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Training a Sigmoidal Node Is Hard

1999
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Neural Computation
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This paper proves that the task of computing near{optimal weights for sigmoidal nodes under the L 1 regression norm is NP{Hard. For the special case where the sigmoid is piecewise{linear we p r o ve a s l i g h tly stronger result, namely that computing the optimal weights is NP{Hard. These results parallel that for the one{node pattern recognition problem, namely that determining the optimal weights for a threshold logic node is also intractable. Our results have important consequences for

doi:10.1162/089976699300016449
fatcat:hdzoobbitjb6bginlypwmfjtnu