Title: ConstraintFlow: A DSL for Specification and Verification of Neural Network Analyses

Abstract: The uninterpretability of DNNs hinders their deployment to safety-critical applications. Recent works have shown that Abstract-Interpretation-based formal certification techniques provide promising avenues for building trust in DNNs to some extent. The intricate mathematical background of Abstract Interpretation poses two challenges: (i) easily designing the algorithms that capture the intricate DNN behavior by balancing cost vs. precision tradeoff, and (ii) maintaining the over-approximation-based soundness of these certifiers.
General-purpose programming languages like C++ provide extensive functionality, however, verifying the soundness of the algorithms written in them can be impractical. The most commonly used DNN certification libraries like auto_LiRPA and ERAN prove the correctness of their analyses. However, they consist of only a few hard-coded abstract domains and abstract transformers (or transfer functions) and do not allow the user to define new analyses. Further, these libraries can handle only specific DNN architectures.
To address these issues, we develop a declarative DSL -- ConstraintFlow -- that can be used to specify Abstract Interpretation-based DNN certifiers. In ConstraintFlow, programmers can easily define various existing and new abstract domains and transformers, all within just a few 10s of Lines of Code as opposed to 1000s of LOCs of existing libraries. We also provide lightweight automatic verification, which can be used to ensure the over-approximation-based soundness of the certifier code written in ConstraintFlow for arbitrary (but bounded) DNN architectures. Using this automated verification procedure, for the first time, we can verify the soundness of state-of-the-art DNN certifiers for arbitrary DNN architectures, all within a few minutes. We prove the soundness of our verification procedure and the completeness of a subset of ConstraintFlow.