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An Overview of Large Language Models for Statisticians

Wenlong Ji, Weizhe Yuan, Emily Getzen, Kyunghyun Cho, Michael I. Jordan, Song Mei, Jason E Weston, Weijie J. Su, Jing Xu, Linjun Zhang

TL;DR

The paper surveys how statisticians can contribute to large language models by integrating statistical rigor into training, evaluation, and deployment to improve trustworthiness. It covers the full LLM lifecycle—from representation learning and Transformer architectures to prompting, fine-tuning, alignment, and self-alignment—with a strong emphasis on uncertainty quantification, privacy, fairness, watermarking, and interpretability. It then articulates how LLMs can empower statistical analysis, data collection, cleaning, and medical research, while discussing the reciprocal role of statisticians in shaping safe and effective AI systems. By offering a structured synthesis and roadmap, the paper advocates closer collaboration between statistics and AI to advance both theoretical foundations and practical societal applications of LLMs.

Abstract

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence (AI), exhibiting remarkable capabilities across diverse tasks such as text generation, reasoning, and decision-making. While their success has primarily been driven by advances in computational power and deep learning architectures, emerging problems -- in areas such as uncertainty quantification, decision-making, causal inference, and distribution shift -- require a deeper engagement with the field of statistics. This paper explores potential areas where statisticians can make important contributions to the development of LLMs, particularly those that aim to engender trustworthiness and transparency for human users. Thus, we focus on issues such as uncertainty quantification, interpretability, fairness, privacy, watermarking and model adaptation. We also consider possible roles for LLMs in statistical analysis. By bridging AI and statistics, we aim to foster a deeper collaboration that advances both the theoretical foundations and practical applications of LLMs, ultimately shaping their role in addressing complex societal challenges.

An Overview of Large Language Models for Statisticians

TL;DR

The paper surveys how statisticians can contribute to large language models by integrating statistical rigor into training, evaluation, and deployment to improve trustworthiness. It covers the full LLM lifecycle—from representation learning and Transformer architectures to prompting, fine-tuning, alignment, and self-alignment—with a strong emphasis on uncertainty quantification, privacy, fairness, watermarking, and interpretability. It then articulates how LLMs can empower statistical analysis, data collection, cleaning, and medical research, while discussing the reciprocal role of statisticians in shaping safe and effective AI systems. By offering a structured synthesis and roadmap, the paper advocates closer collaboration between statistics and AI to advance both theoretical foundations and practical societal applications of LLMs.

Abstract

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence (AI), exhibiting remarkable capabilities across diverse tasks such as text generation, reasoning, and decision-making. While their success has primarily been driven by advances in computational power and deep learning architectures, emerging problems -- in areas such as uncertainty quantification, decision-making, causal inference, and distribution shift -- require a deeper engagement with the field of statistics. This paper explores potential areas where statisticians can make important contributions to the development of LLMs, particularly those that aim to engender trustworthiness and transparency for human users. Thus, we focus on issues such as uncertainty quantification, interpretability, fairness, privacy, watermarking and model adaptation. We also consider possible roles for LLMs in statistical analysis. By bridging AI and statistics, we aim to foster a deeper collaboration that advances both the theoretical foundations and practical applications of LLMs, ultimately shaping their role in addressing complex societal challenges.

Paper Structure

This paper contains 131 sections, 13 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Background and Fundamentals of LLMs
  3. Historical Development of LLMs
  4. Representation Learning
  5. Language Modeling
  6. Architectures of Pre-trained Language Models
  7. Attention Mechanism
  8. Transformer Overview
  9. Multi-head Attention
  10. Variants
  11. LLM Evaluation
  12. Training Pipelines of LLMs
  13. LLM Pre-training
  14. Pre-training Objective
  15. Standard Language Modeling.
  16. ...and 116 more sections

Figures (3)

  • Figure 1: An illustration of next-token prediction by LLMs.
  • Figure 2: Overview of the paper outline.
  • Figure 3: The architecture of a decoder-only Transformer. The model consists of $L$ stacked Transformer decoder layers. Each layer contains a feed-forward network with weight matrices $W_1$ and $W_2$, as well as a multi-head attention module comprising the output matrix ($O_m$), value matrix ($V_m$), key matrix ($K_m$), and query matrix ($Q_m$).