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Matteo Capucci Profile picture
Matteo Capucci
@mattecapu
🇮🇹, PhD @mspstrath, mathematician @ARIA_research (category theory for systems theory & cybernetics), aspiring psycohistorian. shitposting isn't endorsement.
Dec 14, 2024 • 22 tweets • 4 min read
soooo why are proofs cultural objects? here's a quick thread 🧵 here's the deal: proofs are mainly artifacts (usually text, but figures count too!) mathematicians produce to convince other mathematicians of some fact about their *shared* imaginary world. without the *shared* part, they'd mean nothing. 1/n
Feb 6, 2023 • 4 tweets • 2 min read
Two of the most lucid paragraphs on the subject (emergence) I've read recently csc.ucdavis.edu/~cmg/papers/Ca… And now a very interesting concept/observation: some emergent effects have intrinsic significance since they feed back in the components of the system which gave rise to the them:
Dec 12, 2022 • 17 tweets • 5 min read
@math3ma just gave a very interesting talk about this paper, with wonderful intuitions AN ENRICHED CATEGORY THEORY... My understanding of the situation is the following (and I hope she'll correct me if I'm wrong). At a first approximation, a lang model (LM) learns a Markov kernel π:X->X where X is a set of strings.
The question is, what structure shall we expect this kernel to have?
Nov 17, 2022 • 4 tweets • 2 min read
Idea: the structure of scientific revolutions identified by Kuhn is an instance of the more general features of evolutive/inferential dynamics. Available evidence provides the selective pressure for scientific theories. For instance, lack of selective pressure produce adaptive radiation in evolution. en.wikipedia.org/wiki/Adaptive_…
This is analogous to the pre-paradigmatic phase of a science, where lack of evidence produces a plethora of alternative theories and models.
Nov 15, 2022 • 12 tweets • 5 min read
David Spivak delivered one of the best motivational talks about ACT I've ever seen:


It's a replica of his NIST talk from last week, here's a few key points I personally vibed with 👇🧵 First: ACT is about better communication and better language *for SMEs* (Subject Matter Experts).
The corollary (this is me not David) is you shouldn't exact applications from applied category theorists.
It's not our job!
We provide the fishing cane, not the fish. I'm here to help improve co...
Jun 28, 2022 • 10 tweets • 4 min read
👉🏼 Fibred categories are like woven fabric and doing a Grothendieck construction is a like weaving on a loom: a... thread about textile intuitions for fibrations 🧵👇🏼 The threads of woven fabric, when you look up close, are entertwined in a distinctive pattern: some of them run vertically (that's the *weft* or *woof*), and some run horizontally (that's the *warp*). The *bias* is the 'diagonal' direction, along which fabric is easy to stretch From https://www.thesprucecrafts.com/warp-and-weft-1177681
Jun 27, 2022 • 27 tweets • 7 min read
👉🏼 So, what makes games and learners so similar and yet so different from each other?

A 🧵 on an abstract yet very simple (if you're categorically minded) explanation of what 'backpropagation' actually is. 0/n Let's start from gradient-based learners, i.e. machine learning models trained by gradient descent, like NNs.
Their categorical framing has been studied extensively now, starting from arxiv.org/abs/1711.10455 and culminating in arxiv.org/abs/2103.01931 1/n
Jun 27, 2022 • 23 tweets • 8 min read
✨📜 New paper out!

'Diegetic representation of feedback in open games' arxiv.org/abs/2206.12338, accepted for proceedings track at ACT'22

TL;DR: 'reverse-mode diff' for games clarifies game-theoretic structure, fixes conceptual issues and unifies them with learners

🧵 0/n Diegetic representation of feedback in open games Matteo Cap At least two of original inventors of open games, @_julesh_ and @philipp_m_zahn, have been quite enthusiastic about the ideas in the paper (and afaiu also @Anarchia45 liked them :) 1/n
Apr 22, 2022 • 9 tweets • 4 min read
✨📜 As promised, I brushed up and updated my 'old' notes on the Tambara theory of dependent optics.
It's gonna be out on arXiv by Monday, if you can't wait that long here it is matteocapucci.files.wordpress.com/2022/04/main.p… SEEING DOUBLE THROUGH DEPEN... The notes contain an explanation of the idea of action of a bicategory, and then of double categories, on another category/bicategory/double category.
The main contribution is framing Tambara modules as horizontal natural transformations between actions of double categories ImageImage
Mar 31, 2022 • 13 tweets • 4 min read
✨📜 Another paper out today!

'Actegories for the working amthematician', jww @bgavran3
arxiv.org/abs/2203.16351

A 90-pages behemoth on actegories with a focus on their role in optics/categorical cybernetics. Very proud of this one! ACTEGORIES FOR THE WORKING ... This is a theory-heavy paper, which is partly meant to be a reference and partly meant to break theoretical ground for the work we (@mspstrath) have been doing on categories of parametric morphisms and optics. Actegories are the data both these constructions start from.
Mar 30, 2022 • 5 tweets • 2 min read
Out today 👇 'Lenses for compsable servers', jww @andre_videla
arxiv.org/abs/2203.15633

We describe how the technology developed for open games can be repurposed to build web servers in a compositional way. Image This paper is basically a companion to the Idris2 library André wrote, Recombine: gitlab.com/avidela/recomb…
Although it doesn't strictly follow the 'categorical cybernetics' tao, it's still a very neat approach to correct-by-construction servers Image
Jan 9, 2022 • 7 tweets • 3 min read
#PaperADay🦆 today is kindly offered by @jonmsterling & collaborators:

arxiv.org/abs/2107.04663

1/n I'm not going to run a long thread on this because the paper is very detailed and quite enjoyable to read, but here's some of the things I loved 2/n
Jan 6, 2022 • 31 tweets • 5 min read
#PaperADay🦆 time!

Today I read Apolito's essay I announced yersterday.

TL;DR: anarcho-communism should develop a competing alternative to markets for large-scale economical organization, and 'integrated information' is an appealing theoretical framework to look at

1/n First, a reminder that Aurora Apolito is a pseudonym (I don't know if her real name is public knowledge so I'm not gonna dox). But it's cool that the name itself roughly means 'dawn of the stateless [society]', which is really cool 2/n
Dec 22, 2021 • 43 tweets • 14 min read
Today Dylan Braithwaite, @bgavran3, @_julesh_, @AyeGill and myself published the extended abstract of a work that has been cooking for quite a bit (at least a year!)

arxiv.org/abs/2112.11145

What's in there? 1/n Fibre optics (extended abstract) Dylan Braithwaite, Matteo C The problem we're trying to solve is to 'complete this square'. Lenses are modular data accessors for records (i.e. pairs), dep. lenses are modula data accessors for records *with dependency* (i.e. dependent pairs), whereas optics extend lenses to obscene levels of generality 2/n
Nov 27, 2021 • 5 tweets • 2 min read
I'm starting a category theory without context (credit: ) art gallery thread First entry: tonight's diagram chasing
Nov 23, 2021 • 4 tweets • 1 min read
If you didn't get it, the bottom line (or at least *my* bottom line) is semicolon-y coding is obsolete.

We should write code with string diagrams!

It's not about *visual programming*, it's about making concurrency trivial to see and reason about. Also, don't get me wrong, I don't want everything to be a string you plug around. I want string diagrams to be a way to organize code in a file, not as the only programming facility. That's hell.
Nov 23, 2021 • 7 tweets • 2 min read
"We're busy teaching you to program in a programming language that has semicolons all over the place. What that means is that it is not at all obvious how to split those tasks up into things which can be done simultaneously on different cores,... 1/5 Because your program structure says 'first do this and then, maybe, using the results of that, do something else'. And you have no choice but to wait for the first thing to finish before you start the second thing, and... 2/5
Oct 21, 2019 • 16 tweets • 3 min read
Introducing the Pirahã people:
en.wikipedia.org/wiki/Pirah%C3%…
They are a small (800ish) culture leaving in the Amazon forest. Them alone suffice to challenge a lot of our assumptions about human nature. Follow me.

(1/n) They have one of the most interesting culture: very self-sufficient (they call themselves 'the straight ones' and show no major interest in 'developing' themselves), incredibly adapted to their environment. This both reflects and is reflected in their unique language.

(2/n)