Rob Cornish

Neural Network Symmetrisation in Concrete Settings Cornish (2024) recently gave a general theory of neural network symmetrisation in the abstract context of Markov categories. We give a high-level overview of these results, and their concrete implicat...

You can also find an extended abstract of my longer Markov categories paper here: arxiv.org/abs/2412.09469

YouTube video by Zardini Lab ACT4ED Special Lecture - Paolo Perrone, Rob Cornish (Oxford): Markov Categories, Symmetries, & GenAI

If this is of interest to you, here is a recent talk that @paolopmath.bsky.social and I gave for a class at MIT: www.youtube.com/watch?v=ozN4...

This meta-strategy of using category theory to simplify complex reasoning appears useful much more generally, and I think the days of category theory for machine learning are just getting started.

Stochastic Neural Network Symmetrisation in Markov Categories We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $φ: H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-e...

Using Markov categories, this earlier paper explained all previous work on symmetrisation as instances of a single common principle (sec 5 of arxiv.org/abs/2406.11814). It also extended this to methodology suited for *stochastic* models, which our ICLR paper applied to diffusions.

Stochastic Neural Network Symmetrisation in Markov Categories We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $φ: H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-e...

The underlying theory we use here comes from arxiv.org/abs/2406.11814, which studied the problem of symmetrisation using *Markov categories*. Markov categories allow for reasoning about probability in a conceptual, diagrammatic way, while also maintaining full mathematical rigour.

A meta-point of this paper is that category theory has utility for reasoning about current problems of interest in mainstream machine learning. The theory is predictive, not just descriptive. 🧵(1/6)

Neural Network Symmetrisation in Concrete Settings Cornish (2024) recently gave a general theory of neural network symmetrisation in the abstract context of Markov categories. We give a high-level overview of these results, and their concrete implicat...

You can also find an extended abstract of my longer Markov categories paper here: arxiv.org/abs/2412.09469

YouTube video by Zardini Lab ACT4ED Special Lecture - Paolo Perrone, Rob Cornish (Oxford): Markov Categories, Symmetries, & GenAI

If this is of interest to you, here is a recent talk that @paolopmath.bsky.social and I gave for a class at MIT: www.youtube.com/watch?v=ozN4...

This meta-strategy of using category theory to simplify complex reasoning appears useful much more generally, and I think the days of category theory for machine learning are just getting started.

Stochastic Neural Network Symmetrisation in Markov Categories We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $φ: H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-e...

Using Markov categories, this earlier paper explained all previous work on symmetrisation as instances of a single common principle (sec 5 of arxiv.org/abs/2406.11814). It also extended this to methodology suited for *stochastic* models, which our ICLR paper applied to diffusions.

The underlying theory we use here comes from arxiv.org/abs/2406.11814, which studied the problem of symmetrisation using *Markov categories*. Markov categories allow for reasoning about probability in a conceptual, diagrammatic way, while also maintaining full mathematical rigour.

Awesome work by Kia @leoeleoleo1.bsky.social and @rob-cornish.bsky.social !