The computational intractability of training sigmoidal neural networks

We demonstrate that the problem of approximately interpolating a target function by a neural network is computationally intractable. In particular the interpolation training problem for a neural network with two monotone Lipschitzian sigmoidal internal activation functions and one linear output node...

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Veröffentlicht in:IEEE transactions on information theory 1997-01, Vol.43 (1), p.167-173
1. Verfasser: Jones, L.K.
Format: Artikel
Sprache:eng
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Zusammenfassung:We demonstrate that the problem of approximately interpolating a target function by a neural network is computationally intractable. In particular the interpolation training problem for a neural network with two monotone Lipschitzian sigmoidal internal activation functions and one linear output node is shown to be NP-hard and NP-complete if the internal nodes are in addition piecewise ratios of polynomials. This partially answers a question of Blum and Rivest (1992) concerning the NP-completeness of training a logistic sigmoidal 3-node network. An extension of the result is then given for networks with n monotone sigmoidal internal nodes and one convex output node. This indicates that many multivariate nonlinear regression problems may be computationally infeasible.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.567673