Mamba 的上下文学习：面向多任务点云理解的结构感知域泛化
Mamba Learns in Context: Structure-Aware Domain Generalization for Multi-Task Point Cloud Understanding
用基于质心拓扑与测地曲率连续性构造的变换不变序列化替代坐标驱动的序列化，可缓解 Mamba 类点云模型对视角变化与缺失区域的敏感性；其谱域图对齐在测试时无需更新参数即可把目标特征拉向源原型，是一种可直接复用的测试时特征迁移手段。
原文依据 we introduce a lightweight spectral graph alignment (SGA) that shifts target features toward source prototypes in the spectral domain without updating model parameters
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论尽管近期的 Transformer 与 Mamba 架构推动了点云表征学习的发展，但它们通常面向单任务或单域设定设计。将其直接应用于多任务域泛化（DG）会导致性能下降。Transformer 能有效建模全局依赖，但受制于二次注意力开销且缺乏显式的结构顺序；而 Mamba 虽提供线性时间的循环机制，却往往依赖坐标驱动的序列化，该序列化对视角变化和缺失区域敏感，从而引发结构漂移与不稳定的序列建模。本文提出结构感知域泛化（SADG），一个基于 Mamba 的上下文学习框架，可在跨域与跨任务时保持结构层次。我们设计了结构感知序列化（SAS），利用基于质心的拓扑与测地曲率连续性生成变换不变的序列。我们进一步设计了层次化域感知建模（HDM），通过整合域内结构并融合域间关系来稳定跨域推理。在测试阶段，我们引入轻量级的谱图对齐（SGA），在谱域中将目标特征向源原型偏移而无需更新模型参数，从而实现保持结构的测试时特征偏移。此外，我们提出了 MP3DObject，一个用于多任务 DG 评测的真实扫描物体数据集。大量实验表明，所提方法提升了结构保真度，并在重建、去噪与配准等多个任务上持续优于最优方法。
英文原文摘要 1688 字符
While recent Transformer and Mamba architectures have advanced point cloud representation learning, they are typically developed for single-task or single-domain settings. Directly applying them to multi-task domain generalization (DG) leads to degraded performance. Transformers effectively model global dependencies but suffer from quadratic attention cost and lack explicit structural ordering, whereas Mamba offers linear-time recurrence yet often depends on coordinate-driven serialization, which is sensitive to viewpoint changes and missing regions, causing structural drift and unstable sequential modeling. In this paper, we propose Structure-Aware Domain Generalization (SADG), a Mamba-based In-Context Learning framework that preserves structural hierarchy across domains and tasks. We design structure-aware serialization (SAS) that generates transformation-invariant sequences using centroid-based topology and geodesic curvature continuity. We further devise hierarchical domain-aware modeling (HDM) that stabilizes cross-domain reasoning by consolidating intra-domain structure and fusing inter-domain relations. At test time, we introduce a lightweight spectral graph alignment (SGA) that shifts target features toward source prototypes in the spectral domain without updating model parameters, ensuring structure-preserving test-time feature shifting. In addition, we introduce MP3DObject, a real-scan object dataset for multi-task DG evaluation. Comprehensive experiments demonstrate that the proposed approach improves structural fidelity and consistently outperforms state-of-the-art methods across multiple tasks including reconstruction, denoising, and registration.