Carmosino, Marco L. ;
Impagliazzo, Russell ;
Kabanets, Valentine ;
Kolokolova, Antonina
Learning Algorithms from Natural Proofs
Abstract
Based on Hastad's (1986) circuit lower bounds, Linial, Mansour, and Nisan (1993) gave a quasipolytime learning algorithm for AC^0 (constantdepth 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 (constantdepth, 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 = {10:110:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770088},
ISSN = {18688969},
year = {2016},
volume = {50},
editor = {Ran Raz},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5855},
URN = {urn:nbn:de:0030drops58557},
doi = {10.4230/LIPIcs.CCC.2016.10},
annote = {Keywords: natural proofs, circuit complexity, lower bounds, learning, compression}
}
2016
Keywords: 

natural proofs, circuit complexity, lower bounds, learning, compression 
Seminar: 

31st Conference on Computational Complexity (CCC 2016)

Issue date: 

2016 
Date of publication: 

2016 