  Perturbation robustness evaluates the vulnerabilities of models, arising from
a variety of perturbations, such as data corruptions and adversarial attacks.
Understanding the mechanisms of perturbation robustness is critical for global
interpretability. We present a model-agnostic, global mechanistic
interpretability method to interpret the perturbation robustness of image
models. This research is motivated by two key aspects. First, previous global
interpretability works, in tandem with robustness benchmarks, e.g. mean
corruption error (mCE), are not designed to directly interpret the mechanisms
of perturbation robustness within image models. Second, we notice that the
spectral signal-to-noise ratios (SNR) of perturbed natural images exponentially
decay over the frequency. This power-law-like decay implies that: Low-frequency
signals are generally more robust than high-frequency signals -- yet high
classification accuracy can not be achieved by low-frequency signals alone. By
applying Shapley value theory, our method axiomatically quantifies the
predictive powers of robust features and non-robust features within an
information theory framework. Our method, dubbed as \textbf{I-ASIDE}
(\textbf{I}mage \textbf{A}xiomatic \textbf{S}pectral \textbf{I}mportance
\textbf{D}ecomposition \textbf{E}xplanation), provides a unique insight into
model robustness mechanisms. We conduct extensive experiments over a variety of
vision models pre-trained on ImageNet to show that \textbf{I-ASIDE} can not
only \textbf{measure} the perturbation robustness but also \textbf{provide
interpretations} of its mechanisms.
