Cederik Höfs | Searcharxiv

arXiv2026

Rotary Position Encodings for Graphs

We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting performance in synthetic and real-world graph learning tasks. This approach, coined _Wave-Induced Rotary Encodings_ (WIRE), enjoys intriguing theoretical properties: it recovers regular RoPE on grids, and depends asymptotically on the graph effective resistance. Unlike bias-based relative position encodings, WIRE is compatible with linear attention.

cs.LG↗

arXiv2025

Statistical Reconstruction For Anisotropic X-ray Dark-Field Tomography

Anisotropic X-ray Dark-Field Tomography (AXDT) is a novel imaging technology that enables the extraction of fiber structures on the micrometer scale, far smaller than standard X-ray Computed Tomography (CT) setups. Directional and structural information is relevant in medical diagnostics and material testing. Compared to existing solutions, AXDT could prove a viable alternative. Reconstruction methods in AXDT have so far been driven by practicality. Improved methods could make AXDT more accessible. We contribute numerically stable implementations and validation of advanced statistical reconstruction methods that incorporate the statistical noise behavior of the imaging system. We further provide a new statistical reconstruction formulation that retains the advanced noise assumptions of the imaging setup while being efficient and easy to optimize. Finally, we provide a detailed analysis of the optimization behavior for all models regarding AXDT. Our experiments show that statistical reconstruction outperforms the previously used model, and particularly the noise performance is superior. While the previously proposed statistical method is effective, it is computationally expensive, and our newly proposed formulation proves highly efficient with identical performance. Our theoretical analysis opens the possibility to new and more advanced reconstruction algorithms, which in turn enable future research in AXDT.

cs.CE↗