Syntactic and Semantic Soundness of Structural Dataflow Analysis

Cousot, Patrick

doi:10.1007/978-3-030-32304-2_6

Cited by 5 publications

(1 citation statement)

References 26 publications

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“…Unifying Theory of Formal Methods. As a general theory of semantic approximation, abstract interpretation is not only useful to derive new static analyses, but can also model other static analysis methods developed independently, such as data-flow analyses [42] or security analyses [43]. It can also reason about other formal techniques, such as strong typing [39], constraint programming [123], as well as model checking [41] and SMT solving [18].…”

Section: Abstract Interpretationmentioning

confidence: 99%

A Review of Formal Methods applied to Machine Learning

Urban¹,

Miné²

2021

Preprint

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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.

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