mlsanityData to 14 Oct 2026

Teaching Vision-Language Models to Use the Scale They Are Given: Label-Free Equivariance Training for Metric Physical Reasoning

arXiv 2609.00658 ↗First posted 1 Sep 2026cs.CVcited by 0

On the map: LLM reasoning → Spatial and embodied reasoning

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Abstract (arXiv)

Metric questions about video, such as the speed of a moving object, require a vision-language model to convert visual measurements into physical units using a real-world reference supplied in the prompt. We find that current models use this reference only partially. When every world-space quantity in the prompt is multiplied by a common factor, the prompt still describes the same video and the correct answer changes by exactly that factor, but the predictions of eight models change by less, and their accuracy stays concentrated near the scale that the depicted objects usually have. Asked the same physics in a scale-free form, the two models we test recover the closed-form scaling laws on most items, which indicates that the deficit lies in metric grounding and not in knowledge of the physical mechanism. Because the scaling relation is exact, it can serve as supervision without metric annotations. Equivariance Self-Distillation (EquiSD) projects a model's own prediction onto the functions that satisfy this relation and fine-tunes the model on the resulting targets, with one query per training question and no ground truth. Trained on synthetic video only, EquiSD brings a 3B model close to the exact relation on held-out simulated videos, also at scales not seen in training, and improves its accuracy across scales. Without adaptation, it also improves accuracy across scales on the QuantiPhy benchmark, where its gain reaches 93% of that obtained by supervision with exact simulator answers.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. Builds on 17 of its 19 references that are in the map. First posted on arXiv 1 Sep 2026.

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17 of 19 references.

Closest ancestors · 6

Same direction, newest first

  1. 2026Code as Worlds: Agentic Discovery of Executable World Representations for Physical Reasoning27 Aug
  2. 2026PhysMind: From Video to Executable Worlds for Training-Free Physical Reasoning5 Aug
  3. 2025SIMPACT: Simulation-Enabled Action Planning using Vision-Language Models5 Dec
  4. 2024Thinking in Space: How Multimodal Large Language Models See, Remember, and Recall Spaces18 Dec
  5. 2024LLMPhy: Parameter-Identifiable Physical Reasoning Combining Large Language Models and Physics Engines12 Nov
  6. 2024ContPhy: Continuum Physical Concept Learning and Reasoning from Videos9 Feb

Other references · 11

  1. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  2. 2025Qwen2.5-VL Technical Reportcited by 5,587
  3. 2023QLoRA: Efficient Finetuning of Quantized LLMscited by 3,418
  4. 2019CoPhy: Counterfactual Learning of Physical Dynamicscited by 81
  5. 2022Dimensionless machine learning: Imposing exact units equivariancecited by 17
  6. 2022Filtered-CoPhy: Unsupervised Learning of Counterfactual Physics in Pixel Spacecited by 14
  7. 2022CRIPP-VQA: Counterfactual Reasoning about Implicit Physical Properties via Video Question Answeringcited by 13
  8. 2025Test-Time Consistency in Vision Language Modelscited by 5
  9. 2026Deltaynamics: Language-Based Representation for Inferring Rigid-Body Dynamics From Videoscited by 3
  10. 2026Causal Scaffolding for Physical Reasoning: A Benchmark for Causally-Informed Physical World Understanding in VLMscited by 3
  11. 2026Ill-Posed by Design: Probing Evidence Use in VLMscited by 2

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  1. 2025MASS: Motion-Aware Spatial-Temporal Grounding for Physics Reasoning and Comprehension in Vision-Language Models
  2. 2024Physics Context Builders: A Modular Framework for Physical Reasoning in Vision-Language Models
  3. 2026Seeing Is Not Measuring: Tool-Augmented Metric Spatial Reasoning for Vision-Language Models
  4. 2025PhysVidBench: Language-Grounded Evaluation of Physical Commonsense in Text-to-Video Models
  5. 2026Not All Error Yields to Scale: Where Scaling Stops in Vision-Language Inference
  6. 2026Geometric Parrots: Rule Absence vs. Rule Fragility in Spatial and Physical Reasoning for Vision-Language Models
  7. 2024UniBench: Visual Reasoning Requires Rethinking Vision-Language Beyond Scaling
  8. 2025LAST: LeArning to Think in Space and Time for Generalist Vision-Language Models