论文标题

神经网络的定点实现的增量验证

Incremental Verification of Fixed-Point Implementations of Neural Networks

论文作者

Sena, Luiz, Alves, Erickson, Bessa, Iury, Filho, Eddie, Cordeiro, Lucas

论文摘要

人工神经网络(ANN)的实现可能导致故障,由于ANN高度平行,因此在设计阶段几乎没有预测,并且它们的参数几乎无法解释。在这里,我们使用增量有界模型检查(BMC),满意度模型理论(SMT)和不变推理来开发和评估新的符号验证框架,以获取对抗性案例并在多层perceptron(MLP)中验证覆盖方法。我们基于间隔分析利用增量BMC来计算神经元输入的边界。然后,将后者传播以有效地找到神经元的输出,因为它是下一个神经元的输入。本文介绍了第一个基于不变推理的CUDA中ANN的实际实现的第一个比特符号验证框架,因此提供了有关有限优先级的算术及其舍入错误的进一步保证,这些错误在现有文献中通常被忽略。我们已经在有效的SMT有限模型检查器(ESBMC)上实现了建议的方法,其实验结果表明,它可以成功地验证ANN的实际实现,并在MLPS中生成实际对抗性案例。我们的方法能够以不同的输入图像以及与覆盖方法相关的100%的属性来验证和产生21例测试用例中85.8%的对抗性示例。尽管我们的验证时间高于现有方法,但我们的方法可以考虑由最先进的验证方法忽略的定点实现方面。

Implementations of artificial neural networks (ANNs) might lead to failures, which are hardly predicted in the design phase since ANNs are highly parallel and their parameters are barely interpretable. Here, we develop and evaluate a novel symbolic verification framework using incremental bounded model checking (BMC), satisfiability modulo theories (SMT), and invariant inference, to obtain adversarial cases and validate coverage methods in a multi-layer perceptron (MLP). We exploit incremental BMC based on interval analysis to compute boundaries from a neuron's input. Then, the latter are propagated to effectively find a neuron's output since it is the input of the next one. This paper describes the first bit-precise symbolic verification framework to reason over actual implementations of ANNs in CUDA, based on invariant inference, therefore providing further guarantees about finite-precision arithmetic and its rounding errors, which are routinely ignored in the existing literature. We have implemented the proposed approach on top of the efficient SMT-based bounded model checker (ESBMC), and its experimental results show that it can successfully verify safety properties, in actual implementations of ANNs, and generate real adversarial cases in MLPs. Our approach was able to verify and produce adversarial examples for 85.8% of 21 test cases considering different input images, and 100% of the properties related to covering methods. Although our verification time is higher than existing approaches, our methodology can consider fixed-point implementation aspects that are disregarded by the state-of-the-art verification methodologies.

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