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If it looks like they do its reasonable to suggest they do in the same way I don’t know you do I only know it looks like you do. Birds do it, bees do it, even educated fleas do it.
So you don’t know how it works, but you’re positive that it works in this extremely particular way? That’s a minefield of a stance to take.
Yes, LLMs are trained one token at a time and produce one token at a time.
That does not mean that we understand exactly how the encode or process information within their neural networks. Even the most advanced researchers don’t claim that knowledge.
Saying “They don’t reason” without exact knowledge of what they do or a precise definition of what counts as “reasoning” isn’t very useful.
