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The pre-trained ones no (except some of the new ones which have post training data added to pre-training for some reason). The post-trained ones yes (at least all the ones I've seen).

Some of the niche ones I'm not sure about. Like the historical LLMs. I have not tested those yet.

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I think any instruction tuned model is going to "know" it's an LLM.
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Yes. The first step of aligning each and every GPT-based LLM is to suppress the “I am human” kind of responses. It’s baked into the weights.
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Reminds me of old cleverbot conversations where it would always assert it is human and you are the bot.

Trained on previous conversations with people.

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It's also at minimum baked into the system prompt of virtually any LLM.
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That's not "baked" and only applies to remotely hosted LLMs where someone else feeds the prompt into the LLM.
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Without a system prompt no. And in general they “know” nothing and just predict the next best word.
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This is wrong. See other comments.
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For sure, as they are stochastic parrots. My question should have been: what are the odds a llm would react properly to those instruction, but I got lazy and asked if they "know" it, because I presumed most readers here do know how llms are working.
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