Integrating Locality-Aware Attention with Transformers for General Geometry PDEs

Neural operators have emerged as promising frameworks for learning mappings governed by partial differential equations (PDEs), serving as data-driven alternatives to traditional numerical methods. While methods such as the Fourier neural operator (FNO) have demonstrated notable performance, their reliance on uniform grids restricts their applicability to complex geometries and irregular meshes. Recently, Transformer-based neural operators with linear attention mechanisms have shown potential in overcoming these limitations for large-scale PDE simulations. However, these approaches predominantly emphasize global feature aggregation, often overlooking fine-scale dynamics and localized PDE behaviors essential for accurate solutions. To address these challenges, we propose the Locality-Aware Attention Transformer (LA2Former), which leverages K-nearest neighbors for dynamic patchifying and integrates global-local attention for enhanced PDE modeling. By combining linear attention for efficient global context encoding with pairwise attention for capturing intricate local interactions, LA2Former achieves an optimal balance between computational efficiency and predictive accuracy. Extensive evaluations across six benchmark datasets demonstrate that LA2Former improves predictive accuracy by over 50% relative to existing linear attention methods, while also outperforming full pairwise attention under optimal conditions. This work underscores the critical importance of localized feature learning in advancing Transformer-based neural operators for solving PDEs on complex and irregular domains.

TE-TAD: Towards Full End-to-End Temporal Action Detection via Time-Aligned Coordinate Expression

In this paper, we investigate that the normalized coordinate expression is a key factor as reliance on hand-crafted components in query-based detectors for temporal action detection (TAD). Despite significant advancements towards an end-to-end framework in object detection, query-based detectors have been limited in achieving full end-to-end modeling in TAD. To address this issue, we propose \modelname{}, a full end-to-end temporal action detection transformer that integrates time-aligned coordinate expression. We reformulate coordinate expression utilizing actual timeline values, ensuring length-invariant representations from the extremely diverse video duration environment. Furthermore, our proposed adaptive query selection dynamically adjusts the number of queries based on video length, providing a suitable solution for varying video durations compared to a fixed query set. Our approach not only simplifies the TAD process by eliminating the need for hand-crafted components but also significantly improves the performance of query-based detectors. Our TE-TAD outperforms the previous query-based detectors and achieves competitive performance compared to state-of-the-art methods on popular benchmark datasets. Code is available at: https://github.com/Dotori-HJ/TE-TAD