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A Review of Formal Methods applied to Machine Learning
arXiv - CS - Logic in Computer Science Pub Date : 2021-04-06 , DOI: arxiv-2104.02466
Caterina Urban, Antoine Miné

We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability of mature tools, their use is well established in the industry, and in particular to check safety-critical applications as they undergo a stringent certification process. As machine learning is becoming more popular, machine-learned components are now considered for inclusion in critical systems. This raises the question of their safety and their verification. Yet, established formal methods are limited to classic, i.e. non machine-learned software. Applying formal methods to verify systems that include machine learning has only been considered recently and poses novel challenges in soundness, precision, and scalability. We first recall established formal methods and their current use in an exemplar safety-critical field, avionic software, with a focus on abstract interpretation based techniques as they provide a high level of scalability. This provides a golden standard and sets high expectations for machine learning verification. We then provide a comprehensive and detailed review of the formal methods developed so far for machine learning, highlighting their strengths and limitations. The large majority of them verify trained neural networks and employ either SMT, optimization, or abstract interpretation techniques. We also discuss methods for support vector machines and decision tree ensembles, as well as methods targeting training and data preparation, which are critical but often neglected aspects of machine learning. Finally, we offer perspectives for future research directions towards the formal verification of machine learning systems.

中文翻译:

应用于机器学习的形式方法综述

我们回顾了应用于机器学习系统验证新兴领域的最新形式化方法。形式化方法可以为硬件和软件系统提供严格的正确性保证。得益于成熟工具的可用性,它们在行业中已得到广泛使用,尤其是在经过严格的认证过程时检查对安全至关重要的应用程序。随着机器学习的普及,现在考虑将机器学习的组件包含在关键系统中。这就提出了安全性和验证性的问题。但是,已建立的形式化方法仅限于经典(即非机器学习的软件)。直到最近才考虑采用形式化方法来验证包含机器学习的系统,这在稳健性,准确性,和可扩展性。我们首先回想起已建立的形式化方法及其在示例性安全性至关重要的领域(航空电子软件)中的当前使用,重点是基于抽象解释的技术,因为它们可提供高水平的可扩展性。这提供了黄金标准,并为机器学习验证设定了很高的期望。然后,我们将对迄今为止为机器学习开发的形式化方法进行全面而详细的回顾,强调其优势和局限性。他们中的绝大多数验证了训练有素的神经网络,并采用了SMT,优化或抽象解释技术。我们还将讨论支持向量机和决策树集成的方法,以及针对训练和数据准备的方法,这些方法是机器学习的关键但通常被忽略的方面。最后,
更新日期:2021-04-08
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