Title: A Gentle Introduction to LLM Reasoning


Abstract: Large language models are built from three deceptively simple ideas: a parametrized function trained to predict the next word, human feedback that steers those same parameters toward preferred behavior, and a fictional frame made real by intercepting the right tokens. Yet when scaled, these models appear to reason, plan, and solve complex problems. This talk unpacks how modern LLMs reason and how we make them reason better. We trace the path from chain-of-thought prompting through inference-time scaling techniques (self-consistency and self-refinement) to reinforcement learning with verifiable rewards (GRPO) and knowledge distillation. A 0.6B-parameter model can be pushed from 15% to over 50% accuracy on competition math through a combination of these techniques. We discuss the key trade-offs between compute cost, accuracy, and training stability that define this rapidly evolving field.