Complexity of error hypersurfaces in multilayer perceptrons with general multi-input and multi-output architecture

Authors:
Xun Liang
Affiliations:
Institute of Computer Science and Technology, Peking University, Beijing, China
Venue:
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Year:
2005

Citing 3
Cited 0

Combinatorial enumeration of groups, graphs, and chemical compounds

Combinatorial enumeration of groups, graphs, and chemical compounds
Original Contribution: Uniqueness of the weights for minimal feedforward nets with a given input-output map

Neural Networks
On the geometry of feedforward neural network error surfaces

Neural Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 [4] 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.