Bayesian fine-tuning beats gold-answer training: LMs are only as Bayesian as their beliefs allow
tallinzen · x · 2026-10-02
Researchers from Tübingen, MIT and NYU published "As Bayesian as Their Beliefs Allow," asking whether LMs that act Bayesian are actually Bayesian inside.
- On a flight-recommendation task requiring inference of hidden user preferences, an LM fine-tuned on an ideal Bayesian assistant's recommendations (BayesLM) behaves near-Bayesian, while standard fine-tuning on true user answers (OracleLM) falls short.
- The paper tests four increasingly demanding requirements: R1 acting Bayesian, R2 hidden states encoding Bayes-rule quantities, R3 belief edits changing recommendations as Bayes predicts, R4 expected utility converting beliefs into policy.
- Conclusion: LMs are only as Bayesian as their beliefs allow; fine-tuning on the Bayesian assistant yields models that hold and use better beliefs than gold-answer tuning.
- Experiments use three Gemma-2 9B variants (untuned StartLM, BayesLM, OracleLM), with an interactive walkthrough at bayeslm.github.io.
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