Composition and Weight Pushing of Monotonic Subsequential Failure Transducers Representing Probabilistic Models

TL;DR

This paper introduces an efficient method for composing probabilistic subsequential transducers with failure transducers, enabling better weight redistribution and optimization in probabilistic models.

Contribution

It presents a novel construction for composing these transducers and a method for efficient weight pushing under specific conditions, improving model efficiency.

Findings

Efficient composition avoids unnecessary states.

Weights can be redistributed via weight pushing.

Applicable under certain transduction device conditions.

Abstract

We present a construction for the composition of subsequential transducers (representing conditional probabilistic models) with subsequential failure transducers (representing probabilistic models). Under certain conditions, satisfied by the corresponding transduction devices, a more efficient construction is applicable that avoids the creation of unnecessary states. Furthermore, the weights of the resulting failure transducers can be efficiently redistributed via weight pushing in the $\langle \mathbb{R}_+, +, \times, 0, 1 \rangle$ and $\langle \mathbb{R}_+, \max, \times, 0, 1 \rangle$ semirings.