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The computational complexity of the self-attention mechanism in popular transformer architectures poses significant challenges for training and inference, and becomes the bottleneck for long inputs. Is it possible to significantly reduce…

机器学习 · 计算机科学 2024-10-16 Yingyu Liang , Zhizhou Sha , Zhenmei Shi , Zhao Song , Yufa Zhou

The self-attention mechanism is the key to the success of transformers in recent Large Language Models (LLMs). However, the quadratic computational cost $O(n^2)$ in the input sequence length $n$ is a notorious obstacle for further…

机器学习 · 计算机科学 2024-10-17 Yingyu Liang , Heshan Liu , Zhenmei Shi , Zhao Song , Zhuoyan Xu , Junze Yin

In the classical transformer attention scheme, we are given three $n \times d$ size matrices $Q, K, V$ (the query, key, and value tokens), and the goal is to compute a new $n \times d$ size matrix $D^{-1} \exp(QK^\top) V$ where $D =…

数据结构与算法 · 计算机科学 2023-10-09 Josh Alman , Zhao Song

As the demand for processing extended textual data grows, the ability to handle long-range dependencies and maintain computational efficiency is more critical than ever. One of the key issues for long-sequence modeling using attention-based…

计算与语言 · 计算机科学 2025-05-26 Aosong Feng , Rex Ying , Leandros Tassiulas

Attention matrices are fundamental to transformer research, supporting a broad range of applications including interpretability, visualization, manipulation, and distillation. Yet, most existing analyses focus on individual attention heads…

机器学习 · 计算机科学 2026-01-27 Ido Andrew Atad , Itamar Zimerman , Shahar Katz , Lior Wolf

It is straightforward to design an unbiased gradient estimator that stochastically cuts the backpropagation flow through any part of a computational graph. By cutting the parts that have little effect on the computation, one can potentially…

机器学习 · 计算机科学 2025-06-06 Sergey Pankov , Georges Harik

The Rotary Position Embedding (RoPE) mechanism has become a powerful enhancement to the Transformer architecture, which enables models to capture token relationships when encoding positional information. However, the RoPE mechanisms make…

机器学习 · 计算机科学 2026-01-27 Yang Cao , Jiayan Huo , Yingyu Liang , Zhenmei Shi , Zhao Song

In modern machine learning, inner product attention computation is a fundamental task for training large language models such as Transformer, GPT-1, BERT, GPT-2, GPT-3 and ChatGPT. Formally, in this problem, one is given as input three…

机器学习 · 计算机科学 2023-05-11 Josh Alman , Zhao Song

Transformer architectures have led to remarkable progress in many state-of-art applications. However, despite their successes, modern transformers rely on the self-attention mechanism, whose time- and space-complexity is quadratic in the…

机器学习 · 计算机科学 2022-09-13 Feyza Duman Keles , Pruthuvi Mahesakya Wijewardena , Chinmay Hegde

Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences,…

机器学习 · 计算机科学 2020-06-16 Sinong Wang , Belinda Z. Li , Madian Khabsa , Han Fang , Hao Ma

The quadratic complexity of dot-product attention introduced in Transformer remains a fundamental bottleneck impeding the progress of foundation models toward unbounded context lengths. Addressing this challenge, we introduce the Deep…

机器学习 · 计算机科学 2025-09-03 Yifan Zhang

The self-attention mechanism has been a key factor in the advancement of vision Transformers. However, its quadratic complexity imposes a heavy computational burden in high-resolution scenarios, restricting the practical application.…

计算机视觉与模式识别 · 计算机科学 2025-12-29 Dongchen Han , Tianyu Li , Ziyi Wang , Gao Huang

Transformer has been widely-used in many Natural Language Processing (NLP) tasks and the scaled dot-product attention between tokens is a core module of Transformer. This attention is a token-wise design and its complexity is quadratic to…

计算与语言 · 计算机科学 2020-08-13 Shuai Zhang , Peng Zhang , Xindian Ma , Junqiu Wei , Ningning Wang , Qun Liu

Standard inference and training with transformer based architectures scale quadratically with input sequence length. This is prohibitively large for a variety of applications especially in web-page translation, query-answering etc.…

计算与语言 · 计算机科学 2023-03-20 Lovish Madaan , Srinadh Bhojanapalli , Himanshu Jain , Prateek Jain

Previous research has explored the computational expressivity of Transformer models in simulating Boolean circuits or Turing machines. However, the learnability of these simulators from observational data has remained an open question. Our…

机器学习 · 计算机科学 2025-10-27 Morris Yau , Ekin Akyürek , Jiayuan Mao , Joshua B. Tenenbaum , Stefanie Jegelka , Jacob Andreas

Tensor Attention extends traditional attention mechanisms by capturing high-order correlations across multiple modalities, addressing the limitations of classical matrix-based attention. Meanwhile, Rotary Position Embedding…

机器学习 · 计算机科学 2024-12-25 Xiaoyu Li , Yingyu Liang , Zhenmei Shi , Zhao Song , Mingda Wan

We present the Condensate Theorem: attention sparsity is a learned topological property, not an architectural constraint. Through empirical analysis of trained language models, we find that attention mass concentrates on a distinct…

机器学习 · 计算机科学 2026-02-11 Jorge L. Ruiz Williams

The transformer has revolutionized modern AI across language, vision, and beyond. It consists of $L$ layers, each running $H$ attention heads in parallel and feeding the combined output to the subsequent layer. In attention, the input…

计算复杂性 · 计算机科学 2026-03-13 Barna Saha , Yinzhan Xu , Christopher Ye , Hantao Yu

Linear-attention models that compress the entire input sequence into a fixed-size recurrent state offer an efficient alternative to Transformers, but their finite memory induces forgetfulness that harms retrieval-intensive tasks. To…

计算与语言 · 计算机科学 2025-10-27 Mutian He , Philip N. Garner

Transformers have achieved remarkable success in sequence modeling and beyond but suffer from quadratic computational and memory complexities with respect to the length of the input sequence. Leveraging techniques include sparse and linear…

机器学习 · 计算机科学 2022-08-02 Tan Nguyen , Richard G. Baraniuk , Robert M. Kirby , Stanley J. Osher , Bao Wang
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