Revisiting Differential Verification: Equivalence Verification with Confidence

When validated neural networks (NNs) are pruned (and retrained) before deployment, it is desirable to prove that the new NN behaves equivalently to the (original) reference NN. To this end, our paper revisits the idea of differential verification which performs reasoning on differences between NNs: On the one hand, our paper proposes a novel abstract domain for differential verification admitting more efficient reasoning about equivalence. On the other hand, we investigate empirically and theoretically which equivalence properties are (not) efficiently solved using differential reasoning. Based on the gained insights, and following a recent line of work on confidence-based verification, we propose a novel equivalence property that is amenable to Differential Verification while providing guarantees for large parts of the input space instead of small-scale guarantees constructed w.r.t. predetermined input points. We implement our approach in a new tool called VeryDiff and perform an extensive evaluation on numerous old and new benchmark families, including new pruned NNs for particle jet classification in the context of CERN's LHC where we observe median speedups >300x over the State-of-the-Art verifier alpha,beta-CROWN.

An Information-Flow Perspective on Algorithmic Fairness

This work presents insights gained by investigating the relationship between algorithmic fairness and the concept of secure information flow. The problem of enforcing secure information flow is well-studied in the context of information security: If secret information may "flow" through an algorithm or program in such a way that it can influence the program's output, then that is considered insecure information flow as attackers could potentially observe (parts of) the secret. There is a strong correspondence between secure information flow and algorithmic fairness: if protected attributes such as race, gender, or age are treated as secret program inputs, then secure information flow means that these ``secret'' attributes cannot influence the result of a program. While most research in algorithmic fairness evaluation concentrates on studying the impact of algorithms (often treating the algorithm as a black-box), the concepts derived from information flow can be used both for the analysis of disparate treatment as well as disparate impact w.r.t. a structural causal model. In this paper, we examine the relationship between quantitative as well as qualitative information-flow properties and fairness. Moreover, based on this duality, we derive a new quantitative notion of fairness called fairness spread, which can be easily analyzed using quantitative information flow and which strongly relates to counterfactual fairness. We demonstrate that off-the-shelf tools for information-flow properties can be used in order to formally analyze a program's algorithmic fairness properties, including the new notion of fairness spread as well as established notions such as demographic parity.