Large language models (LLMs), although having revolutionized many fields, still suffer from the challenging extrapolation problem, where the inference ability of LLMs sharply declines beyond their max training lengths. In this work, we conduct a theoretical analysis to better understand why No Position Encoding (NoPE) fails outside its effective range, as well as examining the power of Position Encoding (PE) in this context. Our findings reveal that with meticulous weave position, PE can indeed be extended beyond effective range. Our theorems establish that LLMs equipped with weave PE can achieve improved extrapolation performance without additional cost. Furthermore, we introduce a novel weave PE method, Mesa-Extrapolation, which utilizes a chunk-based triangular attention matrix and applies Stair PE to manage the final chunk. This method not only retains competitive performance but also offers substantial benefits such as significantly reduced memory demand and faster inference speed.

Language model architectures are predominantly first created for English and subsequently applied to other languages. It is an open question whether this architectural bias leads to degraded performance for languages that are structurally different from English. We examine one specific architectural choice: positional encodings, through the lens of the trade-off hypothesis: the supposed interplay between morphological complexity and word order flexibility. This hypothesis posits a trade-off between the two: a more morphologically complex language can have a more flexible word order, and vice-versa. Positional encodings are a direct target to investigate the implications of this hypothesis in relation to language modelling. We pretrain monolingual model variants with absolute, relative, and no positional encodings for seven typologically diverse languages and evaluate them on four downstream tasks. Contrary to previous findings, we do not observe a clear interaction between position encodings and morphological complexity or word order flexibility, as measured by various proxies. Our results show that the choice of tasks, languages, and metrics are essential for drawing stable conclusions

This paper presents ViRanker, a cross-encoder reranking model tailored to the Vietnamese language. Built on the BGE-M3 encoder and enhanced with the Blockwise Parallel Transformer, ViRanker addresses the lack of competitive rerankers for Vietnamese, a low-resource language with complex syntax and diacritics. The model was trained on an 8 GB curated corpus and fine-tuned with hybrid hard-negative sampling to strengthen robustness. Evaluated on the MMARCO-VI benchmark, ViRanker achieves strong early-rank accuracy, surpassing multilingual baselines and competing closely with PhoRanker. By releasing the model openly on Hugging Face, we aim to support reproducibility and encourage wider adoption in real-world retrieval systems. Beyond Vietnamese, this study illustrates how careful architectural adaptation and data curation can advance reranking in other underrepresented languages.

Vision transformers have demonstrated significant advantages in computer vision tasks due to their ability to capture long-range dependencies and contextual relationships through self-attention. However, existing position encoding techniques, which are largely borrowed from natural language processing, fail to effectively capture semantic-aware positional relationships between image patches. Traditional approaches like absolute position encoding and relative position encoding primarily focus on 1D linear position relationship, often neglecting the semantic similarity between distant yet contextually related patches. These limitations hinder model generalization, translation equivariance, and the ability to effectively handle repetitive or structured patterns in images. In this paper, we propose 2-Dimensional Semantic-Aware Position Encoding ($\text{SaPE}^2$), a novel position encoding method with semantic awareness that dynamically adapts position representations by leveraging local content instead of fixed linear position relationship or spatial coordinates. Our method enhances the model's ability to generalize across varying image resolutions and scales, improves translation equivariance, and better aggregates features for visually similar but spatially distant patches. By integrating $\text{SaPE}^2$ into vision transformers, we bridge the gap between position encoding and perceptual similarity, thereby improving performance on computer vision tasks.

Vision-language Models (VLMs) have shown remarkable capabilities in advancing general artificial intelligence, yet the irrational encoding of visual positions persists in inhibiting the models' comprehensive perception performance across different levels of granularity. In this work, we propose Pyramid-descent Visual Position Encoding (PyPE), a novel approach designed to enhance the perception of visual tokens within VLMs. By assigning visual position indexes from the periphery to the center and expanding the central receptive field incrementally, PyPE addresses the limitations of traditional raster-scan methods and mitigates the long-term decay effects induced by Rotary Position Embedding (RoPE). Our method reduces the relative distance between interrelated visual elements and instruction tokens, promoting a more rational allocation of attention weights and allowing for a multi-granularity perception of visual elements and countering the over-reliance on anchor tokens. Extensive experimental evaluations demonstrate that PyPE consistently improves the general capabilities of VLMs across various sizes. Code is available at https://github.com/SakuraTroyChen/PyPE.

We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides exact translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers. We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods.

While Rotary Position Embeddings (RoPE) for natural language performs well and has become widely adopted, its adoption for other modalities has been slower. Here, we introduce Lie group Relative position Encodings (LieRE) that goes beyond RoPE in supporting higher dimensional inputs. We evaluate the performance of LieRE on 2D and 3D image classification tasks and observe that LieRE leads to marked improvements in performance (up to 6%), training efficiency (3.5x reduction), data efficiency (30%) compared to the baselines of RoFormer, DeiT III, RoPE-Mixed and Vision-Llama.

Transformers have demonstrated outstanding performance in many applications of deep learning. When applied to time series data, transformers require effective position encoding to capture the ordering of the time series data. The efficacy of position encoding in time series analysis is not well-studied and remains controversial, e.g., whether it is better to inject absolute position encoding or relative position encoding, or a combination of them. In order to clarify this, we first review existing absolute and relative position encoding methods when applied in time series classification. We then proposed a new absolute position encoding method dedicated to time series data called time Absolute Position Encoding (tAPE). Our new method incorporates the series length and input embedding dimension in absolute position encoding. Additionally, we propose computationally Efficient implementation of Relative Position Encoding (eRPE) to improve generalisability for time series. We then propose a novel multivariate time series classification (MTSC) model combining tAPE/eRPE and convolution-based input encoding named ConvTran to improve the position and data embedding of time series data. The proposed absolute and relative position encoding methods are simple and efficient. They can be easily integrated into transformer blocks and used for downstream tasks such as forecasting, extrinsic regression, and anomaly detection. Extensive experiments on 32 multivariate time-series datasets show that our model is significantly more accurate than state-of-the-art convolution and transformer-based models. Code and models are open-sourced at \url{https://github.com/Navidfoumani/ConvTran}.