Neuro-symbolic entropy regularization
Kareem Ahmed, Eric Wang, Kai-Wei Chang, Guy Van den Broeck
Abstract
In structured output prediction, the goal is to jointly predict several output variables that together encode a structured object – a path in a graph, an entity-relation triple, or an ordering of objects. Such a large output space makes learning hard and requires vast amounts of labeled data. Different approaches leverage alternate sources of supervision. One approach – entropy regularization – posits that decision boundaries should lie in low-probability regions. It extracts supervision from unlabeled examples, but remains agnostic to the structure of the output space. Conversely, neuro-symbolic approaches exploit the knowledge that not every prediction corresponds to a valid structure in the output space. Yet, they do not further restrict the learned output distribution.This paper introduces a framework that unifies both approaches. We propose a loss, neuro-symbolic entropy regularization, that encourages the model to confidently predict a valid object. It is obtained by restricting entropy regularization to the distribution over only the valid structures. This loss can be computed efficiently when the output constraint is expressed as a tractable logic circuit. Moreover, it seamlessly integrates with other neuro-symbolic losses that eliminate invalid predictions. We demonstrate the efficacy of our approach on a series of semi-supervised and fully-supervised structured-prediction experiments, where it leads to models whose predictions are more accurate as well as more likely to be valid.
BibTeX
@InProceedings{pmlr-v180-ahmed22a,
title = {Neuro-symbolic entropy regularization},
author = {Ahmed, Kareem and Wang, Eric and Chang, Kai-Wei and Van den Broeck, Guy},
booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence},
pages = {43--53},
year = {2022},
editor = {Cussens, James and Zhang, Kun},
volume = {180},
series = {Proceedings of Machine Learning Research},
month = {01--05 Aug},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v180/ahmed22a/ahmed22a.pdf},
url = {https://proceedings.mlr.press/v180/ahmed22a.html},
abstract = {In structured output prediction, the goal is to jointly predict several output variables that together encode a structured object – a path in a graph, an entity-relation triple, or an ordering of objects. Such a large output space makes learning hard and requires vast amounts of labeled data. Different approaches leverage alternate sources of supervision. One approach – entropy regularization – posits that decision boundaries should lie in low-probability regions. It extracts supervision from unlabeled examples, but remains agnostic to the structure of the output space. Conversely, neuro-symbolic approaches exploit the knowledge that not every prediction corresponds to a valid structure in the output space. Yet, they do not further restrict the learned output distribution.This paper introduces a framework that unifies both approaches. We propose a loss, neuro-symbolic entropy regularization, that encourages the model to confidently predict a valid object. It is obtained by restricting entropy regularization to the distribution over only the valid structures. This loss can be computed efficiently when the output constraint is expressed as a tractable logic circuit. Moreover, it seamlessly integrates with other neuro-symbolic losses that eliminate invalid predictions. We demonstrate the efficacy of our approach on a series of semi-supervised and fully-supervised structured-prediction experiments, where it leads to models whose predictions are more accurate as well as more likely to be valid.}
}