# The Cartesian Shortcut: Re-evaluate Vision Reasoning in Polar Coordinate Space

arXiv: https://arxiv.org/abs/2605.09883 · HTML: https://mlsanity.com/paper/2605.09883/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 17 of 17)

- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [BLINK: Multimodal Large Language Models Can See but Not Perceive](https://mlsanity.com/paper/2404.12390/) (2024)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [CharXiv: Charting Gaps in Realistic Chart Understanding in Multimodal LLMs](https://mlsanity.com/paper/2406.18521/) (2024)
- [MuirBench: A Comprehensive Benchmark for Robust Multi-image Understanding](https://mlsanity.com/paper/2406.09411/) (2024)
- [VisuLogic: A Benchmark for Evaluating Visual Reasoning in Multi-modal Large Language Models](https://mlsanity.com/paper/2504.15279/) (2025)
- [Visionary-R1: Mitigating Shortcuts in Visual Reasoning with Reinforcement Learning](https://mlsanity.com/paper/2505.14677/) (2025)
- [MMIU: Multimodal Multi-image Understanding for Evaluating Large Vision-Language Models](https://mlsanity.com/paper/2408.02718/) (2024)
- [MIRAGE: The Illusion of Visual Understanding](https://mlsanity.com/paper/2603.21687/) (2026)
- [BabyVision: Visual Reasoning Beyond Language](https://mlsanity.com/paper/2601.06521/) (2026)
- [Uni-MMMU: A Massive Multi-discipline Multimodal Unified Benchmark](https://mlsanity.com/paper/2510.13759/) (2025)
- [VGRP-Bench: Visual Grid Reasoning Puzzle Benchmark for Large Vision-Language Models](https://mlsanity.com/paper/2503.23064/) (2025)
- [Lost in Time: Clock and Calendar Understanding Challenges in Multimodal LLMs](https://mlsanity.com/paper/2502.05092/) (2025)
- [GRASP: A Grid-Based Benchmark for Evaluating Commonsense Spatial Reasoning](https://mlsanity.com/paper/2407.01892/) (2024)

## Abstract (arXiv)

As current Multimodal Large Language Models rapidly saturate canonical visual reasoning benchmarks, a key question emerges: do these strong scores genuinely reflect robust visual understanding? We identify a pervasive vulnerability, the Cartesian Shortcut: models frequently discretize the orthogonal grid-based layouts prevalent in visual reasoning benchmarks into explicit textual coordinates, offloading reasoning from visual perception to text-based deduction. To re-evaluate visual reasoning when this shortcut is unavailable, we introduce Polaris-Bench, which re-formulates 53 visual reasoning tasks in Polar coordinate space with paired Cartesian counterparts that preserve task semantics, disrupting the orthogonal structure that models exploit. Comprehensive evaluation across 14 state-of-the-art MLLMs reveals that frontier models achieving 69--83% on Cartesian layouts collapse to 31--39% on Polar equivalents. Moreover, thinking gains largely vanish on Polar layouts, prompting interventions fail to close the gap, and comparable drops arise on other non-orthogonal layouts. These findings reveal that current MLLMs' visual reasoning performance is strongly coupled to orthogonal grid structure, a fragility that is consistent across model families but far smaller in humans, who maintain 88.8% accuracy on Polar layouts. The benchmark, evaluation suite, and leaderboard are publicly available at https://google-deepmind.github.io/polaris-bench.