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Or some randomness is aomehowntroduced in the output, which happens after every word, unless you set the temperature to zero.
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That would not be intuition that is just randomness. Intuition is not randomness.

A jump in intuition comes from automatic processes reorganising the relational structure of conceptual models. There is no reorganisation of the model durring inference.

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> There is no reorganisation of the model durring inference.

one could argue that model can reorganize / interact with prior knowledge captured in text form (edit files) hence there can be reorganisation

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That would "using reason in chain of thought".
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