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There is a growing interest in the ability of neural networks to execute algorithmic tasks (e.g., arithmetic, summary statistics, and sorting). The goal of this work is to better understand the role of attention in Transformers for…

Machine Learning · Computer Science 2025-06-11 Artur Back de Luca , George Giapitzakis , Shenghao Yang , Petar Veličković , Kimon Fountoulakis

We introduce $\Sigma$-Attention, a Transformer-based operator-learning framework to address a key computational challenge in correlated materials. Our approach utilizes an Encoder-Only Transformer as an ansatz to approximate the self-energy…

Strongly Correlated Electrons · Physics 2025-06-02 Yuanran Zhu , Peter Rosenberg , Zhen Huang , Hardeep Bassi , Chao Yang , Shiwei Zhang

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

Computer Vision and Pattern Recognition · Computer Science 2016-04-18 Stephan Zheng , Yang Song , Thomas Leung , Ian Goodfellow

Reinforcement Learning with Verifiable Rewards (RLVR) serves as a cornerstone technique for enhancing the reasoning capabilities of Large Language Models (LLMs). However, its training is often plagued by \emph{entropy collapse}, a rapid…

Machine Learning · Computer Science 2026-04-30 Zhezheng Hao , Hong Wang , Haoyang Liu , Jian Luo , Jiarui Yu , Hande Dong , Qiang Lin , Can Wang , Jiawei Chen

Selective attention helps us focus on task-relevant aspects in the constant flood of our sensory input. This constraint in our perception allows us to robustly generalize under distractions and to new compositions of perceivable concepts.…

Computer Vision and Pattern Recognition · Computer Science 2024-09-17 Ankit Vani , Bac Nguyen , Samuel Lavoie , Ranjay Krishna , Aaron Courville

Previous work on the learnability of transformers \textemdash\ focused primarily on examining their ability to approximate specific algorithmic patterns through training \textemdash\ has largely been data-driven, offering only probabilistic…

Machine Learning · Computer Science 2026-04-23 Debanjan Dutta , Anish Chakrabarty , Faizanuddin Ansari , Swagatam Das

We characterize the pre-softmax attention matrix $\mathbf{QK^\top}$ in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric…

Machine Learning · Computer Science 2026-05-28 Hyunmin Cho , Woo Kyoung Han , Kyong Hwan Jin

The evolution of large language models (LLMs) towards applications with ultra-long contexts faces challenges posed by the high computational and memory costs of the Transformer architecture. While existing sparse and linear attention…

Continual learning (CL) empowers AI systems to progressively acquire knowledge from non-stationary data streams. However, catastrophic forgetting remains a critical challenge. In this work, we identify attention drift in Vision Transformers…

Computer Vision and Pattern Recognition · Computer Science 2026-02-06 Yue Lu , Xiangyu Zhou , Shizhou Zhang , Yinghui Xing , Guoqiang Liang , Wencong Zhang

Self-attention is essential to Transformer architectures, yet how information is embedded in the self-attention matrices and how different objective functions impact this process remains unclear. We present a mathematical framework to…

Machine Learning · Computer Science 2025-06-04 Matteo Saponati , Pascal Sager , Pau Vilimelis Aceituno , Thilo Stadelmann , Benjamin Grewe

Recently, DeepNorm scales Transformers into extremely deep (i.e., 1000 layers) and reveals the promising potential of deep scaling. To stabilize the training of deep models, DeepNorm (Wang et al., 2022) attempts to constrain the model…

Machine Learning · Computer Science 2023-05-05 Yijin Liu , Xianfeng Zeng , Fandong Meng , Jie Zhou

Transformer-based sequential recommendation (SR) has been booming in recent years, with the self-attention mechanism as its key component. Self-attention has been widely believed to be able to effectively select those informative and…

Information Retrieval · Computer Science 2024-03-19 Peilin Zhou , Qichen Ye , Yueqi Xie , Jingqi Gao , Shoujin Wang , Jae Boum Kim , Chenyu You , Sunghun Kim

We introduce the Momentum Transformer, an attention-based deep-learning architecture, which outperforms benchmark time-series momentum and mean-reversion trading strategies. Unlike state-of-the-art Long Short-Term Memory (LSTM)…

Machine Learning · Computer Science 2022-11-24 Kieran Wood , Sven Giegerich , Stephen Roberts , Stefan Zohren

Recent analysis on the training dynamics of Transformers has unveiled an interesting characteristic: the training loss plateaus for a significant number of training steps, and then suddenly (and sharply) drops to near--optimal values. To…

Machine Learning · Computer Science 2024-10-30 Pulkit Gopalani , Ekdeep Singh Lubana , Wei Hu

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Image and Video Processing · Electrical Eng. & Systems 2024-07-10 Mehrsa Pourya , Sebastian Neumayer , Michael Unser

In-context learning (ICL) is a cornerstone of large language model (LLM) functionality, yet its theoretical foundations remain elusive due to the complexity of transformer architectures. In particular, most existing work only theoretically…

Machine Learning · Computer Science 2024-09-18 Siyu Chen , Heejune Sheen , Tianhao Wang , Zhuoran Yang

Transformers have demonstrated exceptional in-context learning capabilities, yet the theoretical understanding of the underlying mechanisms remains limited. A recent work (Elhage et al., 2021) identified a ``rich'' in-context mechanism…

Machine Learning · Computer Science 2025-01-30 Mingze Wang , Ruoxi Yu , Weinan E , Lei Wu

Softmax Self-Attention (SSA) is a key component of Transformer architectures. However, when utilised within skipless architectures, which aim to improve representation learning, recent work has highlighted the inherent instability of SSA…

Machine Learning · Computer Science 2026-02-06 Leo Zhang , James Martens

The decoder-only Transformer architecture with causal masking and relative position encoding (RPE) has become the de facto choice in language modeling. Despite its exceptional performance across various tasks, we have identified two…

Computation and Language · Computer Science 2024-02-08 Qingyu Yin , Xuzheng He , Xiang Zhuang , Yu Zhao , Jianhua Yao , Xiaoyu Shen , Qiang Zhang

While the Self-Attention mechanism in the Transformer model has proven to be effective in many domains, we observe that it is less effective in more diverse settings (e.g. multimodality) due to the varying granularity of each token and the…

Computer Vision and Pattern Recognition · Computer Science 2024-06-06 Wayner Barrios , SouYoung Jin
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