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On the complexity of recognizing iterated differences of polyhedra

  • Part III: Learning: Theory and Algorithms
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Artificial Neural Networks — ICANN'97 (ICANN 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1327))

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Abstract

The iterated difference of polyhedra V = P 1(P 2(...P k )...) has been proposed independently in [11] and [7] as a sufficient condition for V to be exactly computable by a two-layered neural network. An algorithm checking whether V d is an iterated difference of polyhedra is proposed in [11]. However, this algorithm is not practically usable because it has a high computational complexity and it was only conjectured to stop with a negative answer when applied to a region which is not an iterated difference of polyhedra. This paper sheds some light on the nature of iterated difference of polyhedra. The outcomes are : (i) an algorithm which always stops after a small number of iterations, (ii) sufficient conditions for this algorithm to be polynomial and (iii) the proof that an iterated difference of polyhedra can be exactly computed by a two-layered neural network using only essential hyperplanes.

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Wulfram Gerstner Alain Germond Martin Hasler Jean-Daniel Nicoud

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© 1997 Springer-Verlag Berlin Heidelberg

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Mayoraz, E. (1997). On the complexity of recognizing iterated differences of polyhedra. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020200

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  • DOI: https://doi.org/10.1007/BFb0020200

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63631-1

  • Online ISBN: 978-3-540-69620-9

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