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I agree that you can encode any single concept and that the encoding space of a single top pick grows exponentially.

However, I'm talking about the probability distribution of tokens.

I think within the framework of "almost-orthogonal axes" you can still create a vector that has the desired mix of projections onto any combination of these axes?

No. You can fit an exponential number of almost-orthogonal vectors into the input space, but the number of not-too-similar probability distributions over output tokens is also exponential in the output dimension. This is fine if you only care about a small subset of distributions (e.g. those that only assign significant probability to at most k tokens), but if you pick any random distribution, it's unlikely to be represented well. Fortunately, this doesn't seem to be much of an issue in practice and people even do top-k sampling intentionally.

I see. You're right. I was either badly mistaken or only thinking about small k.

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