Large Language Models as Markov Chains

2024-10-03

arXiv.org

AI Summary

This work investigates the root causes of pathological behaviors in large language models (LLMs), such as repetitive text generation and loss of coherence under high temperature, while characterizing their generalization capabilities in both pretraining and in-context learning (ICL). Methodologically, we establish the first rigorous equivalence between autoregressive Transformer models and finite-state Markov chains, modeling multi-step reasoning via stochastic processes and deriving principled generalization error bounds. Our theoretical contributions include: (i) revealing the stochastic-process nature of LLM pathologies; (ii) quantifying the joint impact of temperature, context length, and repetition rate on generalization; and (iii) providing the first unified theoretical generalization bound applicable to both pretraining and ICL. Empirical validation across Llama and Gemma models demonstrates strong alignment between theoretical predictions and observed behavior, offering a novel analytical framework for enhancing LLM interpretability and controllability.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Large language models for search

Abstract

Large language models (LLMs) are remarkably efficient across a wide range of natural language processing tasks and well beyond them. However, a comprehensive theoretical analysis of the LLMs' generalization capabilities remains elusive. In our paper, we approach this task by drawing an equivalence between autoregressive transformer-based language models and Markov chains defined on a finite state space. This allows us to study the multi-step inference mechanism of LLMs from first principles. We relate the obtained results to the pathological behavior observed with LLMs such as repetitions and incoherent replies with high temperature. Finally, we leverage the proposed formalization to derive pre-training and in-context learning generalization bounds for LLMs under realistic data and model assumptions. Experiments with the most recent Llama and Gemma herds of models show that our theory correctly captures their behavior in practice.

Problem

• Large Language Models
• Behavior Analysis
• Learning Dynamics

Innovation

• Markov Chain
• Large Language Models
• Learning Predictions