Graphical Linear Algebra

https://graphicallinearalgebra.net/

by hyperbrainer • 1 year ago

304 26 1 year ago

graphicallinearalgebra.net

lorenzo_medici• 1 year ago

Appreciate the Claude Makelele praise

rurban2• 1 year ago

But nowadays we are calling him the 6. And everybody praises a good 6

Xmd5a• 1 year ago

Generalized Transformers from Applicative Functors

Transformers are a machine-learning model at the foundation of many state-of-the-art systems in modern AI, originally proposed in [arXiv:1706.03762]. In this post, we are going to build a generalization of Transformer models that can operate on (almost) arbitrary structures such as functions, graphs, probability distributions, not just matrices and vectors.
[...]
This work is part of a series of similar ideas exploring machine learning through abstract diagrammatical means.

https://cybercat.institute/2025/02/12/transformers-applicati...

MarkusQ• 1 year ago

I really enjoyed that when it was coming out, and used to follow it with some students. It's a shame it seems to have been abandoned.

Iwan-Zotow• 1 year ago

Who wrote that? Do you know?

pawel ... ?

mattkrause• 1 year ago

Pawel Sobocinski, in collaboration with Filippo Bonchi and Fabio Zanasi

https://graphicallinearalgebra.net/about/

theZilber• 1 year ago

When I read the first meaty chapter about graphs and commutativity I initially thought he just spends too long explaining simple concepts.

But then ai realized I would always forget the names for all the mathy c' words - commutativity commutativity, qssociativity... and for the first time I could actually remember commutativity and what it means, just because he tied it into a graphical representation (which actually made me laugh out loud because, initially, I thought it was a joke). So the concept of "x + y = y + x" always made sense to me but never really stuck like the graphical representation, which also made me remember its name for the first time.

I am sold.

gowld2• 1 year ago

Which chapter is that? It's not in the ToC

memoryfault• 1 year ago

vanderZwan• 1 year ago

It's because the graphs are visual metaphors that encode privileged information[0]. Which is an often overlooked aspect of teaching imo. Your own initial dismissive reaction kind of shows why: people don't really get the point until they realize it works, and even then they're not sure why.

[0] https://web.archive.org/web/20140402025221/http://m.nautil.u...

phforms• 1 year ago

Years ago when I was reading this (just a couple of chapters, not all of it), it opened my eyes to the power of diagrammatic representation in formal reasoning unlike anything before. I never did anything useful with string diagrams, but it was so fun to see what is possible with this system!

elric• 1 year ago

I had a similar revelation when watching 3Blue1Brown's Calculus series. Had they included those kinds of visual representations in school when I was first learning about Calculus, my understanding (and interest) would have been greatly expanded.

Very impressive how some people can create visual representations that enhance understanding.

dclowd9901• 1 year ago

If the internet has taught us anything, it’s that humans + anonymity = unpleasantness.

Aka one of my favorite axioms: https://www.penny-arcade.com/comic/2004/03/19/green-blackboa...

marvinborner• 1 year ago

It's interesting how some of these diagrams are almost equivalent in the context of encoding computation in interaction nets using symmetric interaction combinators [1].

From the perspective of the lambda calculus for example, the duplication of the addition node in "When Adding met Copying" [2] mirrors exactly the iterative duplication of lambda terms - ie. something like (λx.x x) M!

[1] https://ezb.io/thoughts/interaction_nets/lambda_calculus/202...

[2] https://graphicallinearalgebra.net/2015/05/12/when-adding-me...

russfink• 1 year ago

It reads as if Chuck Lorre (The Big Bang Theory) wrote it. Especially chapter two. I love the humor!

webprofusion• 1 year ago

This is nice, my main criticism would be that it uses the language "easy" and "simple" regularly which is a classic mistake in any instructive text (including docs etc).

If the reader was feeling a bit dumb and/or embarrassed that they didn't yet get the concept being explained then this will only make them feel worse and give up.

Language like that is often used to make things feel approachable and worry-free, but can have the opposite effect.

And never ever, ever write "obvious" in a doc explaining something, because if obviousness was at play they wouldn't be reading your doc.

Nevermark• 1 year ago

Excellent point.

I think about wording like that, like the extraneously explicit meta-content that dumbs down so many story plots. A character explicitly says "That makes me angry". When a better written story would make the anger implicitly obvious.

Stories should show not tell.

Make a point, make it clear make it concise, and it will be simple for most readers. Don't talk about making a point, or say a point is clear.

That is projecting attributes or experiences onto readers. But even a very well written point may not appear simple for some readers. Assume (optimistically!) that there will always be some unusually under-prepared but motivated reader. Hooray if you get them! They can handle a challenge every so often.

"Simple" communication is a high priority target, but rarely completely achievable for the total self-selected, beyond intended, audience.

RamblingCTO• 1 year ago

The good ol' "this proof is trivial so we'll skip it" move.

rurban2• 1 year ago

He should have really used the good ol' QED instead, lol

seanhunter• 1 year ago

Oh man. The variant I see so infuriatingly often at the moment is “It is clear that these form a Lie algebra/finite abelian group/Hilbert space/bijective map/<whatever other thing that is long-winded or complex to prove> and I encourage the reader to satisfy themselves that this is the case”.

programjames• 1 year ago

This looks pretty similar to interaction combinators:

1. https://en.wikipedia.org/wiki/Interaction_nets#Interaction_c...

2. https://github.com/HigherOrderCO/Bend

vismit2000• 1 year ago

Immersive Linear Algebra: https://immersivemath.com/ila/index.html HN: https://news.ycombinator.com/item?id=19264048

dtj1123• 1 year ago

I was never able to get my head around it, but this reminds me somewhat of the zx-calculus:

https://en.wikipedia.org/wiki/ZX-calculus

AntonioL• 1 year ago

Reminds me of the work from Bob Coecke at the University of Oxford. He came up with a pictorial language for quantum processes.

gowld2• 1 year ago

ZX-calculus mentioned in https://news.ycombinator.com/item?id=44532535

https://en.wikipedia.org/wiki/ZX-calculus

Graphical Linear Algebra

Related Stories