BRepAssemblyLLM: Reasoning over BReps for Executable CAD Assembly

CAD assembly requires identifying mating entities between parts and estimating a rigid transformation that yields a valid relative pose. Extending large language models (LLMs) to this task is challenging: native Boundary Representations (BReps) exhibit heterogeneous face–edge graph structures, the candidate mating space grows rapidly with entity count, and assembly inherently couples discrete entity correspondence with continuous pose prediction. We present \method, the first geometry-conditioned LLM framework for pairwise CAD assembly. The framework consists of a topology-aware BRep encoder, a lightweight projector, an LLM, and a CAD assembly executor. Given two CAD parts, the BRep encoder jointly encodes face geometry, edge geometry, and their topological relations, while the projector maps the resulting representations into the LLM embedding space. The LLM then predicts a structured assembly action comprising a pair of mating entities and a rigid transformation matrix specifying their relative pose. Subsequently, the CAD assembly executor executes the predicted action and provides contact and interpenetration feedback, which is used to jointly optimize mating-entity selection and pose prediction via reinforcement learning. On the Fusion 360 Gallery benchmark, \method achieves state-of-the-art performance. These results demonstrate that LLMs can move beyond understanding and generating CAD descriptions or code to directly reason over native BReps and produce executable CAD assembly actions. The code will be released.