Paper
Do Foundation Models Know Geometry? Probing Frozen Features for Continuous Physical Measurement
Authors
Yakov Pyotr Shkolnikov
Abstract
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.06459v1</id>\n <title>Do Foundation Models Know Geometry? Probing Frozen Features for Continuous Physical Measurement</title>\n <updated>2026-03-06T16:48:27Z</updated>\n <link href='https://arxiv.org/abs/2603.06459v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.06459v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.CV'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <published>2026-03-06T16:48:27Z</published>\n <arxiv:primary_category term='cs.CV'/>\n <author>\n <name>Yakov Pyotr Shkolnikov</name>\n </author>\n </entry>"
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