1. W. Maass, G. Schnitger, and E.D. Sontag. A comparison of the computational power of sigmoid and Boolean threshold circuits. In V. P. Roychowdhury, Siu K. Y., and Orlitsky A., editors, Theoretical Advances in Neural Computation and Learning, pages 127-151. Kluwer Academic Publishers, 1994. [PDF] Keyword(s): machine learning, neural networks, boolean systems. Abstract:

   We examine the power of constant depth circuits with sigmoid threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size boolean threshold circuits (i.e. circuits with linear threshold gates). On the other hand it turns out that, for any constant depth d, polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same boolean functions as the corresponding circuits with linear threshold gates.

1. W. Maass, G. Schnitger, and E.D. Sontag. On the computational power of sigmoid versus Boolean threshold circuits (extended abstract). In Proceedings of the 32nd annual symposium on Foundations of computer science, Los Alamitos, CA, USA, pages 767-776, 1991. IEEE Computer Society Press. Keyword(s): machine learning, neural networks, theory of computing and complexity.

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