Paper deep dive
PolyComp: A Polycube-based Benchmark for Compositional 3D Spatial Reasoning in Multimodal Models
Siddharth Patel
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
Last extracted: 8/18/2026, 4:32:39 AM
Summary
The paper introduces PolyComp, a procedurally generated benchmark for evaluating compositional 3D spatial reasoning in multimodal models. It consists of 120 problems where models must identify which pair of polycube components forms a target solid. The study evaluates GPT-5.6 Sol, Claude Fable 5, and Gemini 3.1 Pro Preview across three presentation formats, finding that GPT-5.6 Sol achieves the highest accuracy (50.0%) but performance remains near random guessing baselines, highlighting significant gaps in spatial intelligence for current multimodal models.
Entities (10)
Relation Signals (7)
PolyComp → evaluates → GPT 5.6 Sol
confidence 95% · GPT-5.6 Sol with max effort attains 50.0% accuracy
PolyComp → evaluates → Claude-fable-5
confidence 95% · Claude Fable 5 with max effort attains 39.4%
PolyComp → evaluates → Gemini-3.1-Pro-Preview
confidence 95% · Gemini 3.1 Pro Preview with thinking level high attains 27.5%
PolyComp → usesgeometry → Polycube
confidence 95% · The use of polycubes makes the geometry discrete
PolyComp → inspiredby → SpatialBench
confidence 90% · Our use of polycubes is inspired by the SpatialBench repository
GPT 5.6 Sol → outperforms → Claude-fable-5
confidence 90% · GPT-5.6 Sol leads at 50.0% accuracy, followed by Claude Fable 5 at 39.4%
GPT 5.6 Sol → outperforms → Gemini-3.1-Pro-Preview
confidence 90% · GPT-5.6 Sol leads at 50.0% accuracy... and Gemini 3.1 Pro Preview... attains 27.5%
Cypher Suggestions (0)
No Cypher suggestions yet.
Abstract
Abstract:We introduce PolyComp, a procedurally generated and verified benchmark that stresses visual recognition and compositional spatial reasoning. In each problem, a model must identify which of four options shows a pair of polycube components that can be combined to form a target solid. The benchmark contains 120 problems across four geometry families, and each problem has three different presentation formats using either a single image or multiple images. The random guessing baseline is 25%. Across the three presentations (360 presented problems per model), GPT-5.6 Sol with max effort attains 50.0% accuracy (95% problem-cluster CI 43.3-56.7%) at a mean cost of \$0.951 per presented problem, Claude Fable 5 with max effort attains 39.4% (33.1-46.1%) at \$0.701, and Gemini 3.1 Pro Preview with thinking level high attains 27.5% (22.8-32.5%), near the 25% random guessing baseline, at \$0.350. The observed accuracy spread across geometry families is larger than across presentation formats. We present a problem development and evaluation protocol, cost and token accounting, and release the 120 problems.
Tags
Links
- Source: https://arxiv.org/abs/2608.14741v1
- Canonical: https://arxiv.org/abs/2608.14741v1
Trouble viewing inline? Open PDF directly →
Full Text
23,496 characters extracted from source content.
Expand or collapse full text
PolyComp: A Polycube-based Benchmark for Compositional 3D Spatial Reasoning in Multimodal Models Siddharth Patel August 9, 2026 Abstract We introduce PolyComp, a procedurally generated and verified benchmark that stresses visual recognition and compositional spatial reasoning. In each problem, a model must identify which of four options shows a pair of polycube components that can be combined to form a target solid. The benchmark contains 120 problems across four geometry families, and each problem has three different presentation formats using either a single image or multiple images. The random guessing baseline is 25%. Across the three presentations (360 presented problems per model), GPT-5.6 Sol with max effort attains 50.0% accuracy (95% problem-cluster CI 43.3–56.7%) at a mean cost of$0.951 per presented problem, Claude Fable 5 with max effort attains 39.4% (33.1–46.1%) at$0.701, and Gemini 3.1 Pro Preview with thinking level high attains 27.5% (22.8–32.5%), near the 25% random guessing baseline, at$0.350. The observed accuracy spread across geometry families is larger than across presentation formats. We present a problem development and evaluation protocol, cost and token accounting, and release the 120 problems. 1 Introduction Spatial intelligence comprises many capabilities spanning perception (e.g., segmentation, entity detection, identification) and reasoning (e.g., reconciling viewpoints and occlusion, geometric transformations). While multimodal artificial intelligence models have successfully incorporated image processing to extend the considerable capabilities of large language models (LLMs) into new domains [1,2], it remains unclear whether LLM-based models can achieve human-level performance on visual tasks. Targeted diagnostics continue to find failures in visual and spatial reasoning [3–5]. In particular, human-level performance in spatial reasoning may require the ability to develop an internal representation of an object and simulate transformations on that representation. These abilities have been studied through mental rotation [6] and qualitative spatial reasoning [7]. They remain difficult for modern vision-language models, even when the models perform strongly on broad multimodal evaluations [3–5]. Existing benchmarks span synthetic compositional reasoning [8], natural-image relations [9,10], expert multimodal questions [1,2], and 3D scene or video understanding [5,11,12]. PolyComp targets a complementary regime: geometric object perception, rigid body transformation, and composition. The use of polycubes makes the geometry discrete, so that the reasoning task can be solved by identifying a Cartesian frame and counting blocks in three directions. Whether multimodal models build an internal representation that supports this type of reasoning is unknown. The contributions of this paper are: • a procedure to generate and validate a polycube decomposition problem; 1 arXiv:2608.14741v1 [cs.CV] 13 Aug 2026 •a comparison of the performance of three frontier multimodal models on 120 of these problems across three presentations, including accuracy and cost efficiency; • the 120 problems themselves. 2 Related Work 2.1 General multimodal evaluation MMMU and MathVista evaluate deliberate reasoning over heterogeneous visual materials [1,2]. M-Vet emphasizes integrated capabilities and open-ended grading [13]; in contrast, PolyComp uses multiple-choice responses and block geometry. MMStar and MMMU-Pro explicitly address text-only shortcuts, data leakage, and robustness to presentation changes [14,15]. Those concerns motivate our decision to present the same problem in three different presentations. 2.2 Vision-centric and spatial benchmarks BLINK reformulates classic computer-vision tasks, including multi-view reasoning, for multimodal models [3]. CV-Bench evaluates 2D relations and counting as well as 3D depth and distance [16]. VSI-Bench tests spatial memory from video and finds that explicit cognitive maps can help where linguistic chains of thought do not [5]. InternSpatial-Bench broadens single- and multi-view instruction formats [17]; iVISPAR adds interactive planning [18]; SpatialBench proposes a hierarchy from perception to planning [19]. PolyComp is narrower: it isolates whether models can determine exact part-to-whole compatibility under 3D rotation for highly constrained polycube geometry. 2.3 Compositional and 3D reasoning CLEVR established synthetic, programmatically controlled visual diagnostics [8]; GQA extended compositional questions and functional programs to natural images [20]; and NLVR2 tested paired- image reasoning with compositional language [21]. SpatialSense, VSR, and Winoground show persistent failures on relations, reference frames, and minimal compositional contrasts [9,10,22]. ScanQA, SQA3D, and 3D-LLM ground questions and language models in explicit 3D scenes [11,12,23]. Our problem images remove scene semantics and external knowledge, concentrating evaluation on shape, topology, and rigid transformation. Our use of polycubes is inspired by the SpatialBench repository [24]. 2 Figure 1: Example PolyComp problem. The model is given the two views of the target solid and then asked to identify which of options A through D shows two components that together can form the target solid. This is one of the simpler problems missed by the three evaluated models, all of which picked D instead of the correct option A. 3 The PolyComp Benchmark 3.1 Problem Each problem consists of a single target solid polycube presented in two views, followed by four options labeled A through D, each showing two disconnected polycube components. Only one option contains components whose voxel union can equal the target after independent rigid rotations and 3 translations. The model is asked to return one label from A,B,C,D. 3.2 Generation and exact verification Instances are generated as integer-coordinate voxel sets: the whole target solid and a partition of that solid into two components, which are used as the correct option for the multiple-choice decomposition question. The incorrect options are generated by transforming the correct components by moving a cube or by replacing a component with its mirror image. These transformations preserve cube count while violating the assembly condition. A verification routine enumerates the 24 orientation- preserving cube rotations and feasible integer translations, and confirms that exactly one option can form the target without overlaps or missing cubes. The views for the target solid and the components are selected deterministically from sampled camera rotations. We confirm that every incorrect option can be ruled out from the rendered views. Figure 2: Problem generation and validation. The flow chart shows target solid construction, partitioning, incorrect option generation, view selection, geometry verification, rasterization, and asset QA. 3.3 Families and presentations The set of 120 problems contains 65 cases based on rectangular loops, 24 cases inspired by toys, 14 cases based on block cleavage, and 17 inspired by joinery. Every problem is presented in three ways: •a single image with views of the target solid and the options, as in Figure 1, with the accompanying prompt: 4 The image above shows two views of the same target solid in the top row. The four options A through D appear below the top row. Each option shows two component solids. Which option shows two component solids that together can form the target solid? Return only a JSON object with exactly one key and no additional text: - "option": one of "A", "B", "C", or "D" •a multi-image presentation in which one image has two views of the target solid and four more images each have views of an option, with non-descriptive model-facing labelsImage 1 through Image 5; Five images labeled Image 1 through Image 5 appear above. Image 1 shows two views of the same target solid. Image 2 through Image 5 show option A through option D, respectively . Each option image shows two component solids. Which option shows two component solids that together can form the target solid? Return only a JSON object with exactly one key and no additional text: - "option": one of "A", "B", "C", or "D" •a multi-image presentation using the same images as above but with descriptive model-facing labels Target and Option A through Option D. Five images labeled Target and Option A through Option D appear above. The Target image shows two views of the same target solid. Each option image shows two component solids. Which option shows two component solids that together can form the target solid? Return only a JSON object with exactly one key and no additional text: - "option": one of "A", "B", "C", or "D" The intent of varying the formulation is to determine whether a given presentation makes perception easier and enables improved spatial reasoning performance. The single image is generated as vector graphics (SVG) on a 2500×2500 canvas and rasterized to PNG withresvg 0.47.0for submission to the model APIs, without resizing or downsampling. The multi-image target (2440×720) and option images (1200×720) are lossless crops from the same PNG. 3.4 Selection and scope The 120 problems are a subset of 168 submitted in ChatGPT temporary chats using GPT-5.5 at Extra High. The subset comprises 100 problems GPT-5.5 missed and 20 hard ones that it got correct. It is therefore a selected challenge set, not a representative sample of spatial tasks or of the problem generation process’s unconditional distribution. 4 Evaluation Protocol We evaluate GPT-5.6 Sol with max effort, Claude Fable 5 with max effort, and Gemini 3.1 Pro Preview with high thinking level. Each model receives the 120 problems in each of the three presentations. We record one answer per model and compute pass@1 accuracy. A single Claude pre-output refusal remains in the denominator. 5 Table 1: Protocol. Dates identify the evaluation window. Prices are regular API list rates per million tokens, captured July 16 and rechecked July 25, 2026. Sampling parameters were omitted. FieldOpenAIAnthropicGemini Endpoint and mode Batch wrapper around POST /v1/responses /v1/messages/batches :batchGenerateContent Model; dates gpt-5.6-sol; July 20–25 claude-fable-5; July 20 gemini-3.1-pro-preview; July 20 Reasoning and output cap reasoning.effort=max; 128,000 tokens outputconfig.effort=max; managed thinking; 128,000 tokens thinkingLevel=high; 65,536 tokens Image accounting base64 PNG data URL; detail=original base64 image source; provider-managed resolution base64 PNG inline data; MEDIARESOLUTIONHIGH Regular list ratesinput$5; cached$0.50; cache write $6.25; output$30 input$10; cache read$1; 5m/1h write$12.50/$20; output$50 input$2; cached$0.20; output (including thinking)$12 Because each problem appears in all three presentations, the 360 outcomes per model are not independent observations. The reported 95% intervals resample the 120 problem identifiers and retain all presentations for each sampled problem [25]. Presentation-specific intervals use the same problem bootstrap, while presentation contrasts use paired resampling of the two outcomes for each problem. 5 Results 5.1 Overall accuracy and efficiency Table 2: Primary results. Confidence intervals are 95% problem-cluster percentile-bootstrap intervals over 120 problems, with all presentations for a sampled problem resampled together. Token summaries are per final response. Costs are normalized to regular, non-batch API list prices for every provider. ModelAccuracy95% CIMean tok.Median tok.Mean costMedian cost GPT-5.6 Sol50.0%[43.3, 56.7]42,68240,549$0.951$0.881 Claude Fable 539.4%[33.1, 46.1]19,01617,961$0.701$0.634 Gemini 3.1 Pro Preview27.5%[22.8, 32.5]32,56630,430$0.350$0.329 GPT-5.6 Sol leads at 50.0% accuracy, followed by Claude Fable 5 at 39.4% and Gemini 3.1 Pro Preview at 27.5% (Table 2). The uniform random-guessing baseline is 25%. Using normalized regular API list rates, the complete 360-response evaluations cost an estimated $342.41 for GPT-5.6 Sol, $252.36 for Claude Fable 5, and $126.06 for Gemini 3.1 Pro Preview. The corresponding mean costs per response are $0.951, $0.701, and $0.350. 5.2 Presentation and geometry GPT-5.6 Sol’s point estimate rises from 45.0% with a single composite image to 53.3% with separate generic images; Claude’s rises from 34.2% to 42.5% with separate descriptive images. Gemini remains between 26.7% and 28.3%. Paired problem-bootstrap intervals include zero for every separated-minus-single contrast. The pattern is consistent with the possibility that breaking up the single image reduces the perception burden (segmentation, option identification), but that mechanism was not measured. 6 Figure 3: Accuracy versus cost. Each point summarizes one model over 360 problem-presentation responses. The x-axis is mean list-price cost per presented problem; vertical whiskers are 95% problem-cluster bootstrap intervals. The dashed line is the 25% uniform random-guessing baseline. The observed spread across geometry families is larger than across presentation formats. GPT-5.6 Sol reaches 81.0% on block cleavage and 74.5% on joinery, but 34.4% on rectangular loop cases. Claude shows the same ordering at 69.0%, 56.9%, and 28.7%. One possible explanation is that the block cleavage and joinery cases start with rectangular target solids, making some incorrect components easier to rule out when they are missing a corner or have an extra block that exceeds the target solid’s maximum dimension. 5.3 Shared successes and failures On 24 of the 360 problem-presentation cells, all three models answer correctly, and they all answer incorrectly on 91. At the problem level, eight problems are missed in all presentations by all models. Based on qualitative examination, shared successes tend to have diagnostic global silhouettes or large complementary interfaces, while shared failures more often require tracking small cavities, hidden contact surfaces, or multiple locally plausible alignments. These interpretations remain tentative hypotheses for the time being. 6 Release The public GitHub repository athttps://github.com/sidpatelgit/polycompcontains code and frozen manifests for the 120 problems, including exact image-hash and geometry validation. It also contains payload builders for all three presentations, as well as a table with the results from the evaluation of all three models. 7 Figure 4: Accuracy by model and presentation formulation. Whiskers are pointwise 95% problem-bootstrap intervals over 120 problems. The dashed line marks the 25% random guessing baseline. There is weak evidence that the multi-image presentations improved performance for GPT-5.6 Sol and Claude Fable 5 . 7 Limitations •Perception might be a more challenging component of these problems than we expect. Alternate line weights, colors, or image resolutions could improve performance. • We did not test whether variations of the prompt improved performance. •We did not collect a formal human performance baseline. We did verify that each problem can be solved as rendered by rejecting all of the incorrect options, but some problems are still quite challenging. • We did not evaluate run-to-run repeatability in individual model responses or in aggregate performance. • We did not test whether test-time training or a harness would improve performance. 8 8 Conclusion and extensions PolyComp identifies a gap in multimodal model spatial intelligence in a constrained setting: polycube geometry, rotation, and composition. It also presents a method for generating verifiable problems of this class. Future directions include: •further simplifying the perception task by identifying how small of a target solid (i.e., how few cubes in the polycube) still challenges models; • scaffolding the perception task by instructing the model to first create three-dimensional matrices representing the target solid and the component solids in each option; •using the polycube geometry to test understanding of silhouettes, cross sections, interference- free assembly, and other spatial reasoning tasks that may involve internal representations of three-dimensional objects; • isolating what types of disqualifying features for the wrong options the models are able to identify most easily; • moving from polycubes to similar smooth and rounded geometry. Acknowledgments We thank Ranjay Krishna for providing guidance about single vs. multi-image presentations and the evaluation protocol. References [1]Xiang Yue, Yuansheng Ni, Kai Zhang, Tianyu Zheng, Ruoqi Liu, Ge Zhang, Samuel Stevens, Dongfu Jiang, Weiming Ren, Huan Sun, et al. MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024. arXiv:2311.16502. [2] Pan Lu, Hritik Bansal, Tony Xia, Jiacheng Liu, Chunyuan Li, Hannaneh Hajishirzi, Hao Cheng, Kai-Wei Chang, Michel Galley, and Jianfeng Gao. MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts. In International Conference on Learning Representations, 2024. arXiv:2310.02255. [3] Xingyu Fu, Yushi Hu, Bangzheng Li, Yu Feng, Haoyu Wang, Xudong Lin, Dan Roth, Noah A. Smith, Wei-Chiu Ma, and Ranjay Krishna. BLINK: Multimodal Large Language Models Can See but Not Perceive. In Computer Vision – ECCV 2024, volume 15081 of Lecture Notes in Computer Science, pages 148–166. Springer, 2024. doi: 10.1007/978-3-031-73337-69. [4]Shengbang Tong, Zhuang Liu, Yuexiang Zhai, Yi Ma, Yann LeCun, and Saining Xie. Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMs. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9568–9578, 2024. URLhttps://openaccess.thecvf.com/content/CVPR2024/html/Tong_Eyes_Wide_Shut_ Exploring_the_Visual_Shortcomings_of_Multimodal_LLMs_CVPR_2024_paper.html. 9 [5]Jihan Yang,Shusheng Yang,Anjali W. Gupta,Rilyn Han,Li Fei-Fei,and Saining Xie.Thinking in Space:How Multimodal Large Language Models See, Remember, and Recall Spaces. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10632–10643, 2025.URL https://openaccess.thecvf.com/content/CVPR2025/html/Yang_Thinking_in_Space_ How_Multimodal_Large_Language_Models_See_Remember_CVPR_2025_paper.html. [6]Roger N. Shepard and Jacqueline Metzler. Mental Rotation of Three-Dimensional Objects. Science, 171(3972):701–703, 1971. doi: 10.1126/science.171.3972.701. [7] Anthony G. Cohn and Jochen Renz. Qualitative Spatial Representation and Reasoning. In Frank van Harmelen, Vladimir Lifschitz, and Bruce Porter, editors, Handbook of Knowledge Representation, pages 551–596. Elsevier, 2008. [8]Justin Johnson, Bharath Hariharan, Laurens van der Maaten, Li Fei-Fei, C. Lawrence Zitnick, and Ross Girshick. CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2901–2910, 2017. [9]Kaiyu Yang, Olga Russakovsky, and Jia Deng. SpatialSense: An Adversarially Crowdsourced Benchmark for Spatial Relation Recognition. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2051–2060, 2019. [10]Fangyu Liu, Guy Emerson, and Nigel Collier. Visual Spatial Reasoning. Transactions of the Association for Computational Linguistics, 11:635–651, 2023. doi: 10.1162/tacla00566. [11] Daichi Azuma, Taiki Miyanishi, Shuhei Kurita, and Motoaki Kawanabe. ScanQA: 3D Question Answering for Spatial Scene Understanding. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19129–19139, 2022. [12]Xiaojian Ma, Silong Yong, Zilong Zheng, Qing Li, Yitao Liang, Song-Chun Zhu, and Siyuan Huang. SQA3D: Situated Question Answering in 3D Scenes. In International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=IDJx97BC38. [13] Weihao Yu, Zhengyuan Yang, Linjie Li, Jianfeng Wang, Kevin Lin, Zicheng Liu, Xinchao Wang, and Lijuan Wang. M-Vet: Evaluating Large Multimodal Models for Integrated Capabilities. Proceedings of Machine Learning Research, 2024. ICML 2024; arXiv:2308.02490. [14] Lin Chen, Jinsong Li, Xiaoyi Dong, Pan Zhang, Yuhang Zang, Zehui Chen, Haodong Duan, Jiaqi Wang, Yu Qiao, Dahua Lin, and Feng Zhao. Are We on the Right Way for Evaluating Large Vision-Language Models? In Advances in Neural Information Processing Systems, 2024. MMStar; arXiv:2403.20330. [15] Xiang Yue, Tianyu Zheng, Yuansheng Ni, Yubo Wang, Kai Zhang, Shengbang Tong, Yuxuan Sun, Botao Yu, Ge Zhang, Huan Sun, Yu Su, Wenhu Chen, and Graham Neubig. MMMU- Pro: A More Robust Multi-discipline Multimodal Understanding Benchmark. arXiv preprint arXiv:2409.02813, 2024. [16]Shengbang Tong, Ellis Brown, Penghao Wu, Sanghyun Woo, Manoj Middepogu, Sai Charitha Akula, Jihan Yang, Shusheng Yang, Adithya Iyer, Xichen Pan, Ziteng Wang, Rob Fergus, Yann LeCun, and Saining Xie. Cambrian-1: A Fully Open, Vision-Centric Exploration of Multimodal LLMs. Advances in Neural Information Processing Systems, 2024. Introduces CV-Bench; arXiv:2406.16860. 10 [17]Nianchen Deng, Lixin Gu, Shenglong Ye, Yinan He, Zhe Chen, Songze Li, Haomin Wang, Xingguang Wei, Tianshuo Yang, Min Dou, et al. InternSpatial: A Comprehensive Dataset for Spatial Reasoning in Vision-Language Models. arXiv preprint arXiv:2506.18385, 2025. [18]Julius Mayer, Mohamad Ballout, Serwan Jassim, Farbod Nosrat Nezami, and Elia Bruni. iVISPAR — An Interactive Visual-Spatial Reasoning Benchmark for VLMs. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 26757–26781, 2025. doi: 10.18653/v1/2025.emnlp-main.1359. [19]Peiran Xu, Sudong Wang, Yao Zhu, Jianing Li, Gege Qi, and Yunjian Zhang. SpatialBench: Benchmarking Multimodal Large Language Models for Spatial Cognition. arXiv preprint arXiv:2511.21471, 2025. [20] Drew A. Hudson and Christopher D. Manning. GQA: A New Dataset for Real-World Visual Reasoning and Compositional Question Answering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6700–6709, 2019. [21]Alane Suhr, Stephanie Zhou, Ally Zhang, Iris Zhang, Huajun Bai, and Yoav Artzi. A Corpus for Reasoning about Natural Language Grounded in Photographs. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 6418–6428, 2019. doi: 10.18653/v1/P19-1644. [22]Tristan Thrush, Ryan Jiang, Max Bartolo, Amanpreet Singh, Adina Williams, Douwe Kiela, and Candace Ross. Winoground: Probing Vision and Language Models for Visio-Linguistic Compositionality. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5238–5248, 2022. [23] Yining Hong, Haoyu Zhen, Peihao Chen, Shuhong Zheng, Yilun Du, Zhenfang Chen, and Chuang Gan. 3D-LLM: Injecting the 3D World into Large Language Models. In Advances in Neural Information Processing Systems, 2023. URLhttps://openreview.net/forum?id= YQA28p7qNz. [24]Geby Jaff.SpatialBench.GitHub repository, 2026.URLhttps://github.com/ spicylemonade/spatialbench/tree/438d1148a44f10f45d4b2fbea534e95289dab. Ver- sion 0.1.0, commit 438d114; accessed August 13, 2026. [25]C. A. Field and A. H. Welsh. Bootstrapping Clustered Data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69(3):369–390, 2007. doi: 10.1111/j.1467-9868.2007. 00593.x. 11