A Guide to Learning Arithmetic Circuits

Abstract

An \empharithmetic circuit is a directed acyclic graph in which the operations are {+,\times}. In this paper, we exhibit several connections between learning algorithms for arithmetic circuits and other problems. In particular, we show that: \beginitemize \it{em} Efficient learning algorithms for arithmetic circuit classes imply explicit exponential lower bounds. \it{em} General circuits and formulas can be learned efficiently with membership and equivalence queries iff they can be learned efficiently with membership queries only. \it{em} Low-query learning algorithms for certain classes of circuits imply explicit rigid matrices. \it{em} Learning algorithms for multilinear depth-3 and depth-4 circuits must compute square roots. \enditemize

Cite

Text

Volkovich. "A Guide to Learning Arithmetic Circuits." Annual Conference on Computational Learning Theory, 2016.

Markdown

[Volkovich. "A Guide to Learning Arithmetic Circuits." Annual Conference on Computational Learning Theory, 2016.](https://mlanthology.org/colt/2016/volkovich2016colt-guide/)

BibTeX

@inproceedings{volkovich2016colt-guide,
  title     = {{A Guide to Learning Arithmetic Circuits}},
  author    = {Volkovich, Ilya},
  booktitle = {Annual Conference on Computational Learning Theory},
  year      = {2016},
  pages     = {1540-1561},
  url       = {https://mlanthology.org/colt/2016/volkovich2016colt-guide/}
}