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Communication Complexity and Lower Bounds for Threshold Circuits

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Theoretical Advances in Neural Computation and Learning

Abstract

The study of threshold circuits is interesting for several reasons. First, constant-depth threshold circuits are closely related to feed-forward neural networks, a widely studied model. The main difference is that while a threshold gate has Boolean inputs and output, a “neuron” in a neural network can have real numbers as inputs and typically outputs a continuous approximation of a step-function. However, Maass, Schnitger, and Sontag show in [MSS91] that when one considers the computation of Boolean functions the two models are equally powerful (within polynomial factors) (see also Chapter 4).

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Author information

Authors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, NE43-340, Cambridge, MA, 02139, USA

    Mikael Goldmann

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  1. Mikael Goldmann
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Editors and Affiliations

  1. Purdue University, West Lafayette, Indiana, USA

    Vwani Roychowdhury

  2. University of California, Irvine, California, USA

    Kai-Yeung Siu

  3. AT&T Bell Laboratories, Murray Hill, New Jersey, USA

    Alon Orlitsky

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Goldmann, M. (1994). Communication Complexity and Lower Bounds for Threshold Circuits. In: Roychowdhury, V., Siu, KY., Orlitsky, A. (eds) Theoretical Advances in Neural Computation and Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2696-4_3

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  • DOI: https://doi.org/10.1007/978-1-4615-2696-4_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6160-2

  • Online ISBN: 978-1-4615-2696-4

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