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Recurrent Neural Networks were, until recently, one of the best ways to capture the timely dependencies in sequences. However, with the introduction of the Transformer, it has been proven that an architecture with only attention-mechanisms…

Transformers are considered one of the most important deep learning models since 2018, in part because it establishes state-of-the-art (SOTA) records and could potentially replace existing Deep Neural Networks (DNNs). Despite the remarkable…

Transformers have shown great power in time series forecasting due to their global-range modeling ability. However, their performance can degenerate terribly on non-stationary real-world data in which the joint distribution changes over…

State space models (SSMs) have shown impressive results on tasks that require modeling long-range dependencies and efficiently scale to long sequences owing to their subquadratic runtime complexity. Originally designed for continuous…

In exploring Predictive Health Management (PHM) strategies for Proton Exchange Membrane Fuel Cells (PEMFC), the Transformer model, widely used in data-driven approaches, excels in many fields but struggles with time series analysis due to…

The Transformer architecture has revolutionized the field of sequence modeling and underpins the recent breakthroughs in large language models (LLMs). However, a comprehensive mathematical theory that explains its structure and operations…

Transformer-based models have gained large popularity and demonstrated promising results in long-term time-series forecasting in recent years. In addition to learning attention in time domain, recent works also explore learning attention in…

Time series forecasting remains a critical challenge across various domains, often complicated by high-dimensional data and long-term dependencies. This paper presents a novel transformer architecture for time series forecasting,…

Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models…

The transformer architecture is central to the success of modern Large Language Models (LLMs), in part due to its surprising ability to perform a wide range of tasks - including mathematical reasoning, memorization, and retrieval - using…

Transformers have achieved remarkable performance in multivariate time series(MTS) forecasting due to their capability to capture long-term dependencies. However, the canonical attention mechanism has two key limitations: (1) its quadratic…

Deep learning models have been widely applied in various aspects of daily life. Many variant models based on deep learning structures have achieved even better performances. Attention-based architectures have become almost ubiquitous in…

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of…

This paper introduces the Polynomial Mixer (PoM), a novel token mixing mechanism with linear complexity that serves as a drop-in replacement for self-attention. PoM aggregates input tokens into a compact representation through a learned…

Despite advances in the Transformer architecture, their effectiveness for long-term time series forecasting (LTSF) remains controversial. In this paper, we investigate the potential of integrating explicit periodicity modeling into the…

Long-term time series forecasting (LTSF) is a crucial aspect of modern society, playing a pivotal role in facilitating long-term planning and developing early warning systems. While many Transformer-based models have recently been…

Ever since their conception, Transformers have taken over traditional sequence models in many tasks, such as NLP, image classification, and video/audio processing, for their fast training and superior performance. Much of the merit is…

Transformer-based large language models (LLMs) excel in natural language processing tasks by capturing long-range dependencies through self-attention mechanisms. However, long-context modeling faces significant computational inefficiencies…

Over the past few decades, the hydrology community has witnessed notable advancements in streamflow prediction, particularly with the introduction of cutting-edge machine-learning algorithms. Recurrent neural networks, especially Long…

The success of the self-attention mechanism in classical machine learning models has inspired the development of quantum analogs aimed at reducing computational overhead. Self-attention integrates learnable query and key matrices to…