Probabilistic Stability Guarantees for Feature Attributions

Stability guarantees are an emerging tool for evaluating feature attributions, but existing certification methods rely on smoothed classifiers and often yield conservative guarantees. To address these limitations, we introduce soft stability and propose a simple, model-agnostic, and sample-efficient stability certification algorithm (SCA) that provides non-trivial and interpretable guarantees for any attribution. Moreover, we show that mild smoothing enables a graceful tradeoff between accuracy and stability, in contrast to prior certification methods that require a more aggressive compromise. Using Boolean function analysis, we give a novel characterization of stability under smoothing. We evaluate SCA on vision and language tasks, and demonstrate the effectiveness of soft stability in measuring the robustness of explanation methods.