Sample-Efficient Post-Training for LEGO Spatial-Physics Reasoning

• URL: http://arxiv.org/abs/2606.07602v1
• Date: Fri, 29 May 2026 09:31:25 GMT
• Title: Sample-Efficient Post-Training for LEGO Spatial-Physics Reasoning
• Abstract summary: LLM-based LEGO assembly generation requires both semantic grounding and physical feasibility.<n>We propose a model-based data selection approach that uses only a small fraction of the training data.<n>We introduce PVPO, a sample-efficient reinforcement learning method that couples physical feasibility with voxel-space geometric rewards.
• Score: 17.416391606380827
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: LLM-based LEGO assembly generation requires both semantic grounding and physical feasibility. We identify a data-induced failure mode, PhysHack, in which the assemblies satisfy physical-validity constraints while producing structures that are geometrically misaligned, semantically inconsistent, or poorly calibrated. To address this challenge, we propose a model-based data selection approach that uses only a small fraction of the training data while improving physically grounded LEGO assembly generation. Building on the selected trajectories, we introduce PVPO, a sample-efficient reinforcement learning method that couples physical feasibility with voxel-space geometric rewards. Our results show that physical validity alone is an insufficient proxy for reliable physical reasoning: models can learn to generate valid structures without preserving semantic or geometric fidelity. Experiments across model backbones and test-time scaling settings demonstrate that PVPO improves structural and semantic alignment, physical validity, structural stability, and calibration, while reducing reliance on extensive post-hoc rejection sampling. In particular, results on calibration show that PVPO mitigates PhysHack by making test-time selection more predictive of semantic and structural quality.

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