Algorithms and Training for Weighted Multiset Automata and Regular Expressions

Abstract

Multiset automata are a class of automata for which the symbols can be read in any order and obtain the same result. We investigate weighted multiset automata and show how to construct them from weighted regular expressions. We present training methods to learn the weights for weighted regular expressions and for general multiset automata from data. Finally, we examine situations in which inside weights can be computed more efficiently.

Representing Unordered Data Using Complex-Weighted Multiset Automata

“…Definition 2 does not lend itself well to training, because parameter optimization needs to be done subject to the commutativity constraint. Previous work [DeBenedetto and Chiang, 2018] suggested approximating training of a multiset automaton by training a string automaton while using a regularizer to encourage the weight matrices to be close to commuting. However, this strategy cannot make them commute exactly, and the regularizer, which has O(|Σ| 2 ) terms, is expensive to compute.…”