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

Vision-language models (VLMs) struggle with metric and multi-view relationships that remain implicit in RGB observations. Geometry foundation models recover this structure from RGB, but existing methods either fuse the estimated features with visual tokens and learn to use them from question answering alone, or align VLM latents with geometry features. Capturing geometry, however, does not ensure its use: zeroing the aligned latents of a released feature-alignment model leaves its accuracy unchanged. We introduce GeoReader, a framework that learns geometric representations for the VLM that reads them. First, we train lightweight Geometric Readers to produce continuous input tokens, supervising them with geometry descriptions decoded by a frozen VLM, so that the Readers express geometry in a form the target model can already read. We then freeze the Readers to preserve this interface while fine-tuning the VLM on spatial QA, with geometry injection conditioned on the question. Geometry descriptions serve only as training targets: at inference, the VLM answers directly from the continuous geometric tokens without generating a geometry chain of thought. With geometry predicted from RGB images, our approach reaches 94.3 on MindCube-Tiny with Qwen3-VL-4B and, with a multi-source QA mixture, an average of 72.5 across six additional spatial benchmarks with Qwen3.5-9B. These results suggest that a useful geometric representation is one the receiving model can use, not merely one from which geometry can be reconstructed.

Modern Vision-Language Models (VLMs) achieve strong semantic recognition, yet remain brittle on elementary spatial relations such as left of, on, behind, and between. One cause of this failure arises before language reasoning begins: the visual pathway may compress or discard critical 3D structural cues during feature extraction, so the language model receives image representations that are already insufficient for reliable spatial judgment. We introduce GeoWorld-VLM, a VLM-side distillation framework that transfers geometric structure from frozen camera-conditioned video world models into VLMs. GeoWorld-VLM fine-tunes only the image encoder and multimodal projector, aligning post-projector image features with intermediate world-model representations while leaving the main backbone frozen. Given images, a prompt, and a sampled camera trajectory, the world-model teacher converts static visual input into a synthetic multi-view spatial signal. Training combines spatial answer supervision, teacher-student feature alignment, and a preservation anchor to the original VLM. Since the language model remains frozen, GeoWorld-VLM preserves the original model's linguistic capabilities while attributing spatial improvements to the enhanced visual pathway. To evaluate the effectiveness and generality of the proposed method, we apply GeoWorld-VLM to two distinct VLM architectures and observe consistent improvements across both backbones. GeoWorld-VLM improves performance by approximately 4 percent on both the What'sUp and VSR benchmarks, suggesting that world-model-guided visual alignment generalizes across model structures and spatial reasoning datasets.

While recent vision-language models (VLMs) have shown outstanding performance across diverse applications, they tend to under-use visual information and over-rely on textual context. In this work, we propose GeoPID, a training-free framework that analyzes multimodal information within VLMs from a geometric perspective. GeoPID decomposes information into Redundant, Modality-Unique, and Synergistic components through the geometric relationships between visual and textual representation subspaces. Through an extensive analysis across 22 VLMs and 14 benchmarks, we confirm that correct predictions exhibit stronger vision-unique components when questions strongly require visual grounding. Building on this geometric analysis, we introduce a targeted intervention technique that selectively amplifies visual representations along the vision-unique subspace during inference. As a result, visual grounding capabilities were enhanced without any additional model parameter updates, achieving an average relative accuracy gain of 7.63%.