# TangramSR: Can Vision-Language Models Reason in Continuous Geometric Space? arXiv: https://arxiv.org/abs/2602.05570 ยท HTML: https://mlsanity.com/paper/2602.05570/ ## Key facts - Cited by 3 papers in the map (data through 14 Oct 2026). - Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. - Builds on 26 of its 41 references that are in the map. - First posted on arXiv 5 Feb 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, 26 of 26) - [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021) - [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021) - [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022) - [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022) - [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024) - [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023) - [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023) - [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023) - [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016) - [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024) - [LLaMA-Adapter V2: Parameter-Efficient Visual Instruction Model](https://mlsanity.com/paper/2304.15010/) (2023) - [Winoground: Probing Vision and Language Models for Visio-Linguistic Compositionality](https://mlsanity.com/paper/2204.03162/) (2022) - [A Survey of Embodied AI: From Simulators to Research Tasks](https://mlsanity.com/paper/2103.04918/) (2021) - [MMLongBench-Doc: Benchmarking Long-context Document Understanding with Visualizations](https://mlsanity.com/paper/2407.01523/) (2024) - [RoboSpatial: Teaching Spatial Understanding to 2D and 3D Vision-Language Models for Robotics](https://mlsanity.com/paper/2411.16537/) (2024) - [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025) - [Abstract Visual Reasoning with Tangram Shapes](https://mlsanity.com/paper/2211.16492/) (2022) - [Why Vision Language Models Struggle with Visual Arithmetic? Towards Enhanced Chart and Geometry Understanding](https://mlsanity.com/paper/2502.11492/) (2025) - [Unfolding Spatial Cognition: Evaluating Multimodal Models on Visual Simulations](https://mlsanity.com/paper/2506.04633/) (2025) - [Exploiting Temporal State Space Sharing for Video Semantic Segmentation](https://mlsanity.com/paper/2503.20824/) (2025) - [Thinking in Frames: How Visual Context and Test-Time Scaling Empower Video Reasoning](https://mlsanity.com/paper/2601.21037/) (2026) - [The Role of Linguistic Priors in Measuring Compositional Generalization of Vision-Language Models](https://mlsanity.com/paper/2310.02777/) (2023) - [Learning From How Humans Correct](https://mlsanity.com/paper/2102.00225/) (2021) - [Compositional Learning of Visually-Grounded Concepts Using Reinforcement](https://mlsanity.com/paper/2309.04504/) (2023) - [GIQ: Benchmarking 3D Geometric Reasoning of Vision Foundation Models with Simulated and Real Polyhedra](https://mlsanity.com/paper/2506.08194/) (2025) - [Master Rules from Chaos: Learning to Reason, Plan, and Interact from Chaos for Tangram Assembly](https://mlsanity.com/paper/2505.11818/) (2025) ## Built on by (most cited first, 3 of 3) - [A Survey on Self-Improving Test-Time Intelligence: Feedback-Driven Adapting, Learning, and Scaling at Inference](https://mlsanity.com/paper/2609.01679/) (2026) - [Do multimodal models imagine electric sheep?](https://mlsanity.com/paper/2605.09693/) (2026) - [Relational Abstractions for Spatial Reasoning with Diffusion Models](https://mlsanity.com/paper/2610.09780/) (2026) ## Abstract (arXiv) Humans excel at spatial reasoning tasks like Tangram puzzle assembly through cognitive processes involving mental rotation, iterative refinement, and visual feedback. Inspired by how humans solve Tangram puzzles through trial-and-error, observation, and correction, we design a framework that models these human cognitive mechanisms. However, comprehensive experiments across five representative Vision-Language Models (VLMs) reveal systematic failures in continuous geometric reasoning: average IoU of only 0.41 on single-piece tasks, dropping to 0.23 on two-piece composition, far below human performance where children can complete Tangram tasks successfully. This paper addresses a fundamental challenge in self-improving AI: can models iteratively refine their predictions at test time without parameter updates? We introduce a test-time self-refinement framework that combines in-context learning (ICL) with reward-guided feedback loops, inspired by human cognitive processes. Our training-free verifier-refiner agent applies recursive refinement loops that iteratively self-refine predictions based on geometric consistency feedback, achieving IoU improvements from 0.63 to 0.932 on medium-triangle cases without any model retraining. This demonstrates that incorporating human-inspired iterative refinement mechanisms through ICL and reward loops can substantially enhance geometric reasoning in VLMs, moving self-improving AI from promise to practice in continuous spatial domains. Our work is available at this anonymous link https://anonymous.4open.science/r/TangramVLM-F582/.