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There are 2 levels of determinism that matter here IMO. Level 1, given the same input you get the same output. Level 2, you know what to change on the input to get a specific change on the output.

LLMs are currently capable of level 1, but not capable of level 2. Trust follows what is actually deterministic.

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Trust should, but instead is being gulled by those incapable LLMs. And I don't see that changing, given the typical human's seemingly unlimited vulnerability to this con.
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they probably mean deterministic in the sense of traditional computer programs consisting of if-else decision points and ordinary cpu logic, as opposed to numerical models (which can of course be deterministic too, as you pointed out)
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Model inference is just that same logic but faster.

I think the point is determined. No-one can determine what the LLM might do.

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I mean in the traditional software sense. We trust autopilots to fly planes. Would you get on a plane flown by an LLM?
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Then I think I'd rephrase you: There's a reason we trust trusted systems.

:)

Even their fans agree, LLMs are inherently unreliable. The fact some people trust them regardless is due to a deep flaw in human psychology that I believe has not been significantly exploited by any previous tech. There will be tears.

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I think two things contribute to the trust in LLMs:

1. Decades of generally reliable systems (I trust my calculator because it always says 1+1=2) has trained people to believe what computers say.

2. LLMs "speak" with great confidence, which has, as you say, a psychological effect.

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