S-Space: Exploring Spatial Workspace in Multimodal Language Models
Zhiyuan Shi, Xiang Li, Xingzhuo Guo, Shangchen Miao, Weiliang Chen, Qiyu Dai, Jinshan Ren, Jiangran Lyu and 3 others
MirroS
Published October 9, 2026 · on the feed October 12, 2026 · ▲ 294 · arXiv 2610.13527
The abstract
Multimodal language models (MLLMs) exhibit promising spatial reasoning capabilities, yet the internal mechanisms supporting them remain poorly understood. We uncover S-Space, a linear representation subspace in which object-token representations encode continuous coordinates along horizontal, vertical, and distance axes. Although we identify these axes by differentiating spatial-answer scores with respect to object-token activations, S-Space is intrinsic rather than induced by specific data or prompts, remaining readable under non-spatial questions. We show that S-Space functions as an internal spatial workspace of MLLMs. Perception encodes object locations into it, forming spatial representations that can be directly read out to support accurate spatial judgments. Internal reasoning transforms it for changing viewpoints. Verbal responses selectively access it, evidenced by causal interventions that alter spatial judgments while largely preserving non-spatial responses. Case studies further show that S-Space assigns locations to unseen entities and the observer, and connects physical directions with abstract linguistic meanings, suggesting both the capabilities and limitations of large-scale language training. Finally, we use S-Space as a diagnostic tool for spatial reasoning failures. Direction-word readouts reveal systematic coupling between cardinal and image-relative reference frames. More importantly, a perception-computation decomposition exposes a key bottleneck: MLLMs can form capable spatial representations, yet fall short in the spatial transformations required to reason reliably across viewpoint changes.
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Transcript
S-Space. Exploring Spatial Workspace in Multimodal Language Models. By Zhiyuan Shi and ten others, from MirroS. Published on the ninth of October. Its code repository is worked out: about two hundred and fifty source files, with a readme and a licence.
Multimodal language models show promising spatial reasoning, but the internal mechanisms behind it are poorly understood. The claim here is that there is a specific place where that work happens. The authors call it S-Space: a linear representation subspace in which the representations of object tokens encode continuous coordinates along three axes, horizontal, vertical, and distance. And they argue that S-Space functions as an internal spatial workspace for these models.
The axes are identified by differentiating spatial-answer scores with respect to object-token activations. Even so, S-Space is described as intrinsic rather than induced by particular data or prompts, because it stays readable under questions that are not about space at all. Three roles are then traced. Perception writes object locations into it, forming representations that can be read out directly to support accurate spatial judgments. Internal reasoning transforms it when the viewpoint changes. And verbal responses access it selectively. The evidence for that last point is causal: interventions in S-Space alter spatial judgments while largely leaving non-spatial responses alone.
Case studies extend the picture. S-Space assigns locations to unseen entities and to the observer, and it connects physical directions with abstract linguistic meanings. The authors read this as pointing to both the capabilities and the limitations of large-scale language training.
S-Space is also put to work as a diagnostic for spatial reasoning failures, and this is where the limits show. Readouts of direction words reveal a systematic coupling between cardinal reference frames and image-relative ones. More important, a decomposition into perception and computation exposes a key bottleneck. The models can form capable spatial representations. Where they fall short is in the spatial transformations needed to reason reliably across changes of viewpoint. So the claim is not that spatial reasoning works well, but that its representation is in place while the transformation step lags behind.
The value of naming a workspace is that failures can be located. Instead of saying a model is bad at spatial questions, one can ask whether it perceived the layout correctly and then failed to rotate it. On the evidence here, the answer is usually the latter: perception holds up, and the weak link is the computation.
Paper Quest · 7 chapters · about 39 min
Play this paper
Learn it by doing: make the calls the authors made, guess the result before you see it, and defend it in a viva graded on your own words. Chapter 1 is right here.
Chapter 1 🧩 · The problem
The models can see, mostly. The question is where, inside them, the seeing is kept.
You study multimodal language models that answer questions about images, such as which object is left of another. They often get these questions right, and sometimes badly wrong.
The road ahead
- 1 · The problem ~6 min Multimodal models answer spatial questions about images well at times and badly at others, and their answers alone cannot tell you why they fail.
- 2 · What came before ~3 min
- 3 · The key idea ~8 min Three fixed directions inside the model, found from gradients, act as left-right, above-below and close-far axes that the model reads and uses.
- 4 · Choose your own research ~3 min
- 5 · Build the method ~8 min Find three axes from gradients, read object coordinates by projection, edit them to test their causal role, then use them to separate seeing from reasoning.
- 6 · The experiment ~6 min You’ll guess: When multimodal models fail at reasoning across viewpoint changes, where does a perception-computation decomposition place the main bottleneck?
- 7 · The viva ~5 min Three questions from the examiners, answered in your own words. Win it for the paper’s trophy.
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