eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-05-19
10:1
10:24
10.4230/LIPIcs.CCC.2016.10
article
Learning Algorithms from Natural Proofs
Carmosino, Marco L.
Impagliazzo, Russell
Kabanets, Valentine
Kolokolova, Antonina
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].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol050-ccc2016/LIPIcs.CCC.2016.10/LIPIcs.CCC.2016.10.pdf
natural proofs
circuit complexity
lower bounds
learning
compression