$\alpha$-TCAV: A Unified Framework for Testing with Concept Activation Vectors

Abstract:Concept Activation Vectors (CAV) and the Testing with CAVs (TCAV) method are fundamental tools for concept-based explainability in deep learning, yet their practical utility is limited by the variability across different samples of concept and non-concept examples. We analyze this stochastic nature of CAVs, and identify a fundamental flaw in the standard TCAV score, its instability by using a discontinuous indicator function. To address this, we introduce $\alpha$-TCAV, a parameterized unified framework that replaces the discontinuous indicator with a smooth function, which recovers TCAV as a limiting case. Under realistic assumptions, we characterize the score distributions and derive principled parameter choices: one matches the mean of its averaged counterpart, Multi-TCAV, with no larger variance using a single CAV; the other provides a calibrated probability that the concept positively influences the model output. Our analysis and experiments provide practical guidance and challenge the established practice of splitting the sampling budget across multiple CAVs.

Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Probability (math.PR)

arXiv:2605.15688 [stat.ML]

(or arXiv:2605.15688v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2605.15688 Focus to learn more arXiv-issued DOI via DataCite

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