# S-Space: Exploring Spatial Workspace in Multimodal Language Models

arXiv: https://arxiv.org/abs/2610.13527 · HTML: https://mlsanity.com/paper/2610.13527/

## 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 38 of its 47 references that are in the map.
- First posted on arXiv 9 Oct 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, 30 of 38)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Cambrian-1: A Fully Open, Vision-Centric Exploration of Multimodal LLMs](https://mlsanity.com/paper/2406.16860/) (2024)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [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)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [RoboPoint: A Vision-Language Model for Spatial Affordance Prediction for Robotics](https://mlsanity.com/paper/2406.10721/) (2024)
- [NaVid: Video-based VLM Plans the Next Step for Vision-and-Language Navigation](https://mlsanity.com/paper/2402.15852/) (2024)
- [Transcoders Find Interpretable LLM Feature Circuits](https://mlsanity.com/paper/2406.11944/) (2024)
- [Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet](https://mlsanity.com/paper/2605.29358/) (2026)
- [MMSI-Bench: A Benchmark for Multi-Image Spatial Intelligence](https://mlsanity.com/paper/2505.23764/) (2025)
- [EmbSpatial-Bench: Benchmarking Spatial Understanding for Embodied Tasks with Large Vision-Language Models](https://mlsanity.com/paper/2406.05756/) (2024)
- [Why Is Spatial Reasoning Hard for VLMs? An Attention Mechanism Perspective on Focus Areas](https://mlsanity.com/paper/2503.01773/) (2025)
- [MindCube: Spatial Mental Modeling from Limited Views](https://mlsanity.com/paper/2506.21458/) (2025)
- [Verbalizable Representations Form a Global Workspace in Language Models](https://mlsanity.com/paper/2607.15495/) (2026)
- [Seed2.0 Model Card: Towards Intelligence Frontier for Real-World Complexity](https://mlsanity.com/paper/2607.00248/) (2026)
- [MolmoAct2: Action Reasoning Models for Real-world Deployment](https://mlsanity.com/paper/2605.02881/) (2026)
- [BabyVision: Visual Reasoning Beyond Language](https://mlsanity.com/paper/2601.06521/) (2026)
- [Vision-as-Inverse-Graphics Agent via Interleaved Multimodal Reasoning](https://mlsanity.com/paper/2601.11109/) (2026)
- [MMSI-Video-Bench: A Holistic Benchmark for Video-Based Spatial Intelligence](https://mlsanity.com/paper/2512.10863/) (2025)
- [ESI-Bench: Towards Embodied Spatial Intelligence that Closes the Perception-Action Loop](https://mlsanity.com/paper/2605.18746/) (2026)
- [Theory of Space: Can Foundation Models Construct Spatial Beliefs through Active Exploration?](https://mlsanity.com/paper/2602.07055/) (2026)
- [SpatialClaw: Rethinking Action Interface for Agentic Spatial Reasoning](https://mlsanity.com/paper/2606.13673/) (2026)
- [Thinking in 360deg: Humanoid Visual Search in the Wild](https://mlsanity.com/paper/2511.20351/) (2025)
- [InstructPart: Task-Oriented Part Segmentation with Instruction Reasoning](https://mlsanity.com/paper/2505.18291/) (2025)

## Abstract (arXiv)

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.