title: Multi/infinite dimensional neural networks, multi/infinite dimensional logic theory.
abstract: A mathematical model of an arbitrary multi-dimensional neural network is developed and a convergence theorem for an arbitrary multi-dimensional neural network represented by a fully symmetric tensor is stated and proved. The input and output signal states of a multi-dimensional neural network/logic gate are related through an energy function, defined over the fully symmetric tensor (representing the connection structure of a multi-dimensional neural network). The inputs and outputs are related such that the minimum/maximum energy states correspond to the output states of the logic gate/neural network realizing a logic function. Similarly, a logic circuit consisting of the interconnection of logic gates, represented by a block symmetric tensor, is associated with a quadratic/higher degree energy function. Infinite dimensional logic theory is discussed through the utilization of infinite dimension/order tensors.
authors: International Institute of Information Technology (IIIT), Gachibowli, Hyderabad-500019, AP, India. rammurthy@iiit.net
authors: Garimella Rama
authors: GR
authors: Murthy
mesh_terms: D000465:Algorithms; D000818:Animals; D001245:Association Learning / Q000502:physiology; D006801:Humans; D007257:Information Theory; D008128:Logic; D008568:Memory / Q000502:physiology; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology; D016571:Neural Networks, Computer