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arxiv: 2606.04381 · v1 · pith:V6Y2RNJ2new · submitted 2026-06-03 · 💻 cs.LG · cs.AI

From Symbolic to Geometric: Enabling Spatial Reasoning in Large Language Models

Chen Chu , Bita Azarijoo , Li Xiong , Khurram Shafique , Cyrus Shahabi This is my paper

Pith reviewed 2026-06-28 06:57 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords spatial reasoninglarge language modelsmultimodal modelsgeometric reasoningspatial representationsinstruction datasetevaluation benchmark
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The pith

The Spatial Language Model enables geometric spatial reasoning in LLMs by operating directly on learned spatial representations instead of text.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Current large language models handle spatial tasks through symbolic pattern matching over language rather than actual geometric computation over space. The paper introduces the Spatial Language Model as a multimodal architecture that makes location information a primary input type and performs geometric operations inside its inference process. It supports this with a dedicated Spatial Instruction Dataset that pairs spatial representations, atomic geometric operations, and language instructions, plus a new SpatialEval benchmark covering attributes, distance, topology, and relative position. Experiments show the model beats prior LLM approaches that depend on prompt engineering or textual abstraction. A sympathetic reader would care because this shift from symbolic to geometric handling could produce more reliable spatial behavior in applications that require precise spatial understanding.

Core claim

SLM is the first multimodal LLM that treats location information as a first-class modality and directly operates on learned spatial representations rather than textual descriptions of spatial relations, thereby enabling geometric spatial reasoning within the model's inference process.

What carries the argument

The Spatial Language Model (SLM), which integrates learned spatial representations as a native modality alongside language for performing atomic geometric operations during inference.

If this is right

  • SLM outperforms existing LLM-based methods that rely on prompt engineering or textual abstraction across spatial reasoning tasks.
  • The Spatial Instruction Dataset provides aligned training data for spatial representations, geometric operations, and natural language.
  • The SpatialEval benchmark measures performance on attributes, distance, topology, and relative-position problems.
  • Integrating geometric spatial representations produces more robust spatial reasoning than symbolic approaches alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the spatial representations support explicit computation, SLM could extend to dynamic environments such as navigation or manipulation where new geometric relations must be calculated on the fly.
  • The approach suggests that other continuous domains like time or physics might benefit from similar first-class modality treatment in language models.
  • Success on SpatialEval would indicate that the model can generalize geometric operations beyond the specific examples in the instruction dataset.

Load-bearing premise

The learned spatial representations actually enable explicit geometric computation at inference time instead of acting as a more sophisticated form of symbolic pattern matching.

What would settle it

A controlled test in which SLM is forced to answer using only textual descriptions of the same spatial relations instead of its learned representations and shows equivalent performance to standard LLMs on SpatialEval tasks.

Figures

Figures reproduced from arXiv: 2606.04381 by Bita Azarijoo, Chen Chu, Cyrus Shahabi, Khurram Shafique, Li Xiong.

Figure 1
Figure 1. Figure 1: Framework of the proposed Spatial Language Model. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Composition of SpatialEval benchmark. and direct geometric reasoning, thereby enabling assessment of intrinsic spatial reasoning capabilities. Based on this motivation, we design a new spatial reasoning benchmark using the proposed spatial entity grounding method. By replacing the geospatial entity placeholder with different input modalities, such as entity names, coordinate representations, or vector embe… view at source ↗
Figure 3
Figure 3. Figure 3: Zero-shot inference performance of SLM on the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: SLM performance on spatial reasoning queries not [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Performance comparison between symbolic (Qwen3-8B) and geometric (SLM) finetuning methods across different training epochs on the evaluation dataset. To further understand the learning dynamics of our proposed SLM compared to traditional symbolic approaches, we analyze their convergence behaviors during the fine-tuning process [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators. To address this limitation, we introduce the \emph{Spatial Language Model (SLM)}, the first multimodal LLM that treats location information as a first-class modality and enables geometric spatial reasoning within the model's inference process. SLM directly operates on learned spatial representations rather than textual descriptions of spatial relations. To support effective training, we construct a \emph{Spatial Instruction Dataset} that aligns spatial representations, atomic geometric operations, and natural language instructions. We further propose a new benchmark named \emph{SpatialEval}, which is designed to evaluate spatial reasoning across attributes, distance, topology, and relative-position tasks. Extensive experiments show that SLM significantly outperforms existing LLM-based approaches that rely on symbolic reasoning via prompt engineering or textual abstraction, demonstrating the benefits of integrating geometric spatial representations for robust spatial reasoning. Our instruction dataset, evaluation benchmark, model training codes, and models' checkpoints can be found at: \hyperlink{https://github.com/chuchen2017/SLM}{https://github.com/chuchen2017/SLM}.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces the Spatial Language Model (SLM), the first multimodal LLM that treats location information as a first-class modality to enable geometric spatial reasoning by directly operating on learned spatial representations. It constructs a Spatial Instruction Dataset aligning spatial representations, atomic geometric operations, and natural language instructions, and proposes the SpatialEval benchmark to evaluate spatial reasoning across attributes, distance, topology, and relative-position tasks. The central claim is that SLM significantly outperforms existing LLM-based approaches relying on symbolic reasoning via prompt engineering or textual abstraction.

Significance. If the empirical results hold, the work would be significant for addressing LLMs' lack of native support for continuous spatial representations and explicit geometric computation. The open release of the instruction dataset, SpatialEval benchmark, training code, and model checkpoints strengthens reproducibility and enables community follow-up on multimodal spatial reasoning.

major comments (2)
  1. [Abstract] Abstract: the claim of significant outperformance on SpatialEval is asserted without any numerical results, error bars, baseline comparisons, or ablation studies. The experimental section must supply these details (including specific metrics, baselines, and controls) because they are load-bearing for the central empirical claim.
  2. [Method] Method section (description of SLM inference): the distinction that SLM 'directly operates on learned spatial representations rather than textual descriptions of spatial relations' and supports 'explicit geometric computation' is invoked as the key advantage over symbolic approaches. Concrete evidence is needed showing how geometric operators are applied at inference time (e.g., via explicit distance or topology computations) rather than learned pattern matching, as this premise underpins the geometric-vs-symbolic framing.
minor comments (1)
  1. [Abstract] The GitHub link is provided but the manuscript should confirm that all released artifacts (dataset, benchmark, code, checkpoints) are complete and documented.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and outline revisions to improve clarity and empirical presentation while preserving the manuscript's core contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of significant outperformance on SpatialEval is asserted without any numerical results, error bars, baseline comparisons, or ablation studies. The experimental section must supply these details (including specific metrics, baselines, and controls) because they are load-bearing for the central empirical claim.

    Authors: We agree that the abstract would be strengthened by referencing specific results. In the revised manuscript we will update the abstract to include key quantitative outcomes (e.g., accuracy on SpatialEval tasks with comparisons to prompt-based baselines) while keeping it concise. The experimental section already reports full metrics, error bars from multiple runs, baseline comparisons (including GPT variants with symbolic prompting and other multimodal models), ablation studies on the spatial modality and instruction dataset, and controls for task variants. We will add explicit cross-references from the abstract to these tables and figures. revision: yes

  2. Referee: [Method] Method section (description of SLM inference): the distinction that SLM 'directly operates on learned spatial representations rather than textual descriptions of spatial relations' and supports 'explicit geometric computation' is invoked as the key advantage over symbolic approaches. Concrete evidence is needed showing how geometric operators are applied at inference time (e.g., via explicit distance or topology computations) rather than learned pattern matching, as this premise underpins the geometric-vs-symbolic framing.

    Authors: We will revise the method section to include a dedicated inference subsection with a step-by-step description and pseudocode of the forward pass. Spatial tokens produced by the dedicated encoder are concatenated with text tokens and processed by the transformer; geometric relations (distance, topology, relative position) emerge from attention and feed-forward operations over the continuous spatial embeddings rather than from textual symbolic manipulation. While the model does not invoke separate hand-coded geometric primitives at inference (as it is an end-to-end neural architecture), the training on aligned spatial representations and atomic operations enables direct geometric computation in representation space. We will clarify this distinction and contrast it explicitly with the textual abstraction used by symbolic baselines. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper introduces SLM as a multimodal model, constructs a new Spatial Instruction Dataset and SpatialEval benchmark, and reports empirical outperformance versus symbolic LLM baselines. No equations, parameter fits, or self-citations are present in the provided text that reduce the central claim (geometric vs. symbolic reasoning) to quantities defined by the paper's own inputs or prior self-referential results. The distinction between operating on learned spatial representations versus textual descriptions is framed as an outcome of training on the new dataset and evaluation on the new benchmark, making the claims self-contained against external evaluation resources rather than internally circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 3 invented entities

The central claim rests on the effectiveness of adding a spatial modality and aligned dataset; no explicit free parameters are described, and the only background assumption is that multimodal extension is feasible.

axioms (1)
  • domain assumption Multimodal LLMs can be extended with an additional spatial modality that supports geometric operations.
    Invoked in the design of SLM and the claim that it enables geometric reasoning.
invented entities (3)
  • Spatial Language Model (SLM) no independent evidence
    purpose: Multimodal LLM that treats location as first-class modality for geometric spatial reasoning.
    New model introduced by the paper.
  • Spatial Instruction Dataset no independent evidence
    purpose: Training data aligning spatial representations, geometric operations, and language instructions.
    New dataset constructed for the work.
  • SpatialEval benchmark no independent evidence
    purpose: Evaluation suite for spatial reasoning across attributes, distance, topology, and relative position.
    New benchmark proposed in the paper.

pith-pipeline@v0.9.1-grok · 5790 in / 1416 out tokens · 26954 ms · 2026-06-28T06:57:05.242358+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

35 extracted references · 10 canonical work pages

  1. [1]

    Conference acronym ’XX, June 03–05, 2018, Woodstock, NY Trovato et al

    Kai Chen, Yunhao Gou, Runhui Huang, Zhili Liu, Daxin Tan, Jing Xu, Chunwei Wang, Yi Zhu, Yihan Zeng, Kuo Yang, Dingdong Wang, Kun Xiang, Haoyuan Li, Haoli Bai, Jianhua Han, Xiaohui Li, Weike Jin, Nian Xie, Yu Zhang, James T. Conference acronym ’XX, June 03–05, 2018, Woodstock, NY Trovato et al. Kwok, Hengshuang Zhao, Xiaodan Liang, Dit-Yan Yeung, Xiao Che...

    2018

  2. [2]

    An-Chieh Cheng, Hongxu Yin, Yang Fu, Qiushan Guo, Ruihan Yang, Jan Kautz, Xiaolong Wang, and Sifei Liu. 2024. SpatialRGPT: Grounded Spatial Reasoning in Vision-Language Models. InNeurIPS

    2024

  3. [3]

    Chen Chu and Cyrus Shahabi. 2026. Geo2Vec: Shape- and Distance-Aware Neural Representation of Geospatial Entities.Proceedings of the AAAI Conference on Artificial Intelligence40, 23 (Mar. 2026), 18985–18993. doi:10.1609/aaai.v40i23. 38970

    work page doi:10.1609/aaai.v40i23 2026

  4. [4]

    Gheorghe Comanici, Eric Bieber, Mike Schaekermann, and et al. 2025. Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities. arXiv:2507.06261 [cs.CL] https: //arxiv.org/abs/2507.06261

    Pith/arXiv arXiv 2025

  5. [5]

    Jie Feng, Tianhui Liu, Yuwei Du, Siqi Guo, Yuming Lin, and Yong Li. 2025. CityGPT: Empowering Urban Spatial Cognition of Large Language Models. In Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2(Toronto ON, Canada)(KDD ’25). Association for Computing Machinery, New York, NY, USA, 591–602. doi:10.1145/3711896.3736878

    work page doi:10.1145/3711896.3736878 2025

  6. [6]

    Jie Feng, Shengyuan Wang, Tianhui Liu, Yanxin Xi, and Yong Li. 2025. Urban- LLaVA: A Multi-modal Large Language Model for Urban Intelligence with Spatial Reasoning and Understanding. arXiv:2506.23219 [cs.CV] https://arxiv.org/abs/ 2506.23219

    arXiv 2025

  7. [7]

    Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, and et al. 2024. The Llama 3 Herd of Models. arXiv:2407.21783 [cs.AI] https://arxiv.org/abs/2407.21783

    Pith/arXiv arXiv 2024

  8. [8]

    Daya Guo, Dejian Yang, Haowei Zhang, and et al. Song. 2025. DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning.Nature645, 8081 (Sept. 2025), 633–638. doi:10.1038/s41586-025-09422-z

    work page doi:10.1038/s41586-025-09422-z 2025

  9. [9]

    Wes Gurnee and Max Tegmark. 2023. Language Models Represent Space and Time.arXiv preprint arXiv:2310.02207(2023)

    arXiv 2023

  10. [10]

    Jiaming Han, Kaixiong Gong, Yiyuan Zhang, Jiaqi Wang, Kaipeng Zhang, Dahua Lin, Yu Qiao, Peng Gao, and Xiangyu Yue. 2024. OneLLM: One Framework to Align All Modalities with Language. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

    2024

  11. [11]

    Xixuan Hao, Wei Chen, Yibo Yan, Siru Zhong, Kun Wang, Qingsong Wen, and Yuxuan Liang. 2025. UrbanVLP: multi-granularity vision-language pretraining for urban socioeconomic indicator prediction. InProceedings of the Thirty-Ninth AAAI Conference on Artificial Intelligence (AAAI 2025). AAAI Press, Article 3126, 9 pages. doi:10.1609/aaai.v39i27.35024

    work page doi:10.1609/aaai.v39i27.35024 2025

  12. [12]

    Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen

    Edward J. Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. 2021. LoRA: Low-Rank Adaptation of Large Language Models. arXiv:2106.09685 [cs.CL] https://arxiv.org/abs/2106.09685

    Pith/arXiv arXiv 2021

  13. [13]

    Yuhan Ji, Song Gao, Ying Nie, Ivan Majić, and Krzysztof Janowicz. 2025. Founda- tion models for geospatial reasoning: assessing the capabilities of large language models in understanding geometries and topological spatial relations.Inter- national Journal of Geographical Information Science39, 9 (2025), 1866–1903. arXiv:https://doi.org/10.1080/13658816.20...

    work page doi:10.1080/13658816.2025.2511227 2025

  14. [14]

    Siyu Li, Toan Tran, Haowen Lin, John Krumm, Cyrus Shahabi, Lingyi Zhao, Khurram Shafique, and Li Xiong. 2025. Geo-Llama: Leveraging LLMs for Human Mobility Trajectory Generation with Spatiotemporal Constraints. arXiv:2408.13918 [cs.AI] https://arxiv.org/abs/2408.13918

    arXiv 2025

  15. [15]

    Bin Lin, Yang Ye, Bin Zhu, Jiaxi Cui, Munan Ning, Peng Jin, and Li Yuan. 2024. Video-LLaVA: Learning United Visual Representation by Alignment Before Pro- jection. InProceedings of the 2024 Conference on Empirical Methods in Natu- ral Language Processing, Yaser Al-Onaizan, Mohit Bansal, and Yun-Nung Chen (Eds.). Association for Computational Linguistics, ...

    2024

  16. [16]

    doi:10.18653/v1/2024.emnlp-main.342

    work page doi:10.18653/v1/2024.emnlp-main.342 2024

  17. [17]

    Haotian Liu, Chunyuan Li, Qingyang Wu, and Yong Jae Lee. 2023. Visual Instruc- tion Tuning. arXiv:2304.08485 [cs.CV] https://arxiv.org/abs/2304.08485

    Pith/arXiv arXiv 2023

  18. [18]

    G. Mai, K. Janowicz, R. Zhu, L. Cai, and N. Lao. 2021. Geographic Question Answering: Challenges, Uniqueness, Classification, and Future Directions.AGILE: GIScience Series2 (2021), 8. doi:10.5194/agile-giss-2-8-2021

    work page doi:10.5194/agile-giss-2-8-2021 2021

  19. [19]

    Gengchen Mai, Chiyu Jiang, Weiwei Sun, Rui Zhu, Yao Xuan, Ling Cai, Krzysztof Janowicz, Stefano Ermon, and Ni Lao. 2023. Towards general-purpose represen- tation learning of polygonal geometries.GeoInformatica27, 2 (2023), 289–340

    2023

  20. [20]

    Gengchen Mai, Xiaobai Yao, Yiqun Xie, Jinmeng Rao, Hao Li, Qing Zhu, Ziyuan Li, and Ni Lao. 2024. SRL: Towards a General-Purpose Framework for Spatial Representation Learning. InProceedings of the 32nd ACM International Conference on Advances in Geographic Information Systems(Atlanta, GA, USA)(SIGSPATIAL ’24). Association for Computing Machinery, New York...

    arXiv 2024

  21. [21]

    Rohin Manvi, Samar Khanna, Gengchen Mai, Marshall Burke, David Lobell, and Stefano Ermon. 2024. GeoLLM: Extracting Geospatial Knowledge from Large Language Models. arXiv:2310.06213 [cs.CL] https://arxiv.org/abs/2310.06213

    arXiv 2024

  22. [22]

    2025.Introducing GPT-5

    OpenAI. 2025.Introducing GPT-5. https://openai.com/index/introducing-gpt-5/ Accessed: 2026-02-02

    2025

  23. [23]

    Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever. 2021. Learning Transferable Visual Models From Natural Language Supervision. arXiv:2103.00020 [cs.CV] https://arxiv.org/ abs/2103.00020

    Pith/arXiv arXiv 2021

  24. [24]

    Jonathan Roberts, Timo Lüddecke, Sowmen Das, Kai Han, and Samuel Al- banie. 2023. GPT4GEO: How a Language Model Sees the World’s Geography. arXiv:2306.00020 [cs.CL] https://arxiv.org/abs/2306.00020

    arXiv 2023

  25. [25]

    Maria Despoina Siampou, Jialiang Li, John Krumm, Cyrus Shahabi, and Hua Lu. 2025. Poly2Vec: Polymorphic Fourier-Based Encoding of Geospatial Objects for GeoAI Applications. InForty-second International Conference on Machine Learning

    2025

  26. [26]

    Smith, Daniel Khashabi, and Hannaneh Hajishirzi

    Yizhong Wang, Yeganeh Kordi, Swaroop Mishra, Alisa Liu, Noah A. Smith, Daniel Khashabi, and Hannaneh Hajishirzi. 2023. Self-Instruct: Aligning Language Mod- els with Self-Generated Instructions. InProceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), Anna Rogers, Jordan Boyd-Graber, and Naoaki Oka...

    work page doi:10.18653/v1/2023.acl- 2023

  27. [27]

    Zehui Wang, Wolfram Höpken, and Dietmar Jannach. 2025. Beyond Visit Trajec- tories: Enhancing POI Recommendation via LLM-Augmented Text and Image Representations. InProceedings of the Nineteenth ACM Conference on Recom- mender Systems (RecSys ’25). Association for Computing Machinery, New York, NY, USA, 521–526. doi:10.1145/3705328.3748014

    work page doi:10.1145/3705328.3748014 2025

  28. [28]

    Shaolin Xie, Shang-Ling Hsu, Qihan Zhang, Yiming Gao, Cyrus Shahabi, and Ibrahim Sabek. 2025. Evaluating Intrinsic Geospatial Topological Reasoning in LLMs. InProceedings of the 1st ACM SIGSPATIAL International Workshop on Gen- erative and Agentic AI for Multi-Modality Space-Time Intelligence(The Graduate Hotel Minneapolis, Minneapolis, MN, USA)(GeoGenAge...

    work page doi:10.1145/3764915.3770722 2025

  29. [29]

    Runsen Xu, Xiaolong Wang, Tai Wang, Yilun Chen, Jiangmiao Pang, and Dahua Lin. 2024. PointLLM: Empowering Large Language Models to Understand Point Clouds. arXiv:2308.16911 [cs.CV] https://arxiv.org/abs/2308.16911

    arXiv 2024

  30. [30]

    Ziwei Xu, Sanjay Jain, and Mohan Kankanhalli. 2025. Hallucination is Inevitable: An Innate Limitation of Large Language Models. arXiv:2401.11817 [cs.CL] https: //arxiv.org/abs/2401.11817

    Pith/arXiv arXiv 2025

  31. [31]

    An Yang, Anfeng Li, Baosong Yang, and et al. 2025. Qwen3 Technical Report. arXiv preprint arXiv:2505.09388(2025)

    Pith/arXiv arXiv 2025

  32. [32]

    Tianyi Zhou, Deqing Fu, Mahdi Soltanolkotabi, Robin Jia, and Vatsal Sharan

  33. [33]

    arXiv:2502.09741 [cs.CL] https://arxiv.org/abs/2502.09741

    FoNE: Precise Single-Token Number Embeddings via Fourier Features. arXiv:2502.09741 [cs.CL] https://arxiv.org/abs/2502.09741

    Pith/arXiv arXiv

  34. [34]

    Zhilun Zhou, Jingyang Fan, Yu Liu, Fengli Xu, Depeng Jin, and Yong Li. 2024. Synergizing LLM Agents and Knowledge Graph for Socioeconomic Prediction in LBSN. arXiv:2411.00028 [cs.CL] https://arxiv.org/abs/2411.00028

    arXiv 2024

  35. [35]

    Zhilun Zhou, Yuming Lin, Depeng Jin, and Yong Li. 2024. Large Language Model for Participatory Urban Planning. arXiv:2402.17161 [cs.AI] https://arxiv.org/abs/ 2402.17161 From Symbolic to Geometric: Enabling Spatial Reasoning in Large Language Models Conference acronym ’XX, June 03–05, 2018, Woodstock, NY Appendix A Experiment details All experiments and m...

    arXiv 2024