For the general multi-input and multi-output architecture of multilayer perceptrons, the issue of classes of congruent error hypersurfaces is converted into the issue of classes of congruent pattern sets. By finding the latter number which is much smaller than the total number of error hypersurfaces, the complexity of error hypersurfaces is reduced. This paper accomplishes the remaining work left by which only addresses multi-input and single-output architecture. It shows that from the input side, group G(N) includes all the possible orthogonal operations which make the error hypersurfaces congruent. In addition, it extends the results from the case of single output to the case of multiple outputs by finding the group S(M) of orthogonal operations. Also, the paper shows that from the output side, group S(M) includes all the possible orthogonal operations which make the error hypersurfaces congruent. The results in this paper simplify the complexity of error hypersurfaces in multilayer perceptrons.
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