Neuro-Symbolic Entropy Regularization

• URL: http://arxiv.org/abs/2201.11250v1
• Date: Tue, 25 Jan 2022 06:23:10 GMT
• Title: Neuro-Symbolic Entropy Regularization
• Authors: Kareem Ahmed, Eric Wang, Kai-Wei Chang, Guy Van den Broeck
• Abstract summary: In structured prediction, the goal is to jointly predict many output variables that together encode a structured object. One approach -- entropy regularization -- posits that decision boundaries should lie in low-probability regions. We propose a loss, neuro-symbolic entropy regularization, that encourages the model to confidently predict a valid object.
• Score: 78.16196949641079
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In structured prediction, the goal is to jointly predict many 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 does 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 valid structures. This loss is efficiently computed 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 we find that it leads to models whose predictions are more accurate and more likely to be valid.

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