Differential privacy representation geometry for medical image analysis
This work addresses the problem of understanding privacy-induced utility degradation for medical imaging researchers, offering a diagnostic framework, but it is incremental as it builds on existing differential privacy methods without introducing a new paradigm.
The authors tackled the unclear mechanism of how differential privacy causes utility loss in medical imaging by introducing DP-RGMI, a framework that decomposes performance degradation into encoder geometry and task-head utilization, showing across over 594,000 chest X-ray images that DP consistently creates a utilization gap while altering representation anisotropy in non-monotonic ways.
Differential privacy (DP)'s effect in medical imaging is typically evaluated only through end-to-end performance, leaving the mechanism of privacy-induced utility loss unclear. We introduce Differential Privacy Representation Geometry for Medical Imaging (DP-RGMI), a framework that interprets DP as a structured transformation of representation space and decomposes performance degradation into encoder geometry and task-head utilization. Geometry is quantified by representation displacement from initialization and spectral effective dimension, while utilization is measured as the gap between linear-probe and end-to-end utility. Across over 594,000 images from four chest X-ray datasets and multiple pretrained initializations, we show that DP is consistently associated with a utilization gap even when linear separability is largely preserved. At the same time, displacement and spectral dimension exhibit non-monotonic, initialization- and dataset-dependent reshaping, indicating that DP alters representation anisotropy rather than uniformly collapsing features. Correlation analysis reveals that the association between end-to-end performance and utilization is robust across datasets but can vary by initialization, while geometric quantities capture additional prior- and dataset-conditioned variation. These findings position DP-RGMI as a reproducible framework for diagnosing privacy-induced failure modes and informing privacy model selection.