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Forecasting multivariate time series data, such as prediction of electricity consumption, solar power production, and polyphonic piano pieces, has numerous valuable applications. However, complex and non-linear interdependencies between…

Machine Learning · Computer Science 2019-09-20 Shun-Yao Shih , Fan-Keng Sun , Hung-yi Lee

Transformer-based models have emerged as powerful tools for multivariate time series forecasting (MTSF). However, existing Transformer models often fall short of capturing both intricate dependencies across variate and temporal dimensions…

Machine Learning · Computer Science 2024-06-10 Juncheng Liu , Chenghao Liu , Gerald Woo , Yiwei Wang , Bryan Hooi , Caiming Xiong , Doyen Sahoo

The rapid progress seen in terms of large-scale generative AI is largely based on the attention mechanism. It is conversely non-trivial to conceive small-scale applications for which attention-based architectures outperform traditional…

Machine Learning · Computer Science 2025-08-07 Claudius Gros

Time series forecasting faces two important but often overlooked challenges. Firstly, the inherent random noise in the time series labels sets a theoretical lower bound for the forecasting error, which is positively correlated with the…

Machine Learning · Computer Science 2025-09-26 Tianyi Shi , Zhu Meng , Yue Chen , Siyang Zheng , Fei Su , Jin Huang , Changrui Ren , Zhicheng Zhao

Recently, Transformer-based models for long sequence time series forecasting have demonstrated promising results. The self-attention mechanism as the core component of these Transformer-based models exhibits great potential in capturing…

Machine Learning · Computer Science 2024-12-17 Zhicheng Zhang , Yong Wang , Shaoqi Tan , Bowei Xia , Yujie Luo

Softmax Self-Attention (SSA) is a key component of Transformer architectures. However, when utilised within skipless architectures, which aim to improve representation learning, recent work has highlighted the inherent instability of SSA…

Machine Learning · Computer Science 2026-02-06 Leo Zhang , James Martens

Time-series data in real-world medical settings typically exhibit long-range dependencies and are observed at non-uniform intervals. In such contexts, traditional sequence-based recurrent models struggle. To overcome this, researchers…

Machine Learning · Statistics 2024-03-18 Fernando Moreno-Pino , Álvaro Arroyo , Harrison Waldon , Xiaowen Dong , Álvaro Cartea

Multivariate time series (MTS) forecasting is vital across various domains but remains challenging due to the need to simultaneously model temporal and inter-variate dependencies. Existing channel-dependent models, where Transformer-based…

Machine Learning · Computer Science 2025-02-03 Junwoo Ha , Hyukjae Kwon , Sungsoo Kim , Kisu Lee , Seungjae Park , Ha Young Kim

Transformer self-attention computes pairwise token interactions, yet protein sequence to phenotype relationships often involve cooperative dependencies among three or more residues that dot product attention does not capture explicitly. We…

Machine Learning · Computer Science 2026-03-13 Shirin Amiraslani , Xin Gao

Time series forecasting has made significant advances, including with Transformer-based models. The attention mechanism in Transformer effectively captures temporal dependencies by attending to all past inputs simultaneously. However, its…

Machine Learning · Computer Science 2025-11-04 Xiongxiao Xu , Canyu Chen , Yueqing Liang , Baixiang Huang , Guangji Bai , Liang Zhao , Kai Shu

Scaling attention faces a critical bottleneck: the $\mathcal{O}(n^2)$ quadratic computational cost of softmax attention, which limits its application in long-sequence domains. While linear attention mechanisms reduce this cost to…

Machine Learning · Computer Science 2025-12-10 Ashkan Shahbazi , Ping He , Ali Abbasi , Yikun Bai , Xinran Liu , Elaheh Akbari , Darian Salehi , Navid NaderiAlizadeh , Soheil Kolouri

The attention mechanism is an important reason for the success of transformers. It relies on computing pairwise relations between tokens. To reduce the high computational cost of standard quadratic attention, linear attention has been…

Artificial Intelligence · Computer Science 2026-02-13 Hanno Ackermann , Hong Cai , Mohsen Ghafoorian , Amirhossein Habibian

Time-series forecasting has seen significant advancements with the introduction of token prediction mechanisms such as multi-head attention. However, these methods often struggle to achieve the same performance as in language modeling,…

Machine Learning · Computer Science 2024-12-03 Panayiotis Christou , Shichu Chen , Xupeng Chen , Parijat Dube

Recurrent Neural Networks (RNNs) have shown great success in modeling time-dependent patterns, but there is limited research on their learned representations of latent temporal features and the emergence of these representations during…

Machine Learning · Computer Science 2023-06-13 Peter DelMastro , Rushiv Arora , Edward Rietman , Hava T. Siegelmann

Attention mechanism is a significant part of Transformer models. It helps extract features from embedded vectors by adding global information and its expressivity has been proved to be powerful. Nevertheless, the quadratic complexity…

Machine Learning · Computer Science 2025-11-11 Hanwen Liu , Yixuan Ma , Shi Jin , Yuguang Wang

Existing research largely attributes the global sequence modeling capability of Transformers to the explicit computation of attention weights, a process that inherently incurs quadratic computational complexity. In this work, we offer a…

Computer Vision and Pattern Recognition · Computer Science 2026-05-07 Ruize He , Dongchen Han , Gao Huang

Soft attention is a critical mechanism powering LLMs to locate relevant parts within a given context. However, individual attention weights are determined by the similarity of only a single query and key token vector. This "single token…

Computation and Language · Computer Science 2025-07-14 Olga Golovneva , Tianlu Wang , Jason Weston , Sainbayar Sukhbaatar

The attention mechanism is the computational core of modern Transformer architectures, but its quadratic complexity in the input sequence length is the bottleneck for large-scale inference. This has motivated a rapidly growing body of work…

The forecasting of irregular multivariate time series (IMTS) is crucial in key areas such as healthcare, biomechanics, climate science, and astronomy. However, achieving accurate and practical predictions is challenging due to two main…

Machine Learning · Computer Science 2025-11-18 Xvyuan Liu , Xiangfei Qiu , Xingjian Wu , Zhengyu Li , Chenjuan Guo , Jilin Hu , Bin Yang

As a consequence of the high variability of load demand and renewable generation, long-term and high-resolution inputs are required for power system expansion planning, making the problem intractable in real-world applications. Time series…

Optimization and Control · Mathematics 2025-10-29 Ruiqi Zhang , Ensieh Sharifnia , Simon H. Tindemans