α-TCAV unifies CAV explainability with stable, smooth concept scores

Concept Activation Vectors (CAVs) are widely used to interpret deep learning models by measuring how much a concept (e.g., 'stripes') influences predictions. However, the standard Testing with CAVs (TCAV) method suffers from statistical instability. In a new paper, Ekkehard Schnoor and colleagues analyze the stochastic nature of CAVs and identify a fundamental flaw: the TCAV score uses a discontinuous indicator function that introduces non-decaying variance, making results unreliable even with increased sampling. The authors prove this flaw affects major CAV variants like PatternCAV, FastCAV, and ridge regression-based CAVs, and show that current state-of-the-art choices lack theoretical justification.

To solve this, the team introduces α-TCAV, a generalized framework that replaces the indicator with a smooth, parameterized function. This yields a unified probabilistic formulation that subsumes both TCAV and Multi-TCAV. The parameter α can be tuned either to imitate Multi-TCAV at substantially lower computational cost or to obtain a calibrated Bayes-optimal probabilistic measure of a concept's influence. The paper provides principled guidance on setting α and delivers a surprising practical recommendation: for maximum reliability, allocate the full sampling budget to a single CAV rather than splitting it across several. This work promises more robust and theoretically sound explainability for critical AI applications.