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, as the standard self-attention mechanism of the Transformer uses $O(n^2)$ time and space with respect to sequence length. In this paper, we demonstrate that the self-attention mechanism can be approximated by a low-rank matrix. We further exploit this finding to propose a new self-attention mechanism, which reduces the overall self-attention complexity from $O(n^2)$ to $O(n)$ in both time and space. The resulting linear transformer, the \textit{Linformer}, performs on par with standard Transformer models, while being much more memory- and time-efficient.
Although Transformer models such as Google's BERT and OpenAI's GPT-3 are successful in many natural language processing tasks, training and deploying these models are costly and inefficient.Even if pre-trained models are used, deploying these models still remained a challenge due to their large size. Apart from deployment, these models take higher time during inference restricting user-friendliness. The main bottleneck is self-attention which uses quadratic time and space with respect to the sequence length. In order to reduce the quadratic time complexity of the self-attention mechanism, Linf…
LinFormer: A Linear-based Lightweight Transformer Architecture For Time-Aware MIMO Channel Prediction
School of Communication and Information Engineering, Shanghai University（上海大学通信与信息工程学院）；School of Information Science and Engineering, Southeast University（东南大学信息科学与工程学院）
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. Consequently, several approaches have been developed recently to speedup attention computation by enforcing different attention structures such as sparsity, low-rank, approximating attention using kernels. In this work, we view attention computation as that of nearest neighbor retrieval, and use decision tree based hierarchical navigation to reduce the retrieval cos…
The dot product self-attention is known to be central and indispensable to state-of-the-art Transformer models. But is it really required? This paper investigates the true importance and contribution of the dot product-based self-attention mechanism on the performance of Transformer models. Via extensive experiments, we find that (1) random alignment matrices surprisingly perform quite competitively and (2) learning attention weights from token-token (query-key) interactions is useful but not that important after all. To this end, we propose \textsc{Synthesizer}, a model that learns synthetic …
MetaLA: Unified Optimal Linear Approximation to Softmax Attention Map
The Hong Kong Polytechnic University（香港理工大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；UC Santa Cruz（加州大学圣克鲁兹分校）；Shanghai AI Lab（上海人工智能实验室）
Although transformers have become the neural architectures of choice for natural language processing, they require orders of magnitude more training data, GPU memory, and computations in order to compete with convolutional neural networks for computer vision. The attention mechanism of transformers scales quadratically with the length of the input sequence, and unrolled images have long sequence lengths. Plus, transformers lack an inductive bias that is appropriate for images. We tested three modifications to vision transformer (ViT) architectures that address these shortcomings. Firstly, we a…
EMAGN: Efficient Multi-Attention Graph Network via Learned Clustering for Scalable Traffic Forecasting
Shanghai Jiao Tong University（上海交通大学）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）；University of California, Berkeley（加利福尼亚大学伯克利分校）；Cornell University（康奈尔大学）；Technische Universität Dresden（德累斯顿工业大学）；Carnegie Mellon University（卡内基梅隆大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
Polytechnique Montréal（蒙特利尔理工学院）；Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）
Recurrent neural networks are effective models to process sequences. However, they are unable to learn long-term dependencies because of their inherent sequential nature. As a solution, Vaswani et al. introduced the Transformer, a model solely based on the attention mechanism that is able to relate any two positions of the input sequence, hence modelling arbitrary long dependencies. The Transformer has improved the state-of-the-art across numerous sequence modelling tasks. However, its effectiveness comes at the expense of a quadratic computational and memory complexity with respect to the seq…
Exploring Self-Attention Mechanisms for Speech Separation
Université Laval（拉瓦尔大学）；Concordia University（康考迪亚大学）；Mila-Quebec AI Institute（米拉-魁北克人工智能研究所）；Università Politecnica delle Marche（马尔凯理工大学）；Université de Sherbrooke（舍布鲁克大学）
Harvard University（哈佛大学）；Microsoft Research NYC（微软研究院纽约）
Self-attention, an architectural motif designed to model long-range interactions in sequential data, has driven numerous recent breakthroughs in natural language processing and beyond. This work provides a theoretical analysis of the inductive biases of self-attention modules. Our focus is to rigorously establish which functions and long-range dependencies self-attention blocks prefer to represent. Our main result shows that bounded-norm Transformer networks "create sparse variables": a single self-attention head can represent a sparse function of the input sequence, with sample complexity sca…
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 length of the input. Several approaches have been proposed to speed up self-attention mechanisms to achieve sub-quadratic running time; however, the large majority of these works are not accompanied by rigorous error guarantees. In this work, we establish lower bounds on the computational complexity of self-attention in a number of scenarios. We prove that the…
The attention module, which is a crucial component in Transformer, cannot scale efficiently to long sequences due to its quadratic complexity. Many works focus on approximating the dot-then-exponentiate softmax function in the original attention, leading to sub-quadratic or even linear-complexity Transformer architectures. However, we show that these methods cannot be applied to more powerful attention modules that go beyond the dot-then-exponentiate style, e.g., Transformers with relative positional encoding (RPE). Since in many state-of-the-art models, relative positional encoding is used as…
The University of Hong Kong（香港大学）；ByteDance Inc.（字节跳动公司）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）
Recently, random feature attentions (RFAs) are proposed to approximate the softmax attention in linear time and space complexity by linearizing the exponential kernel. In this paper, we first propose a novel perspective to understand the bias in such approximation by recasting RFAs as self-normalized importance samplers. This perspective further sheds light on an \emph{unbiased} estimator for the whole softmax attention, called randomized attention (RA). RA constructs positive random features via query-specific distributions and enjoys greatly improved approximation fidelity, albeit exhibiting…
Institute of Informatics, LMU Munich（慕尼黑大学信息学研究所）；Corporate Technology, Siemens AG（西门子公司企业技术部）
Transformers have improved the state-of-the-art across numerous tasks in sequence modeling. Besides the quadratic computational and memory complexity w.r.t the sequence length, the self-attention mechanism only processes information at the same scale, i.e., all attention heads are in the same resolution, resulting in the limited power of the Transformer. To remedy this, we propose a novel and efficient structure named Adaptive Multi-Resolution Attention (AdaMRA for short), which scales linearly to sequence length in terms of time and space. Specifically, we leverage a multi-resolution multi-he…
Meta AI；The Chinese University of Hong Kong（香港中文大学）
Efficient transformer variants with linear time complexity have been developed to mitigate the quadratic computational overhead of the vanilla transformer. Among them are low-rank projection methods such as Linformer and kernel-based Transformers. Despite their unique merits, they usually suffer from a performance drop comparing with the vanilla transformer on many sequence generation tasks, and often fail to obtain computation gain when the generation is short. We propose MemSizer, an approach towards closing the performance gap while improving the efficiency even with short generation. It pr…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Amazon Alexa AI（亚马逊 Alexa 人工智能）
Transformer-based models are not efficient in processing long sequences due to the quadratic space and time complexity of the self-attention modules. To address this limitation, Linformer and Informer are proposed to reduce the quadratic complexity to linear (modulo logarithmic factors) via low-dimensional projection and row selection respectively. These two models are intrinsically connected, and to understand their connection, we introduce a theoretical framework of matrix sketching. Based on the theoretical analysis, we propose Skeinformer to accelerate self-attention and further improve th…
The University of Hong Kong（香港大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）
Transformer architectures are now central to sequence modeling tasks. At its heart is the attention mechanism, which enables effective modeling of long-term dependencies in a sequence. Recently, transformers have been successfully applied in the computer vision domain, where 2D images are first segmented into patches and then treated as 1D sequences. Such linearization, however, impairs the notion of spatial locality in images, which bears important visual clues. To bridge the gap, we propose ripple attention, a sub-quadratic attention mechanism for vision transformers. Built upon the recent k…
In pursuit of faster computation, Efficient Transformers demonstrate an impressive variety of approaches -- models attaining sub-quadratic attention complexity can utilize a notion of sparsity or a low-rank approximation of inputs to reduce the number of attended keys; other ways to reduce complexity include locality-sensitive hashing, key pooling, additional memory to store information in compacted or hybridization with other architectures, such as CNN. Often based on a strong mathematical basis, kernelized approaches allow for the approximation of attention with linear complexity while retai…
Self-attention has recently been adopted for a wide range of sequence modeling problems. Despite its effectiveness, self-attention suffers from quadratic compute and memory requirements with respect to sequence length. Successful approaches to reduce this complexity focused on attending to local sliding windows or a small set of locations independent of content. Our work proposes to learn dynamic sparse attention patterns that avoid allocating computation and memory to attend to content unrelated to the query of interest. This work builds upon two lines of research: it combines the modeling fl…
Australian National University（澳大利亚国立大学）；Google Brain（谷歌大脑）
The sparse transformer can reduce the computational complexity of the self-attention layers to $O(n)$, whilst still being a universal approximator of continuous sequence-to-sequence functions. However, this permutation variant operation is not appropriate for direct application to sets. In this paper, we proposed an $O(n)$ complexity sampled transformer that can process point set elements directly without any additional inductive bias. Our sampled transformer introduces random element sampling, which randomly splits point sets into subsets, followed by applying a shared Hamiltonian self-attent…
This paper analyzes three formal models of Transformer encoders that differ in the form of their self-attention mechanism: unique hard attention (UHAT); generalized unique hard attention (GUHAT), which generalizes UHAT; and averaging hard attention (AHAT). We show that UHAT and GUHAT Transformers, viewed as string acceptors, can only recognize formal languages in the complexity class AC$^0$, the class of languages recognizable by families of Boolean circuits of constant depth and polynomial size. This upper bound subsumes Hahn's (2020) results that GUHAT cannot recognize the DYCK languages or …
Autoregressive Transformers are strong language models but incur O(T) complexity during per-token generation due to the self-attention mechanism. Recent work proposes kernel-based methods to approximate causal self-attention by replacing it with recurrent formulations with various update rules and feature maps to achieve O(1) time and memory complexity. We explore these approaches and find that they are unnecessarily complex, and propose a simple alternative - decaying fast weights - that runs fast on GPU, outperforms prior methods, and retains 99% of attention's performance for GPT-2. We also…
University of California, Santa Barbara（加州大学圣巴巴拉分校）
Transformers are the mainstream of NLP applications and are becoming increasingly popular in other domains such as Computer Vision. Despite the improvements in model quality, the enormous computation costs make Transformers difficult at deployment, especially when the sequence length is large in emerging applications. Processing attention mechanism as the essential component of Transformer is the bottleneck of execution due to the quadratic complexity. Prior art explores sparse patterns in attention to support long sequence modeling, but those pieces of work are on static or fixed patterns. We…
Hierarchical Shift Mixing -- Beyond Dense Attention in Transformers
Dept. of Electrical Engineering, Linköping University, Linköping, Sweden（电子工程系，林霍普大学）；RISE Research Institutes of Sweden, Linköping, Sweden（瑞典RISE研究机构）
University of California, Santa Barbara（加州大学圣巴巴拉分校）；ALIBABA DAMO Academy（阿里巴巴达摩院）
Transformers are becoming the mainstream solutions for various tasks like NLP and Computer vision. Despite their success, the high complexity of the attention mechanism hinders them from being applied to latency-sensitive tasks. Tremendous efforts have been made to alleviate this problem, and many of them successfully reduce the asymptotic complexity to linear. Nevertheless, most of them fail to achieve practical speedup over the original full attention under moderate sequence lengths and are unfriendly to finetuning. In this paper, we present DFSS, an attention mechanism that dynamically prun…
University of Southern California（南加州大学）；Meta AI Research（Meta人工智能研究院）；Carnegie Mellon University（卡内基梅隆大学）；Shanghai Jiao Tong University（上海交通大学）
The design choices in the Transformer attention mechanism, including weak inductive bias and quadratic computational complexity, have limited its application for modeling long sequences. In this paper, we introduce Mega, a simple, theoretically grounded, single-head gated attention mechanism equipped with (exponential) moving average to incorporate inductive bias of position-aware local dependencies into the position-agnostic attention mechanism. We further propose a variant of Mega that offers linear time and space complexity yet yields only minimal quality loss, by efficiently splitting the …
Efficient Context Propagating Perceiver Architectures for Auto-Regressive Language Modeling
Department of Computer Science and Statistics, University of Rhode Island, Kingston, RI, USA（计算机科学与统计学系，罗德岛大学，金斯敦，罗德岛州，美国）；Department of Computer Science, Stevens Institute of Technology, Hoboken, New Jersey, USA（计算机科学系，史蒂文斯理工学院，霍博肯，新泽西州，美国）
College of Intelligence and Computing, Tianjin University（天津大学智能与计算学部）
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 the length of sequence, limiting its application potential for long sequence tasks. In this paper, we propose a dimension-wise attention mechanism based on which a novel language modeling approach (namely TensorCoder) can be developed. The dimension-wise attention can reduce the attention complexity from the original $O(N^2d)$ to $O(Nd^2)$, where $N$ is the l…
The University of Hong Kong（香港大学）；ByteDance Inc.（字节跳动有限公司）；Apple Inc.（苹果公司）
Random-feature-based attention (RFA) is an efficient approximation of softmax attention with linear runtime and space complexity. However, the approximation gap between RFA and conventional softmax attention is not well studied. Built upon previous progress of RFA, we characterize this gap through the lens of control variates and show that RFA can be decomposed into a sum of multiple control variate estimators for each element in the sequence. This new framework reveals that exact softmax attention can be recovered from RFA by manipulating each control variate. Besides, it allows us to develop…
AWS Shanghai AI Lab（AWS上海人工智能实验室）；Fudan University（复旦大学）；New York University Shanghai（上海纽约大学）
The Transformer model is widely successful on many natural language processing tasks. However, the quadratic complexity of self-attention limit its application on long text. In this paper, adopting a fine-to-coarse attention mechanism on multi-scale spans via binary partitioning (BP), we propose BP-Transformer (BPT for short). BPT yields $O(k\cdot n\log (n/k))$ connections where $k$ is a hyperparameter to control the density of attention. BPT has a good balance between computation complexity and model capacity. A series of experiments on text classification, machine translation and language mo…
Transformers based on the attention mechanism have achieved impressive success in various areas. However, the attention mechanism has a quadratic complexity, significantly impeding Transformers from dealing with numerous tokens and scaling up to bigger models. Previous methods mainly utilize the similarity decomposition and the associativity of matrix multiplication to devise linear-time attention mechanisms. They avoid degeneration of attention to a trivial distribution by reintroducing inductive biases such as the locality, thereby at the expense of model generality and expressiveness. In th…
The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所先进智能项目中心）
Time-series data analysis is important because numerous real-world tasks such as forecasting weather, electricity consumption, and stock market involve predicting data that vary over time. Time-series data are generally recorded over a long period of observation with long sequences owing to their periodic characteristics and long-range dependencies over time. Thus, capturing long-range dependency is an important factor in time-series data forecasting. To solve these problems, we proposed two novel modules, Grouped Self-Attention (GSA) and Compressed Cross-Attention (CCA). With both modules, we…
