With the rapid development of deep learning techniques, various recent work has tried to apply graph neural networks (GNNs) to solve NP-hard problems such as Boolean Satisfiability (SAT), which shows the potential in bridging the gap between machine learning and symbolic reasoning. However, the quality of solutions predicted by GNNs has not been well investigated in the literature. In this paper, we study the capability of GNNs in learning to solve Maximum Satisfiability (MaxSAT) problem, both from theoretical and practical perspectives. We build two kinds of GNN models to learn the solution of MaxSAT instances from benchmarks, and show that GNNs have attractive potential to solve MaxSAT problem through experimental evaluation. We also present a theoretical explanation of the effect that GNNs can learn to solve MaxSAT problem to some extent for the first time, based on the algorithmic alignment theory.

State-of-the-art deep NLP models have achieved impressive improvements on many tasks. However, they are found to be vulnerable to some perturbations. Before they are widely adopted, the fundamental issues of robustness need to be addressed. In this paper, we design a robustness enhancement method to defend against word substitution perturbation, whose basic idea is to fight perturbation with perturbation. We find that: although many well-trained deep models are not robust in the setting of the presence of adversarial samples, they satisfy weak robustness. That means they can handle most non-crafted perturbations well. Taking advantage of the weak robustness property of deep models, we utilize non-crafted perturbations to resist the adversarial perturbations crafted by attackers. Our method contains two main stages. The first stage is using randomized perturbation to conform the input to the data distribution. The second stage is using randomized perturbation to eliminate the instability of prediction results and enhance the robustness guarantee. Experimental results show that our method can significantly improve the ability of deep models to resist the state-of-the-art adversarial attacks while maintaining the prediction performance on the original clean data.

This paper introduces a notation of 𝜀-weakened robustness for analyzing the reliability and stability of deep neural networks (DNNs). Unlike the conventional robustness, which focuses on the "perfect" safe region in the absence of adversarial examples, 𝜀-weakened robustness focuses on the region where the proportion of adversarial examples is bounded by user-specified 𝜀. Smaller 𝜀 means a smaller chance of failure. Under such robustness definition, we can give conclusive results for the regions where conventional robustness ignores. We prove that the 𝜀-weakened robustness decision problem is PP-complete and give a statistical decision algorithm with user-controllable error bound. Furthermore, we derive an algorithm to find the maximum 𝜀-weakened robustness radius. The time complexity of our algorithms is polynomial in the dimension and size of the network. So, they are scalable to large real-world networks. Besides, We also show its potential application in analyzing quality issues.

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