Complexity of error hypersurfaces in multilayer perceptrons.
Error hypersurfaces are very valuable to study because of their unique status in multilayer perceptron research. Given the architecture of a multilayer perceptron, if the pattern sets are different, so are the respective error hypersurfaces in the multilayer perceptron. Using the theory of groups and Polya Theorem, this paper constructs classes of congruent pattern sets and classes of congruent error hypersurfaces, and proves that the number of classes of congruent pattern sets is equal to the number of congruent error hypersurfaces. Calculation results lead to much fewer classes of congruent error hypersurfaces than the total error hypersurfaces, and show that as the input dimension N increases, the former number increases at a much lower rate than the latter number, thus simplifying the understanding of the complexity of classes of error hypersurfaces.
Liang
Xun
X
Institute of Computer Science and Technology, Peking University, Beijing 100871, China. liangxun@founder.com
D000465:Algorithms; D001185:Artificial Intelligence; D008959:Models, Neurological; D015233:Models, Statistical; D016571:Neural Networks, Computer