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Life sciences · Preprint
arXiv · September 10, 2026
Early or partial results. Treat as a signal, not a conclusion.
This preprint proposes that spectral metrics derived from neural network weights—specifically stable rank and Log alpha-Norm—correlate with membership inference attack success and may offer a computationally cheaper alternative to shadow-model-based privacy auditing. The work is exploratory and presents correlations rather than a validated predictive framework; it has not undergone peer review and requires independent validation before adoption in privacy assessment workflows.
Computational observational study. Neural network models trained for image and tabular classification. Intervention: Computation of spectral metrics (stable rank, Log alpha-Norm) from model weight matrices. Compared with: Generalisation gap and membership inference attack success rates.
Stable rank exhibits a strong positive correlation with overall MIA success across datasets Log alpha-Norm shows a consistent negative correlation with MIA vulnerability at the low false-positive regime Associations with spectral metrics are observed to be stronger than those obtained using the generalisation gap
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Early-stage computational study proposing spectral metrics as proxies for privacy risk, without validation against gold-standard privacy attacks or real-world deployment data; findings are exploratory and require confirmation.
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Membership inference attacks (MIAs) are widely used to audit the privacy disclosure risk of machine learning models, however current state-of-the-art attacks require training computationally expensive shadow models, making large-scale privacy evaluation impractical. In this work, we investigate whether inexpensive spectral metrics derived from the heavy-tailed self-regularisation framework can serve as proxies for MIA vulnerability. We evaluate several WeightWatcher spectral metrics on image and tabular classification tasks and compare their relationship with MIA privacy leakage against conventional measures of generalisation. Across datasets, stable rank exhibits a strong positive correlation with overall MIA success, while Log alpha-Norm shows a consistent negative correlation with MIA vulnerability at the low false-positive regime. These associations are observed to be stronger than those obtained using the generalisation gap. The results indicate that neural network spectra may contain information about privacy leakage that is not fully captured by conventional measures of overfitting, motivating spectral analysis as a promising direction for scalable privacy auditing.
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