使用符号传播分析深度神经网络：实现更高的精度和更快的验证
Analyzing Deep Neural Networks with Symbolic Propagation: Towards Higher Precision and Faster Verification
摘要：
深度神经网络（DNN）已经被证明缺乏鲁棒性，因为它们的分类容易受到输入上的小扰动的影响。这导致了将DNN应用于安全关键域的安全问题。已经开发了几种验证方法来自动证明或反驳DNN的安全属性。然而，这些方法遭受可扩展性问题，即，只能处理小的DNN，或者精度问题，即，得到的边界是松散的。本文改进了最近提出的分析DNN通过经典的抽象解释技术，通过一种新的符号传播技术。更具体地说，神经元的值被符号化地表示，并在抽象域之上从输入层向前传播到输出层。我们表明，我们的方法可以实现显着更高的精度，从而可以证明更多的属性比只使用抽象域。此外，我们表明，来自我们的方法对隐藏的神经元的界限，当应用到一个国家的最先进的SMT基于验证工具，可以提高其性能。我们将我们的方法实现到一个软件工具中，并在一些在MNIST等基准数据集上训练的DNN上对其进行验证。
英文摘要：
Deep neural networks (DNNs) have been shown lack of robustness for the vulnerability of their classification to small perturbations on the inputs. This has led to safety concerns of applying DNNs to safety-critical domains. Several verification approaches have been developed to automatically prove or disprove safety properties of DNNs. However, these approaches suffer from either the scalability problem, i.e., only small DNNs can be handled, or the precision problem, i.e., the obtained bounds are loose. This paper improves on a recent proposal of analyzing DNNs through the classic abstract interpretation technique, by a novel symbolic propagation technique. More specifically, the values of neurons are represented symbolically and propagated forwardly from the input layer to the output layer, on top of abstract domains. We show that our approach can achieve significantly higher precision and thus can prove more properties than using only abstract domains. Moreover, we show that the bounds derived from our approach on the hidden neurons, when applied to a state-of-the-art SMT based verification tool, can improve its performance. We implement our approach into a software tool and validate it over a few DNNs trained on benchmark datasets such as MNIST, etc.
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