LLMs dont do gradient descent to generate tokens.
replyThey are trained by gradient descent, but inference doesnt involve it.
I don't think there's anything like that going on. They just word vomit into a secondary area, and then there is an internal prompt that says "clean this up and summarize for the user".
replyLess "internal prompt" and more "they are trained to summarize after a </think> token"
replyThe training methods try not to apply any particular rules to the contents of the thinking text. That's called "optimization pressure on CoT" and is thought to reduce safety by inducing the model to lie (or stop clearly printing its intentions) in the thinking text.
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