Multidimensional Neural Networks Unified Theory by G. Rama Murthy
By G. Rama Murthy
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Extra info for Multidimensional Neural Networks Unified Theory
The results are interpreted as the dual to the ones in the previous section for defining the Maximum Likelihood Decoding (MLD) problem. In section 5, the results are generalized to nonbinary codes. Further, in section 6, the results are generalized to non-linear multidimensional codes. In section 7, by means of a decomposition principle, theorems related to optimization of tensor based (based on the components of a tensor) multivariate polynomials over arbitrary open/closed sets are proved. Also, various innovative ideas on the utilization of results in previous sections, to derive very general results in static optimization are described.
The set over which optimization is carried out is the unbounded unit hypercube (countable number of entries in the infinite dimensional state vector), a subset of the lattice ( based on one independent variable ). The following theorem is concerned with the points on the lattice in multi/infinite dimensions. This theorem is the infinite dimensional extension of the result proved in section 3. 4: Let MN = (S, T) be an infinite dimensional neural network of order n/ infinite and dimension infinity (number of neurons in each dimension).
Utilizing the convergence theorem, multidimensional logic functions are defined and multidimensional logic synthesis is discussed. Infinite dimensional logic synthesis is briefly described. Various constrained static optimization problems of utility in control, communication, computation and other applications are summarized. Several innovative themes on one/multidimensional neural networks are summarized. 26 Multidimensional Neural Networks: Unified Theory REFERENCES (BoT) A. I. Borisenko and I.