# Dynamic Universal Approximation Theory: The Basic Theory for Transformer-based Large Language Models

arXiv: https://arxiv.org/abs/2407.00958 · HTML: https://mlsanity.com/paper/2407.00958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 20 of 20)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [O(n) Connections are Expressive Enough: Universal Approximability of Sparse Transformers](https://mlsanity.com/paper/2006.04862/) (2020)
- [Universal Approximation Under Constraints is Possible with Transformers](https://mlsanity.com/paper/2110.03303/) (2021)
- [Sumformer: Universal Approximation for Efficient Transformers](https://mlsanity.com/paper/2307.02301/) (2023)

## Abstract (arXiv)

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.