MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks

Nicholas Hoernle, Rafael Michael Karampatsis, Vaishak Belle, Kobi Gal

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

17 Scopus citations


We propose a novel way to incorporate expert knowledge into the training of deep neural networks. Many approaches encode domain constraints directly into the network architecture, requiring non-trivial or domain-specific engineering. In contrast, our approach, called MultiplexNet, represents domain knowledge as a quantifier-free logical formula in disjunctive normal form (DNF) which is easy to encode and to elicit from human experts. It introduces a latent Categorical variable that learns to choose which constraint term optimizes the error function of the network and it compiles the constraints directly into the output of existing learning algorithms. We demonstrate the efficacy of this approach empirically on several classical deep learning tasks, such as density estimation and classification in both supervised and unsupervised settings where prior knowledge about the domains was expressed as logical constraints. Our results show that the MultiplexNet approach learned to approximate unknown distributions well, often requiring fewer data samples than the alternative approaches. In some cases, MultiplexNet finds better solutions than the baselines; or solutions that could not be achieved with the alternative approaches. Our contribution is in encoding domain knowledge in a way that facilitates inference. We specifically focus on quantifier-free logical formulae that are specified over the output domain of a network. We show that this approach is both efficient and general; and critically, our approach guarantees 100% constraint satisfaction in a network's output.

Original languageEnglish
Title of host publicationAAAI-22 Technical Tracks 5
PublisherAssociation for the Advancement of Artificial Intelligence
Number of pages10
ISBN (Electronic)1577358767, 9781577358763
StatePublished - 30 Jun 2022
Event36th AAAI Conference on Artificial Intelligence, AAAI 2022 - Virtual, Online
Duration: 22 Feb 20221 Mar 2022

Publication series

NameProceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022


Conference36th AAAI Conference on Artificial Intelligence, AAAI 2022
CityVirtual, Online

ASJC Scopus subject areas

  • Artificial Intelligence


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