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Right, but all of that is still in the weights. The point of the article/joke isn’t literally that there is no grammar, it’s that there is no grammar separate from the weights. It’s all in the weights. And yes, it’s absurd. It’s a joke, but a thought provoking one.

by throwaway17373814 hours ago|

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So basically there are rules, we just can’t articulate them and so we can’t decode them from the weights. The Goedel Numbering metaphor is pretty appealing to me. You can represent any finite series of real numbers with a series of computations performed on some other finite series of real numbers. We just happen to be using matrices because the math is easy to parallelize. The trick is to realize that when you know the sequence you have and the sequence you want then you can compute the calculations. If you constrain the calculations to only matrix multiplication then you arrive at the scheme we have.

by teiferer13 hours ago|

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> You can represent any finite series of real numbers with a series of computations performed on some other finite series of real numbers.

That statement caught my eye. It's either trivially true or quite clearly wrong, depending on how you mean it.

In the literal meaning it's true. Given any finite set of real numbers, I can easily produce a different set (like taking the original set and adding a number which wasn't in there like one plus the largest or so) from which you can trivially produce the original set computationally.

But if you mean you give me both sets then that can't be true. For example if you give me a single real number as set A and the empty set as set B then I can't create a program which generates set A from set B. Your real number in set A could encode anything.

by skydhash7 hours ago|

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> For example if you give me a single real number as set A and the empty set as set B then I can't create a program which generates set A from set B. Your real number in set A could encode anything.

And that’s why in computation theory, the set of symbols is the union of the input and output. As set B is a subset of set A, then the set that govern any program from B to A has set A as its domain.