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1. ART: Abstraction Refinement-Guided Training for Provably Correct Neural Networks

   https://doi.org/10.34727/2020/isbn.978-3-85448-042-6_22  

   Lin, Xuankang; Zhu, He; Samanta, Roopsha; Jagannathan, Suresh (January 2020, Formal Methods in Computer-Aided Design)

   Ivrii, Alexander; Strichman, Ofer (Ed.)

   Artificial Neural Networks (ANNs) have demonstrated remarkable utility in various challenging machine learning applications. While formally verified properties of their behaviors are highly desired, they have proven notoriously difficult to derive and enforce. Existing approaches typically formulate this problem as a post facto analysis process. In this paper, we present a novel learning framework that ensures such formal guarantees are enforced by construction. Our technique enables training provably correct networks with respect to a broad class of safety properties, a capability that goes well-beyond existing approaches, without compromising much accuracy. Our key insight is that we can integrate an optimization-based abstraction refinement loop into the learning process and operate over dynamically constructed partitions of the input space that considers accuracy and safety objectives synergistically. The refinement procedure iteratively splits the input space from which training data is drawn, guided by the efficacy with which such partitions enable safety verification. We have implemented our approach in a tool (ART) and applied it to enforce general safety properties on unmanned aviator collision avoidance system ACAS Xu dataset and the Collision Detection dataset. Importantly, we empirically demonstrate that realizing safety does not come at the price of much accuracy. Our methodology demonstrates that an abstraction refinement methodology provides a meaningful pathway for building both accurate and correct machine learning networks. 

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2. Verifying Binary Neural Networks on Continuous Input Space using Star Reachability

   https://doi.org/10.1109/FormaliSE58978.2023.00009  

   Ivashchenko, Mykhailo; Choi, Sung Woo; Nguyen, Luan Viet; Tran, Hoang-Dung (May 2023, 2023 IEEE/ACM 11th International Conference on Formal Methods in Software Engineering (FormaliSE))

   Deep Neural Networks (DNNs) have become a popular instrument for solving various real-world problems. DNNs’ sophisticated structure allows them to learn complex representations and features. For this reason, Binary Neural Networks (BNNs) are widely used on edge devices, such as microcomputers. However, architecture specifics and floating-point number usage result in an increased computational operations complexity. Like other DNNs, BNNs are vulnerable to adversarial attacks; even a small perturbation to the input set may lead to an errant output. Unfortunately, only a few approaches have been proposed for verifying BNNs.This paper proposes an approach to verify BNNs on continuous input space using star reachability analysis. Our approach can compute both exact and overapproximate reachable sets of BNNs with Sign activation functions and use them for verification. The proposed approach is also efficient in constructing a complete set of counterexamples in case a network is unsafe. We implemented our approach in NNV, a neural network verification tool for DNNs and learning-enabled Cyber-Physical Systems. The experimental results show that our star-based approach is less conservative, more efficient, and scalable than the recent SMT-based method implemented in Marabou. We also provide a comparison with a quantization-based tool EEVBNN. 

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3. An Abstraction-Refinement Approach to Verifying Convolutional Neural Networks

   https://doi.org/10.1007/978-3-031-19992-9_25  

   Ostrovsky, Matan; Barrett, Clark; Katz, Guy (October 2022, Proceedings of the 20th International Symposium on Automated Technology for Verification and Analysis (ATVA))

   Bouajjani, Ahmed; Holk, Lukas; Wu, Zhilin (Ed.)

   Convolutional neural networks (CNNs) have achieved immense popularity in areas like computer vision, image processing, speech proccessing, and many others. Unfortunately, despite their excellent performance, they are prone to producing erroneous results — for example, minor perturbations to their inputs can result in severe classification errors. In this paper, we present the CNN-ABS framework, which implements an abstraction-refinement based scheme for CNN verification. Specifically, CNN-ABS simplifies the verification problem through the removal of convolutional connections in a way that soundly creates an over-approximation of the original problem; it then iteratively restores these connections if the resulting problem becomes too abstract. CNN-ABS is designed to use existing verification engines as a backend, and our evaluation demonstrates that it can significantly boost the performance of a state-of-the-art DNN verification engine, reducing runtime by 15.7% on average. 

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4. Harnessing Neuron Stability to Improve DNN Verification

   https://doi.org/10.1145/3643765  

   Duong, Hai; Xu, Dong; Nguyen, Thanhvu; Dwyer, Matthew B (July 2024, Proceedings of the ACM on Software Engineering)

   Deep Neural Networks (DNN) have emerged as an effective approach to tackling real-world problems. However, like human-written software, DNNs are susceptible to bugs and attacks. This has generated significant interest in developing effective and scalable DNN verification techniques and tools. Recent developments in DNN verification have highlighted the potential of constraint-solving approaches that combine abstraction techniques with SAT solving. Abstraction approaches are effective at precisely encoding neuron behavior when it is linear, but they lead to overapproximation and combinatorial scaling when behavior is non-linear. SAT approaches in DNN verification have incorporated standard DPLL techniques, but have overlooked important optimizations found in modern SAT solvers that help them scale on industrial benchmarks. In this paper, we present VeriStable, a novel extension of the recently proposed DPLL-based constraint DNN verification approach. VeriStable leverages the insight that while neuron behavior may be non-linear across the entire DNN input space, at intermediate states computed during verification many neurons may be constrained to have linear behavior – these neurons are stable. Efficiently detecting stable neurons reduces combinatorial complexity without compromising the precision of abstractions. Moreover, the structure of clauses arising in DNN verification problems shares important characteristics with industrial SAT benchmarks. We adapt and incorporate multi-threading and restart optimizations targeting those characteristics to further optimize DPLL-based DNN verification. We evaluate the effectiveness of VeriStable across a range of challenging benchmarks including fully- connected feedforward networks (FNNs), convolutional neural networks (CNNs) and residual networks (ResNets) applied to the standard MNIST and CIFAR datasets. Preliminary results show that VeriStable is competitive and outperforms state-of-the-art DNN verification tools, including α-β-CROWN and MN-BaB, the first and second performers of the VNN-COMP, respectively. 

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5. Harnessing Neuron Stability to Improve DNN Verification

   Duong, Hai; Xu, Dong; Nguyen, Thanhvu; Dwyer, Matthew B (July 2024, Proceedings of the ACM on Software Engineering)

   Deep Neural Networks (DNN) have emerged as an effective approach to tackling real-world problems. However, like human-written software, DNNs are susceptible to bugs and attacks. This has generated significant interests in developing effective and scalable DNN verification techniques and tools. Recent developments in DNN verification have highlighted the potential of constraint-solving approaches that combine abstraction techniques with SAT solving. Abstraction approaches are effective at precisely encode neuron behavior when it is linear, but they lead to overapproximation and combinatorial scaling when behavior is non-linear. SAT approaches in DNN verification have incorporated standard DPLL techniques, but have overlooked important optimizations found in modern SAT solvers that help them scale on industrial benchmarks. In this paper, we present VeriStable, a novel extension of recently proposed DPLL-based constraint DNN verification approach. VeriStable leverages the insight that while neuron behavior may be non-linear across the entire DNN input space, at intermediate states computed during verification many neurons may be constrained to have linear behavior – these neurons are stable. Efficiently detecting stable neurons reduces combinatorial complexity without compromising the precision of abstractions. Moreover, the structure of clauses arising in DNN verification problems shares important characteristics with industrial SAT benchmarks. We adapt and incorporate multi-threading and restart optimizations targeting those characteristics to further optimize DPLL-based DNN verification. We evaluate the effectiveness of VeriStable across a range of challenging benchmarks including fully- connected feedforward networks (FNNs), convolutional neural networks (CNNs) and residual networks (ResNets) applied to the standard MNIST and CIFAR datasets. Preliminary results show that VeriStable is competitive and outperforms state-of-the-art DNN verification tools, including 𝛼-𝛽-CROWN and MN-BaB, the first and second performers of the VNN-COMP, respectively. 

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