An algebraic model for generating and adapting neural networks by means ofoptimization methods

This paper describes a new scheme of binary codification of artificial neur al networks designed to generate automatically neural networks using any op timization method. Instead of using direct mapping of strings of bits in ne twork connectivities, this particular codification abstracts binary encodin g so that it does not reference the artificial indexing of network nodes; t his codification employs shorter string length and avoids illegal points in the search space, but does not exclude any legal neural network. With thes e goals in mind, an Abelian semi-group structure with neutral element is ob tained in the set of artificial neural networks with a particular internal operation called superimposition that allows building complex neural nets f rom minimum useful structures. This scheme preserves the significant featur e that similar neural networks only differ in one bit, which is desirable w hen using search algorithms. Experimental results using this codification w ith genetic algorithms are reported and compared to other codification meth ods in terms of speed of convergence and the size of the networks obtained as a solution.