Learning the Latent Rules of a Game from Data: A Chess Story

Abstract: We demonstrate that small pretrained foundational generative LLMs with millions of parameters can learn the latent rules of a process from data associated with the process. Inspired by Stefan Zweig's novella "Schachnovelle," also known as "The Royal Game" in English, we show that 28M and 125M parameter pretrained foundational small LLMs (SLMs) can be instruction fine-tuned with 1,000-to-1,000,000 examples to learn the rules of chess, propose legal moves, and accurately solve chess problems. We also explore the impact of successive LLM fine-tuning epochs on improved outcomes and demonstrate reductions in model hallucinations by increasing the number of instruction fine-tuning examples.