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Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to $O(n \sqrt{n})$. We also…

Machine Learning · Computer Science 2019-04-25 Rewon Child , Scott Gray , Alec Radford , Ilya Sutskever

Many real-world time series exhibit strong periodic structures arising from physical laws, human routines, or seasonal cycles. However, modern deep forecasting models often fail to capture these recurring patterns due to spectral bias and a…

Machine Learning · Computer Science 2025-08-05 Menglin Kong , Vincent Zhihao Zheng , Lijun Sun

Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the…

Machine Learning · Computer Science 2022-11-01 Junlong Tong , Liping Xie , Wankou Yang , Kanjian Zhang

Transformers have demonstrated remarkable efficacy in forecasting time series data. However, their extensive dependence on self-attention mechanisms demands significant computational resources, thereby limiting their practical applicability…

Machine Learning · Computer Science 2024-06-26 Cat P. Le , Chris Cannella , Ali Hasan , Yuting Ng , Vahid Tarokh

Multi-horizon forecasting problems often contain a complex mix of inputs -- including static (i.e. time-invariant) covariates, known future inputs, and other exogenous time series that are only observed historically -- without any prior…

Machine Learning · Statistics 2020-09-29 Bryan Lim , Sercan O. Arik , Nicolas Loeff , Tomas Pfister

Reliable uncertainty quantification is critical in multivariate time series forecasting problems arising in domains such as energy systems and transportation networks, among many others. Although Transformer-based architectures have…

Machine Learning · Computer Science 2026-03-13 Rajdeep Pathak , Rahul Goswami , Madhurima Panja , Palash Ghosh , Tanujit Chakraborty

Large Language Models (LLMs) based on autoregressive, decoder-only Transformers generate text one token at a time, where a token represents a discrete unit of text. As each newly produced token is appended to the partial output sequence,…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-06 Dimitrios Kafetzis , Ramin Khalili , Iordanis Koutsopoulos

Transformer models achieve state-of-the-art performance on a wide range of NLP tasks. They however suffer from a prohibitive limitation due to the self-attention mechanism, inducing $O(n^2)$ complexity with regard to sequence length. To…

Computation and Language · Computer Science 2022-10-28 Charles Condevaux , Sébastien Harispe

The increasing severity of climate change necessitates an urgent transition to renewable energy sources, making the large-scale adoption of wind energy crucial for mitigating environmental impact. However, the inherent uncertainty of wind…

Machine Learning · Computer Science 2024-10-18 Chongyang Wan , Shunbo Lei , Yuan Luo

Recently, learned image compression methods have outperformed traditional hand-crafted ones including BPG. One of the keys to this success is learned entropy models that estimate the probability distribution of the quantized latent…

Image and Video Processing · Electrical Eng. & Systems 2022-07-22 Jun-Hyuk Kim , Byeongho Heo , Jong-Seok Lee

Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world data-scarce scenarios, which can be concealed due to the performance saturation with…

Machine Learning · Computer Science 2024-10-21 Yong Liu , Haoran Zhang , Chenyu Li , Xiangdong Huang , Jianmin Wang , Mingsheng Long

Transformer is the state-of-the-art model for many natural language processing, computer vision, and audio analysis problems. Transformer effectively combines information from the past input and output samples in auto-regressive manner so…

Machine Learning · Computer Science 2025-03-14 Joni-Kristian Kämäräinen

Long-term time-series forecasting is essential for planning and decision-making in economics, energy, and transportation, where long foresight is required. To obtain such long foresight, models must be both efficient and effective in…

Machine Learning · Computer Science 2025-09-05 Chao Ma , Yikai Hou , Xiang Li , Yinggang Sun , Haining Yu , Zhou Fang , Jiaxing Qu

Multivariate long-term time series forecasting aims to predict future sequences by utilizing historical observations, with a core focus on modeling intra-sequence and cross-channel dependencies. Numerous studies have developed diverse…

Machine Learning · Computer Science 2026-02-03 Gaoxiang Zhao , Chunmao Huang , Li Zhou , Xiaoqiang Wang

Time series forecasting is a critical task in domains such as energy, finance, and meteorology, where accurate long-term predictions are essential. While Transformer-based models have shown promise in capturing temporal dependencies, their…

Machine Learning · Computer Science 2024-12-10 Zhenkai Qin , Baozhong Wei , Caifeng Gao , Jianyuan Ni

Long-term load forecast (LTLF) for area distribution feeders is one of the most critical tasks frequently performed in electric distribution utility companies. For a specific planning area, cost-effective system upgrades can only be planned…

Systems and Control · Electrical Eng. & Systems 2020-07-02 Ming Dong , Jian Shi , QingXin Shi

It has been challenging to model the complex temporal-spatial dependencies between agents for trajectory prediction. As each state of an agent is closely related to the states of adjacent time steps, capturing the local temporal dependency…

Computer Vision and Pattern Recognition · Computer Science 2025-07-08 Yixin Yan , Yang Li , Yuanfan Wang , Xiaozhou Zhou , Beihao Xia , Manjiang Hu , Hongmao Qin

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

This paper proposes an efficient memory transformer Emformer for low latency streaming speech recognition. In Emformer, the long-range history context is distilled into an augmented memory bank to reduce self-attention's computation…

One critical component in lossy deep image compression is the entropy model, which predicts the probability distribution of the quantized latent representation in the encoding and decoding modules. Previous works build entropy models upon…

Image and Video Processing · Electrical Eng. & Systems 2023-03-16 Yichen Qian , Ming Lin , Xiuyu Sun , Zhiyu Tan , Rong Jin