  Language models have emerged as a critical area of focus in artificial
intelligence, particularly with the introduction of groundbreaking innovations
like ChatGPT. Large-scale Transformer networks have quickly become the leading
approach for advancing natural language processing algorithms. Built on the
Transformer architecture, these models enable interactions that closely mimic
human communication and, equipped with extensive knowledge, can even assist in
guiding human tasks. Despite their impressive capabilities and growing
complexity, a key question remains-the theoretical foundations of large
language models (LLMs). What makes Transformer so effective for powering
intelligent language applications, such as translation and coding? What
underlies LLMs' ability for In-Context Learning (ICL)? How does the LoRA scheme
enhance the fine-tuning of LLMs? And what supports the practicality of pruning
LLMs? To address these critical questions and explore the technological
strategies within LLMs, we leverage the Universal Approximation Theory (UAT) to
offer a theoretical backdrop, shedding light on the mechanisms that underpin
these advancements.
