No abstract

We discuss the multi-dimensional Exclusive-OR (EOR) problems and the extension, general classification problem. These problems can be solved by multi-layer neural networks and the back propagation learning (BP) in systematic processing. However, the solution is reasonable in case of small dimension, i.e., under 6th, where the number of data is 26=64. Over 7th..., we haven't effective approach yet. It is very hard to find convergence path toward the global minimum to classify general cases. To break the limitation, we propose a partial stepwise learning for the BP, which is derived by a kind of symmetric character found in teaching data set. Where, there is no clear-cut symmetry but indistinct one; that is, the symmetry is defined for most of elements, but not for small parts. We used the ambiguous symmetric idea to get initial-guess for connections among neurons. Thus; we got a stepwise learning, and had solve EOR and generalized classifications less than Ith./10th.