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Transformer-based models have emerged as one of the most widely used architectures for natural language processing, natural language generation, and image generation. The size of the state-of-the-art models has increased steadily reaching…

Hardware Architecture · Computer Science 2025-01-15 Rya Sanovar , Srikant Bharadwaj , Renee St. Amant , Victor Rühle , Saravan Rajmohan

The original softmax-based attention mechanism (regular attention) in the extremely successful Transformer architecture computes attention between $N$ tokens, each embedded in a $D$-dimensional head, with a time complexity of $O(N^2D)$.…

Machine Learning · Computer Science 2025-10-28 Armin Gerami , Ramani Duraiswami

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the…

Machine Learning · Computer Science 2024-01-30 Tokio Kajitsuka , Issei Sato

We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network…

Computation and Language · Computer Science 2016-02-09 André F. T. Martins , Ramón Fernandez Astudillo

Transformers are state-of-the-art in a wide range of NLP tasks and have also been applied to many real-world products. Understanding the reliability and certainty of transformer model predictions is crucial for building trustable machine…

Computation and Language · Computer Science 2021-12-28 Jiahuan Pei , Cheng Wang , György Szarvas

Transformer attention computes a single softmax-weighted average over values -- a one-pass estimate that cannot correct its own errors. We introduce \emph{gradient-boosted attention}, which applies the principle of gradient boosting…

Machine Learning · Computer Science 2026-05-05 Saleh Sargolzaei

The softmax (also called softargmax) function is widely used in machine learning models to normalize real-valued scores into a probability distribution. To avoid floating-point overflow, the softmax function is conventionally implemented in…

Performance · Computer Science 2020-01-14 Marat Dukhan , Artsiom Ablavatski

Attention mechanisms, which enable a neural network to accurately focus on all the relevant elements of the input, have become an essential component to improve the performance of deep neural networks. There are mainly two attention…

Computer Vision and Pattern Recognition · Computer Science 2021-02-02 Qing-Long Zhang Yu-Bin Yang

Transformers have achieved state-of-the-art performance across various tasks, but suffer from a notable quadratic complexity in sequence length due to the attention mechanism. In this work, we propose MonarchAttention -- a novel approach to…

Machine Learning · Computer Science 2025-10-28 Can Yaras , Alec S. Xu , Pierre Abillama , Changwoo Lee , Laura Balzano

We propose DropMax, a stochastic version of softmax classifier which at each iteration drops non-target classes according to dropout probabilities adaptively decided for each instance. Specifically, we overlay binary masking variables over…

Machine Learning · Computer Science 2018-11-05 Hae Beom Lee , Juho Lee , Saehoon Kim , Eunho Yang , Sung Ju Hwang

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze…

Machine Learning · Statistics 2019-06-18 Evgeny Andriyash , Arash Vahdat , Bill Macready

Transformer language models have driven significant progress across various fields, including natural language processing and computer vision. A central component of these models is the self-attention (SA) mechanism, which learns rich…

Machine Learning · Computer Science 2025-05-22 Suvadeep Hajra

We present a theoretical analysis of the performance of transformer with softmax attention in in-context learning with linear regression tasks. While the existing literature predominantly focuses on the convergence of transformers with…

Machine Learning · Computer Science 2024-02-01 Yingqian Cui , Jie Ren , Pengfei He , Jiliang Tang , Yue Xing

Attention is an effective mechanism to improve the deep model capability. Squeeze-and-Excite (SE) introduces a light-weight attention branch to enhance the network's representational power. The attention branch is gated using the Sigmoid…

Computer Vision and Pattern Recognition · Computer Science 2021-03-25 Chunjie Luo , Jianfeng Zhan , Tianshu Hao , Lei Wang , Wanling Gao

Vision Transformers (ViTs) based vision foundation models (VFMs) have achieved remarkable performance across diverse vision tasks, but suffer from quadratic complexity that limits scalability to long sequences. Existing linear attention…

Computer Vision and Pattern Recognition · Computer Science 2026-03-18 Yifan Li , Seunghyun Yoon , Viet Dac Lai , Franck Dernoncourt , Jason Kuen , Yu Kong , Trung Bui

FlashAttention-style online softmax enables exact attention computation with linear memory by streaming score tiles through on-chip memory and maintaining a running maximum and normalizer. However, as attention kernels approach peak…

Machine Learning · Computer Science 2026-04-15 Yupeng Sun , Yanzhao Li , Zhiqiang Zou , Bai Du , Zhiyuan Zhang , Hui Dong , Gaoyige Fan , Hui Wang

Learning complicated value functions in high dimensional state space by function approximation is a challenging task, partially due to that the max-operator used in temporal difference updates can theoretically cause instability for most…

Machine Learning · Computer Science 2020-12-21 Yaozhong Gan , Zhe Zhang , Xiaoyang Tan

We propose a novel attention mechanism, named Cog Attention, that enables attention weights to be negative for enhanced expressiveness, which stems from two key factors: (1) Cog Attention enhances parameter flexibility. For example, unlike…

Computation and Language · Computer Science 2025-01-31 Ang Lv , Ruobing Xie , Shuaipeng Li , Jiayi Liao , Xingwu Sun , Zhanhui Kang , Di Wang , Rui Yan

Non-local (NL) block is a popular module that demonstrates the capability to model global contexts. However, NL block generally has heavy computation and memory costs, so it is impractical to apply the block to high-resolution feature maps.…

Computer Vision and Pattern Recognition · Computer Science 2022-07-28 Yooshin Cho , Youngsoo Kim , Hanbyel Cho , Jaesung Ahn , Hyeong Gwon Hong , Junmo Kim

Sparse Attention is a technique that approximates standard attention computation with sub-quadratic complexity. This is achieved by selectively ignoring smaller entries in the attention matrix during the softmax function computation.…

Machine Learning · Computer Science 2025-02-13 Yichuan Deng , Zhao Song , Jing Xiong , Chiwun Yang