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Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to…

Machine Learning · Computer Science 2024-07-04 Kaiying Hou , David Brandfonbrener , Sham Kakade , Samy Jelassi , Eran Malach

Recent work has shown that Transformers trained from scratch can successfully solve various arithmetic and algorithmic tasks, such as adding numbers and computing parity. While these Transformers generalize well on unseen inputs of the same…

Machine Learning · Computer Science 2025-05-13 Ying Fan , Yilun Du , Kannan Ramchandran , Kangwook Lee

Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness. However, whether Transformers can learn to generalize to CoT traces longer than…

Machine Learning · Computer Science 2026-04-29 Oliver Kraus , Yash Sarrof , Yuekun Yao , Alexander Koller , Michael Hahn

Mathematical reasoning is one of the most impressive achievements of human intellect but remains a formidable challenge for artificial intelligence systems. In this work we explore whether modern deep learning architectures can learn to…

Machine Learning · Computer Science 2022-07-07 Samuel Cognolato , Alberto Testolin

The Transformer based neural networks have been showing significant advantages on most evaluations of various natural language processing and other sequence-to-sequence tasks due to its inherent architecture based superiorities. Although…

Computation and Language · Computer Science 2019-10-31 Hailiang Li , Adele Y. C. Wang , Yang Liu , Du Tang , Zhibin Lei , Wenye Li

There has been great progress in unifying various table-to-text tasks using a single encoder-decoder model trained via multi-task learning (Xie et al., 2022). However, existing methods typically encode task information with a simple dataset…

Computation and Language · Computer Science 2022-12-20 Jifan Chen , Yuhao Zhang , Lan Liu , Rui Dong , Xinchi Chen , Patrick Ng , William Yang Wang , Zhiheng Huang

Large language models demonstrate the intriguing ability to perform unseen tasks via in-context learning. However, it remains unclear what mechanisms inside the model drive such task-level generalization. In this work, we approach this…

Computation and Language · Computer Science 2026-03-05 Qinyuan Ye , Robin Jia , Xiang Ren

Transformer network architecture has proven effective in speech enhancement. However, as its core module, self-attention suffers from quadratic complexity, making it infeasible for training on long speech utterances. In practical scenarios,…

Audio and Speech Processing · Electrical Eng. & Systems 2025-06-10 Qiquan Zhang , Hongxu Zhu , Xinyuan Qian , Eliathamby Ambikairajah , Haizhou Li

Transformer models are permutation equivariant. To supply the order and type information of the input tokens, position and segment embeddings are usually added to the input. Recent works proposed variations of positional encodings with…

Computation and Language · Computer Science 2021-11-04 Pu-Chin Chen , Henry Tsai , Srinadh Bhojanapalli , Hyung Won Chung , Yin-Wen Chang , Chun-Sung Ferng

Preventing the performance decay of Transformers on inputs longer than those used for training has been an important challenge in extending the context length of these models. Though the Transformer architecture has fundamentally no limits…

Transformers are widely deployed in large language models (LLMs), yet most models still fail on basic arithmetic tasks such as multidigit addition. In contrast, we show that small transformers trained from scratch can solve n-digit addition…

Machine Learning · Computer Science 2025-10-06 Philip Quirke , Clement Neo , Fazl Barez

Meta-learning has proven to be a powerful paradigm for transferring the knowledge from previous tasks to facilitate the learning of a novel task. Current dominant algorithms train a well-generalized model initialization which is adapted to…

Machine Learning · Computer Science 2021-06-11 Huaxiu Yao , Longkai Huang , Linjun Zhang , Ying Wei , Li Tian , James Zou , Junzhou Huang , Zhenhui Li

Length generalization, the ability to generalize from small training context sizes to larger ones, is a critical challenge in the development of Transformer-based language models. Positional encoding (PE) has been identified as a major…

Computation and Language · Computer Science 2023-11-08 Amirhossein Kazemnejad , Inkit Padhi , Karthikeyan Natesan Ramamurthy , Payel Das , Siva Reddy

Positional encodings enable Transformers to incorporate sequential information, yet their theoretical understanding remains limited to two properties: distance attenuation and translation invariance. Because natural language lacks purely…

Machine Learning · Computer Science 2026-02-11 Zihan Gu , Ruoyu Chen , Han Zhang , Hua Zhang , Yue Hu

Position modeling plays a critical role in Transformers. In this paper, we focus on length extrapolation, i.e., training on short texts while evaluating longer sequences. We define attention resolution as an indicator of extrapolation. Then…

Computation and Language · Computer Science 2022-12-21 Yutao Sun , Li Dong , Barun Patra , Shuming Ma , Shaohan Huang , Alon Benhaim , Vishrav Chaudhary , Xia Song , Furu Wei

Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…

Populations and Evolution · Quantitative Biology 2012-04-16 Ilmari Karonen

Large Language Models (LLMs) have made significant strides in natural language processing, and a precise understanding of the internal mechanisms driving their success is essential. In this work, we analyze the trajectories of token…

Machine Learning · Computer Science 2025-03-06 Murdock Aubry , Haoming Meng , Anton Sugolov , Vardan Papyan

Positional encoding plays a crucial role in transformers, significantly impacting model performance and length generalization. Prior research has introduced absolute positional encoding (APE) and relative positional encoding (RPE) to…

Computation and Language · Computer Science 2024-11-06 Chuanyang Zheng , Yihang Gao , Han Shi , Minbin Huang , Jingyao Li , Jing Xiong , Xiaozhe Ren , Michael Ng , Xin Jiang , Zhenguo Li , Yu Li

Due to long-distance correlation and powerful pretrained models, transformer-based methods have initiated a breakthrough in visual object tracking performance. Previous works focus on designing effective architectures suited for tracking,…

Computer Vision and Pattern Recognition · Computer Science 2023-09-18 Jie Zhao , Johan Edstedt , Michael Felsberg , Dong Wang , Huchuan Lu

Length generalization is the ability of language models to maintain performance on inputs longer than those seen during pretraining. In this work, we introduce a simple yet powerful position encoding (PE) strategy, Random Float Sampling…

Machine Learning · Computer Science 2026-02-17 Atsushi Shimizu , Shohei Taniguchi , Yutaka Matsuo