Teaching LLMs to reason like Bayesians
LLMs often struggle to update their beliefs as new evidence arrives, relying instead on simplistic heuristics. Google Research tested whether training models to imitate an optimal Bayesian assistant could improve this capability. The results show that Bayesian teaching substantially improves recommendation accuracy, adaptation across interactions, and generalization to other tasks—more effectively than training on always-correct answers. ## Testing Bayesian Reasoning in LLMs - Researchers created a five-round flight recommendation task involving three options with different: - Departure times - Flight durations - Number of stops - Costs - Simulated users had hidden preferences, such as strong, weak, or no preference for high or low values of each feature. - After every recommendation, the user revealed the correct choice, giving the assistant new evidence. - The benchmark compared: - Off-the-shelf LLMs - Human participants - An optimal Bayesian assistant - The Bayesian assistant maintained a probability distribution over possible user preferences and updated it using Bayes’ rule. - Most LLMs performed substantially worse and often stopped improving after the first interaction, showing limited ability to incorporate information over time. - Humans improved more than most LLMs but still failed to match the Bayesian assistant. ## Bayesian Teaching Framework - Bayesian reasoning requires an agent to: - Start with a prior belief about the world - Incorporate new evidence - Produce a posterior belief - Use that posterior as the prior for future reasoning - For LLMs, the “world state” includes facts, relationships, concepts, and inferred user preferences. - Researchers used supervised fine-tuning on many simulated user interactions to teach models this update process. ## Oracle Teaching vs. Bayesian Teaching - **Oracle teaching** trained models on interactions with an assistant that knew the user’s preferences perfectly and always selected the correct option. - **Bayesian teaching** trained models to imitate an assistant that estimated preferences probabilistically and sometimes made mistakes, especially during early uncertain rounds. - The researchers argued that Bayesian examples better preserve uncertainty and demonstrate how beliefs should change as evidence accumulates. - This approach resembles knowledge distillation: the LLM learns to reproduce the predictions of a more principled teacher rather than memorizing only correct outcomes. ## Results and Generalization - Both fine-tuning strategies improved performance compared with the original LLMs. - Bayesian teaching consistently outperformed oracle teaching. - Models trained on Bayesian predictions more often agreed with the optimal Bayesian assistant. - Improvements extended beyond the original flight recommendation task, suggesting the models learned a broader approximation of probabilistic reasoning rather than merely memorizing task-specific patterns. - The findings indicate that LLMs can acquire reasoning strategies from examples and apply them in new domains. The practical implication is that training models on the behavior of an optimal probabilistic reasoner may be more effective than supplying only correct answers. For agents that must learn user preferences or update beliefs over time, examples that explicitly preserve uncertainty and demonstrate evidence-based belief revision could produce more reliable behavior.
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