cs.CVOct 9, 2026

S-Space: Exploring Spatial Workspace in Multimodal Language Models

Authors: Zhiyuan Shi, Xiang Li, Xingzhuo Guo, Shangchen Miao, Weiliang Chen, Qiyu Dai, Jinshan Ren, Jiangran Lyu, +3 more

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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.

Figures & tables

Figure 1: Object coordinates read out from S-Space across MLLMs. For each input image and caption, the intermediate representations of object-name tokens are linearly projected onto the three axes of S-Space to obtain continuous coordinates. Colors and numbers link object names, image regions, and their corresponding coordinates.
Figure 2: Linear spatial representation in S-Space. An object’s spatial coordinates (left) are linearly embedded in its high-dimensional token representation. Horizontal, vertical, and distance directions span a three-dimensional S-Space (middle) . Projections onto them recover viewer-centered coordinates (right) .
Figure 3: Accuracy of S-Space. (a-b) S-Space coordinates read from layer 21 of Molmo2-ER versus ground-truth object positions, with Spearman correlations and least-squares fits. (c) Spatial QA accuracy across benchmarks and models, comparing S-Space readouts with models’ direct answers.
Figure 4: Causal intervention of S-Space. (a) Different coordinate-editing and question configurations. (b) Answer retention under different interventions and edit scales. Experiments use Molmo2-ER at layer 17 (L17). See Appendix C.3 for details.
Figure 5: S-Space persists across prompts. The same S-Space readout continues to support accurate spatial judgments on CV-Bench, EmbSpatial, and SpatialTunnel (b-d) across pairwise spatial, single-object, and non-spatial prompts (a) .
Figure 6: S-Space beyond visible objects. It localizes off-screen entities (a) , places the invisible observer (b) , and reflects relations implied by language (c-d) . Readout from Molmo2-ER L17. Bars show 95% prompt-template bootstrap intervals.
Figure 7: S-Space beyond physical space . Socialist and conservative project toward opposite ends of the horizontal axis of S-Space, mirroring the linguistic metaphor of political left and right.
Figure 8: Perception-Computation decomposition via S-Space. (a) Perspective-taking question and the optional w/ premise setting. (b) We separate spatial perception from spatial computation by reading object coordinates from S-Space, applying the viewpoint transformation explicitly, and deriving the answer with a deterministic spatial rule.
 \mirrosth w/o premise\mirrosth w/ premise
\mirrosth Model\mirrosth Direct\mirrosth Reasoning\mirrosth S-Space + Rotation\mirrosth Direct\mirrosth Reasoning\mirrosth S-Space + Rotation
Molmo2-ER60.96—94.52 (+33.56)61.81—99.31 (+37.50)
Qwen3.5-4B60.9662.33 (+1.37)91.10 (+30.14)60.4272.22 (+11.80)97.92 (+37.50)
Qwen3.6-27B60.9683.56 (+22.60)95.21 (+34.25)72.9291.67 (+18.75)99.31 (+26.39)
Table 1: SpinBench perspective-taking accuracy. Numbers in parentheses show gains over direct answers in the same setting, in percentage points; dashes indicate no reasoning mode.
Figure 9: Chain-of-thought progressively transforms S-Space. (a) S-Space coordinates read out from object names at successive stages of a controlled CoT. (b) Qwen3.6-27B L43 readout accuracy on SpinBench with and without explicit viewpoint rotation.
Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

\mirrosth Molmo2-ER\mirrosth MolmoAct2 Pretrain\mirrosth MolmoAct2\mirrosth Qwen3.5-4B\mirrosth Qwen3.6-27B
\mirrosth Layer\mirrosth Acc.\mirrosth Layer\mirrosth Acc.\mirrosth Layer\mirrosth Acc.\mirrosth Layer\mirrosth Acc.\mirrosth Layers 0–31\mirrosth Layers 32–62
        \mirrosth Layer\mirrosth Acc.\mirrosth Layer\mirrosth Acc.
0\cellcolor SweepPurple!4.6555.170\cellcolor SweepPurple!6.9057.670\cellcolor SweepPurple!5.6556.280\cellcolor SweepPurple!2.3552.610\cellcolor SweepPurple!7.4058.2232\cellcolor SweepPurple!34.6588.50
1\cellcolor SweepPurple!4.9055.441\cellcolor SweepPurple!7.8558.721\cellcolor SweepPurple!7.7058.561\cellcolor SweepPurple!2.2552.501\cellcolor SweepPurple!6.4057.1133\cellcolor SweepPurple!33.5587.28
2\cellcolor SweepPurple!6.0556.722\cellcolor SweepPurple!8.4059.332\cellcolor SweepPurple!7.1557.942\cellcolor SweepPurple!4.0554.502\cellcolor SweepPurple!6.9057.6734\cellcolor SweepPurple!33.3087.00
3\cellcolor SweepPurple!6.4057.113\cellcolor SweepPurple!8.8559.833\cellcolor SweepPurple!7.2558.063\cellcolor SweepPurple!5.7056.333\cellcolor SweepPurple!5.8556.5035\cellcolor SweepPurple!36.7090.78
Appendix
Table 2: Layer sweeping accuracy on the COCO validation set. Layer indices start at zero. Darker purple indicates higher accuracy, and bold marks the selected layer. Qwen3.6-27B is split into two consecutive layer ranges.
Figure 11: S-Space beyond visible objects. Images, prompts, and horizontal or distance readouts for an unseen ball, owner, train, the observer, and a robot moving past or toward. Readouts use Molmo2-ER L17. Means and 95% bootstrap intervals are computed across prompt templates.
Figure 12: Political semantics in S-Space. Standardized horizontal readouts across five models.

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