Hairy neuron convergence theorems without the precision of timing

The author assumes arbitrary timing and individual time scales for each McCulloch-Pitts neurons, and proved the convergences of computational energies for a hard-wired Hopfield-like E(V_i), a soft-wired Rumelhart-like E(W_ij) and a brittal-wired Hairy-Neuron E(V_i, T_ij) neurocomputers. All assume the characteristic of an inhomogeneous architecture and imprecise timing. An important question for practical applications is how to speed up the training process and to ensure a fast convergence of weight adjustment? The authors have suggested a general procedure of Taylor series expansion of the clustering-declustering mini-max cost energy to estimate the synaptic weights (IJCNN-89 vol.1, p.485). They augment the Taylor expansion procedure by a self-consistently variational technique, so that a fast training is mathematically equivalent to make the truncated higher order terms of the Taylor series negligable. A typical mini-max cost function consists of (1) the sample variance of each class in the numerator, and (2) separation of the center of each class in the denominator. Thus, when the total cost energy is minimized, the conflicting goals of intraclass clustering and interclass segregation are achieved simultaneously. This Taylor expansion variable is a neuronic vector representation which traces along a Peano´s curve