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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…

Machine Learning · Computer Science 2025-09-05 Yihe Dong , Lorenzo Noci , Mikhail Khodak , Mufan Li

Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by self-attention. However, the employment of self-attention modules results in a quadratic…

Computer Vision and Pattern Recognition · Computer Science 2022-05-03 Jiachen Lu , Jinghan Yao , Junge Zhang , Xiatian Zhu , Hang Xu , Weiguo Gao , Chunjing Xu , Tao Xiang , Li Zhang

We study the training dynamics of gradient descent in a softmax self-attention layer trained to perform linear regression and show that a simple first-order optimization algorithm can converge to the globally optimal self-attention…

Machine Learning · Computer Science 2026-03-03 Gautam Goel , Mahdi Soltanolkotabi , Peter Bartlett

Recently, it has been argued that encoder-decoder models can be made more interpretable by replacing the softmax function in the attention with its sparse variants. In this work, we introduce a novel, simple method for achieving sparsity in…

Computation and Language · Computer Science 2021-10-07 Biao Zhang , Ivan Titov , Rico Sennrich

While linear-complexity attention mechanisms offer a promising alternative to Softmax attention for overcoming the quadratic bottleneck, training such models from scratch remains prohibitively expensive. Inheriting weights from pretrained…

Computer Vision and Pattern Recognition · Computer Science 2026-05-29 Yining Li , Dongchen Han , Zeyu Liu , Hanyi Wang , Yulin Wang , Gao Huang

Self-attention in Transformers relies on globally normalized softmax weights, causing all tokens to compete for influence at every layer. When composed across depth, this interaction pattern induces strong synchronization dynamics that…

Machine Learning · Computer Science 2026-05-26 Jingkun Liu , Yisong Yue , Max Welling , Yue Song

Kernel ridge regression (KRR) is widely used for nonparametric regression over reproducing kernel Hilbert spaces. It offers powerful modeling capabilities at the cost of significant computational costs, which typically require $O(n^3)$…

Methodology · Statistics 2024-03-18 Xiaowu Dai , Huiying Zhong

Despite their central role in the success of foundational models and large-scale language modeling, the theoretical foundations governing the operation of Transformers remain only partially understood. Contemporary research has largely…

Machine Learning · Computer Science 2025-06-02 Sagar Ghosh , Kushal Bose , Swagatam Das

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…

Machine Learning · Computer Science 2025-10-27 Morris Yau , Ekin Akyürek , Jiayuan Mao , Joshua B. Tenenbaum , Stefanie Jegelka , Jacob Andreas

Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with…

Transformers are extremely successful machine learning models whose mathematical properties remain poorly understood. Here, we rigorously characterize the behavior of transformers with hardmax self-attention and normalization sublayers as…

Computation and Language · Computer Science 2026-05-14 Albert Alcalde , Giovanni Fantuzzi , Enrique Zuazua

Linear attentions have shown potential for improving Transformer efficiency, reducing attention's quadratic complexity to linear in sequence length. This holds exciting promise for (1) training linear Transformers from scratch, (2)…

Machine Learning · Computer Science 2024-02-08 Michael Zhang , Kush Bhatia , Hermann Kumbong , Christopher Ré

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

Machine Learning · Statistics 2023-12-14 Tomoharu Iwata , Atsutoshi Kumagai

Transformer-based large language models have displayed impressive in-context learning capabilities, where a pre-trained model can handle new tasks without fine-tuning by simply augmenting the query with some input-output examples from that…

Machine Learning · Computer Science 2024-06-18 Hongkang Li , Meng Wang , Songtao Lu , Xiaodong Cui , Pin-Yu Chen

Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight-even at…

Machine Learning · Computer Science 2025-10-03 Yifei Zuo , Yutong Yin , Zhichen Zeng , Ang Li , Banghua Zhu , Zhaoran Wang

Pretrained Transformers demonstrate remarkable in-context learning (ICL) capabilities, enabling them to adapt to new tasks from demonstrations without parameter updates. However, theoretical studies often rely on simplified architectures…

Machine Learning · Statistics 2026-02-06 Samet Demir , Zafer Dogan

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

Transformer-based deep learning models have achieved state-of-the-art performance across numerous language and vision tasks. While the self-attention mechanism, a core component of transformers, has proven capable of handling complex data…

Machine Learning · Computer Science 2025-08-05 Laziz Abdullaev , Tan M. Nguyen

Transformers excel through content-addressable retrieval and the ability to exploit contexts of, in principle, unbounded length. We recast associative memory at the level of probability measures, treating a context as a distribution over…

Machine Learning · Statistics 2026-02-03 Ryotaro Kawata , Taiji Suzuki

Transformers have proven highly effective across various applications, especially in handling sequential data such as natural languages and time series. However, transformer models often lack clear interpretability, and the success of…

Machine Learning · Computer Science 2025-12-01 Wei Shi , Yuan Cao