Paper review · October 13, 2026
S-Space: Exploring the Spatial Workspace Inside Multimodal Language Models
S-Space: Exploring Spatial Workspace in Multimodal Language Models
The authors find a 3D linear subspace (S-Space) in MLLM internal Representations, made up of left-right, up-down and distance axes, and show that spatial reasoning failures come more from viewpoint-transformation computation than from perception.
Problem
Multimodal language models (MLLMs) show spatial reasoning ability, but little is known about how spatial information is represented and used inside them. This makes it hard to diagnose where spatial reasoning fails.
Method
The method uses relative-position questions such as "Is the apple to the left or right of the cup?". It takes the gradient of the correct-answer logit difference with respect to the Hidden Representation of object tokens, then averages the gradient difference between the query object and the reference object across prompts, object orders and examples to obtain three axes: horizontal, vertical and distance. Projecting object tokens onto these axes gives readable continuous coordinates. The authors also ran causal intervention experiments that edit these coordinates and write them back. They further built a diagnostic pipeline that combines coordinate reading with explicit rotation to separate perception from computation. The models studied are Molmo2-ER, Qwen3.5-4B and Qwen3.6-27B.
Results
- Spatial QA accuracy using only S-Space coordinates was similar to the models' own direct-answer accuracy on CV-Bench, EmbSpatial and SpatialTunnel. It also generalized to benchmarks not used to find the axes.
- Editing S-Space coordinates changed spatial judgments substantially while leaving non-spatial judgments such as color mostly unchanged. The coordinates could still be read even in non-spatial prompts asking about color.
- On the SpinBench perspective-taking task, Qwen3.6-27B scored 60.96% with direct answers and 83.56% with CoT reasoning. Applying rotation to S-Space coordinates gave 95.21%.
- Molmo2-ER rose from 60.96% with direct answers to 94.52% with S-Space+rotation. When the correct relation in the original viewpoint was given as a premise, S-Space+rotation reached up to 99.31%.
- In a case study, 'socialist' projected to the left on the horizontal axis and 'conservative' to the right. This shows that physical direction and abstract linguistic meaning are mixed.
Limitations
The horizontal and vertical axes are image-plane coordinates, not world coordinates, and perspective effects from depth are not separated out. Only three models were analyzed. The explanation that S-Space emerges from predicting spatial language is at the level of the authors' hypothesis. The viewpoint-transformation experiments were run mainly on a single benchmark, SpinBench.
Why it matters
It shows that MLLMs already hold enough spatial information yet fail at viewpoint-transformation computation. This suggests that improving models for robotics and navigation should target spatial computation rather than perception.
Key terms
- Linear Representation hypothesis
- The hypothesis that concepts inside a model are represented as specific direction vectors, so projecting onto that direction reads out the concept's value.
- Causal Intervention
- An interpretability technique that directly changes a specific component of an internal Representation, observes how the output changes, and thereby checks whether the component is actually used.
- Perspective-taking
- A task that asks how relations between objects would look when the observer's viewpoint shifts to the left, right, behind and so on.
Original
Authors: Zhiyuan Shi, Xiang Li, Xingzhuo Guo, Shangchen Miao, Weiliang Chen, Qiyu Dai, Jinshan Ren, Jiangran Lyu, et al. · Posted 2026-10-09 · License CC BY-NC-SA 4.0 · Based on the full text
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