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

TL;DR

This paper reveals that current multimodal large language models rely on a Cartesian shortcut in visual reasoning tasks, which can be broken by reformulating tasks in Polar coordinates, exposing their lack of topology-invariant reasoning.

Contribution

The authors introduce Polaris-Bench, a benchmark reformulating visual reasoning tasks in Polar coordinates to evaluate and expose the reliance of models on Cartesian shortcuts.

Findings

Models' performance drops from 70-83% to 31-39% on Polar layouts.

Reasoning improvements on Cartesian layouts do not transfer to Polar equivalents.

Current models lack topology-invariant visual reasoning capabilities.

Abstract

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 \textbf{Cartesian Shortcut}: visual reasoning benchmarks prevalently build on orthogonal grid-based layouts that can be readily discretized into explicit textual coordinates. Models systematically exploit this property, heavily leveraging text-based deductive reasoning to assist visual problem-solving. To systematically dismantle this shortcut, we introduce \textbf{Polaris-Bench}, which re-formulates 53 visual reasoning tasks in Polar coordinate space with paired Cartesian counterparts as reference, while preserving consistent logical constraints and task semantics -- thus fundamentally breaking the orthogonal prior that models exploit. Comprehensive evaluation across $14$ state-of-the-art MLLMs reveals that frontier models achieving $70$--$83\%$ on Cartesian layouts collapse to $31$--$39\%$ on Polar equivalents, with degradation persisting even under complete logical equivalence. Moreover, reasoning gains observed on Cartesian layouts are severely diminished on Polar equivalents. These findings expose a critical deficiency in current MLLMs: the lack of topology-invariant visual reasoning.