PoPE: Legendre Orthogonal Polynomials Based Position Encoding for Large Language Models

There are several improvements proposed over the baseline Absolute Positional Encoding (APE) method used in original transformer. In this study, we aim to investigate the implications of inadequately representing positional encoding in higher dimensions on crucial aspects of the attention mechanism, the model's capacity to learn relative positional information, and the convergence of models, all stemming from the choice of sinusoidal basis functions. Through a combination of theoretical insights and empirical analyses, we elucidate how these challenges extend beyond APEs and may adversely affect the performance of Relative Positional Encoding (RPE) methods, such as Rotatory Positional Encoding (RoPE). Subsequently, we introduce an innovative solution termed Orthogonal Polynomial Based Positional Encoding (PoPE) to address some of the limitations associated with existing methods. The PoPE method encodes positional information by leveraging Orthogonal Legendre polynomials. Legendre polynomials as basis functions offers several desirable properties for positional encoding, including improved correlation structure, non-periodicity, orthogonality, and distinct functional forms among polynomials of varying orders. Our experimental findings demonstrate that transformer models incorporating PoPE outperform baseline transformer models on the $Multi30k$ English-to-German translation task, thus establishing a new performance benchmark. Furthermore, PoPE-based transformers exhibit significantly accelerated convergence rates. Additionally, we will present novel theoretical perspectives on position encoding based on the superior performance of PoPE.

Breast Cancer Immunohistochemical Image Generation: a Benchmark Dataset and Challenge Review

For invasive breast cancer, immunohistochemical (IHC) techniques are often used to detect the expression level of human epidermal growth factor receptor-2 (HER2) in breast tissue to formulate a precise treatment plan. From the perspective of saving manpower, material and time costs, directly generating IHC-stained images from hematoxylin and eosin (H&E) stained images is a valuable research direction. Therefore, we held the breast cancer immunohistochemical image generation challenge, aiming to explore novel ideas of deep learning technology in pathological image generation and promote research in this field. The challenge provided registered H&E and IHC-stained image pairs, and participants were required to use these images to train a model that can directly generate IHC-stained images from corresponding H&E-stained images. We selected and reviewed the five highest-ranking methods based on their PSNR and SSIM metrics, while also providing overviews of the corresponding pipelines and implementations. In this paper, we further analyze the current limitations in the field of breast cancer immunohistochemical image generation and forecast the future development of this field. We hope that the released dataset and the challenge will inspire more scholars to jointly study higher-quality IHC-stained image generation.