Hint for authors: when discussing linear algebra (or really most other kinds of math), follow normal conventions. In this case, the convention would be that - (the minus sign) means subtraction. It does not mean "and also", especially when you sandwich it between two variables that represent matrices.

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.

I can see why the QKV gets used but I can't help but think that thete's got to be a better mechanism with turning a pair of vectors into a new vector and a significance field.

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.

Somewhat relevant is a blog-post that likens attention to kernel smoothing: https://bactra.org/notebooks/nn-attention-and-transformers.h... (as discussed before in https://news.ycombinator.com/item?id=38756888)

Will be great and amusing if it actually turns out that we have been doing transformer overly-complex. The code repo is missing tho...

Gemma-4 E2B/E4B models reuses K-V cache from other layers, which do things in a "transposed" way: not reuse Q/K/V matrices within a single layer, but reuse across different layers.

These types of ablation studies are always good. However, I'm not sure how generalizable the language model findings here are.

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).

Can anyone explain to me why Q and K are both needed? They only ever appear as a pair, so why can’t you just define a matrix A = QK and learn that directly?

V being collinear is obvious, the question is/was also which additional orthogonal projections such as camera position for vision would improve the transformer.

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I would not be surprised if it turned out the exact attention mechanism does not really matter, similarly to the sigmoid, ReLU, GELU movement, only the speed on calculation - and QKV is pretty good at that on the GPUs.

It's interesting to see people are still experimenting with the core concepts of transformers

I'm terribly sorry, but scaling curves or GTFO. Any random pile of linear algebra works fine-ish at small scales. Very few random piles of linear algebra push the Pareto envelope at large scales.

More evidence that the original Transformer authors didn't really know what they were doing, but they did have access to more cheap compute than anyone else.

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No one got fired for choosing QKV I guess