Open-Vocabulary 3D Part Segmentation with Semantic Propagation Hawkes Process

Existing open-vocabulary 3D part segmentation methods typically rely on point–text matching, where semantic organization is shaped implicitly by the training loss, and both training and inference lack an explicit forward semantic optimization mechanism. We address this limitation with a framework of forward semantic dynamics, implemented with coupled semantic-dynamics blocks that organize part semantics within a single forward pass. Specifically, differentiable forward low-rank semantic shaping constrains point features to a prompt-conditioned semantic subspace, suppressing semantic drift and improving intra-part consistency. Built on this shaped state, a finite-depth spatial Hawkes process for semantic propagation models high-confidence prompt responses as sparse semantic events and propagates them across multiple steps to provide reliable evidence for ambiguous regions. The propagated context is further fed back into later feature shaping, coupling semantic organization and evidence propagation without test-time iterative optimization or additional post-processing. Extensive experiments on multiple open-vocabulary 3D part segmentation benchmarks show that our method establishes a new state of the art, outperforming the previous comparable SOTA method on all 16 reported evaluation slices by 1.88 to 5.31 mIoU points (3.84 on average) and achieving the overall best results on 14 of them.