I read the paper with much head scratching all the way through sections 1 and 2 and part of 3 before I figured out that, no, really, the description "Q-K=V" does not mean "Q minus K equals V" (the head scratching was because a bunch of their descriptions and symmetry comments really make little sense if you think "Q minus K equals V"). If you want to say that "K equals V", please spell it "K=V" :)

I am curious whether it makes any sense at all to enforce a more general linear constraint on the query, key and value attention matrices along the line of Q-K=V.

It is an entertaining paper. I admit I'm surprised that K=V appears to work as well as it does -- it seems like it's almost enforcing a sort of model where the query is a guess as to what the value is and the attention head returns a (softmaxed) value that is closest to the query's guess. Maybe it works because the sequences are short and the dimension is high and there's plenty of room for interesting results to fit in the merged key/value space.

Geometrically I imagine the process of attention like picking up a bunch of vectots and spinning and squishing them in many-D until you can find a crack where you can see all the way through, then leveraging that crack to seperate what you want.

I doubt that's strictly accurate, but it might be close enough that it makes me think that if you were doing that with a bunch of bananas, it would be much easier to find the way through if you could also bend the bunch so they were all straight.

It's always the trade off of a smart complex operation against an absolute crapload of dumb ones.

Their 1.2B model was trained on only 10B tokens, which is less than half of the chinchilla compute optimal number. Modern overtrained 1B LLMs are trained on the order of 10T tokens (1000x more).

This is important because, from my own experience, simplifications and alternatives to standard attention can look fine in the under-trained regime but lag after over-training. This happens because attention has very little out-of-the-gate inductive bias, so it takes a lot of training for the expressiveness to really shine through.

I can't fault the authors since longer training runs cost money, but it warrants pointing out.

I'm also disappointed that they didn't report reasoning benchmark results for the Q=K-V case, since that is by far the most theoretically interesting case (in my eyes).