Transformers rely on position embedding mechanisms in long context modeling in most cases. Rotary Position Embedding (RoPE) embeds positional information with independent 2D rotations, forming relative position terms in self-attention. However, its pairwise, block-based, and decoupled structure limits deep mixing and robustness across channels. We propose HD-RoPE, which extends RoPE from independent 2D rotations to higher-dimensional rotations and introduces a Paley-I orthogonal basis to obtain balanced, isotropic, and dense phase mixing within each rotation subspace. This significantly enhances channel coupling and rotational degrees of freedom while maintaining orthogonal stability and the relative position closure property. Furthermore, HD-RoPE is easily optimized for engineering efficiency without introducing additional trainable parameters. We have conducted extensive evaluation results demonstrating that HD-RoPE achieves significant performance improvements over standard RoPE across various popular benchmarks and in both long and short contexts.
Link prediction aims to identify potential or future connections within a given graph structure. Position information is essential for link prediction, as it distinguishes homogeneous nodes through their relative relationships, facilitating the accurate capture of structural patterns and implicit connections. Previous studies derive node positional information as distances to single-granularity landmarks, defined as the centers of homophilic regions, while neglecting the multi-granularity nature of homophilic structures and their hierarchical interrelations. We propose the Multi-Granularity Position Embedding of Graphs via Granular-Ball for Link Prediction (MGLP) method to obtain multi-granularity position embedding of graphs. Specifically, MGLP introduces an Adaptive Granular-Ball Graph Refinement mechanism to adaptively refine the graph into homophilic subdomains with optimal levels of granularity. The central nodes within subdomains are treated as landmarks, which form a Hierarchical Central Graph. Moreover, a novel Multi-granularity Hierarchical Distance encoding mechanism is proposed to capture both the homophilic structures within a graph and their hierarchical correlations, improving the discriminative power of nodes. Experimental results demonstrate that the multi-granularity position embedding generated by our method exhibits excellent performance and strong competitiveness compared to baseline algorithms for link prediction. Our codes are available in https://anonymous.4open.science/r/MGLP-D3C5/.
Panoptic segmentation in complex scenes remains challenging because of occlusions, yet modern approaches often neglect occlusion modelling. In this paper, we propose Position Embedding Modulation with Occlusion Level Attention (PEMOLA), a novel occlusion-aware module that can be seamlessly integrated into transformer-based panoptic segmentation. To obtain occlusion cues, we train an occlusion classifier on the COCO-OLAC dataset. The classifier derives the occlusion-level attention, which serves as spatial guidance, while the occlusion labels are encoded into a learnable embedding to produce channel-wise weights. Through joint modulation, PEMOLA elegantly introduces the occlusion priors into the position embedding, thereby improving the occlusion modelling. We further annotate the Cityscapes dataset with occlusion levels, termed Cityscapes Occlusion Labels for All Computer Vision Tasks (Cityscapes-OLAC), following the same labelling protocol as COCO-OLAC, to evaluate the cross-dataset generalisation ability of PEMOLA. Extensive experiments on COCO-OLAC and Cityscapes-OLAC demonstrate that PEMOLA consistently improves panoptic segmentation quality while introducing minimal computational overhead. These results highlight the importance of occlusion modelling, where incorporating occlusion-level attention helps deliver robust panoptic segmentation under occlusion. Code and dataset are available at https://github.com/wenbo-wei/PEMOLA.
Rotary Position Embedding (RoPE) is widely adopted in Transformer models, yet its extension to high-dimensional domains lacks a unified theoretical formulation. Most existing approaches either apply rotations independently along each axis or empirically mix frequencies, which limits cross-dimensional interactions and yields direction-dependent representations. To address these limitations, we propose nD-RoPE, a decomposition-free generalization of RoPE to arbitrary dimensions. From a translation-invariant formulation in continuous Hilbert space, we derive a spectral condition for isotropy that requires treating positions and frequencies as coupled \(n\)-dimensional vectors. We instantiate this formulation with a multi-scale regular-simplex wave-vector design, which provides non-degenerate spatial coverage and a symmetric, directionally balanced second-order response. Experiments across images, videos, and point clouds demonstrate consistent performance gains and improved generalization in high-dimensional settings.