If you've been curious what I've been up to, the recently published report from GLAIVE reveals a part of it: https://glaive-research.org/2025/12/08/q4-report.html

Different products of containers, with examples on the List container: List ⊗ List -> rectangular array List ∘ List -> ragged array List × List -> two lists List + List -> a boolean value and a list

Remember kids, theoretical physicists have irreparably ruined public trust in science by saying they *hope* we *could* find BSM evidence at the LHC, but Elon gets to predict his products will "do the sci-fi" and be wrong 100 times per year for profit but he's just giving them hope

Had an absolutely fantastic time in Scotland. It's been great seeing a lot of friendly faces, and making exciting research progress with Glaive

London ---🚅---> Glasgow

Containers and quotient containers can be interpreted as choices of a category S with some constraints on it, and a functor S -> Set. For an ordinary container, S has to be a discrete category, i.e. a set.

Para construction for double categories https://arxiv.org/abs/2510.26465

Stumbled upon this on HN: "Categorical foundations for CuTe layouts" https://research.colfax-intl.com/categorical-foundations-for-cute-layouts/

Stumbled upon the paper "Sorting with Bialgebras and Distributive Laws" ( https://www.cs.ox.ac.uk/people/nicolas.wu/papers/Sorting.pdf ) which introdued me to the idea that certain sorting algorithms can be considered 'duals' of others:

I have been thinking about fixpoints of containers recently, and noticed that there seems to be a close correspondence between fixpoints of extensions of containers \mu(Ext(C)) and iterated compositions I + C + C o C + C o C o C ... Has this been formally established somewhere?

Interestingly, this is still a question I do not have a good answer for, and a question that I didn't see tackled by the deep learning community at all.

Unbelievable! Today, San Diego witnessed a government-sanctioned kidnapping. ICE stormed Buona Forchetta in military gear ripping workers away, then unleashing tear gas and smoke on the terrified community. Full on police state, fascism now used on American citizens. Stay aware. #OnYourSide

Stumbled upon a peculiar paper: Aggregating time-series and image data: functors and double functors https://arxiv.org/abs/2504.05274

I've always wanted someone to write a type-safe framework for tensor manipulation that a) fully leverages first-class types, and b) is ergonomic Maybe that someone has to be me; I wrote a proof-of-concept in Idris and used it to implement transformers: github.com/bgavran/Type...

Coming to an ICML near you arxiv.org/abs/2502.03689

London --🚄--> Edinburgh

Stumbled upon an Idris implementation of type-safe tensor computation (alongside many other things) https://github.com/joelberkeley/spidr/tree/master

Spotted at EPFL

I've been playing with provably correct list sorting ( https://gist.github.com/bgavran/e6ef899a86223d32e25adde4ce884a64 ), and internalising a very unintuitive fact: there exists a *type of sorted lists*. It's something I would have never came up with myself. Hence makes me wonder, what *else* is

After a multi-year collaboration with Martin Biehl, @mattecapu.bsky.social and @nathanielvirgo.bsky.social, I’m stoked to share the first of (hopefully) many outputs: “A Bayesian Interpretation of the Internal Model Principle” arxiv.org/abs/2503.00511. 1/

Provably correct FizzBuzz: https://github.com/0xd34df00d/fizzbuzz-i

I never thought about the underlying implementation of typed holes in languages like Idris/Agda before. Are they just implemented as a nullary constructor of an inductive type? ``` data Expr : Type where Num : Nat -> Expr Add : Expr -> Expr -> Expr Hole : Expr ```

Reading about linters, and I ran into a lovely example of what they keep you from doing: (from the International obfuscated C code contest https://github.com/ioccc-src/winner/blob/master/2011/goren/goren.c )

Fun fact I just learned: gunpowder was created by alchemists as a byproduct of trying to create the elixir of life. https://en.wikipedia.org/wiki/Gunpowder

Discovered a gem of a paper, which merges two things I am very excited about: DeepRL + (dependently) type-directed program search. Highly recommended read. https://arxiv.org/abs/2407.00695

I'm writing a new blog series on practical implementation of substructural type systems, in Idris! The first blog post will look at substructural polymorphism and why it's *hard*, harder than people assume on first glance! zanzix.github.io/posts/5-subs...

What separates life from death? Mary Shelley once wrote: "To understand life, we first need to understand death". In this movie, we see how a single-celled organism dies. The same matter in both pictures. It is not the same state or the same integrated complexity. youtube.com/watch?v=4bj6...

I'm hoping starting to post more both on Bluesky and Mathstodon. Is there a good client for crossposting I ought to use? (as opposed to what I'm doing now, which is pasting the same message twice)

An Invitation to Neuroalgebraic Geometry https://arxiv.org/abs/2501.18915

The takeover of Twitter was a preview of what we're all living with now and a stark example of why you can't let any one person have too much money: they go insane and make themselves everybody's problem

This post by @zanzi on the Cybercat blog is the one I've been the most excited for in a very long time: Optics for UI 1: Deconstructing React with Parametrised Lenses https://cybercat.institute/2025/01/21/ui-para-optic/

This has been a long time coming! Have you ever wondered what lenses and UI programming have in common? Can we recreate React, Elm, and Redux entirely using pure category theory? Read this series to find out. cybercat.institute/2025/01/21/u...

Dropping in with some good news that two of the last papers from my PhD have recently been accepted to their respective journals, SciPost and PhysRevLett :))) Many thanks to the hard work of all my collaborators! 1/3

🥰 🎄

I have an unfortunate personal announcement: I was fired from Symbolica. This was a complete surprise. I am in shock and, honestly, still not sure how to process this. If you've been following me, you understand just how excited and optimistic I am about the programme of categorical deep learning.

Rewatched “My Neighbour Totoro” with @bgavran.bsky.social yesterday and was once again reminded of the goodness in humanity, if only for a little bit :) deeply recommend doing so given the state of the world these days

🌟Noether's razor⭐️ Our NeurIPS 2024 paper connects ML symmetries to conserved quantities through a seminal result in mathematical physics: Noether's theorem. We can learn neural network symmetries from data by learning associated conservation laws. Learn more👇. 1/16🧵

I've been thinking about how 'First Class Types' feels like a much better name for 'Dependent Types' than 'Dependent Types'. The fact that we can treat types as first-class objects seems of primary value, and the fact that they types arise as outputs of functions sometimes seems secondary.

Reposting with alt text!

"Categories and Compositionality with a view to Applications" z7-stage-act4e-book.zuper.ai/sync/ACT4E/A...

A fundamental puzzle of programming is how to lessen the enormous cost of good programming abstractions. I didn't mean things like functional vs imperative languages. I mean more fundamental things, like the choice between a CPU with an instruction set, vs circuit level hardware design.

A random selection of thoughts from my history, from the old bird site, pasted here!

"According to Eastern traditions, all dollars are not the same. It matters where you get it from. In Buddhism this is called “right livelihood”. In Chinese culture, it is Qi (energy) It is believed that working for unethical or toxic companies gives you toxic or tainted money"

A welcome property of Para(Optic) framework for studying deep learning is that it does not impose any conceptual separation between training and inference stages - meaning in-context learning exhibited by Transformers is not automatically ruled out as in some classical frameworks.

Luc's ten commandments of authorship luc.devroye.org/commandments...

One of my deep beliefs is that the transition from the human to an "artificial" intelligence is a natural progression, rather than something to be feared or resisted. It often sounds like we're overemphasizing what "human values" mean, even though we can't agree on what they mean.

Neural networks, seen as processes, have 3 distinct properties. They are: * parametric * bidirectional * defined functorially by differentiation Using the category Poly to model them blends these distinctions. I'm still trying to decide whether that's a good or a bad thing.

"CT is an emergent inevitability in response to the structure which underpins our world"

There is more than one way to skin a cat, but only one way to preserve its structure.

"Just because you know something, it doesn't mean that you know that you know it." A random piece of thought that I heard in @davidcorfield.bsky.social's talk that resonated with me