Extensive research on formal verification of machine learning systems indicates that learning from data alone often fails to capture underlying background knowledge such as specifications implicitly available in the data. Various neural network verifiers have been developed to ensure that a machine-learnt model satisfies correctness and safety properties, however, they typically assume a trained network with fixed weights. A promising approach for creating machine learning models that inherently satisfy constraints after training is to encode background knowledge as explicit logical constraints that guide the learning process via so-called differentiable logics. In this paper, we experimentally compare and evaluate various logics from the literature, presenting our findings and highlighting open problems for future work.

翻译：对机器学习系统形式化验证的广泛研究表明，仅从数据中学习往往无法捕捉潜在的背景知识，例如数据中隐含可用的规范。尽管已开发出多种神经网络验证器来确保机器学习模型满足正确性与安全性属性，但这些方法通常假设网络权重在训练完成后固定不变。一种有前景的创建满足约束的机器学习模型的方法，是将背景知识编码为显式逻辑约束，通过所谓的可微逻辑来指导学习过程。本文通过实验比较和评估了文献中的多种逻辑方法，呈现了我们的研究发现，并指出了未来工作中待解决的开放性问题。