Representational similarity analysis and related methods have become standard tools for comparing the internal geometries of neural networks and biological systems. These methods measure what is represented, the alignment between two representational spaces, but not whether that structure is robust. We introduce geometric stability, a distinct dimension of representational quality that quantifies how reliably a representation's pairwise distance structure holds under perturbation. Our metric, Shesha, measures self-consistency through split-half correlation of representational dissimilarity matrices constructed from complementary feature subsets. A key formal property distinguishes stability from similarity: Shesha is not invariant to orthogonal transformations of the feature space, unlike CKA and Procrustes, enabling it to detect compression-induced damage to manifold structure that similarity metrics cannot see. Spectral analysis reveals the mechanism: similarity metrics collapse after removing the top principal component, while stability retains sensitivity across the eigenspectrum. Across 2463 encoder configurations in seven domains -- language, vision, audio, video, protein sequences, molecular profiles, and neural population recordings -- stability and similarity are empirically uncorrelated ($ρ=-0.01$). A regime analysis shows this independence arises from opposing effects: geometry-preserving transformations make the metrics redundant, while compression makes them anti-correlated, canceling in aggregate. Applied to 94 pretrained models across 6 datasets, stability exposes a "geometric tax": DINOv2, the top-performing model for transfer learning, ranks last in geometric stability on 5/6 datasets. Contrastive alignment and hierarchical architecture predict stability, providing actionable guidance for model selection in deployment contexts where representational reliability matters.

翻译：表征相似性分析及相关方法已成为比较神经网络与生物系统内部几何结构的标准工具。这些方法度量的是"表征内容"——两个表征空间之间的对齐程度，但未能评估其结构是否鲁棒。我们提出"几何稳定性"这一表征质量的独立维度，用于量化表征的成对距离结构在扰动下的可靠保持程度。我们的指标Shesha通过互补特征子集构建的表征差异矩阵的分半相关性来测量自一致性。一项关键的形式属性将稳定性与相似性区分开来：与CKA和Procrustes不同，Shesha对特征空间的正交变换不具不变性，因此能检测相似性指标无法识别的压缩引起的流形结构损伤。谱分析揭示了其机制：移除主成分后相似性指标失效，而稳定性在整个特征谱区间保持敏感度。在涵盖语言、视觉、音频、视频、蛋白质序列、分子谱及神经群体记录七个领域共2463个编码器配置中，稳定性与相似性在经验上不相关（ρ=-0.01）。状态空间分析表明这种独立性源于对抗效应：保几何变换使指标冗余，而压缩使其负相关，最终在总体中相互抵消。针对6个数据集的94个预训练模型应用显示，稳定性揭示了"几何代价"：迁移学习最优模型DINOv2在5/6个数据集的几何稳定性排名垫底。对比对齐与层级化架构可预测稳定性，为需要表征可靠性的部署场景提供了可操作的模型选择指导。