Differential privacy representation geometry for medical image analysis

TL;DR

This paper introduces DP-RGMI, a framework that interprets differential privacy in medical imaging as a structured transformation of representation space, revealing how privacy mechanisms affect utility and representation geometry.

Contribution

The paper presents DP-RGMI, a novel interpretative framework that decomposes privacy-induced utility loss into geometric and utilization components in medical imaging.

Findings

DP consistently causes a utilization gap even with preserved linear separability.

Representation displacement and spectral dimension change non-monotonically depending on initialization and dataset.

Geometric quantities reveal dataset- and initialization-dependent variations in privacy effects.

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.