Yi Yang

Meiling Wang, Guangyan Chen, Yi Yang et al.

Point cloud registration is a fundamental task in the fields of computer vision and robotics. Recent developments in transformer-based methods have demonstrated enhanced performance in this domain. However, the standard attention mechanism utilized in these methods often integrates many low-relevance points, thereby struggling to prioritize its attention weights on sparse yet meaningful points. This inefficiency leads to limited local structure modeling capabilities and quadratic computational complexity. To overcome these limitations, we propose the Point Tree Transformer (PTT), a novel transformer-based approach for point cloud registration that efficiently extracts comprehensive local and global features while maintaining linear computational complexity. The PTT constructs hierarchical feature trees from point clouds in a coarse-to-dense manner, and introduces a novel Point Tree Attention (PTA) mechanism, which follows the tree structure to facilitate the progressive convergence of attended regions towards salient points. Specifically, each tree layer selectively identifies a subset of key points with the highest attention scores. Subsequent layers focus attention on areas of significant relevance, derived from the child points of the selected point set. The feature extraction process additionally incorporates coarse point features that capture high-level semantic information, thus facilitating local structure modeling and the progressive integration of multiscale information. Consequently, PTA empowers the model to concentrate on crucial local structures and derive detailed local information while maintaining linear computational complexity. Extensive experiments conducted on the 3DMatch, ModelNet40, and KITTI datasets demonstrate that our method achieves superior performance over the state-of-the-art methods.

Xihang Yue, Yi Yang, Linchao Zhu

The limited availability of high-quality training data poses a major obstacle in data-driven PDE solving, where expensive data collection and resolution constraints severely impact the ability of neural operator networks to learn and generalize the underlying physical system. To address this challenge, we propose DeltaPhi, a novel learning framework that transforms the PDE solving task from learning direct input-output mappings to learning the residuals between similar physical states, a fundamentally different approach to neural operator learning. This reformulation provides implicit data augmentation by exploiting the inherent stability of physical systems where closer initial states lead to closer evolution trajectories. DeltaPhi is architecture-agnostic and can be seamlessly integrated with existing neural operators to enhance their performance. Extensive experiments demonstrate consistent and significant improvements across diverse physical systems including regular and irregular domains, different neural architectures, multiple training data amount, and cross-resolution scenarios, confirming its effectiveness as a general enhancement for neural operators in data-limited PDE solving.