Episode Details

tl;dr I tested GPT-6 Astra on randomized Boolean logic problems. Astra can solve surprisingly complex logic problems without chain-of-thought, and its performance improves significantly with more filler tokens. Astra is also able to combine prior probabilities with constraints to find the most likely solution, and can output surprisingly accurate posterior marginal probabilities. By extending a cached prompt with progressively more filler tokens, I created visualizations of Astra's per-variable confidence scores at different points in the computations. These values tend to oscillate for a while and then eventually converge toward the exact marginal probabilities. Together, these results suggest that Astra performs some kind of iterative, belief-propagation-like probabilistic inference internally.

In my previous post, I hypothesised that Astra (and to a lesser extent other LLMs) may be performing some form of speculative reasoning when solving specially crafted logic problems without chain-of-thought, and provided some experimental results supporting this hypothesis. One question those experiments didn't answer is whether Astra is keeping track of not just the speculative values of intermediate results, but also its level of confidence in them. If Astra is doing the latter, speculative evaluation turns into something much more powerful: a form of belief propagation.

Belief propagation, also known [...]

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Outline:

(03:24) Decoding BCH codes

(07:02) Impact of phrasing

(09:34) Can we just supply probabilities directly?

(15:05) Visualizing confidence values over time

(19:53) Conclusion

The original text contained 3 footnotes which were omitted from this narration.

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First published:
September 14th, 2026

Source:
https://www.lesswrong.com/posts/PAHqDoFrp9fybcSn2/astra-appears-to-perform-belief-propagation-like-inference

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Narrated by TYPE III AUDIO.

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