The paper establishes a theoretical framework for analyzing LLMs by modeling them as finite-state Markov chains.
📚 https://arxiv.org/pdf/2410.02724
Original Problem 🧠:
- A comprehensive theoretical analysis of the impressive performance of large language models (LLMs) remains elusive.
- There is no widely accepted agreement on how LLMs achieve reasoning capabilities beyond their training data.
-----
Solution in this Paper 💡:
- Draws an equivalence between generic autoregressive language models and Markov chains on a finite state space
- Analyzes the transition matrix of the equivalent Markov chain
- Proves existence and uniqueness of stationary distribution
- Derives convergence rate to stationary distribution
- Proves pre-training and in-context generalization bounds
-----
Key Insights from this Paper 💡:
- LLMs can be modeled as finite-state Markov chains despite their seemingly infinite generation capacity
- Stationary distribution captures LLM's understanding of natural language in its token space
- Convergence to stationary distribution depends on context window size and model temperature
- Generalization bounds depend on model depth, dictionary size, dataset size, and properties of training sequences
-----
Results 📊:
- Recent LLMs (2023-2024) obey in-context scaling laws predicted by theoretical results
- LLMs are better Markov chain learners than minimax optimal frequentist approach
- Experimental validation on Mistral 7B, Llama2, and Gemma models
Share this post