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Efficient Neural Network Verification via Order Leading Exploration of Branch-and-Bound Trees

Authors Guanqin Zhang , Kota Fukuda , Zhenya Zhang , H.M.N. Dilum Bandara , Shiping Chen , Jianjun Zhao , Yulei Sui

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Subject Classification

ACM Subject Classification
  • Software and its engineering → Formal software verification
  • Software and its engineering → Software testing and debugging
Keywords
  • neural network verification
  • branch and bound
  • counterexample potentiality
  • simulated annealing
  • stochastic optimization

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Abstract

The vulnerability of neural networks to adversarial perturbations has necessitated formal verification techniques that can rigorously certify the quality of neural networks. As the state-of-the-art, branch-and-bound (BaB) is a "divide-and-conquer" strategy that applies off-the-shelf verifiers to sub-problems for which they perform better. While BaB can identify the sub-problems that are necessary to be split, it explores the space of these sub-problems in a naive "first-come-first-served" manner, thereby suffering from an issue of inefficiency to reach a verification conclusion. To bridge this gap, we introduce an order over different sub-problems produced by BaB, concerning with their different likelihoods of containing counterexamples. Based on this order, we propose a novel verification framework Oliva that explores the sub-problem space by prioritizing those sub-problems that are more likely to find counterexamples, in order to efficiently reach the conclusion of the verification. Even if no counterexample can be found in any sub-problem, it only changes the order of visiting different sub-problems and so will not lead to a performance degradation. Specifically, Oliva has two variants, including Oliva^GR, a greedy strategy that always prioritizes the sub-problems that are more likely to find counterexamples, and Oliva^SA, a balanced strategy inspired by simulated annealing that gradually shifts from exploration to exploitation to locate the globally optimal sub-problems. We experimentally evaluate the performance of Oliva on 690 verification problems spanning over 5 models with datasets MNIST and CIFAR-10. Compared to the state-of-the-art approaches, we demonstrate the speedup of Oliva for up to 25× in MNIST, and up to 80× in CIFAR-10.

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Guanqin Zhang, Kota Fukuda, Zhenya Zhang, H.M.N. Dilum Bandara, Shiping Chen, Jianjun Zhao, and Yulei Sui. Efficient Neural Network Verification via Order Leading Exploration of Branch-and-Bound Trees. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 36:1-36:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ECOOP.2025.36

Author Details

Guanqin Zhang
  • University of New South Wales, Sydney, Australia
  • CSIRO’s Data61, Sydney, Australia
Kota Fukuda
  • Kyushu University, Fukuoka, Japan
Zhenya Zhang
  • Kyushu University, Fukuoka, Japan
  • National Institute of Informatics, Tokyo, Japan
H.M.N. Dilum Bandara
  • CSIRO’s Data61, Sydney, Australia
  • University of New South Wales, Sydney, Australia
Shiping Chen
  • CSIRO’s Data61, Sydney, Australia
  • University of New South Wales, Sydney, Australia
Jianjun Zhao
  • Kyushu University, Fukuoka, Japan
Yulei Sui
  • University of New South Wales, Sydney, Australia

Funding

  • Zhang, Guanqin: CSIRO’s Data61 PhD Scholarship
  • Fukuda, Kota: JST BOOST Grant No. JPMJBS2406
  • Zhang, Zhenya: JST BOOST Grant No. JPMJBY24D7 and JSPS Grant No. JP25K21179
  • Zhao, Jianjun: JSPS KAKENHI Grant No. JP23H0337
  • Sui, Yulei: Australian Research Council Grants No. FT220100391 and No. DP250101396

Supplementary Materials

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