Abstract
We construct a predicate that is computable by a perceptron with linear size, order 1, and exponential weights, but which cannot be computed by any perceptron having subexponential\((2^{n^{o(1)} } )\) size, subpolynomial (n o(1)) order and subxponential weights. A consequence is that there is an oracle relative to which PNP is not contained in PP.
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Beigel, R. Perceptrons, PP, and the polynomial hierarchy. Comput Complexity 4, 339–349 (1994). https://doi.org/10.1007/BF01263422
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DOI: https://doi.org/10.1007/BF01263422