• Corpus ID: 245424756

Learning with distributional inverters

@article{Binnendyk2021LearningWD,
  title={Learning with distributional inverters},
  author={Eric Binnendyk and Marco Carmosino and Antonina Kolokolova and Ramyaa and Manuel Sabin},
  journal={ArXiv},
  year={2021},
  volume={abs/2112.12340}
}

• Eric Binnendyk, M. Carmosino, +2 authors Manuel Sabin
• Published 23 December 2021
• Mathematics, Computer Science
• ArXiv

We generalize the “indirect learning” technique of Furst et al. (1991) to reduce from learning a concept class over a samplable distribution µ to learning the same concept class over the uniform distribution. The reduction succeeds when the sampler for µ is both contained in the target concept class and efficiently invertible in the sense of Impagliazzo and Luby (1989). We give two applications. • We show that AC 0 [ q ] is learnable over any succinctly-described product distribution. AC 0 [ q ] is the class of constant-depth Boolean circuits of polynomial size with AND, OR, NOT, and counting modulo q gates of unbounded fanins. Our algorithm runs in randomized quasi-polynomial time and uses membership queries. • If there is a strongly useful natural property in the sense of Razborov and Rudich (1997) — an efficient algorithm that can distinguish between random strings and strings of non-trivial circuit complexity — then general polynomial-sized Boolean circuits are learnable over any efficiently samplable distribution in randomized polynomial time, given membership queries to the target funuction.