display. We conclude with implications made when contrasting our time-based neural computation systems to ANN for what real brain computations might involve.