A Semidefinite Relaxation based Branch-and-Bound Method for Tight Neural Network Verification

Lan, J. , Bruckner, B. and Lomuscio, A. (2023) A Semidefinite Relaxation based Branch-and-Bound Method for Tight Neural Network Verification. In: 37th AAAI Conference on Artificial Intelligence (AAAI-23), Washington, DC, USA, 7-14 Feb 2023, pp. 14946-14954. ISBN 9781577358800 (doi: 10.1609/aaai.v37i12.26745)

Abstract

We introduce a novel method based on semidefinite program (SDP) for the tight and efficient verification of neural networks. The proposed SDP relaxation advances the present state of the art in SDP-based neural network verification by adding a set of linear constraints based on eigenvectors. We extend this novel SDP relaxation by combining it with a branch-and-bound method that can provably close the relaxation gap up to zero. We show formally that the proposed approach leads to a provably tighter solution than the present state of the art. We report experimental results showing that the proposed method outperforms baselines in terms of verified accuracy while retaining an acceptable computational overhead.

• Item Type: Conference Proceedings
• Additional Information: Jianglin Lan is supported by a Leverhulme Trust Early Career Fellowship under Award ECF-2021-517. Benedikt Bruckner is supported by the UKRI Centre for Doctoral Training in Safe and Trusted Artificial Intelligence [grant number EP/S023356/1]. Alessio Lomuscio is supported by a Royal Academy of Engineering Chair in Emerging Technologies.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Lan, Dr Jianglin
• Authors: Lan, J., Bruckner, B., and Lomuscio, A.
• College/School: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• ISSN: 2374-3468
• ISBN: 9781577358800
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Proceedings of the AAAI Conference on Artificial Intelligence, 37(12), 14946-14954.
• Publisher Policy: Reproduced with the permission of the publisher

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