The problem with probabilistic DAG automata for semantic graphs

TL;DR

This paper critically examines probabilistic DAG automata for semantic graphs, revealing fundamental limitations in their ability to model probabilities effectively across various DAG variants.

Contribution

It demonstrates that many DAG automata cannot be converted into useful probabilistic models using standard weighting strategies, highlighting a key limitation.

Findings

Certain DAG automata cannot be probabilistically modeled with transition weights

The problem affects single-rooted, multi-rooted, and unbounded-degree DAG automata

Planar DAG automata are not affected by this issue

Abstract

Semantic representations in the form of directed acyclic graphs (DAGs) have been introduced in recent years, and to model them, we need probabilistic models of DAGs. One model that has attracted some attention is the DAG automaton, but it has not been studied as a probabilistic model. We show that some DAG automata cannot be made into useful probabilistic models by the nearly universal strategy of assigning weights to transitions. The problem affects single-rooted, multi-rooted, and unbounded-degree variants of DAG automata, and appears to be pervasive. It does not affect planar variants, but these are problematic for other reasons.