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Transformers excel through content-addressable retrieval and the ability to exploit contexts of, in principle, unbounded length. We recast associative memory at the level of probability measures, treating a context as a distribution over…

Machine Learning · Statistics 2026-02-03 Ryotaro Kawata , Taiji Suzuki

Do autoregressive Transformer language models require explicit positional encodings (PEs)? The answer is 'no' provided they have more than one layer -- they can distinguish sequences with permuted tokens without the need for explicit PEs.…

Machine Learning · Computer Science 2025-06-03 Kazuki Irie

Transformer architectures rely on explicit position encodings in order to preserve a notion of word order. In this paper, we argue that existing work does not fully utilize position information. For example, the initial proposal of a…

Computation and Language · Computer Science 2020-09-30 Zhiheng Huang , Davis Liang , Peng Xu , Bing Xiang

Multi-head self-attention-based Transformers have shown promise in different learning tasks. Albeit these models exhibit significant improvement in understanding short-term and long-term contexts from sequences, encoders of Transformers and…

Computation and Language · Computer Science 2023-10-24 Ayan Sengupta , Md Shad Akhtar , Tanmoy Chakraborty

Positional encoding (PE) is a core architectural component of Transformers, yet its impact on the Transformer's generalization and robustness remains unclear. In this work, we provide the first generalization analysis for a single-layer…

Machine Learning · Statistics 2026-03-25 Weiyi He , Yue Xing

Many recent text-to-speech (TTS) systems are built on transformer architectures and employ cross-attention mechanisms for text-speech alignment. Within these systems, rotary position embedding (RoPE) is commonly used to encode positional…

Audio and Speech Processing · Electrical Eng. & Systems 2025-09-16 Hyeongju Kim , Juheon Lee , Jinhyeok Yang , Jacob Morton

Transformer is the backbone of modern NLP models. In this paper, we propose RealFormer, a simple and generic technique to create Residual Attention Layer Transformer networks that significantly outperform the canonical Transformer and its…

Machine Learning · Computer Science 2021-09-14 Ruining He , Anirudh Ravula , Bhargav Kanagal , Joshua Ainslie

Linear attention has emerged as a promising direction for scaling Vision Transformers beyond the quadratic cost of dense self-attention. A prevalent strategy is to compress spatial tokens into a compact set of intermediate proxies that…

Computer Vision and Pattern Recognition · Computer Science 2026-05-15 Yuntong Li , Hainuo Wang , Hengxing Liu , Mingjia Li , Xiaojie Guo

We introduce a new way of learning to encode position information for non-recurrent models, such as Transformer models. Unlike RNN and LSTM, which contain inductive bias by loading the input tokens sequentially, non-recurrent models are…

Machine Learning · Computer Science 2020-03-23 Xuanqing Liu , Hsiang-Fu Yu , Inderjit Dhillon , Cho-Jui Hsieh

Existing research largely attributes the global sequence modeling capability of Transformers to the explicit computation of attention weights, a process that inherently incurs quadratic computational complexity. In this work, we offer a…

Computer Vision and Pattern Recognition · Computer Science 2026-05-07 Ruize He , Dongchen Han , Gao Huang

Tables are ubiquitous across various domains for concisely representing structured information. Empowering large language models (LLMs) to reason over tabular data represents an actively explored direction. However, since typical LLMs only…

Computation and Language · Computer Science 2024-10-21 Jia-Nan Li , Jian Guan , Wei Wu , Zhengtao Yu , Rui Yan

In sequence to sequence learning, the self-attention mechanism proves to be highly effective, and achieves significant improvements in many tasks. However, the self-attention mechanism is not without its own flaws. Although self-attention…

Computation and Language · Computer Science 2019-11-22 Guangxiang Zhao , Xu Sun , Jingjing Xu , Zhiyuan Zhang , Liangchen Luo

Recently, the Transformer model that is based solely on attention mechanisms, has advanced the state-of-the-art on various machine translation tasks. However, recent studies reveal that the lack of recurrence hinders its further improvement…

Computation and Language · Computer Science 2019-04-08 Jie Hao , Xing Wang , Baosong Yang , Longyue Wang , Jinfeng Zhang , Zhaopeng Tu

Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale regimes. While Transformer-based neural…

Machine Learning · Computer Science 2026-03-04 Pengyu Lai , Yixiao Chen , Dewu Yang , Rui Wang , Feng Wang , Hui Xu

Length generalization, defined as the ability to extrapolate from shorter training sequences to longer test ones, is a significant challenge for language models. This issue persists even with large-scale Transformers handling relatively…

Machine Learning · Computer Science 2024-02-15 Yongchao Zhou , Uri Alon , Xinyun Chen , Xuezhi Wang , Rishabh Agarwal , Denny Zhou

Despite the significant progress made by transformer models in machine reading comprehension tasks, they still fall short in handling complex reasoning tasks due to the absence of explicit knowledge in the input sequence. To address this…

Computation and Language · Computer Science 2024-01-17 Shima Foolad , Kourosh Kiani

Rotary Position Embedding (RoPE) is the de facto positional encoding in large language models due to its ability to encode relative positions and support length extrapolation. When adapted to vision transformers, the standard axial…

Computer Vision and Pattern Recognition · Computer Science 2026-02-04 Haoyu Liu , Sucheng Ren , Tingyu Zhu , Peng Wang , Cihang Xie , Alan Yuille , Zeyu Zheng , Feng Wang

We investigate the universal approximation property (UAP) of transformer-type architectures, providing a unified theoretical framework that extends prior results on residual networks to models incorporating attention mechanisms. Our work…

Machine Learning · Computer Science 2025-10-22 Jingpu Cheng , Ting Lin , Zuowei Shen , Qianxiao Li

This study reports an unintuitive finding that positional encoding enhances learning of recurrent neural networks (RNNs). Positional encoding is a high-dimensional representation of time indices on input data. Most famously, positional…

Machine Learning · Computer Science 2024-11-28 Takashi Morita

Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of…

Machine Learning · Computer Science 2026-03-04 Linyan Gu , Lihua Yang , Feng Zhou