# ORIGAMISPACE: Benchmarking Multimodal LLMs in Multi-Step Spatial Reasoning with Mathematical Constraints

arXiv: https://arxiv.org/abs/2511.18450 · HTML: https://mlsanity.com/paper/2511.18450/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 23 Nov 2025.

## 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, 20 of 20)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [MiniCPM-V: A GPT-4V Level MLLM on Your Phone](https://mlsanity.com/paper/2408.01800/) (2024)
- [VideoLLaMA 2: Advancing Spatial-Temporal Modeling and Audio Understanding in Video-LLMs](https://mlsanity.com/paper/2406.07476/) (2024)
- [DeepSeek-VL2: Mixture-of-Experts Vision-Language Models for Advanced Multimodal Understanding](https://mlsanity.com/paper/2412.10302/) (2024)
- [MM-LLMs: Recent Advances in MultiModal Large Language Models](https://mlsanity.com/paper/2401.13601/) (2024)
- [NVILA: Efficient Frontier Visual Language Models](https://mlsanity.com/paper/2412.04468/) (2024)
- [The Revolution of Multimodal Large Language Models: A Survey](https://mlsanity.com/paper/2402.12451/) (2024)
- [RoboSpatial: Teaching Spatial Understanding to 2D and 3D Vision-Language Models for Robotics](https://mlsanity.com/paper/2411.16537/) (2024)
- [Super-CLEVR: A Virtual Benchmark to Diagnose Domain Robustness in Visual Reasoning](https://mlsanity.com/paper/2212.00259/) (2022)
- [StepGame: A New Benchmark for Robust Multi-Hop Spatial Reasoning in Texts](https://mlsanity.com/paper/2204.08292/) (2022)
- [LEGO-Puzzles: How Good Are MLLMs at Multi-Step Spatial Reasoning?](https://mlsanity.com/paper/2503.19990/) (2025)
- [A Survey of State of the Art Large Vision Language Models: Alignment, Benchmark, Evaluations and Challenges](https://mlsanity.com/paper/2501.02189/) (2025)
- [Mind the Gap: Benchmarking Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2503.19707/) (2025)
- [NLVR2 Visual Bias Analysis](https://mlsanity.com/paper/1909.10411/) (2019)
- [VLUE: A Multi-Task Benchmark for Evaluating Vision-Language Models](https://mlsanity.com/paper/2205.15237/) (2022)

## Built on by (most cited first, 7 of 7)

- [TangramPuzzle: Evaluating Multimodal Large Language Models with Compositional Spatial Reasoning](https://mlsanity.com/paper/2601.16520/) (2026)
- [Can AI Understand the Language of Origami?](https://mlsanity.com/paper/2603.13856/) (2026)
- [World Craft: Agentic Framework to Create Visualizable Worlds via Text](https://mlsanity.com/paper/2601.09150/) (2026)
- [COrigami: An AI Pipeline for Co-Designing Flat-Foldable Visually Recognisable Origami](https://mlsanity.com/paper/2606.26299/) (2026)
- [FoldingAgent: Inferring Parametric Origami Procedures from Demonstration Videos](https://mlsanity.com/paper/2609.00377/) (2026)
- [MindTopo: Can Foundation Models Reason in Topological Space?](https://mlsanity.com/paper/2609.11900/) (2026)
- [PolyBridgeBench: Benchmarking Multimodal LLMs for Physics-Grounded Bridge Design](https://mlsanity.com/paper/2609.21493/) (2026)

## Abstract (arXiv)

Spatial reasoning is a key capability in the field of artificial intelligence, especially crucial in areas such as robotics, computer vision, and natural language understanding. However, evaluating the ability of multimodal large language models(MLLMs) in complex spatial reasoning still faces challenges, particularly in scenarios requiring multi-step reasoning and precise mathematical constraints. This paper introduces ORIGAMISPACE, a new dataset and benchmark designed to evaluate the multi-step spatial reasoning ability and the capacity to handle mathematical constraints of MLLMs through origami tasks. The dataset contains 350 data instances,each comprising a strictly formatted crease pattern (CP diagram), the Compiled Flat Pattern, the complete Folding Process, and the final Folded Shape Image. We propose four evaluation tasks: Pattern Prediction, Multi-step Spatial Reasoning, Spatial Relationship Prediction, and End-to-End CP Code Generation. For the CP code generation task, we design an interactive environment and explore the possibility of using reinforcement learning methods to train MLLMs. Through experiments on existing MLLMs, we initially reveal the strengths and weaknesses of these models in handling complex spatial reasoning tasks.