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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…

Machine Learning · Computer Science 2026-04-14 Xue-Cheng Tai , Hao Liu , Lingfeng Li , Raymond H. Chan

Augmenting large language models (LLMs) with auxiliary tokens has emerged as a promising strategy for enhancing model performance. In this work, we introduce a lightweight method termed latent tokens; these are dummy tokens that may be…

Machine Learning · Computer Science 2025-05-20 Yuchang Sun , Yanxi Chen , Yaliang Li , Bolin Ding

Self-attention is usually described as a flexible, content-adaptive way to mix a token with information from its past. We reinterpret causal self-attention transformers, the backbone of modern foundation models, within a probabilistic…

Machine Learning · Computer Science 2026-03-24 Deepak Agarwal , Dhyey Dharmendrakumar Mavani , Suyash Gupta , Karthik Sethuraman , Tejas Dharamsi

Transformers have become the dominant architecture for natural language processing. Part of their success is owed to a remarkable capability known as in-context learning (ICL): they can acquire and apply novel associations solely from their…

Artificial Intelligence · Computer Science 2026-01-12 Tiberiu Musat , Tiago Pimentel , Lorenzo Noci , Alessandro Stolfo , Mrinmaya Sachan , Thomas Hofmann

In this paper, we trace the history of neural networks applied to natural language understanding tasks, and identify key contributions which the nature of language has made to the development of neural network architectures. We focus on the…

Computation and Language · Computer Science 2020-06-12 James Henderson

The transformer architecture has prevailed in various deep learning settings due to its exceptional capabilities to select and compose structural information. Motivated by these capabilities, Sanford et al. proposed the sparse token…

Machine Learning · Statistics 2024-06-12 Zixuan Wang , Stanley Wei , Daniel Hsu , Jason D. Lee

Transformers have the capacity to act as supervised learning algorithms: by properly encoding a set of labeled training ("in-context") examples and an unlabeled test example into an input sequence of vectors of the same dimension, the…

Machine Learning · Computer Science 2024-12-16 Spencer Frei , Gal Vardi

Empirical studies have identified a range of learnability biases and limitations of transformers, such as a persistent difficulty in learning to compute simple formal languages such as PARITY, and a bias towards low-degree functions.…

Machine Learning · Computer Science 2024-05-28 Michael Hahn , Mark Rofin

Large language models (LLMs) often exhibit unexpected errors or unintended behavior, even at scale. While recent work reveals the discrepancy between LLMs and humans in skill compositions, the learning dynamics of skill compositions and the…

Machine Learning · Computer Science 2026-02-02 Xingyu Zhao , Darsh Sharma , Rheeya Uppaal , Yiqiao Zhong

While transformer-based models achieve strong performance on text classification, we explore whether masking input tokens can further enhance their effectiveness. We propose token masking regularization, a simple yet theoretically motivated…

Computation and Language · Computer Science 2025-05-20 Xianglong Xu , John Bowen , Rojin Taheri

Vision Transformers (ViTs) lack the hierarchical inductive biases inherent to Convolutional Neural Networks (CNNs), theoretically allowing them to maintain high-dimensional representations throughout all layers. However, recent observations…

Computer Vision and Pattern Recognition · Computer Science 2025-12-09 Kanishk Awadhiya

The sudden appearance of modern machine learning (ML) phenomena like double descent and benign overfitting may leave many classically trained statisticians feeling uneasy -- these phenomena appear to go against the very core of statistical…

Machine Learning · Statistics 2024-09-30 Alicia Curth

In recent years, transformer-based models have revolutionized deep learning, particularly in sequence modeling. To better understand this phenomenon, there is a growing interest in using Markov input processes to study transformers.…

Machine Learning · Computer Science 2024-06-28 Ashok Vardhan Makkuva , Marco Bondaschi , Chanakya Ekbote , Adway Girish , Alliot Nagle , Hyeji Kim , Michael Gastpar

Since language models are used to model a wide variety of languages, it is natural to ask whether the neural architectures used for the task have inductive biases towards modeling particular types of languages. Investigation of these biases…

Computation and Language · Computer Science 2021-06-03 Jennifer C. White , Ryan Cotterell

In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…

Machine Learning · Computer Science 2021-03-09 Yan Zhang

While modern Transformer-based language models (LMs) have achieved major success in multi-task generalization, they often struggle to capture long-range dependencies within their context window. This work introduces a novel approach using…

Computation and Language · Computer Science 2025-09-23 Alok N. Shah , Khush Gupta , Keshav Ramji , Pratik Chaudhari

Transformers excel at discovering patterns in sequential data, yet their fundamental limitations and learning mechanisms remain crucial topics of investigation. In this paper, we study the ability of Transformers to learn pseudo-random…

Machine Learning · Computer Science 2025-07-10 Tao Tao , Darshil Doshi , Dayal Singh Kalra , Tianyu He , Maissam Barkeshli

Sampling biases can cause distribution shifts between train and test datasets for supervised learning tasks, obscuring our ability to understand the generalization capacity of a model. This is especially important considering the wide…

Machine Learning · Computer Science 2024-02-05 Max Vargas , Adam Tsou , Andrew Engel , Tony Chiang

Training Transformers on algorithmic tasks frequently demonstrates an intriguing abrupt learning phenomenon: an extended performance plateau followed by a sudden, sharp improvement. This work investigates the underlying mechanisms for such…

Machine Learning · Computer Science 2025-10-24 Pulkit Gopalani , Wei Hu

Transformers were initially introduced for natural language processing (NLP) tasks, but fast they were adopted by most deep learning fields, including computer vision. They measure the relationships between pairs of input tokens (words in…

Computer Vision and Pattern Recognition · Computer Science 2023-03-22 Robin Courant , Maika Edberg , Nicolas Dufour , Vicky Kalogeiton