Types and Neural Networks
LLMs generate code as flat token sequences, then typecheck after the fact. Can we make the output space itself be typed?
Bruno Gavranović's blog posts
Blog post from the website www.brunogavranovic.com
Latest posts
My PhD Thesis is out!
After four years in the making, I've finally defended, and published my PhD thesis.
Two kinds of Prisms
In this short blog post I describe two different notions of a prism, describe their relationship, and outline reasons for why one gives us a cleaner operational interpretation than the other.
Graph Convolutional Neural Networks as Parametric CoKleisli morphisms
This is a short blog post accompanying the latest preprint of Mattia Villani and myself which you can now find [on the ArXiv](https://arxiv.org/abs/2212.00542).
Optics vs Lenses, Operationally
I've been thinking about lenses and optics a lot lately. They're both abstract gadgets that model various sorts of bidirectional processes, appearing in machine learning, game theory, database systems, and so on. While optics are more general, it's understood that they're equivalent to lenses in the special case of a cartesian monoidal category $\mathcal{C}$. In this blog post I'll explain how…
Lenses to the left of me, Prisms to the right
There's an interesting way to think about lenses and prisms. Lenses model processes that perform internal computation and interact with the environment. Prisms model processes that perform internal computation or interact with the environment. Let me explain what I mean.
Meta-learning and Monads
Meta learning is an exciting approach to machine learning. Instead of training models to do particular tasks, it trains these models to learn how to do those tasks. Meta learning is essentially learning squared':' learning how to learn. There's been plenty of exciting developments in this area, but in this blog post I want to explore one foundational aspect of it what it means to meta learn.
Riding upon the fields on the horse of mathematics
I admire the elegance of your method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot. This quote from Einstein resonates with me in a pretty surprising context. Einstein said this in a letter to Levi-Civita, praising what's now called the Einstein notation. After watching Kevin Buzzard's…
Towards Categorical Foundations of Learning
Having posted our paper on Categorical Foundations of Gradient-Based Learning on arXiv, I decided to write a short update on the progress we made, and the staggering amount of potential I believe Category Theory has in the field of Deep Learning.
Dinatural transformations
In this blog post I will talk about dinatural transformations, which is a concept found in category theory. I'll describe the intuition behind them, and how you could have arrived at their definition yourself.