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

Researchers reveal that multimodal large language models achieve high visual reasoning benchmark scores by exploiting a 'Cartesian Shortcut'—leveraging grid-based layouts that convert to explicit text coordinates rather than performing genuine visual understanding. The Polaris-Bench study shows frontier models collapse from 70-83% accuracy to 31-39% when benchmarks are reformulated in polar coordinate space, exposing critical deficiencies in topology-invariant reasoning.

Current multimodal large language models demonstrate a fundamental weakness masked by strong benchmark performance. The research identifies that high scores on visual reasoning tasks stem largely from models exploiting orthogonal grid structures that naturally discretize into textual coordinates—allowing models to reduce visual problems to text-based deductive reasoning rather than true visual understanding. This 'Cartesian Shortcut' represents a systemic evaluation gap across the field.

The Polaris-Bench benchmark addresses this vulnerability by reformulating 53 visual reasoning tasks in polar coordinate space while maintaining logical equivalence to Cartesian counterparts. The dramatic performance degradation—with frontier models dropping 40+ percentage points—reveals that state-of-the-art MLLMs lack genuine topology-invariant visual reasoning capabilities. This finding gains significance as these models increasingly guide decisions in vision-critical domains from autonomous systems to medical imaging.

For the AI industry, these results necessitate fundamental architectural reassessment. Current transformer-based approaches appear inherently biased toward exploitable grid structures, suggesting that achieving robust visual understanding requires new approaches to spatial representation and reasoning. The persistence of performance gaps even under complete logical equivalence indicates the problem transcends simple coordinate transformation and points to deeper limitations in how models process visual information.

Moving forward, the field should prioritize coordinate-system-agnostic benchmarks and develop MLLMs capable of reasoning about spatial relationships independent of underlying representation frameworks. This research directly challenges claims of visual understanding advancement and establishes a new quality bar for evaluating genuine multimodal reasoning capabilities.

• →Frontier MLLMs achieve 70-83% accuracy on Cartesian visual benchmarks but collapse to 31-39% on logically equivalent polar coordinate versions
• →Models exploit grid-based layouts by converting visual problems into text-based coordinate deduction rather than performing genuine visual reasoning
• →Polaris-Bench reformulates 53 tasks in polar space to eliminate the Cartesian shortcut while preserving logical constraints and semantics
• →Current MLLMs fundamentally lack topology-invariant visual reasoning, a critical deficiency for real-world vision applications
• →Performance degradation persists even under complete logical equivalence, indicating deep architectural limitations beyond coordinate transformation