61–70 of 134 posts
Earlier quoted context omitted.
"you could have..." is among the top insulting phrases used by maths-adjacent people. Others in that league are "it should now be obvious...", "it's abundantly clear...", "it can be easily shown that...", "this is nothing but..." etc. The rest of us reading this are like, holy batman, what the fuck was that?!
Also the proof is so trivial that it’s left to the reader.
Earlier quoted context omitted.
One of the more annoying parts of my physics study was getting used to the new matrix multiplication notation they came up with every semester.
bra-ket is the (most?) general form of tensor manipulation. Raising and lowering operators for summation notation are the beginner tools for covariant derivatives of the metric tensor. Christoffel symbols are where it's at, if you need to write out the Ricci tensor. The more constrained the space the more concise the notation can be. Note that MechE tensor notation has an even more compact (eigen) form for principal…
It is what has separated me from being able to code just about anything on a GPU and being known for some of that work and coming up with a better way to run ab initio quantum chemistry on them.
It truly has been my Waterloo for many years. So make me wrong.
after a cursory read, I can confidently say I could not, in fact, have come up with Kimi Delta Attention.
"you could have..." is among the top insulting phrases used by maths-adjacent people. Others in that league are "it should now be obvious...", "it's abundantly clear...", "it can be easily shown that...", "this is nothing but..." etc. The rest of us reading this are like, holy batman, what the fuck was that?!
You could have your own hacker news, it's just a textbox, a bunch of tables and headings! Once you add these, it'll be abundantly clear that you also need a database. It should now be obvious that you also need a user system and it can be easily shown that needs a backend. Admin tools, tests, statistics, performance checks and so on can easily be derived from such backend.
Machine learning could need, and probably has needed, some unified math notation for the past 15 years IMO. With that said, it was worse back in the day - when ML papers were the products of researchers from all over, you'd see some wild notation. Many will likely disagree with me, but inconsistent notation (across papers!) is to me friction. At least in this article the author explicitly explains the notation at the…
I never understood people who preferred traditional math notation (e.g. single letter symbols, weird characters like ∣q⟩ instead of writing down an explicit type, etc.). I guess the main advantage is terseness? To me, the mathematical expressions would be so much easier to understand if they were just written in pseudo code or an actual programming language like Python.
Remember that the oft-used e^x is actually an infinite series, even writing it out in summation form would be quite verbose given its frequency in many equations.
[1] I specifically mean those who are able to hold very big complex ideas and systems in their head, and reason about them, which seems to be an important talent for mathematicians.
Earlier quoted context omitted.
bra-ket is the (most?) general form of tensor manipulation. Raising and lowering operators for summation notation are the beginner tools for covariant derivatives of the metric tensor. Christoffel symbols are where it's at, if you need to write out the Ricci tensor. The more constrained the space the more concise the notation can be. Note that MechE tensor notation has an even more compact (eigen) form for principal…
All of this is true, but I don't believe and I want to be wrong about this that there is something in this notation that starts at an ELI 5 level and gently guides you to physicist level expertise. I all but majored in math (deriving back prop was trivial once it was clear it was the chain rule as one example) but I have never been able to keep bra ket notation straight in my head for the more exotic operations. Eins…
I will say that seeing transformers written this way gives me a bit more intuition for what is going on (being able to identify correct equations), but there's enough complexity in actual transformer implementations, that it still feels like I'm fooling myself.
Conceivably, I think you could use Feynman diagrams to talk about phonon dispersion in (eg asymetric crystaline) solids, but even though they're a "simplification", they're overkill for the problem.
after a cursory read, I can confidently say I could not, in fact, have come up with Kimi Delta Attention.
"you could have..." is among the top insulting phrases used by maths-adjacent people. Others in that league are "it should now be obvious...", "it's abundantly clear...", "it can be easily shown that...", "this is nothing but..." etc. The rest of us reading this are like, holy batman, what the fuck was that?!
A piece like this which uses it in a headline but in no way makes an average reader feel like they could have come up with it is just badly misjudging how good of an explanation it is.