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Syntactic vs Semantic Linear Abstraction and Refinement of Neural Networks

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Automated Technology for Verification and Analysis (ATVA 2023)

Abstract

Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that is similar enough. We can classify the similarity as defined either syntactically (using quantities on the connections between neurons) or semantically (on the activation values of neurons for various inputs). Unfortunately, the previous approaches only achieve moderate reductions, when implemented at all. In this work, we provide a more flexible framework, where a neuron can be replaced with a linear combination of other neurons, improving the reduction. We apply this approach both on syntactic and semantic abstractions, and implement and evaluate them experimentally. Further, we introduce a refinement method for our abstractions, allowing for finding a better balance between reduction and precision.

This research was funded in part by the German Research Foundation (DFG) project 427755713 GoPro, the German Federal Ministry of Education and Research (BMBF) within the project SEMECO Q1 (03ZU1210AG), and the DFG research training group ConVeY (GRK 2428).

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Notes

  1. 1.

    Please note that this statement is slightly different from the paper (\((2a)^k\) instead of \((2/a)^k\)), which we believe to be a typo in the paper.

  2. 2.

    https://github.com/cxlvinchau/LiNNA.

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Correspondence to Stefanie Mohr .

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Chau, C., Křetínský, J., Mohr, S. (2023). Syntactic vs Semantic Linear Abstraction and Refinement of 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_19

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  • DOI: https://doi.org/10.1007/978-3-031-45329-8_19

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