# Measuring Representation Robustness in Large Language Models for Geometry

arXiv: https://arxiv.org/abs/2604.16421 · HTML: https://mlsanity.com/paper/2604.16421/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
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- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [Is ChatGPT a General-Purpose Natural Language Processing Task Solver?](https://mlsanity.com/paper/2302.06476/) (2023)
- [Reasoning with Language Model Prompting: A Survey](https://mlsanity.com/paper/2212.09597/) (2022)
- [A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level](https://mlsanity.com/paper/2112.15594/) (2021)

## Abstract (arXiv)

Large language models (LLMs) are increasingly evaluated on mathematical reasoning, yet their robustness to equivalent problem representations remains poorly understood. In geometry, identical problems can be expressed in Euclidean, coordinate, or vector forms, but existing benchmarks report accuracy on fixed formats, implicitly assuming representation invariance and masking failures caused by representational changes alone. We propose GeoRepEval, a representation-aware evaluation framework that measures correctness, invariance, and consistency at the problem level across parallel formulations, combining strict answer matching, bootstrap confidence intervals, paired McNemar tests, representation-flip analyses, and regression controls for surface complexity. We prove that our Invariance@3 metric decomposes accuracy into robust and fragile components and is bounded by the weakest representation. Evaluating eleven LLMs on 158 curated high-school geometry problems (474 instances), we find accuracy gaps of up to 14 percentage points induced solely by representation choice. Vector formulations emerge as a consistent failure point, with Invariance@3 as low as 0.044 even after controlling for length and symbolic complexity. A convert-then-solve prompting intervention improves vector accuracy by up to 52 percentage points for high-capacity models, suggesting that failures reflect representation sensitivity rather than inability; however, low-capacity models show no gains, indicating deeper limitations. These results suggest that current models rely on representation-specific heuristics rather than abstract geometric reasoning. All datasets, prompts, and scripts are released at https://github.com/vedjaw/GeoRepEval.