# SPACENUM: Revisiting Spatial Numerical Understanding in VLMs

arXiv: https://arxiv.org/abs/2605.23898 · HTML: https://mlsanity.com/paper/2605.23898/

## Key facts

- Cited by 3 papers in the map (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 25 of its 33 references that are in the map.
- First posted on arXiv 22 May 2026.

## Placed in

- 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, 25 of 25)

- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [AI2-THOR: An Interactive 3D Environment for Visual AI](https://mlsanity.com/paper/1712.05474/) (2017)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [Thinking in Space: How Multimodal Large Language Models See, Remember, and Recall Spaces](https://mlsanity.com/paper/2412.14171/) (2024)
- [SpatialRGPT: Grounded Spatial Reasoning in Vision Language Models](https://mlsanity.com/paper/2406.01584/) (2024)
- [Visual Spatial Reasoning](https://mlsanity.com/paper/2205.00363/) (2022)
- [What's "up" with vision-language models? Investigating their struggle with spatial reasoning](https://mlsanity.com/paper/2310.19785/) (2023)
- [Imagine while Reasoning in Space: Multimodal Visualization-of-Thought](https://mlsanity.com/paper/2501.07542/) (2025)
- [SAT: Dynamic Spatial Aptitude Training for Multimodal Language Models](https://mlsanity.com/paper/2412.07755/) (2024)
- [OmniSpatial: Towards Comprehensive Spatial Reasoning Benchmark for Vision Language Models](https://mlsanity.com/paper/2506.03135/) (2025)
- [Ovis2.5 Technical Report](https://mlsanity.com/paper/2508.11737/) (2025)
- [EmbSpatial-Bench: Benchmarking Spatial Understanding for Embodied Tasks with Large Vision-Language Models](https://mlsanity.com/paper/2406.05756/) (2024)
- [MM-Spatial: Exploring 3D Spatial Understanding in Multimodal LLMs](https://mlsanity.com/paper/2503.13111/) (2025)
- [SpatialReasoner: Towards Explicit and Generalizable 3D Spatial Reasoning](https://mlsanity.com/paper/2504.20024/) (2025)
- [SpatialPIN: Enhancing Spatial Reasoning Capabilities of Vision-Language Models through Prompting and Interacting 3D Priors](https://mlsanity.com/paper/2403.13438/) (2024)
- [Reasoning Paths with Reference Objects Elicit Quantitative Spatial Reasoning in Large Vision-Language Models](https://mlsanity.com/paper/2409.09788/) (2024)
- [MindJourney: Test-Time Scaling with World Models for Spatial Reasoning](https://mlsanity.com/paper/2507.12508/) (2025)
- [Image Textualization: An Automatic Framework for Creating Accurate and Detailed Image Descriptions](https://mlsanity.com/paper/2406.07502/) (2024)
- [GSR-BENCH: A Benchmark for Grounded Spatial Reasoning Evaluation via Multimodal LLMs](https://mlsanity.com/paper/2406.13246/) (2024)
- [SpaceTools: Tool-Augmented Spatial Reasoning via Double Interactive RL](https://mlsanity.com/paper/2512.04069/) (2025)
- [EarthSpatialBench: Benchmarking Spatial Reasoning Capabilities of Multimodal LLMs on Earth Imagery](https://mlsanity.com/paper/2602.15918/) (2026)
- [Video2Layout: Recall and Reconstruct Metric-Grounded Cognitive Map for Spatial Reasoning](https://mlsanity.com/paper/2511.16160/) (2025)
- [Hydra-Nav: Object Navigation via Adaptive Dual-Process Reasoning](https://mlsanity.com/paper/2602.09972/) (2026)

## Built on by (most cited first, 3 of 3)

- [LENS: Adaptive Spatio-Temporal Zooming for Keyframe Sampling in Long-Form Videos](https://mlsanity.com/paper/2607.25125/) (2026)
- [AnnotateAnything: Automatic Annotation of 3D Assets for Robot Manipulation](https://mlsanity.com/paper/2606.17446/) (2026)
- [MagicSim: A Unified Infrastructure for Executable Embodied Interaction](https://mlsanity.com/paper/2606.17511/) (2026)

## Abstract (arXiv)

Vision-Language Models (VLMs) are increasingly deployed in embodied environments, where they need produce numerical outputs such as action magnitudes and spatial coordinates. Although these numbers appear meaningful, it remains unclear whether these numerical outputs are genuinely grounded in spatial perception. Therefore, in this work, we revisit spatial numerical understanding through SpaceNum, a unified framework that captures two complementary settings: numbers as dynamic transitions during spatial exploration, and numbers as static layouts in spatial reasoning. We formulate two bidirectional tasks, Num2Space and Space2Num, to evaluate how well VLMs map between vision-side spatial structure and language-side numerical representations. We systematically study whether current VLMs truly understand numerical values in spatial settings. Across dynamic transitions and static layouts, we find that models largely fail to ground numbers in spatial meaning and often perform close to random guess. Through error analysis, reasoning trace analysis, and controlled interventions, we show that current VLMs rely heavily on shallow spatial cues, struggle to build stable coordinate-aware representations, and fail to abstract structured spatial layouts from visual observations. We further show that explicit reasoning provides only marginal gains, while tuning can partially improve spatial numerical understanding and transfer to external spatial reasoning benchmarks.