Minimizing the Quadratic Training Error of a Sigmoid Neuron is Hard

0404256 - UIVT-O 20010079 RIV DE eng C - Conference Paper (international conference)
Šíma, Jiří
Minimizing the Quadratic Training Error of a Sigmoid Neuron is Hard.
Algorithmic Learning Theory. Berlin: Springer, 2001 - (Abe, N.; Khardon, R.; Zeugmann, T.), s. 92-105. Lecture Notes in Computer Science, 2225. ISBN 3-540-42875-5.
[ALT'2001. International Conference /12./. Washington (US), 25.11.2001-28.11.2001]
R&D Projects: GA AV ČR IAB2030007; GA ČR GA201/00/1489
Institutional research plan: AV0Z1030915
Keywords : loading problem * learning complexity * NP-hardness * sigmoid neuron * back-propagation * constructive learning
Subject RIV: BA - General Mathematics

We first present a brief survey of hardness results for training feedforward neural networks. These results are then completed by the proof that the simplest architecture containing only a single neuron that applies the standard (logistic) activation function to the weighted sum of n inputs is hard to train. In particular,the problem of finding the weights of such a unit that minimize the relative quadratic training error within 1 or its average (over a training set) within 13/(31n) of its infimum proves...
Permanent Link: http://hdl.handle.net/11104/0124519