# Unraveling Text Generation in LLMs: A Stochastic Differential Equation Approach

arXiv: https://arxiv.org/abs/2408.11863 · HTML: https://mlsanity.com/paper/2408.11863/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 17 Aug 2024.

## Builds on (most cited first, 12 of 12)

- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [DriveGPT4: Interpretable End-to-end Autonomous Driving via Large Language Model](https://mlsanity.com/paper/2310.01412/) (2023)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning](https://mlsanity.com/paper/2310.01061/) (2023)
- [Language in a Bottle: Language Model Guided Concept Bottlenecks for Interpretable Image Classification](https://mlsanity.com/paper/2211.11158/) (2022)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Can Large Language Models Explain Themselves? A Study of LLM-Generated Self-Explanations](https://mlsanity.com/paper/2310.11207/) (2023)
- [SelfIE: Self-Interpretation of Large Language Model Embeddings](https://mlsanity.com/paper/2403.10949/) (2024)
- [Sequential Integrated Gradients: a simple but effective method for explaining language models](https://mlsanity.com/paper/2305.15853/) (2023)
- [Language modeling via stochastic processes](https://mlsanity.com/paper/2203.11370/) (2022)
- [Automatically Generate Steganographic Text Based on Markov Model and Huffman Coding](https://mlsanity.com/paper/1811.04720/) (2018)
- [Improving Human Text Comprehension through Semi-Markov CRF-based Neural Section Title Generation](https://mlsanity.com/paper/1904.07142/) (2019)

## Abstract (arXiv)

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.