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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 36 / No. 5: AAAI-22 Technical Tracks 5

MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks

February 1, 2023

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Authors

Nick Hoernle

University of Edinburgh


Rafael Michael Karampatsis

University of Edinburgh


Vaishak Belle

University of Edinburgh The Alan Turing Institute


Kobi Gal

University of Edinburgh Ben Gurion University


DOI:

10.1609/aaai.v36i5.20512


Abstract:

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.

Topics: AAAI

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HOW TO CITE:

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks Proceedings of the AAAI Conference on Artificial Intelligence (2022) 5700-5709.

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks AAAI 2022, 5700-5709.

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal (2022). MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 5700-5709.

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal. MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks. Proceedings of the AAAI Conference on Artificial Intelligence 2022 p.5700-5709.

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal. 2022. MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks. "Proceedings of the AAAI Conference on Artificial Intelligence". 5700-5709.

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal. (2022) "MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks", Proceedings of the AAAI Conference on Artificial Intelligence, p.5700-5709

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal, "MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks", AAAI, p.5700-5709, 2022.

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal. "MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks". Proceedings of the AAAI Conference on Artificial Intelligence, 2022, p.5700-5709.

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal. "MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks". Proceedings of the AAAI Conference on Artificial Intelligence, (2022): 5700-5709.

Nick Hoernle||Rafael Michael Karampatsis||Vaishak Belle||Kobi Gal. MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks. AAAI[Internet]. 2022[cited 2023]; 5700-5709.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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