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

LLM-based LEGO assembly requires both semantic grounding and physical feasibility. In this paper, we identify a data-induced failure mode, physhack, in which generated assemblies satisfy physical-validity constraints while remaining geometrically misaligned, semantically inconsistent, or poorly calibrated. To address this challenge, we propose a model-based data selection approach that uses only 5% of the original training data while improving semantic and structural alignment across multiple independent evaluators. We further introduce PVPO, a reinforcement learning method that couples physical-validity and voxel-space geometric rewards to strengthen the LEGO synthesis capabilities of LLMs. PVPO-trained DeepSeek-Llama-8B outperforms the frontier VLM Kimi-K3 across semantic, structural, and physical evaluation dimensions, even when Kimi-K3 is provided with a ground-truth image as an additional reference.