arXiv AI By Tong Xiao, Jingbo Zhu

Foundations of Large Language Models

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Foundations of Large Language Models is a book that focuses on core concepts of large language models rather than exhaustive coverage of the latest technologies. It is organized into six chapters covering pre‑training, generative models, prompting, alignment, inference, and reasoning. The book targets college students, professionals, and practitioners in NLP and related fields, serving as a reference for anyone interested in large language models.

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arXiv Machine Learning
Aug 19

Large Language Models: A Mathematical Formulation

The article presents a mathematical framework for large language models (LLMs), detailing how text sequences are encoded into tokens, how next‑token prediction architectures are defined, and how these models are trained and deployed for tasks such as summarization, recommendation, software writing, and quantitative problem solving. It emphasizes that the framework relies on basic concepts from information theory, probability, and optimization, yet captures the complex algorithmic structure responsible for LLMs’ empirical successes. The authors argue that this formalism enables the study of accuracy, efficiency, and robustness, and points toward new methodological developments.

By Ricardo Baptista, Andrew Stuart, Son Tran