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An Automata-Theoretic Approach to Synthesizing Binarized Neural Networks

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Automated Technology for Verification and Analysis (ATVA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14215))

Abstract

Deep neural networks, (DNNs, a.k.a. NNs), have been widely used in various tasks and have been proven to be successful. However, the accompanied expensive computing and storage costs make the deployments in resource-constrained devices a significant concern. To solve this issue, quantization has emerged as an effective way to reduce the costs of DNNs with little accuracy degradation by quantizing floating-point numbers to low-width fixed-point representations. Quantized neural networks (QNNs) have been developed, with binarized neural networks (BNNs) restricted to binary values as a special case. Another concern about neural networks is their vulnerability and lack of interpretability. Despite the active research on trustworthy of DNNs, few approaches have been proposed to QNNs. To this end, this paper presents an automata-theoretic approach to synthesizing BNNs that meet designated properties. More specifically, we define a temporal logic, called BLTL, as the specification language. We show that each BLTL formula can be transformed into an automaton on finite words. To deal with the state-explosion problem, we provide a tableau-based approach in real implementation. For the synthesis procedure, we utilize SMT solvers to detect the existence of a model (i.e., a BNN) in the construction process. Notably, synthesis provides a way to determine the hyper-parameters of the network before training. Moreover, we experimentally evaluate our approach and demonstrate its effectiveness in improving the individual fairness and local robustness of BNNs while maintaining accuracy to a great extent.

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Acknowledgement

This work is partially supported by the National Key R & D Program of China (2022YFA1005101), the National Natural Science Foundation of China (61872371, 62072309, 62032024), CAS Project for Young Scientists in Basic Research (YSBR-040), and ISCAS New Cultivation Project (ISCAS-PYFX-202201).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, National University of Defense Technology, Changsha, China

    Ye Tao, Wanwei Liu & Hongxu Zhu

  2. School of Information Science and Technology, ShanghaiTech University, Shanghai, China

    Fu Song

  3. Institute of Software, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China

    Fu Song

  4. Automotive Software Innovation Center, Shanghai, China

    Fu Song

  5. Institute for Quantum Information and State Key Laboratory for High Performance Computing, National University of Defense Technology, Changsha, China

    Zhen Liang & Ji Wang

Authors
  1. Ye Tao
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  2. Wanwei Liu
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  3. Fu Song
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  4. Zhen Liang
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  5. Ji Wang
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  6. Hongxu Zhu
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Corresponding author

Correspondence to Wanwei Liu .

Editor information

Editors and Affiliations

  1. Université Sorbonne Paris Nord, Villetaneuse, France

    Étienne André

  2. Singapore Management University, Singapore, Singapore

    Jun Sun

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Tao, Y., Liu, W., Song, F., Liang, Z., Wang, J., Zhu, H. (2023). An Automata-Theoretic Approach to Synthesizing Binarized Neural Networks. In: André, É., Sun, J. (eds) Automated Technology for Verification and Analysis. ATVA 2023. Lecture Notes in Computer Science, vol 14215. Springer, Cham. https://doi.org/10.1007/978-3-031-45329-8_18

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  • DOI: https://doi.org/10.1007/978-3-031-45329-8_18

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  • Print ISBN: 978-3-031-45328-1

  • Online ISBN: 978-3-031-45329-8

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