The toroidal neural networks

In this paper we present the toroidal neural networks (TNN), a new class of neural network derived from discrete time-cellular neural networks (DT-CNN). TNN are characterized by 2D toroidal topology with local connections, by binary outputs and by a simple equation describing the dynamic of neuron states; binary outputs are obtained comparing initial and final states. Due to the expression of state dynamic, TNN learning has a very appealing geometric interpretation: a transformation, specified by means of a training input sequence, is represented through a polyhedron in the TNN weight space. Along with the definition and theory of TNN, we present a learning algorithm which, for a given transformation expressed by means of a training sequence, gives the set of TNN weights (if existing) which exactly implement the transformation: such a set of weights is a point belonging to the polyhedron representing the training sequence. Furthermore, the algorithm gives the exact minimal spatial locality characterizing the problem; in order to reduce the number of TNN weights, a heuristic is used to try to move neuron connectivity from the spatial to the temporal dimension