GeoPhys: The Geometry of
Physical Plausibility

Abstract

While humans can identify physically implausible events within milliseconds, machine learning approaches addressing the same problem are extremely slow and expensive. They either rely on external multimodal-LLM judges or require ad-hoc modifications to the training procedure. In this work, we argue that indicators of physical plausibility are implicitly captured by five geometric properties of the per-frame embeddings produced by frozen image encoders. In aggregate, we call them GeoPhys.

The Setup

A frozen backbone maps each frame to a pooled feature; stacking them across time gives a trajectory. Plausible videos trace smooth, locally linear paths. Violations bend.

The five signals. Each measures one way a trajectory can betray a physics violation, computed directly on the per-frame features with no learned parameters.

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(paper Figure 1: plausible vs. violated trajectories)

On the trajectory ${\Gamma }_{\theta }(V)=({\bar{z}}_1,\dots ,{\bar{z}}_T)$, with step $v_t={\bar{z}}_{t+1}-{\bar{z}}_t$, turning angle ${\theta }_t=\arccos \frac{⟨v_t,v_{t+1}⟩}{\Vert v_t\Vert \Vert v_{t+1}\Vert }$, acceleration $a_t={\bar{z}}_{t+2}-2{\bar{z}}_{t+1}+{\bar{z}}_t$, and residual ${\epsilon }_t={\bar{z}}_{t+1}-{\hat{\bar{z}}}_{t+1}$ of a linear predictor ${\hat{\bar{z}}}_{t+1}$ on ${\bar{z}}_{1:t}$. All statistics run over $t$; larger values mean less regular dynamics.

Four frozen backbones. The score runs on self-supervised transformers and explicit models of primate visual cortex. None is trained on video or physics. For each backbone we pick the readout layer that maximises the plausible-versus-violated curvature gap on a held-out split. Backbones are complementary: each specialises in a different signal and wins a different physics domain.

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(paper Figure 2: GeoPhys pipeline)

It tracks the brain

A useful signal should reflect a real phenomenon, not an artefact of pretraining statistics. We compare per-frame GeoPhys signals against human EEG on matched violation-of-expectation stimuli.

On two object-permanence scenarios, Create (one object enters an occluder, two emerge) and Vanish (two enter, one emerges), CORnet-S IT speed follows the contralateral delay activity, an EEG marker of visual working memory. Both rise and stay elevated after the violation, and the GeoPhys signal scales with the number of tracked objects.

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(paper Figure 4: model and brain comparison)

It detects violations at scale

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L LikePhys
detection

650 matched Blender pairs across 12 scenarios in four physics domains: rigid-body, continuum, fluid and optical.

arXiv:2510.11512 ↗

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I IntPhys 2
detection

506 photorealistic Unreal Engine pairs probing four core-knowledge properties: permanence, solidity, continuity, immutability.

arXiv:2506.09849 ↗

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P PhysicsIQ
generation

396 real-world videos over 66 scenarios in solid mechanics, fluid dynamics, optics, thermodynamics and magnetism.

physics-iq.github.io ↗

A leave-one-scene-out linear probe on the same DINOv3 features reaches only 62.4% on LikePhys, so the gain comes from trajectory geometry, not the backbone alone.

It steers video generation

Beyond passive measurement, GeoPhys transfers to active control. As a best-of-N verifier it reranks a generator's candidates by plausibility, with no learned ranker and no PhysicsIQ-specific tuning.

On PhysicsIQ GeoPhys outscores every inference-time verifier and closes more of the gap to the oracle ceiling than a billion-parameter world model.

PhysicsIQ score (%, higher is better). I2V settings score lower than the V2V setting; GeoPhys leads the real verifiers in every column.

Test-time scaling. More candidates, better physics. As the best-of-N budget grows, GeoPhys keeps climbing toward the oracle ceiling while cheaper verifiers and the no-verifier baseline plateau, so spending compute at inference pays off only with the right plausibility signal.

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(paper Figure 8: test-time scaling)

Results in motion. Pick a physics family, then drag the divider to compare the no-verifier baseline against the GeoPhys best-of-N selection.

Same scenario, same candidate pool. The baseline takes a random sample; GeoPhys reranks by plausibility. Δ is the per-scenario PhysicsIQ gain over baseline.

Cheaper Frozen image encoders cost a fraction of a video-pretrained world model.

1.5× lower wall-clock and 4.65× lower memory than the world-model verifier. At a fixed budget that is roughly 5× more candidates.

Citation (BibTeX)

If you find this work useful, please cite it.

@misc{interno2026geophys,
  title   = {GeoPhys: The Geometry of Physical Plausibility},
  author  = {Intern\`{o}, Christian and Pondaven, Alexander and Issa, Habon
             and Pizzati, Fabio and Pinto, Francesco and Olhofer, Markus
             and Laptev, Ivan and Torr, Philip and Simoncelli, Eero P.
             and Hammer, Barbara and Klindt, David},
  year    = {2026},
  url     = {https://christianinterno.github.io/GeoPhys/}
}