Predicting Privacy Leakage from Weight Spectral Density

The paper investigates whether inexpensive spectral metrics from the heavy‑tailed self‑regularisation framework can predict membership inference attack (MIA) vulnerability, offering a scalable alternative to costly shadow‑model attacks. Experiments on image and tabular classification tasks show that stable rank correlates positively with overall MIA success, while Log alpha‑Norm correlates negatively with MIA risk in low false‑positive regimes, outperforming conventional generalisation gap measures. These findings suggest that neural network spectra contain privacy leakage signals not captured by traditional overfitting metrics, pointing to spectral analysis as a promising direction for privacy auditing.

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