Principia: Relational Physics Tests for Video Models

Forum topic · 小凯 · 2026-09-05

Summary

Principia is a benchmark that evaluates Newtonian physics understanding in video models through relational consistency between paired objects. Instead of relying on absolute motion measurements—which depend on frame rate, object scale, and camera calibration that are often ambiguous in generated videos—Principia exploits the fact that objects in the same scene must obey predictable, calibration-independent relations. The benchmark covers eight phenomena: gravity, coefficient of restitution, friction, moment of inertia, projectile motion, momentum, pendulums, and mass-spring oscillation, spanning translational, rotational, collisional, and oscillatory dynamics using real-world scenes recorded under controlled protocols. It also introduces a calibration-independent consistency score that quantifies physical violations directly in image space. Across thousands of generations from six state-of-the-art video generators, no model exceeds 0.42 on Principia despite all scoring around 0.8 on VBench. Vision-language models also perform poorly at detecting relational physics violations, with the best reaching only 67% accuracy while most are near chance.

Paper Overview

Field: Computer Vision
Authors: Varun Varma Thozhiyoor, Shivam Tripathi, Venkatesh Babu Radhakrishnan
Published: 2026-09-03
arXiv: 2609.04200

Abstract

Evaluating physical reasoning in video models is difficult because absolute motion measurements depend on frame rate, object scale, and camera calibration—all of which are often ambiguous or unavailable in generated videos. The authors take a different approach: when two objects in the same scene follow the same physical laws, their motions must satisfy predictable relations, and these relations are independent of calibration.

They introduce Principia, a benchmark that evaluates Newtonian physics through relational consistency between paired objects. Principia covers eight phenomena—gravity, coefficient of restitution, friction, moment of inertia, projectile motion, momentum, pendulums, and mass-spring oscillation—spanning translational, rotational, collisional, and oscillatory dynamics, using real-world scenes recorded under controlled protocols. The benchmark also introduces a calibration-independent consistency score that quantifies physical violations directly in image space.

Key Findings

Across thousands of generations from six state-of-the-art video generators, no model exceeds 0.42 on Principia, despite all scoring around 0.8 on VBench.
Vision-language models also perform disappointingly at detecting relational physics violations: the best model reaches only 67% accuracy, while most are near chance level.

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*Originally collected on zhichai.net, 2026-09-05.*