Approximating probabilistic models as weighted finite automata
This work addresses the need for efficient representation of probabilistic models in applications like language modeling, though it is incremental as it builds on existing WFA methods.
The authors tackled the problem of approximating arbitrary probabilistic sequence models as weighted finite automata (WFA) by developing an algorithm that minimizes Kullback-Leibler divergence, and demonstrated its utility in tasks like distilling n-gram models from neural models and building compact language models.
Weighted finite automata (WFA) are often used to represent probabilistic models, such as $n$-gram language models, since they are efficient for recognition tasks in time and space. The probabilistic source to be represented as a WFA, however, may come in many forms. Given a generic probabilistic model over sequences, we propose an algorithm to approximate it as a weighted finite automaton such that the Kullback-Leiber divergence between the source model and the WFA target model is minimized. The proposed algorithm involves a counting step and a difference of convex optimization step, both of which can be performed efficiently. We demonstrate the usefulness of our approach on various tasks, including distilling $n$-gram models from neural models, building compact language models, and building open-vocabulary character models. The algorithms used for these experiments are available in an open-source software library.