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Constant depth circuits, Fourier transform, and learnability
Open accessAbstract
In this paper, Boolean functions in ,4C0 are studied using harmonic analysis on the cube.The main result is that an ACO Boolean function has almost all of its "power spectrum" on the low-order coefficients.An important ingredient of the proof is Hastad's switching lemma [8].This result implies several new properties of functions in -4C[': Functions in AC() have low "average sensitivity;" they may be approximated well by a real polynomial of low degree and they cannot be pseudorandom function generators.Perhaps the most interesting application is an O(n POIYIOg(n ')-time algorithm for learning functions in ACO.The algorithm observes the behavior of an AC'" function on O(nPO'Y'Og(n)) randomly chosen inputs, and derives a good approximation for the Fourier transform of the function.This approximation allows the algorithm to predict, with high probability, the value of the function on other randomly chosen inputs.
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Valiant, L. G. (1984) · Communications of the ACM · doi:10.1145/1968.1972 · Cited by 3,279
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Diakonikolas, I., O'Donnell, R., Servedio, R. A., & Wu, Y. (2011) · Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms · doi:10.1137/1.9781611973082.123 · Cited by 6
Metadata
- Authors
- Linial, N., Mansour, Y., & Nisan, N.
- Venue
- Journal of the ACM
- Published
- 1993-07
- Volume
- 40
- Issue
- 3
- Pages
- 607-620
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2042194938
- Cited by
- 572
- References
- 1
- FWCI
- 9.03
- Type
- journal article
- Language
- en
- Open access
- bronze
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