# NoReGeo: Non-Reasoning Geometry Benchmark

arXiv: https://arxiv.org/abs/2601.10254 · HTML: https://mlsanity.com/paper/2601.10254/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 25 of 25)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [ALFRED: A Benchmark for Interpreting Grounded Instructions for Everyday Tasks](https://mlsanity.com/paper/1912.01734/) (2019)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [BabyAI: A Platform to Study the Sample Efficiency of Grounded Language Learning](https://mlsanity.com/paper/1810.08272/) (2018)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [3DSRBench: A Comprehensive 3D Spatial Reasoning Benchmark](https://mlsanity.com/paper/2412.07825/) (2024)
- [Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2406.17294/) (2024)
- [XGrammar: Flexible and Efficient Structured Generation Engine for Large Language Models](https://mlsanity.com/paper/2411.15100/) (2024)
- [MultiMath: Bridging Visual and Mathematical Reasoning for Large Language Models](https://mlsanity.com/paper/2409.00147/) (2024)
- [Unlocking Multimodal Mathematical Reasoning via Process Reward Model](https://mlsanity.com/paper/2501.04686/) (2025)
- [SpatialSense: An Adversarially Crowdsourced Benchmark for Spatial Relation Recognition](https://mlsanity.com/paper/1908.02660/) (2019)
- [General Scene Adaptation for Vision-and-Language Navigation](https://mlsanity.com/paper/2501.17403/) (2025)
- [GeoGramBench: Benchmarking the Geometric Program Reasoning in Modern LLMs](https://mlsanity.com/paper/2505.17653/) (2025)
- [FloorplanQA: A Benchmark for Spatial Reasoning in LLMs using Structured Representations](https://mlsanity.com/paper/2507.07644/) (2025)
- [CLEVR-POC: Reasoning-Intensive Visual Question Answering in Partially Observable Environments](https://mlsanity.com/paper/2403.03203/) (2024)

## Built on by (most cited first, 2 of 2)

- [From Seeing to Thinking: Decoupling Perception and Reasoning Improves Post-Training of Vision-Language Models](https://mlsanity.com/paper/2605.20177/) (2026)
- [Large Language Models and their Awareness of Mechanics and Spatial Geometry](https://mlsanity.com/paper/2608.14615/) (2026)

## Abstract (arXiv)

We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models' proficiency in reasoning-based geometry-where solutions are derived using algebraic methods-NoReGeo focuses on evaluating whether LLMs can inherently encode spatial relationships and recognize geometric properties directly. Our benchmark comprises 2,500 trivial geometric problems spanning 25 categories, each carefully crafted to be solvable purely through native geometric understanding, assuming known object locations. We assess a range of state-of-the-art models on NoReGeo, including frontier models like GPT-4, observing that even the most advanced systems achieve an overall maximum of 65% accuracy in binary classification tasks. Further, our ablation experiments demonstrate that such geometric understanding does not emerge through fine-tuning alone, indicating that effective training for geometric comprehension requires a specialized approach from the outset. Our findings highlight a significant gap in current LLMs' ability to natively grasp geometric concepts, providing a foundation for future research toward models with true geometric cognition.