arXiv:2607.05268cs.CVcs.LG2026-07

实证检验超球视觉语言模型是否真用几何层次,发现多数模型未激活预期结构。

Is the Geometry Doing the Work? An Operating-Point Audit of Hierarchy in Hyperbolic Vision-Language Models

论文配图:Is the Geometry Doing the Work? An Operating-Point Audit of Hierarchy in Hyperbolic Vision-Language Models
图 1 · 摘自论文原文
  • 通过多维度诊断区分几何与角度效应,验证模型是否真正利用超球几何
  • 最大半径仅0.37,远低于10%局部畸变阈值0.84,接近欧氏空间
  • 模型依赖低曲率捷径,而非真正学习概念层级关系,适合研究架构机制者

超球视觉语言模型旨在以几何方式编码抽象:通用概念位于原点附近,具体概念则更远离中心,蕴含蕴含锥体表示有向顺序。我们检验了训练后的MERU、HyCoCLIP和PHyCLIP模型是否实际使用这些机制。对七个已发布检查点及对应从头训练干预进行审计,采用能区分活跃超球几何、角结构与监督效应的诊断方法。所有审计收敛检查点在无量纲半径 $u=\sqrt{c}ρ$ 上仍接近欧氏空间,图像端最大观测值为0.37,显著低于 $u\approx0.84$(此时局部度量畸变达10%)。释放曲率下限虽改变曲率与范数,但未改变此区域,下游性能变化有限且普遍温和。训练后的蕴含锥体趋于饱和或几乎饱和,因此低违反率可能源于锥体过宽而非学习到真实顺序。预注册语义遍历检测到分支内弱顺序,但未发现操作性全层级读取。随机化控制测试显示,已发布检查点中无配对特定径向排序,且三个匹配ViT-B种子无一致正结果。根源在于低曲率捷径:降低曲率可扩大蕴含锥体并抑制违反,无需学习顺序。在探测轨迹中,梯度分解表明蕴含是导致曲率下降的主要压力。然而,即使移除蕴含,曲率仍收缩,说明该捷径非唯一原因。根据诊断,审计的模型未展现有效的径向或锥基层级结构。我们提炼出五数值几何报告,用于评估未来层级声称。

原文摘要 · Abstract (English)

Hyperbolic vision-language models are designed to encode abstraction geometrically: general concepts near the origin, specific ones farther out, and entailment cones representing directed order. We ask whether trained MERU, HyCoCLIP, and PHyCLIP models actually use these mechanisms. We audit seven released checkpoints and matched from-scratch interventions, using diagnostics that distinguish active hyperbolic geometry from angular structure and supervision effects. All audited converged checkpoints remain near-Euclidean in the dimensionless radius $u=\sqrt{c}ρ$, which measures how strongly embeddings experience hyperbolic geometry: the largest observed image-side value is $0.37$ -- well below $u\approx0.84$, where local metric distortion reaches $10\%$. Releasing the curvature floor changes curvature and norms but not this regime, with mixed, generally modest downstream shifts. Trained entailment cones are saturated or nearly saturated, so low violation rates can arise from trivially wide cones rather than learned order. Preregistered semantic traversal detects weak within-branch order but no operative full-hierarchy readout. Shuffle-controlled tests detect no pair-specific radial ordering in released checkpoints, and no positive result is consistent across all three matched ViT-B seeds. We trace this to a low-curvature shortcut: lowering curvature widens entailment cones and suppresses violations without learning order. In the probed trajectories, gradient decomposition identifies entailment as the dominant curvature-lowering pressure during collapse. Yet curvature contracts even when entailment is removed, so the shortcut is not the sole cause. Under our diagnostics, the audited formulations do not demonstrate an operative radial or cone-based hierarchy. We distill the audit into a five-number geometry report for evaluating future hierarchy claims.

超球模型层级结构几何审计视觉语言

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