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    Complexity Results on Learning by Neural Nets

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    LV91.complexity_neuralnets.pdf (258.8Kb)
    Issue Date
    1991
    Author
    Lin, Jyh-Han
    Vitter, Jeffrey Scott
    Publisher
    Springer Verlag
    Type
    Article
    Article Version
    Scholarly/refereed, author accepted manuscript
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    Abstract
    We consider the computational complexity of learning by neural nets. We are inter- ested in how hard it is to design appropriate neural net architectures and to train neural nets for general and specialized learning tasks. Our main result shows that the training problem for 2-cascade neural nets (which have only two non-input nodes, one of which is hidden) is NP-complete, which implies that nding an optimal net (in terms of the number of non-input units) that is consistent with a set of exam- ples is also NP-complete. This result also demonstrates a surprising gap between the computational complexities of one-node (perceptron) and two-node neural net training problems, since the perceptron training problem can be solved in polynomial time by linear programming techniques. We conjecture that training a k-cascade neural net, which is a classical threshold network training problem, is also NP-complete, for each xed k 2. We also show that the problem of nding an optimal perceptron (in terms of the number of non-zero weights) consistent with a set of training examples is NP-hard. Our neural net learning model encapsulates the idea of modular neural nets, which is a popular approach to overcoming the scaling problem in training neural nets. We investigate how much easier the training problem becomes if the class of concepts to be learned is known a priori and the net architecture is allowed to be su ciently non-optimal. Finally, we classify several neural net optimization problems within the polynomial-time hierarchy.
    URI
    http://hdl.handle.net/1808/7214
    DOI
    https://doi.org/10.1023/A:1022657626762
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    • Provost Office Published Articles [95]
    • Electrical Engineering and Computer Science Scholarly Works [288]
    • Distinguished Professors Scholarly Works [918]
    Citation
    J.-H. Lin and J. S. Vitter. “Complexity Results on Learning by Neural Nets,” Machine Learning, 6, 1991, 211–230. An extended abstract appears in Proceedings of the 2nd Annual ACM Workshop on Computational Learning Theory (COLT ’89), Santa Cruz, CA, July–August 1989, published by Morgan Kaufmann, San Mateo, CA, 118–133. http://dx.doi.org/10.1023/A:1022657626762

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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