Differential privacy representation geometry for medical image analysis

2026-03-01

AI Summary

This work addresses the unclear mechanisms underlying utility degradation in medical image analysis under differential privacy (DP). We propose DP-RGMI, a framework that, for the first time, disentangles DP’s impact on representation space into three interpretable dimensions: geometric displacement, spectral effective dimensionality, and utilization gap. Through comprehensive analyses—including representation displacement metrics, spectral decomposition, linear probing, and end-to-end evaluation across over 594,000 chest X-ray images—we reveal that DP induces non-monotonic, initialization- and dataset-dependent anisotropic reshaping of representations. Our findings demonstrate that DP consistently introduces a utilization gap between the learned representations and downstream task heads, while geometric changes are highly sensitive to pretraining initialization and data distribution. These insights provide reproducible criteria for diagnosing and selecting privacy-preserving models in clinical imaging applications.

Technology Category

• Machine Learning: Privacy
• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• Differential Privacy
• Medical Image Analysis
• Representation Geometry
• Utility Loss
• Privacy-Utility Tradeoff

Innovation

• differential privacy
• representation geometry
• medical image analysis
• spectral effective dimension
• utilization gap