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，尤其是神经网络的日益普及，人们对其可信度产生了担忧，特别是在安全关键型应用中（例如，自动驾驶车辆的动作必须安全）。现有方法可以训练神经网络将此类领域需求作为约束来强制执行，但它们要么无法保证所有可能的预测（甚至包括未见数据）都满足该约束，要么在可强制执行的约束类型上存在局限性。在本文中，我们提出了一种训练神经网络的方法，该方法能够强制执行多种约束，并保证所有可能的预测都满足这些约束。该方法建立在将线性模型学习表述为约束满足问题（CSP）的先前工作基础上。为了使这一思想适用于神经网络，我们添加了两个关键的新要素：跨网络层的约束传播，以及基于梯度下降与CSP求解混合的权重更新。对多种机器学习任务的评估表明，我们的方法足够灵活，能够强制执行各种领域约束，并能保证这些约束在神经网络中得以实现。