# Do Foundation Models Know Geometry? Probing Frozen Features for Continuous Physical Measurement

arXiv: https://arxiv.org/abs/2603.06459 · HTML: https://mlsanity.com/paper/2603.06459/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Embodied and 3D vision-language models, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 43 of its 54 references that are in the map.
- First posted on arXiv 6 Mar 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)
- Mechanistic interpretability / [Interpreting vision and multimodal models](https://mlsanity.com/mechinterp/interpreting-vision-and-multimodal-models/)

## Builds on (most cited first, 30 of 43)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [InternVL: Scaling up Vision Foundation Models and Aligning for Generic Visual-Linguistic Tasks](https://mlsanity.com/paper/2312.14238/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [How Far Are We to GPT-4V? Closing the Gap to Commercial Multimodal Models with Open-Source Suites](https://mlsanity.com/paper/2404.16821/) (2024)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMs](https://mlsanity.com/paper/2401.06209/) (2024)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [DeiT III: Revenge of the ViT](https://mlsanity.com/paper/2204.07118/) (2022)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Reconstructing Hands in 3D with Transformers](https://mlsanity.com/paper/2312.05251/) (2023)
- [FreiHAND: A Dataset for Markerless Capture of Hand Pose and Shape from Single RGB Images](https://mlsanity.com/paper/1909.04349/) (2019)
- [Probing the 3D Awareness of Visual Foundation Models](https://mlsanity.com/paper/2404.08636/) (2024)
- [MediaPipe Hands: On-device Real-time Hand Tracking](https://mlsanity.com/paper/2006.10214/) (2020)
- [It's Written All Over Your Face: Full-Face Appearance-Based Gaze Estimation](https://mlsanity.com/paper/1611.08860/) (2016)
- [Reliability of CKA as a Similarity Measure in Deep Learning](https://mlsanity.com/paper/2210.16156/) (2022)
- [Improving 2D Feature Representations by 3D-Aware Fine-Tuning](https://mlsanity.com/paper/2407.20229/) (2024)
- [BRAVE: Broadening the visual encoding of vision-language models](https://mlsanity.com/paper/2404.07204/) (2024)
- [6D Rotation Representation For Unconstrained Head Pose Estimation](https://mlsanity.com/paper/2202.12555/) (2022)

## Abstract (arXiv)

Vision-language models encode continuous geometry that their text pathway fails to express: a 6,000-parameter linear probe extracts hand joint angles at 6.1 degrees MAE from frozen features, while the best text output achieves only 20.0 degrees -- a 3.3x bottleneck. LoRA fine-tuning (r=16, 2,000 images) narrows this gap to 6.5 degrees, providing evidence for a pathway-training deficit rather than a representational one. Training objective determines accuracy more than architecture: five encoders spanning self-supervised, contrastive, and hybrid paradigms converge to statistically equivalent accuracy (R^2 approximately 0.55, TOST-equivalent at delta=0.03) despite sharing as little as CKA=0.41 representational similarity -- functional convergence without representational convergence. Autoregressive generation damages geometric fidelity, but the damage originates in the generation process, not in language alignment: Qwen2.5-VL's LLM layers actually improve probe accuracy over its raw vision encoder. Layer-wise analysis reveals a universal mid-network accuracy peak across all architectures, with attention heads in layers 18-22 carrying disproportionate geometric signal. These findings enable a single frozen backbone to function as a multi-task geometric sensor through lightweight probes, without fine-tuning or text generation.