Is the Geometry Doing the：它和通用视觉自监督的关系在于：审计 MERU/HyCoCLIP/PHyCLIP 是否真正使用 hyperbolic geometry，适合作为层级 V-L 表征评估反例
中相关；详见方法、贡献和实验边界。
Is the Geometry Doing the Work? An Operating-Point Audit of Hierarchy in Hyperbolic Vision-Language Models arXiv new/cross; TMLR under review; V-L representation audit 原文链接
Figureure 2 · : Dimensionless radius $\sqrt { c } \rho$ for current-GRIT baseline (fFigure 2: Dimensionless radius $\sqrt { c } \rho$ for current-GRIT baseline (filled circles) and clampOf (open diamonds) across the three families and both ViT sizes (image side; seed-0 values from Table 15). Arrows trace the baseline→clampOf shift. Every model sits at $\sqrt { c } \rho \approx 0 . 2 – 0 . 3$ deep inside the locally-Euclidean region (shaded) and far from the threshold $\sqrt { c } \rho = 1$ (dashed)—so releasing the floor moves c and $\rho$ but keeps the operating point near-Euclidean: HyCoCLIP barely moves (inset), MERU drops further, PHyCLIP between. Table 2 reports the corresponding seed means.这张图/表用于判断 Is the Geometry Doing the 的实验收益来自哪里。重点看替换、消融或跨模型设置下趋势是否一致，而不是只看单个最高分。Figureure 3 · : Radial parent–child consistency (ViT-B released) against each model’Figure 3: Radial parent–child consistency (ViT-B released) against each model’s 10,000-permutation shufle null $( \pm 1 \sigma , \pm 2 \sigma$ bands; null mean as vertical tick; ±1.6σ detection threshold dashed). The three hyperbolic models lie within ±1σ of their nulls. The only crossing is the Euclidean CLIP-B baseline $( z = + 1 . 7 3 ) \mathrm { \mathrm { - \ a } }$ model that by construction encodes no radial hierarchy—so a crossing at this level reflects the near-unitnorm marginal artifact rather than radial depth, and it does not survive a multiple-comparison correction (Table 29). Raw consistencies span 22–61%, but each sits at its own shufle null, not above it.这张图/表用于判断 Is the Geometry Doing the 的实验收益来自哪里。重点看替换、消融或跨模型设置下趋势是否一致，而不是只看单个最高分。
