# @kazani: Google taught LLMs to reason like Bayesians via supervised fine-tuning

Source: https://farcaster.xyz/kazani/0xd34ec9fb
Kiwi News: https://news.kiwistand.com/stories/kazani-Google-taught-LLMs-to-reason-like-Bayesians-via-supervised-fine-tuning?index=0x69aac54efcc2edbe66e6e1edf85da659c7eb929efca5145c4732970452085f45aa6506af
Submitted by @kazani on 2026-03-06 UTC, 3 upvotes, 0 comments

## Summary

Google researchers report that they compressed a classical symbolic Bayesian model into a neural network using supervised fine-tuning. Models trained only on synthetic flight data transferred their probabilistic reasoning to different domains, including hotel recommendations and real-world web shopping, which the post says suggests they internalized general Bayesian principles. The post states that demonstrations of how to reason, rather than correct answers alone, can unlock capabilities that prompting cannot. It also cites three other research examples, including QED-Nano, a 4B parameter model trained to write Olympiad-level proofs.

## Article

Teaching LLMs to reason like Bayesians

Google compressed a classical symbolic Bayesian model into a neural network via supervised fine-tuning. 

Generalization: Models trained only on synthetic flight data successfully transferred their probabilistic reasoning to entirely different domains like hotel recommendations and real-world web shopping. This suggests the LLMs internalized general Bayesian reasoning principles, not just task-specific patterns.

The right training signal (demonstrations of how to reason, not just correct answers) can unlock capabilities that prompting alone can't.

Read more: https://research.google/blog/teaching-llms-to-reason-like-bayesians/

P.S. There has been so much exciting foundational research lately that I'm more convinced than ever that there is not only no wall but that progress will accelerate.

Three of many examples:

1. SOAR ("Teaching Models to Teach Themselves"), which shows that an AI model can generate useful intermediate problems (stepping stones) for tasks it cannot itself solve. https://arxiv.org/abs/2601.18778

2. QED-Nano, a tiny 4B parameter model, was trained to write Olympiad-level mathematical proofs that compete with models 50x its size. The key technique: instead of reasoning in one long pass, the model reasons in cycles: thinking, summarizing what it's learned, then thinking again conditioned on that summary. This lets it reason effectively across 1.5 million tokens without losing the thread. https://huggingface.co/spaces/lm-provers/qed-nano-blogpost

3. Recursive Language Models (RLMs): Instead of stuffing everything into the model's context window where it degrades, the model treats its input as an external object it can programmatically slice, examine, and recursively call itself on, handling inputs 100x larger than its context window. https://arxiv.org/abs/2512.24601