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

arXiv: https://arxiv.org/abs/2606.07602 · HTML: https://mlsanity.com/paper/2606.07602/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 68 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 30 of 33)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Measuring Progress on Scalable Oversight for Large Language Models](https://mlsanity.com/paper/2211.03540/) (2022)
- [EmbodiedBench: Comprehensive Benchmarking Multi-modal Large Language Models for Vision-Driven Embodied Agents](https://mlsanity.com/paper/2502.09560/) (2025)
- [Natural Emergent Misalignment from Reward Hacking in Production RL](https://mlsanity.com/paper/2511.18397/) (2025)
- [MiMo-VL Technical Report](https://mlsanity.com/paper/2506.03569/) (2025)
- [Subliminal Learning: Language models transmit behavioral traits via hidden signals in data](https://mlsanity.com/paper/2507.14805/) (2025)
- [LEGO-Puzzles: How Good Are MLLMs at Multi-Step Spatial Reasoning?](https://mlsanity.com/paper/2503.19990/) (2025)
- [LLMPhy: Parameter-Identifiable Physical Reasoning Combining Large Language Models and Physics Engines](https://mlsanity.com/paper/2411.08027/) (2024)
- [Chinese Tiny LLM: Pretraining a Chinese-Centric Large Language Model](https://mlsanity.com/paper/2404.04167/) (2024)
- [Building LEGO Using Deep Generative Models of Graphs](https://mlsanity.com/paper/2012.11543/) (2020)
- [Generating Symbolic World Models via Test-time Scaling of Large Language Models](https://mlsanity.com/paper/2502.04728/) (2025)
- [PAPO: Stabilizing Rubric Integration Training via Decoupled Advantage Normalization](https://mlsanity.com/paper/2603.26535/) (2026)
- [Benchmarks for Physical Reasoning AI](https://mlsanity.com/paper/2312.10728/) (2023)
- [VoxelCodeBench: Benchmarking 3D World Modeling Through Code Generation](https://mlsanity.com/paper/2604.02580/) (2026)
- [Symbolic Graphics Programming with Large Language Models](https://mlsanity.com/paper/2509.05208/) (2025)
- [BrickNet: Graph-Backed Generative Brick Assembly](https://mlsanity.com/paper/2604.22984/) (2026)
- [Budget-Aware Sequential Brick Assembly with Efficient Constraint Satisfaction](https://mlsanity.com/paper/2210.01021/) (2022)

## Built on by (most cited first, 1 of 1)

- [ScaffoldM3C: A Multimodal Sequential Monte Carlo Framework for Generative Stable Construction Planning](https://mlsanity.com/paper/2610.00487/) (2026)

## Abstract (arXiv)

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.