For those who are not math people, this comment is referring to the fact that "attention" is formally equivalent[1] to Nadaraya-Watson kernel smoothing, which is a kind of weighted average. Yes! Incredibly, attention is
just a weighted average.
Imagine you have a series of (x,y) coordinates. You receive a new x coordinate, and you'd like to predict the corresponding y. So, the absolute dumbest thing you can do is find the nearest x, and then report its corresponding y as your prediction. The second dumbest thing you can do is find the n closest x coordinates, and then average their y values together, and output that as your predicted value. And the third-dumbest thing you can do is that n-closest-average thing, but give the "closest" x coordinates the most "weight" when you average them. (Technically, not always "closest": you have some "kernel" function which does the weighting, but "closeness" is a good kernel so I will use it here.)
That third-dumbest thing is Nadaraya-Watson kernel smoothing. And that's what attention does. You have a big list of vectors. You compute a weighted average of those vectors. You now have a new vector. You can do what you want with it, but LLMs will generally turn that into a distribution over token types, from which you'll generally want to select either the top one, or weighted-randomly one from the top k (known as "increasing the temperature").
With all that said, I'm not sure "Kernel smoothing is all you need" is actually materially better than "attention is all you need" for 99.999% of humans. :)
[1]: https://arxiv.org/abs/1908.11775
Imagine you have a series of (x,y) coordinates. You receive a new x coordinate, and you'd like to predict the corresponding y. So, the absolute dumbest thing you can do is find the nearest x, and then report its corresponding y as your prediction. The second dumbest thing you can do is find the n closest x coordinates, and then average their y values together, and output that as your predicted value. And the third-dumbest thing you can do is that n-closest-average thing, but give the "closest" x coordinates the most "weight" when you average them. (Technically, not always "closest": you have some "kernel" function which does the weighting, but "closeness" is a good kernel so I will use it here.)
That third-dumbest thing is Nadaraya-Watson kernel smoothing. And that's what attention does. You have a big list of vectors. You compute a weighted average of those vectors. You now have a new vector. You can do what you want with it, but LLMs will generally turn that into a distribution over token types, from which you'll generally want to select either the top one, or weighted-randomly one from the top k (known as "increasing the temperature").
With all that said, I'm not sure "Kernel smoothing is all you need" is actually materially better than "attention is all you need" for 99.999% of humans. :)
[1]: https://arxiv.org/abs/1908.11775