Iteratively Enhanced Semidefinite Relaxations for Efficient Neural Network Verification

Lan, J. , Zheng, Y. and Lomuscio, A. (2023) Iteratively Enhanced Semidefinite Relaxations for Efficient Neural Network Verification. In: 37th AAAI Conference on Artificial Intelligence (AAAI-23), Washington, DC, USA, 7-14 Feb 2023, pp. 14937-14945. (doi: 10.1609/aaai.v37i12.26744)

Abstract

We propose an enhanced semidefinite program (SDP) relaxation to enable the tight and efficient verification of neural networks (NNs). The tightness improvement is achieved by introducing a nonlinear constraint to existing SDP relaxations previously proposed for NN verification. The efficiency of the proposal stems from the iterative nature of the proposed algorithm in that it solves the resulting non-convex SDP by recursively solving auxiliary convex layer-based SDP problems. We show formally that the solution generated by our algorithm is tighter than state-of-the-art SDP-based solutions for the problem. We also show that the solution sequence converges to the optimal solution of the non-convex enhanced SDP relaxation. The experimental results on standard benchmarks in the area show that our algorithm achieves the state-of-the-art performance whilst maintaining an acceptable computational cost.

• Item Type: Conference Proceedings
• Additional Information: Jianglin Lan is supported by a Leverhulme Trust Early Career Fellowship under Award ECF-2021-517. Yang Zheng is supported by the National Science Foundation under Grant No. ECCS-2154650. 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., Zheng, Y., and Lomuscio, A.
• College/School: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• ISSN: 2159-5399
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Proceedings of the AAAI Conference on Artificial Intelligence, 37(12), 14937-14945.
• Publisher Policy: Reproduced with the permission of the publisher

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