As machine learning models, specifically neural networks, are becoming increasingly popular, there are concerns regarding their trustworthiness, specially in safety-critical applications, e.g. actions of an autonomous vehicle must be safe. There are approaches that can train neural networks where such domain requirements are enforced as constraints, but they either cannot guarantee that the constraint will be satisfied by all possible predictions (even on unseen data) or they are limited in the type of constraints that can be enforced. In this paper, we present an approach to train neural networks which can enforce a wide variety of constraints and guarantee that the constraint is satisfied by all possible predictions. The approach builds on earlier work where learning linear models is formulated as a constraint satisfaction problem (CSP). To make this idea applicable to neural networks, two crucial new elements are added: constraint propagation over the network layers, and weight updates based on a mix of gradient descent and CSP solving. Evaluation on various machine learning tasks demonstrates that our approach is flexible enough to enforce a wide variety of domain constraints and is able to guarantee them in neural networks.

翻译：随着机器学习模型（尤其是神经网络）日益普及，其可信度问题备受关注，尤其在安全关键型应用中（例如自动驾驶车辆的行为必须确保安全）。现有方法虽可在训练神经网络时将领域需求作为约束强制施加，但要么无法保证所有可能预测（甚至包括未见数据）均满足约束，要么所能施加的约束类型极为有限。本文提出一种训练神经网络的方法，既能施加多样化约束，又可保证所有可能预测均满足约束。该方法基于早期将线性模型学习形式化为约束满足问题（CSP）的研究成果。为将其推广至神经网络，我们新增两个关键要素：网络层间的约束传播，以及基于梯度下降与CSP求解混合机制的权重更新。在多种机器学习任务上的评估表明，本方法兼具灵活性以施加多样化领域约束，并能确保神经网络对这些约束的严格满足。