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We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the…

Machine Learning · Computer Science 2024-10-31 Mingze Wang , Weinan E

Increasing the size of a Transformer does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, the model's enhanced performance is closely associated with its memorization…

Machine Learning · Computer Science 2024-12-02 Xueyan Niu , Bo Bai , Lei Deng , Wei Han

We propose the first method to show theoretical limitations for one-layer softmax transformers with arbitrarily many precision bits (even infinite). We establish those limitations for three tasks that require advanced reasoning. The first…

Transformer-based deep learning models have achieved state-of-the-art performance across numerous language and vision tasks. While the self-attention mechanism, a core component of transformers, has proven capable of handling complex data…

Machine Learning · Computer Science 2025-08-05 Laziz Abdullaev , Tan M. Nguyen

The Transformer architecture consists of self-attention and feed-forward networks (FFNs) which can be viewed as key-value memories according to previous works. However, FFN and traditional memory utilize different activation functions…

Computation and Language · Computer Science 2023-02-14 Kai Shen , Junliang Guo , Xu Tan , Siliang Tang , Rui Wang , Jiang Bian

We propose a contrastive attention mechanism to extend the sequence-to-sequence framework for abstractive sentence summarization task, which aims to generate a brief summary of a given source sentence. The proposed contrastive attention…

Computation and Language · Computer Science 2019-10-31 Xiangyu Duan , Hoongfei Yu , Mingming Yin , Min Zhang , Weihua Luo , Yue Zhang

The transformer architecture has driven breakthroughs in recent years on tasks which require modeling pairwise relationships between sequential elements, as is the case in natural language understanding. However, long seqeuences pose a…

Computation and Language · Computer Science 2024-03-26 Heejun Lee , Jina Kim , Jeffrey Willette , Sung Ju Hwang

The Transformer architecture model, based on self-attention and multi-head attention, has achieved remarkable success in offline end-to-end Automatic Speech Recognition (ASR). However, self-attention and multi-head attention cannot be…

Computation and Language · Computer Science 2022-10-03 Chendong Zhao , Jianzong Wang , Wen qi Wei , Xiaoyang Qu , Haoqian Wang , Jing Xiao

Modern autoregressive models rely on attention, yet the Softmax full attention in Transformers scales quadratically with sequence length. Sliding Window Attention (SWA) achieves linear-time encoding/decoding by constraining the attention…

Machine Learning · Computer Science 2026-01-08 Jiaxu Liu , Yuhe Bai , Xiangyu Yin , Christos-Savvas Bouganis

In this paper, we share our reflections and insights on understanding Transformer architectures through the lens of associative memory--a classic psychological concept inspired by human cognition. We start with the basics of associative…

Machine Learning · Computer Science 2025-05-27 Shu Zhong , Mingyu Xu , Tenglong Ao , Guang Shi

Recently, it has been argued that encoder-decoder models can be made more interpretable by replacing the softmax function in the attention with its sparse variants. In this work, we introduce a novel, simple method for achieving sparsity in…

Computation and Language · Computer Science 2021-10-07 Biao Zhang , Ivan Titov , Rico Sennrich

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

Transformers are among the state of the art for many tasks in speech, vision, and natural language processing, among others. Self-attentions, which are crucial contributors to this performance have quadratic computational complexity, which…

Computation and Language · Computer Science 2022-12-21 Roshan Sharma , Bhiksha Raj

Transformers are extremely successful machine learning models whose mathematical properties remain poorly understood. Here, we rigorously characterize the behavior of transformers with hardmax self-attention and normalization sublayers as…

Computation and Language · Computer Science 2026-05-14 Albert Alcalde , Giovanni Fantuzzi , Enrique Zuazua

Self-attention mechanisms are foundational to Transformer architectures, supporting their impressive success in a wide range of tasks. While there are many self-attention variants, their robustness to noise and spurious correlations has not…

Machine Learning · Computer Science 2025-09-09 Camilo Tamayo-Rousseau , Yunjia Zhao , Yiqun Zhang , Randall Balestriero

The key to a Transformer model is the self-attention mechanism, which allows the model to analyze an entire sequence in a computationally efficient manner. Recent work has suggested the possibility that general attention mechanisms used by…

Machine Learning · Computer Science 2020-01-01 Thomas Dowdell , Hongyu Zhang

Motivated by the factorization inherent in the original fast multipole method and the improved fast Gauss transform we introduce a factorable form of attention that operates efficiently in high dimensions. This approach reduces the…

Machine Learning · Computer Science 2024-02-13 Armin Gerami , Monte Hoover , Pranav S. Dulepet , Ramani Duraiswami

Understanding the expressive power of transformers has recently attracted attention, as it offers insights into their abilities and limitations. Many studies analyze unique hard attention transformers, where attention selects a single…

Machine Learning · Computer Science 2025-11-14 Selim Jerad , Anej Svete , Jiaoda Li , Ryan Cotterell

Softmax is the de facto standard in modern neural networks for language processing when it comes to normalizing logits. However, by producing a dense probability distribution each token in the vocabulary has a nonzero chance of being…

Computation and Language · Computer Science 2022-05-20 Maxat Tezekbayev , Vassilina Nikoulina , Matthias Gallé , Zhenisbek Assylbekov

While Transformers have revolutionized deep learning, their quadratic attention complexity hinders their ability to process infinitely long inputs. We propose Feedback Attention Memory (FAM), a novel Transformer architecture that leverages…

Machine Learning · Computer Science 2024-05-08 Dongseong Hwang , Weiran Wang , Zhuoyuan Huo , Khe Chai Sim , Pedro Moreno Mengibar