Unraveling Text Generation in LLMs: A Stochastic Differential Equation Approach

TL;DR

This paper models the text generation process of Large Language Models using Stochastic Differential Equations to provide a mathematical framework that captures both deterministic and stochastic aspects of language generation.

Contribution

It introduces a novel SDE-based approach to interpret LLMs' text generation, offering new insights into their dynamics and potential for optimization.

Findings

SDE effectively models LLM text generation dynamics

Analysis reveals deterministic and stochastic influences on output

Provides a new perspective for diagnosing and improving LLMs

Abstract

This paper explores the application of Stochastic Differential Equations (SDE) to interpret the text generation process of Large Language Models (LLMs) such as GPT-4. Text generation in LLMs is modeled as a stochastic process where each step depends on previously generated content and model parameters, sampling the next word from a vocabulary distribution. We represent this generation process using SDE to capture both deterministic trends and stochastic perturbations. The drift term describes the deterministic trends in the generation process, while the diffusion term captures the stochastic variations. We fit these functions using neural networks and validate the model on real-world text corpora. Through numerical simulations and comprehensive analyses, including drift and diffusion analysis, stochastic process property evaluation, and phase space exploration, we provide deep insights into the dynamics of text generation. This approach not only enhances the understanding of the inner workings of LLMs but also offers a novel mathematical perspective on language generation, which is crucial for diagnosing, optimizing, and controlling the quality of generated text.