Differential privacy representation geometry for medical image analysis

• URL: http://arxiv.org/abs/2603.01098v1
• Date: Sun, 01 Mar 2026 13:30:36 GMT
• Title: Differential privacy representation geometry for medical image analysis
• Abstract summary: Differential privacy (DP)'s effect in medical imaging is typically evaluated only through end-to-end performance.<n>We introduce Differential Privacy Representation Geometry for Medical Imaging (DP-RGMI), a framework that interprets DP as a structured transformation of representation space.<n>We show that DP is consistently associated with a utilization gap even when linear separability is largely preserved.
• Score: 1.828619151598757
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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