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

arXiv: https://arxiv.org/abs/2607.05268 · HTML: https://mlsanity.com/paper/2607.05268/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompt learning and adaptation of CLIP, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Prompt learning and adaptation of CLIP](https://mlsanity.com/mllm/prompt-learning-and-adaptation-of-clip/)

## Builds on (most cited first, 18 of 18)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Kosmos-2: Grounding Multimodal Large Language Models to the World](https://mlsanity.com/paper/2306.14824/) (2023)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [SugarCrepe: Fixing Hackable Benchmarks for Vision-Language Compositionality](https://mlsanity.com/paper/2306.14610/) (2023)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [VL-CheckList: Evaluating Pre-trained Vision-Language Models with Objects, Attributes and Relations](https://mlsanity.com/paper/2207.00221/) (2022)
- [Order-Embeddings of Images and Language](https://mlsanity.com/paper/1511.06361/) (2015)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers](https://mlsanity.com/paper/2107.11472/) (2021)
- [HiCLIP: Contrastive Language-Image Pretraining with Hierarchy-aware Attention](https://mlsanity.com/paper/2303.02995/) (2023)
- [PHyCLIP: ℓ1-Product of Hyperbolic Factors Unifies Hierarchy and Compositionality in Vision-Language Representation Learning](https://mlsanity.com/paper/2510.08919/) (2025)
- [Embedding Geometries of Contrastive Language-Image Pre-Training](https://mlsanity.com/paper/2409.13079/) (2024)
- [Comparing Euclidean and Hyperbolic Embeddings on the WordNet Nouns Hypernymy Graph](https://mlsanity.com/paper/2109.07488/) (2021)
- [ARGENT: Adaptive Hierarchical Image-Text Representations](https://mlsanity.com/paper/2603.23311/) (2026)

## Abstract (arXiv)

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=√cρ, which measures how strongly embeddings experience hyperbolic geometry: the largest observed image-side value is 0.37 -- well below u≈0.84, 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.