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I come back to this every so often as well. After so many years of looking at Markov chain outputs that almost looked like they made sense or chatbot systems rewriting your sentence back at you, software which can simply talk is a heady thing.
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I would say that the LLM is something completly different especiayll as its not a normal algorithm but is very close to what brains do.
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Ah yes, matrix multiplication is "not a normal algorithm", surely.
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The matrix multilication underneath a large language model is the hardware but the data and the forming weights is not.

A quick sort sorts a list. A LLM depends on its learning data.

You train a model and then you use the model.

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The LLM is still a "normal algorithm", just one with a fairly large dataset to use. Assigning the algorithm part of LLMs magical properties hinders understanding. The work needed to pick the next output token is very much a classical algorithm.

Algorithms can be based on training and/or use data just fine, too. https://arxiv.org/abs/1712.01208

(Now, the weights used, those we kinda really don't understand the same way we understand the processing, and the approach to looking for structures in weights sometimes looks more like archeology or anthropology than computer science.)

It sounds like you're trying to express some kind of "but LLMs are so much more" thought. Yes, very much, they are. It's because of the size of the data, there's interesting emergence there. They're still a normal algorithm. (And our brains aren't quite like that; biological things are much more random/chaotic and generally non-reproducible. And the data and algorithm aren't separate.)

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LLMs have really changed the world. I didn’t think something like then would be possible in my lifetime
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It came out of nowhere. It’s all emergent. I’m convinced this is possible with just about anything given enough data. We will be seeing a near magical physical outputs LLM in the near future. It’s going to take in video and sounds and spit out physical movements that will be just as mind blowing as when 3.5 came out and it will come out of nowhere.
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if youve ever seen a pile of wrinkly mush and wondered.. pretty damn crazy too

https://web.mit.edu/people/dpolicar/writing/prose/text/think...

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