Probability of an LLM Trajectory: Starting from the Chain Rule (www.sithankanna.com)

A new article has been released that delves into the foundational aspect of modeling trajectories in reinforcement learning, specifically for language models (LLMs), by employing the chain rule in probability theory. It starts by analyzing a trajectory defined by a sequence of states and actions, emphasizing that the probability of this trajectory can be articulated mathematically based on defined states and actions over parameters of a model (policy). The derivation is significant for the AI/ML community as it clarifies how initial states and actions contribute to token generation, detailing the transition probabilities involved in generating language sequences. The article highlights that while the policy impacts the actions taken, the environmental transitions remain fixed once a state and action are established, adhering to Markov assumptions. It systematically outlines how the trajectory's probability simplifies in the context of token generation by LLMs, ultimately producing a clean formula that delineates the generation process based on initial prompts and subsequent tokens. This insight is crucial for refining model training methods, especially in applying policy gradients effectively, showcasing the underpinnings of successful LLM operations that leverage these principles in generating coherent text sequences.