google/polaris-bench

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

Polaris-Bench: Official Evaluation Dataset

Xia Hu¹, Zhenrui Yue¹, Brian Potetz¹, Howard Zhou¹, Leonidas Guibas^1,2, Chun-Ta Lu³, Zhicheng Wang^1
1Google DeepMind   ²Stanford University   ³Google Research

Overview

As current Multimodal Large Language Models (MLLMs) rapidly saturate canonical visual reasoning benchmarks, a key question emerges: do these strong scores genuinely reflect robust visual understanding? In our paper, The Cartesian Shortcut: Re-evaluate Vision Reasoning in Polar Coordinate Space, we identify a pervasive vulnerability: the 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 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. 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. These findings expose a critical deficiency in current MLLMs: the lack of topology-invariant visual reasoning.

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Dataset Summary

• Total Problem Instances: 10,800 evaluation problems with ground-truth answers and high-resolution visual diagrams.
• Tasks: 53 distinct visual reasoning tasks spanning 5 cognitive categories.
• Coordinate Spaces:
  • Cartesian: 5,300 instances (53 tasks x 100 examples)
  • Polar: 5,300 instances (53 tasks x 100 examples)
  • Hexagonal: 100 instances (Word Search intermediate coordinate ablation)
  • Octagonal: 100 instances (Word Search intermediate coordinate ablation)
• Pairwise Controlled Evaluation: Every problem instance has a paired counterpart between Cartesian and Polar coordinate systems under consistent logical constraints and task semantics.

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Task Taxonomy

Polaris-Bench covers 53 tasks organized into 5 cognitive categories:

Category	Count	Tasks
Visual Pattern Matching	11	pattern_completion, pattern_prediction, layer_completion, shape_completion, shape_fitting, jigsaw_matching, odd_piece_out, fragment_matching, anomaly_detection, template_matching, impossible_shape
Spatial Transformation & Geometry	13	grid_rotation, pivot_rotation, mirror_reflection, grid_folding, rotation_center, rotation_matching, area_balancing, minimum_flips, wall_follower, letter_collection, turn_counting, pipe_lengths, word_search
Navigation & Routing	14	maze, shortest_path, bounded_path_finding, wrapping_path_finding, bounded_diagonal_paths, wrapping_diagonal_paths, bounded_knight_paths, knight_paths, checkpoint_paths, monotonic_path, rule_based_navigation, absolute_navigation, egocentric_navigation, wrapping_navigation
Combinatorics & Probability	9	path_counting, lattice_paths, area_counting, edge_counting, uncut_cells, maximum_collection, longest_path, largest_number_path, curve_length
Algorithmic Logic & Simulation	6	sudoku, four_color, n_queens, random_walk, collision_detection, bouncing_point

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Files & Data Structure

This repository provides multiple ways to access and consume the benchmark:

google/polaris-bench/
├── data/
│   ├── test-00000-of-00005.parquet   # Sharded Parquet with embedded PIL images (2,160 rows)
│   ├── test-00001-of-00005.parquet   # Sharded Parquet with embedded PIL images (2,160 rows)
│   ├── test-00002-of-00005.parquet   # Sharded Parquet with embedded PIL images (2,160 rows)
│   ├── test-00003-of-00005.parquet   # Sharded Parquet with embedded PIL images (2,160 rows)
│   └── test-00004-of-00005.parquet   # Sharded Parquet with embedded PIL images (2,160 rows)
├── polaris_bench.json                # Complete benchmark metadata (10,800 records) in JSON
├── polaris_bench.parquet             # Lightweight metadata-only Parquet (without binary images)
├── images.zip                        # Complete visual asset archive (10,800 PNG images, 2.67 GB)
└── README.md                         # Dataset card and documentation

Data Fields & Schema

Each record contains the following fields:

Field	Type	Description
task	string	Task identifier (e.g., "sudoku", "maze", "shape_fitting").
index	string	Unique problem instance identifier within the task (e.g., "example_001").
question_type	string	Coordinate representation: "cartesian", "polar", "hexagonal", or "octagonal".
image	Image	Decoded PIL Image object (available when loading through datasets).
image_path	string	Relative path to the visual diagram (e.g., "images/sudoku/sudoku_example_001_polar.png").
question	string	Full problem prompt, instructions, and multiple-choice options.
answer	string	Ground-truth answer (option labels, digits, coordinates, strings, or lists).

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How to Use the Dataset

Method 1: Hugging Face datasets Library (Recommended)

from datasets import load_dataset

# Load the full benchmark test split
dataset = load_dataset("google/polaris-bench", split="test")

# Inspect an example
sample = dataset[0]
print(f"Task: {sample['task']}")
print(f"Coordinate System: {sample['question_type']}")
print(f"Question:\n{sample['question']}")
print(f"Answer: {sample['answer']}")

# Display the image (sample['image'] is a PIL Image object)
sample["image"].show()

Method 2: Official Polaris-Bench Evaluation Toolkit

Use the official open-source evaluation suite from GitHub:

git clone https://github.com/google-deepmind/polaris-bench.git
cd polaris-bench
pip install -r requirements.txt

Then load paired Cartesian-Polar evaluation sets directly:

from evaluation import PolarisDataLoader, Evaluator

# Loads directly from Hugging Face Hub
loader = PolarisDataLoader("google/polaris-bench")

# Get paired instances for controlled Cartesian vs. Polar evaluation
paired_dataset = loader.get_paired_dataset()
print(f"Loaded {len(paired_dataset)} paired evaluation tasks.")

# Inspect paired problem
pair = paired_dataset[0]
print("Task:", pair["task"])
print("Cartesian Question:", pair["cartesian"]["question"][:100])
print("Polar Question:", pair["polar"]["question"][:100])

Method 3: Direct Download via huggingface_hub

import json
import zipfile
from huggingface_hub import hf_hub_download
from PIL import Image

# 1. Download benchmark metadata JSON
json_file = hf_hub_download(
    repo_id="google/polaris-bench",
    repo_type="dataset",
    filename="polaris_bench.json"
)
with open(json_file, "r") as f:
    benchmark_data = json.load(f)

print(f"Loaded {len(benchmark_data)} records.")

# 2. Download the complete image archive (2.67 GB)
zip_file = hf_hub_download(
    repo_id="google/polaris-bench",
    repo_type="dataset",
    filename="images.zip"
)
with zipfile.ZipFile(zip_file, "r") as zf:
    zf.extractall("polaris_images")

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Benchmark Results (High Reasoning Mode)

All models evaluated under high reasoning mode. Sorted by Polar accuracy (P). Full per-category results on the project page.

#	Model	Type	Cartesian (%)	Polar (%)	Drop (Δ)
👤	Human	Baseline	94.5	88.8	-5.7
1	GPT-5.2	Closed	77.4	39.2	-38.2
2	Gemini-3.1-Pro	Closed	82.6	35.9	-46.7
3	Qwen3.5-397B-A17B	Open	72.9	35.0	-37.9
4	Gemini-3-Flash	Closed	71.0	33.8	-37.2
5	Kimi-k2.5	Open	69.0	31.1	-37.8
6	Gemma-4-31B	Open	60.5	31.0	-29.5
7	Claude-Sonnet-4.6	Closed	44.4	25.9	-18.5
8	Gemini-2.5-Pro	Closed	38.4	25.3	-13.2
9	Gemini-3.1-Flash-Lite	Closed	46.8	24.6	-22.2
10	Gemma-4-26B	Open	47.2	22.9	-24.4
11	Grok-4-Fast-Reasoning	Closed	31.0	22.3	-8.7
12	Grok-4-0709	Closed	33.0	21.8	-11.2
13	Gemini-2.5-Flash	Closed	32.2	21.1	-11.2
14	Mistral-Small-2503	Open	19.4	19.0	-0.4
-	Random Baseline	Baseline	15.8	15.8	0.0

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Licensing & Disclaimer

Copyright 2026 Google LLC

All software is licensed under the Apache License, Version 2.0 (Apache 2.0); you may not use this file except in compliance with the Apache 2.0 license. You may obtain a copy of the Apache 2.0 license at: https://www.apache.org/licenses/LICENSE-2.0

All other materials are licensed under the Creative Commons Attribution 4.0 International License (CC-BY). You may obtain a copy of the CC-BY license at: https://creativecommons.org/licenses/by/4.0/legalcode

Some data was created with inspiration from:

• Babyvision, which is available at https://github.com/UniPat-AI/BabyVision under the Creative Commons Attribution 4.0 International License (CC-BY). You may obtain a copy of the CC-BY license at: https://creativecommons.org/licenses/by/4.0/legalcode.
• EMMA-Bench, which is available at https://github.com/EMMA-Bench/EMMA.
• MathVista, which is available at https://github.com/lupantech/MathVista under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0). You may obtain a copy of the CC BY-SA 4.0 license at: https://creativecommons.org/licenses/by-sa/4.0/legalcode.
• MEGABench, which is available at https://github.com/TIGER-AI-Lab/MEGA-Bench.

Unless required by applicable law or agreed to in writing, all software and materials distributed here under the Apache 2.0 or CC-BY licenses are distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the licenses for the specific language governing permissions and limitations under those licenses.

This is not an official Google product.

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Citation

@misc{hu2026cartesianshortcutreevaluatevision,
      title={The Cartesian Shortcut: Re-evaluate Vision Reasoning in Polar Coordinate Space},
      author={Xia Hu and Zhenrui Yue and Brian Potetz and Howard Zhou and Leonidas Guibas and Chun-Ta Lu and Zhicheng Wang},
      year={2026},
      eprint={2605.09883},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2605.09883},
}