# Geometric Encoding for Spatial Reasoning in Vision-Language Models

arXiv: https://arxiv.org/abs/2609.34148 · HTML: https://mlsanity.com/paper/2609.34148/

## 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 21 of its 25 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 21 of 21)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [Video-LLaVA: Learning United Visual Representation by Alignment Before Projection](https://mlsanity.com/paper/2311.10122/) (2023)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [Thinking in Space: How Multimodal Large Language Models See, Remember, and Recall Spaces](https://mlsanity.com/paper/2412.14171/) (2024)
- [YOLO-World: Real-Time Open-Vocabulary Object Detection](https://mlsanity.com/paper/2401.17270/) (2024)
- [SpatialRGPT: Grounded Spatial Reasoning in Vision Language Models](https://mlsanity.com/paper/2406.01584/) (2024)
- [Spatial-MLLM: Boosting MLLM Capabilities in Visual-based Spatial Intelligence](https://mlsanity.com/paper/2505.23747/) (2025)
- [VLM-3R: Vision-Language Models Augmented with Instruction-Aligned 3D Reconstruction](https://mlsanity.com/paper/2505.20279/) (2025)
- [SpaceR: Reinforcing MLLMs in Video Spatial Reasoning](https://mlsanity.com/paper/2504.01805/) (2025)
- [ViewSpatial-Bench: Evaluating Multi-perspective Spatial Localization in Vision-Language Models](https://mlsanity.com/paper/2505.21500/) (2025)
- [SpatialLadder: Progressive Training for Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2510.08531/) (2025)
- [Beyond Semantics: Rediscovering Spatial Awareness in Vision-Language Models](https://mlsanity.com/paper/2503.17349/) (2025)
- [Thinking with Spatial Code for Physical-World Video Reasoning](https://mlsanity.com/paper/2603.05591/) (2026)

## Abstract (arXiv)

Vision-Language Models (VLMs) are far more reliable at recognizing what appears in a video than at reasoning about its spatial and temporal properties, such as metric distances, object dimensions, and consistent object identities across frames. We present Geometric Code, a perception-to-geometry pipeline that computes explicit spatial structure from video and supplies it to VLMs as context to augment reasoning. A perception layer segments and classifies objects and recovers depth, camera pose, and intrinsics from monocular RGB video. A deterministic geometric engine then back-projects, merges, and cleans these outputs into a spatial code, including per-object positions, dimensions, counts, inter-object distances, appearance order, and room geometry. The code is serialized into VLMs' prompts, either alongside the video or replacing it entirely. Specifically, there is no component trained or fine-tuned in our approach. On VSI-Bench, augmenting 2B and 4B open models with the spatial code improves average accuracy by +4.1 points over the frames-only baseline, with the largest gains on numeric estimation tasks such as absolute distance (+24.1 points). The results suggest that explicitly computed geometry, delivered through the language channel, recovers spatial competence that small VLMs cannot extract from pixels alone.