A Review of Formal Methods applied to Machine Learning

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

Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning

Learning-based pattern classifiers, including deep networks, have shown impressive performance in several application domains, ranging from computer vision to cybersecurity. However, it has also been shown that adversarial input perturbations carefully crafted either at training or at test time can easily subvert their predictions. The vulnerability of machine learning to such wild patterns (also referred to as adversarial examples), along with the design of suitable countermeasures, have been investigated in the research field of adversarial machine learning. In this work, we provide a thorough overview of the evolution of this research area over the last ten years and beyond, starting from pioneering, earlier work on the security of non-deep learning algorithms up to more recent work aimed to understand the security properties of deep learning algorithms, in the context of computer vision and cybersecurity tasks. We report interesting connections between these apparently-different lines of work, highlighting common misconceptions related to the security evaluation of machine-learning algorithms. We review the main threat models and attacks defined to this end, and discuss the main limitations of current work, along with the corresponding future challenges towards the design of more secure learning algorithms.Comment: Accepted for publication on Pattern Recognition, 201

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review

Context: Machine Learning (ML) has been at the heart of many innovations over the past years. However, including it in so-called 'safety-critical' systems such as automotive or aeronautic has proven to be very challenging, since the shift in paradigm that ML brings completely changes traditional certification approaches. Objective: This paper aims to elucidate challenges related to the certification of ML-based safety-critical systems, as well as the solutions that are proposed in the literature to tackle them, answering the question 'How to Certify Machine Learning Based Safety-critical Systems?'. Method: We conduct a Systematic Literature Review (SLR) of research papers published between 2015 to 2020, covering topics related to the certification of ML systems. In total, we identified 217 papers covering topics considered to be the main pillars of ML certification: Robustness, Uncertainty, Explainability, Verification, Safe Reinforcement Learning, and Direct Certification. We analyzed the main trends and problems of each sub-field and provided summaries of the papers extracted. Results: The SLR results highlighted the enthusiasm of the community for this subject, as well as the lack of diversity in terms of datasets and type of models. It also emphasized the need to further develop connections between academia and industries to deepen the domain study. Finally, it also illustrated the necessity to build connections between the above mention main pillars that are for now mainly studied separately. Conclusion: We highlighted current efforts deployed to enable the certification of ML based software systems, and discuss some future research directions.Comment: 60 pages (92 pages with references and complements), submitted to a journal (Automated Software Engineering). Changes: Emphasizing difference traditional software engineering / ML approach. Adding Related Works, Threats to Validity and Complementary Materials. Adding a table listing papers reference for each section/subsection