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.

翻译：差分隐私在医学影像中的影响通常仅通过端到端性能进行评估，导致隐私引致效用损失的机制尚不明确。我们提出医学影像差分隐私表示几何框架（DP-RGMI），该框架将差分隐私诠释为一种对表示空间的结构化变换，并将性能退化分解为编码器几何与任务头利用率两部分。其中，几何特性通过表示相对于初始化的位移和谱有效维数进行量化，而利用率则通过线性探针与端到端效用之间的差距来衡量。基于来自四个胸部X光数据集、超过59.4万张图像以及多种预训练初始化的实验，我们表明：即使在线性可分性基本得以保持的情况下，差分隐私始终与利用率差距相关。与此同时，位移和谱维数表现出非单调、依赖于初始化和数据集的重新塑造特性，这表明差分隐私改变的是表示的各向异性而非均匀塌缩特征。相关性分析表明，端到端性能与利用率之间的关联在不同数据集上具有鲁棒性，但可能因初始化而异，而几何量则能捕捉额外的先验与数据集条件变异。这些发现使DP-RGMI成为一个可复现的框架，用于诊断隐私引致的故障模式并指导隐私模型选择。