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Apple-$\pi$: Benchmarking Thinking with Video Towards Law-Grounded Physical Intelligence
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Introduces Apple-π, a law-grounded benchmark (400-video Orchard mechanics dataset, three-stage Perception/Formulation/Deduction chain-of-frames protocol, hybrid MLLM and physics-grounded metrics) for testing whether video and unified models reason physically, evaluating 11 models.
Problem
Existing video-generation physics benchmarks evaluate only output plausibility, not whether models reach outputs through law-grounded reasoning, so it is unclear whether video models internalize physical laws.
Approach
Anchors video-model evaluation in classical-mechanics laws using infographic-annotated first frames and chain-of-frames prompts, splitting evaluation into Perception, Formulation, and Deduction stages with stage-resolved hybrid metrics (MLLM judge plus physics-grounded IoU and trajectory error).
Key results
- Best video model Seedance 2.0 scores 0.473 average, while GPT Image 2 and Nano Banana 2 reach 0.704 and 0.699.
- Deduction is the hardest stage; even the strongest unified models score only around 0.40 on Deduction.
- Video and unified models both score lower on real-world than simulated cases, indicating a Sim-to-Real gap.
Surprising findings
- Unified image-generation models (GPT Image 2, Nano Banana 2) substantially outperform video models on the benchmark average.
- Text-parameter prompting of physical quantities is nearly neutral versus infographic overlays.
Limitations
- Covers only ten classical-mechanics task families with four primitive object shapes.
- Deduction and Formulation scores depend on an MLLM judge (Gemini 3 Flash) for subjective criteria.
Experimental setup
Datasets: Orchard
Benchmarks: Apple-π
Metrics: MLLM subjective score segmentation IoU pixel-level fidelity spatiotemporal mask overlap 3D velocity error
Baselines: Wan2.2 HunyuanVideo-1.5 VBVR-Wan2.2 Veo 3.1 BAGEL OmniGen2 SenseNova-U1-8B-MoT
Builds on: chain-of-frames VideoPhy Physics-IQ
Closest papers by meaning
- SciVideoBench: Benchmarking Scientific Video Reasoning in Large Multimodal Models (ICML 2026 · similarity 0.87)
- Towards World Simulator: Crafting Physical Commonsense-Based Benchmark for Video Generation (ICML 2025 · similarity 0.87)
- How Far Is Video Generation from World Model: A Physical Law Perspective (ICML 2025 · similarity 0.87)
- QUANTIPHY: A Quantitative Benchmark Evaluating Physical Reasoning Abilities of Vision-Language Models (CVPR 2026 · similarity 0.87)
- VideoHallu: Evaluating and Mitigating Multi-modal Hallucinations on Synthetic Video Understanding (NeurIPS 2025 · similarity 0.86)
- Principia: Relational Physics Tests for Video Models (NeurIPS 2026 · similarity 0.86)
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