Nonlinear Weighted Finite Automata

Weighted finite automata (WFA) can expressively model functions defined over strings but are inherently linear models.Given the recent successes of non-linear models in machine learning, it is natural to wonder whether extending WFA to the non-linearsetting would be beneficial.In this paper, we propose a novel model of neural network based nonlinear WFA model (NL-WFA) along with a learning algorithm. Our learning algorithm is inspired by the spectral learning algorithm for WFA and relies on a non-linear decomposition of the so-called Hankel matrix, by means of an auto-encoder network. The expressive power of NL-WFA and the proposed learning algorithm are assessed on both synthetic and real world data, showing that NL-WFA can infer complex grammatical structures from data.