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General-purpose computation with neural networks: a survey of complexity theoretic results

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This work surveys and summarizes the literature on the computational aspects of neural network models by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics, mainly on the digital computation whose inputs and outputs are binary in nature, although their values are quite often encoded as analog neuron states.
Abstract
We survey and summarize the literature on the computational aspects of neural network models by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics. The criteria of classification include the architecture of the network (feedforward versus recurrent), time model (discrete versus continuous), state type (binary versus analog), weight constraints (symmetric versus asymmetric), network size (finite nets versus infinite families), and computation type (deterministic versus probabilistic), among others. The underlying results concerning the computational power and complexity issues of perceptron, radial basis function, winner-take-all, and spiking neural networks are briefly surveyed, with pointers to the relevant literature. In our survey, we focus mainly on the digital computation whose inputs and outputs are binary in nature, although their values are quite often encoded as analog neuron states. We omit the important learning issues.

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Sima, Jiri; Orponen, Pekka
General purpose computation with neural networks: a survey of complexity theoretic results
Published in:
Neural Computation
DOI:
10.1162/089976603322518731
Published: 01/01/2003
Document Version
Peer reviewed version
Please cite the original version:
Sima, J., & Orponen, P. (2003). General purpose computation with neural networks: a survey of complexity
theoretic results. Neural Computation, 15(12), 2727-2778. https://doi.org/10.1162/089976603322518731

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TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
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This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form.