Sample-Efficient Post-Training for LEGO Spatial-Physics Reasoning
Authors: Yuhuan Yuan, Zhouliang Yu, Minghao Liu, Weiyang Liu, Ge Lin Kan
Organizations: HKUST(GZ) · CUHK · ZODA
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.
We train a language model to generate LEGO-brick build sequences. While prior work has been restricted to discrete, voxel-like towers, we consider a much broader set of pieces, encompassing thousands of part types with diverse connection semantics. To enable this, we first collect a large-scale dataset of over 100,000 human-designed LDraw brick objects and scenes. The complexity of our setting makes it challenging to autoregressively assemble structures that satisfy physical constraints. When predicting block pose directly, build sequences quickly become invalid after a small number of steps. Although pieces are placed in 3D space, it is the spatial relationships of the parts which define the whole. With this in mind, we design a graph-based program representation that parametrizes structure through connectivity, improving the physical grounding of generated sequences. To enable future applications, we make our dataset and models available for research purposes. https://kulits.github.io/BrickNet
We introduceWorkBenchMark, a LEGO Duplo-based robotic assembly benchmark motivated by the RoboCup Smart Manufacturing League. Robotic assembly couples low-level manipulation with task-level symbolic reasoning under physical constraints, a combination that current end-to-end learning methods do not yet solve reliably. The benchmark provides 400 tasks across four complexity tiers. We provide an open-vocabulary perception, Assembly-by-Disassembly baseline solution. Our planning-based pipeline outperforms a modern vision-language-action approach across all tiers. The benchmark, simulation environment, and baseline implementation will be released openly to support the broader robotic assembly community.
We dream of AI agents that can read arbitrary designs and construct real-world objects from reusable building blocks. As a first step toward this vision, we study whether multimodal large language models (MLLMs) possess the visual grounding and spatial reasoning capabilities required for brick assembly. We formulate brick assembly as a sequential decision-making problem, where each step involves two subtasks: brick selection, identifying the target brick from candidate components, and brick pose estimation, predicting where and how the selected brick should be placed. To support this study, we introduce BC-Bench (Brick Construction Benchmark), the first benchmark for evaluating MLLMs on assembly with diverse bricks. Experiments show that current state-of-the-art MLLMs remain far from reliable builders, struggling with fine-grained brick selection and failing at precise pose estimation. To bridge this gap, we propose Brick-Composer, a learning framework that equips MLLMs with assembly skills through three complementary signals: Human Design Sparks, which provide affordance-rich construction demonstrations; World Feedback, which grounds predicted actions in visual and physical consequences; and Synthetic Experience, which scales learning beyond existing object designs. Brick-Composer improves brick selection accuracy by over three times, substantially reduces pose estimation errors, and raises strict step-level assembly success from less than 1% to around 15%. After training, a Qwen-3-8B can correctly compose up to 42% of the steps for a complete object, suggesting that MLLMs can acquire assembly capabilities through targeted, physically grounded learning.