MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks

Nick Hoernle, Rafael Karampatsis, Vaishak Belle, Yakov Kobi Gal

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 publicationProceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI 2022)
Subtitle of host publicationVol. 36 No. 5: AAAI-22 Technical Tracks 5
Place of PublicationPalo Alto, California, USA
PublisherAssociation for the Advancement of Artificial Intelligence AAAI
Number of pages13
ISBN (Electronic)1-57735-876-7, 978-1-57735-876-3
Publication statusPublished - 30 Jun 2022
Event36th AAAI Conference on Artificial Intelligence - Virtual Conference
Duration: 22 Feb 20221 Mar 2022

Publication series

NameThirty-Sixth AAAI Conference on Artificial Intelligence
ISSN (Print)2159-5399
ISSN (Electronic)2374-3468


Conference36th AAAI Conference on Artificial Intelligence
Abbreviated titleAAAI 2022
Internet address


  • Knowledge Representation And Reasoning (KRR)


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