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Is "token" a directly perceivable unit for the LLM? If you ask it "how many tokens are in this sentence?" can it count them (again, not guessing or making a tool call)?

I've never tried it and it might take some thought and effort to conduct an experiment to find out properly, but I would be interested in the answer.

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I dont think so. This is akin to asking a person, what is the frequency of the light hitting your eye when watching a leaf for example. You either know the (approximate) answer by knowing the frequency of green, or use a tool to measure it. If the LLM gives the correct answer it is either.guessing based on intution(and this intuition is based on pairs of word to tokenization length in text form in training data), writing code(or executing a tokenizer) or running a tokenizer mentally (reasoning via CoT).

Not the point: the simulated intelligence in this context needs to create proper representation. It is not a matter of what it sees but of what it can see.

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