I feel like n^10 attention can capture patterns that lower complexity attention may not. So it seems arbitrary that we have n^2 attention.
Keep in mind that LLMs have many many layers, so they have plenty of opportunity to model higher-order interactions without needing to brute force every possible combination of 10 previous tokens, of which the vast majority will be useless. Empirically, even full "quadratic" attention is not always necessary, as evidenced by the existence of linear/sparse attention variants that perform almost as well.
Less so in practice. You saturate the memory of a b200 with a few dozen tokens on attentions higher than order 4. Training is even worse.
To paraphrase Knuth: high order polynomials are much more unimaginably large than mere infinity.
Another thing to consider is that transformers are very general computers. You can encode many many more complex architectures in simpler, multi layer transformers.
Here's what attention does: every token looks at every other token to decide what's relevant. If you have n tokens, and each one looks at n others, you get n * n = n^2 operations.
Put another way: n^2 is when every token gets to look at every other token. What would n^3 be? n^10?
(sibling comment has same interpretation as you, then handwaves transformers can emulate more complex systems)
I was wondering - I've been thinking about switching to AI systems programming (I know, easy task), but from what I understand, industry cloud GPUs are the main winners, right? Nobody's going to pay me (assuming I even had the skills) to optimize for consumer GPUs?
From what I understand, it's not just number + capacity + performance, it's literal core primitives. I don't think any of the "Blackwell" chips like the grace one or rtx 5090 have for example SM pairs in their ISA? And likewise similar fundamental differences between consumer and cloud hopper (where the majority of the perf is the cloud one's ISA?)
So I guess I'm wondering if I should buy a GPU myself or should I just rent on the cloud if I wanted to start getting some experience in this field. How do you even get experience in this normally anyways, do you get into really good schools and into their AI labs which have a lot of funding?