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Causal-PIK: Causality-based Physical Reasoning with a Physics-Informed Kernel

ICML 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Counterfactual identification and bounds

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Proposes Causal-PIK, a Bayesian optimization method whose GP kernel is a causal-similarity function computed from a learned RPIN dynamics model's predicted action effects, evaluated on Virtual Tools and PHYRE-1B Cross.

Problem

Single-intervention physical reasoning puzzles with unknown dynamics require finding a successful action in as few attempts as possible; existing methods either use dynamics models to rank actions or operate on reduced action spaces.

Approach

A physics-informed GP kernel that measures similarity between actions by comparing the object state changes a learned dynamics model predicts they cause (directional cosine and magnitude similarity, counterfactually normalized), used within UCB Bayesian optimization over the full continuous/discrete action space.

Key results

• On Virtual Tools (max 10 attempts), Causal-PIK achieves AUCCESS 65.0 versus 58.0 for SSUP and 42.0 for the RBF-kernel ablation.
• On PHYRE-1B Cross (max 100 attempts), Causal-PIK achieves AUCCESS 41.6 versus 42.2 for RPIN-based ranking and 30.24 for the best full-action-space baseline, and 27.7 for the RBF variant.
• Per-puzzle correlation with human scores is highest for SSUP on Virtual Tools (r=0.71) and for Causal-PIK on PHYRE (r=0.73).

Measured effects reported in the paper

Surprising findings

• Causal-PIK with a dynamics model trained on unseen puzzles reaches AUCCESS 41.6, while a model trained on test-template puzzles (L2 error 3.56 vs 19.3) reaches only 45, suggesting robustness to prediction noise.
• Causal-PIK is outperformed by the RPIN-based ranking baseline on PHYRE at 100 attempts in terms of AUCCESS (41.6 vs 42.2), and with a 10-attempt cap it drops to 24.8, below humans at 36.6.

Limitations

• No knowledge sharing across tasks.
• Performance depends on noisy causal effect predictions from the dynamics model.
• Evaluated only on 3D action spaces; scaling to higher dimensions requires changes to the causal effect predictor.

Experimental setup

Datasets: Virtual Tools PHYRE-1B

Benchmarks: Virtual Tools PHYRE-1B Cross

Metrics: AUCCESS

Baselines: SSUP RAND DQN MEM RBF kernel BO Dec [Joint] RPIN-based dynamics ranking

Builds on: Bayesian optimization Region Proposal Interaction Networks SSUP UCB acquisition

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