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

Abstract

Abstract:In the context of the modeling and simulation of neural nets, we formulate definitions for the 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 earlier generations of neural net models, third generation spiking neural nets exhibit important temporal and dynamic properties, and random neural nets provide alternative probabilistic approaches. Our definitions of realization are based on the Discrete Event System Specification (DEVS) formalism that fundamentally include temporal and probabilistic characteristics of neuron system inputs, state, and outputs. The realizations that we construct-in particular for the Exclusive Or (XOR) logic gate-provide insight into the temporal and probabilistic characteristics that real neural systems might display. Our results provide a solid system-theoretical foundation and simulation modeling framework for the high-performance computational support of such applications.

DEVS-Based Building Blocks and Architectural Patterns for Intelligent Hybrid Cyberphysical System Design

“…Definitions for state-based realization of cognitive behaviors based on mathematical system theory and DEVS fundamentally include temporal and probabilistic characteristics of neuron system inputs, state, and outputs [1] and provide a solid system-theoretical foundation and simulation modeling framework for the high-performance computational support of such applications. Spiking neural nets (SNN), [20][21][22][23][24][25] a form of hybrid continuous discrete event abstraction, have demonstrated potential for solving complicated time-dependent pattern recognition problems because of their inclusion of temporal and dynamic behavior [3]. Realizations of SNN's in DEVS have been shown [25,26].…”

“…Discrete Event System Specification (DEVS) and its extensions to hybrid modeling and simulation [1][2][3] are increasingly being adopted as the preferred approach to intelligent hybrid (continuous and discrete) cyberphysical system design [4][5][6][7][8][9]. After decades of developments in its theory, software support, and breadth of applications, the DEVS formalism has been recognized to support generic open architectures that allows incorporating multiple engineering domains within integrated simulation models.…”