Google researchers have developed a method to teach large language models Bayesian reasoning by training them to mimic optimal probabilistic inference patterns. The approach, detailed in a new paper, addresses a fundamental limitation where LLMs default to simple heuristics rather than inferring user-specific preferences through multiple interactions.

In experiments using a flight recommendation task, off-the-shelf LLMs performed significantly worse than a Bayesian assistant that updates its probability estimates using Bayes' rule. While the Bayesian model gradually improved its recommendations as it received more information about user choices, standard LLMs plateaued after just one interaction, showing limited ability to adapt to new evidence.

The researchers employed two teaching strategies: Oracle teaching, where models learned from perfect assistants, and Bayesian teaching, where models mimicked the probabilistic reasoning of Bayesian assistants. The latter proved more effective, enabling models to maintain uncertainty and update beliefs more realistically. Fine-tuned models achieved 80% agreement with mathematical ideals and generalized their reasoning skills to new domains like web shopping, demonstrating that probabilistic inference can be taught rather than being an innate capability.