Recent advances in machine learning and artificial intelligence are now being considered in safety-critical autonomous systems where software defects may cause severe harm to humans and the environment. Design organizations in these domains are currently unable to provide convincing arguments that their systems are safe to operate when machine learning algorithms are used to implement their software.

In this paper, we present an efficient method to extract equivalence classes from decision trees and tree ensembles, and to formally verify that their input-output mappings comply with requirements. The idea is that, given that safety requirements can be traced to desirable properties on system input-output patterns, we can use positive verification outcomes in safety arguments. This paper presents the implementation of the method in the tool VoTE (Verifier of Tree Ensembles), and evaluates its scalability on two case studies presented in current literature. We demonstrate that our method is practical for tree ensembles trained on low-dimensional data with up to 25 decision trees and tree depths of up to 20. Our work also studies the limitations of the method with high-dimensional data and preliminarily investigates the trade-off between large number of trees and time taken for verification.

如今，在安全关键的自治系统中考虑了机器学习和人工智能的最新进展，其中软件缺陷可能对人类和环境造成严重伤害。这些领域的设计组织当前无法提供令人信服的论点，即使用机器学习算法实现其软件时，其系统可以安全运行。

在本文中，我们提出了一种有效的方法来从决策树和树集成中提取等价类，并正式验证其输入输出映射是否符合要求。这个想法是，鉴于安全需求可以追溯到系统输入输出模式的理想特性，我们可以在安全论证中使用肯定的验证结果。本文介绍了该方法在工具VoTE（Tree Ensembles的验证程序）中的实现，并根据当前文献中提供的两个案例研究评估了该方法的可扩展性。我们证明了我们的方法对于在低维数据上训练的树集成体是实用的，该树集成体具有多达25个决策树和多达20个树深。