Murthy G.R. Multidimensional Neural Networks. Unified Theory

New Age, 2005, -168 p.This book deals with a novel paradigm of neural networks, called multidimensional neural networks. It also provides comprehensive description of a certain unified theory of control, communication and computation. This book can serve as a textbook for an advanced course on neural networks or computational intelligence/cybernetics. Both senior undergraduate and graduate students can get benefit from such a course. It can also serve as a reference book for practicising engineers utilizing neural networks. Further more, the book can be used as a research monograph by neural network researchers.
In the field of electrical engineering, researchers have innovated sub-fields such as control theory, communication theory and computation theory. Concepts such as logic gates, error correcting codes and optimal control vectors arise in the computation, communication and control theories respectively. In one dimensional systems, the concept of error correcting codes, logic gates are related to neural networks. The author, in his research efforts showed that the optimal control vectors (associated with a one dimensional linear system) constitute the stable states of a neural network. Thus unified theory is discovered and formalized in one dimensional systems. Questioning the possibility of logic gates operating on higher dimensional arrays resulted in the discovery as well as formalisation of the research area of multi/infinite dimensional logic theory. The author has generalised the known relationship between one dimensional logic theory and one dimensional neural networks to multiple dimensions. He has also generalised the relationship between one dimensional neural networks and error correcting codes to multidimensions (using generator tensor).
On the way to unification in multidimensional systems the author has discovered and formalised the concept of tensor state space representation of certain multidimensional linear systems. It is well accepted that the area of complex valued neural networks is a very promising research area. The author has proposed a novel activation function called the complex signum function. This function has enabled proposing a complex valued neural associative memory on the complex hypercube. He also proposed novel models of neuron (such as linear filter model of synapse).Multi/Infinite Dimensional Neural Networks, Multi/Infinite Dimensional Logic Theory
Multi/Infinite Dimensional Coding Theory: Multi/Infinite Dimensional Neural Networks — Constrained Static Optimization
Tensor State Space Representation: Multidimensional Systems
Unified Theory of Control, Communication and Computation: Multidimensional Neural Networks
Complex Valued Neural Associative Memory on the Complex Hypercube
Optimal Binary Filters: Neural Networks
Linear Filter Model of a Synapse: Associated Novel Real/Complex Valued Neural Networks
Novel Complex Valued Neural Networks
Advanced Theory of Evolution of Living Systems