License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2016.10
URN: urn:nbn:de:0030-drops-58557
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5855/
Go to the corresponding LIPIcs Volume Portal

Carmosino, Marco L. ; Impagliazzo, Russell ; Kabanets, Valentine ; Kolokolova, Antonina

Learning Algorithms from Natural Proofs

pdf-format:
34.pdf (0.7 MB)

Abstract

Based on Hastad's (1986) circuit lower bounds, Linial, Mansour, and Nisan (1993) gave a quasipolytime learning algorithm for AC^0 (constant-depth circuits with AND, OR, and NOT gates), in the PAC model over the uniform distribution. It was an open question to get a learning algorithm (of any kind) for the class of AC^0[p] circuits (constant-depth, with AND, OR, NOT, and MOD_p gates for a prime p).

Our main result is a quasipolytime learning algorithm for AC^0[p] in the PAC model over the uniform distribution with membership queries. This algorithm is an application of a general connection we show to hold between natural proofs (in the sense of Razborov and Rudich (1997)) and learning algorithms. We argue that a natural proof of a circuit lower bound against any (sufficiently powerful) circuit class yields a learning algorithm for the same circuit class. As the lower bounds against AC^0[p] by Razborov (1987) and Smolensky (1987) are natural, we obtain our learning algorithm for AC^0[p].

BibTeX - Entry

@InProceedings{carmosino_et_al:LIPIcs:2016:5855,
  author =	{Marco L. Carmosino and Russell Impagliazzo and Valentine Kabanets and Antonina Kolokolova},
  title =	{{Learning Algorithms from Natural Proofs}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{10:1--10:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Ran Raz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5855},
  URN =		{urn:nbn:de:0030-drops-58557},
  doi =		{10.4230/LIPIcs.CCC.2016.10},
  annote =	{Keywords: natural proofs, circuit complexity, lower bounds, learning, compression}
}

Keywords: natural proofs, circuit complexity, lower bounds, learning, compression
Collection: 31st Conference on Computational Complexity (CCC 2016)
Issue Date: 2016
Date of publication: 19.05.2016

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI