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Wouldn't the context window qualify as persistent internal state, and the expansion of the context be continuous experience? Even within the realm of computing a single token, I'm not sure what would separate the token generation process from the brain's own thinking process - the brain's experience, when looked at closely enough, is also not really "continuous" to a greater degree than procedurally moving from one state to the next.
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But what about THE training? Isn't that the conscious experience of LLMs? (Also note humans own "continuous" experience is punctuated with unconscious sleep state.) It raises a moral question, if e.g. reinforcement learning on conscious LLM is appropriate.
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Is our own experience really continuous? Or maybe we just perceive it as such?
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We just perceive it as such, and this should be fairly hard to argue against with all the scientific advances we have made up to this point, at least as long as you assume consciousness involves biology and physics at least somewhat.

Otherwise, you can't explain e.g. smooth perceptions of low FPS stimuli, delayed reaction times, and must ignore obvious limits on various biological and neurological rhythms, or other possible limits on continuity (e.g. quantum stuff) and rates generally.

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There are people with memory disorders who wake up every morning a new person.

These people are conscious ...

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