Dr. Paul Lessard and his collaborators have written a paper on "Categorical Deep Learning and Algebraic Theory of Architectures". They aim to make neural networks more interpretable, composable and amenable to formal reasoning. The key is mathematical abstraction, as exemplified by category theory - using monads to develop a more principled, algebraic approach to structuring neural networks.

We also discussed the limitations of current neural network architectures in terms of their ability to generalise and reason in a human-like way. In particular, the inability of neural networks to do unbounded computation equivalent to a Turing machine. Paul expressed optimism that this is not a fundamental limitation, but an artefact of current architectures and training procedures.

The power of abstraction - allowing us to focus on the essential structure while ignoring extraneous details. This can make certain problems more tractable to reason about. Paul sees category theory as providing a powerful "Lego set" for productively thinking about many practical problems.

Towards the end, Paul gave an accessible introduction to some core concepts in category theory like categories, morphisms, functors, monads etc. We explained how these abstract constructs can capture essential patterns that arise across different domains of mathematics.

Paul is optimistic about the potential of category theory and related mathematical abstractions to put AI and neural networks on a more robust conceptual foundation to enable interpretability and reasoning. However, significant theoretical and engineering challenges remain in realising this vision.

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Links:

Categorical Deep Learning: An Algebraic Theory of Architectures

Bruno Gavranović, Paul Lessard, Andrew Dudzik,

Tamara von Glehn, João G. M. Araújo, Petar Veličković

Paper: https://categoricaldeeplearning.com/

Symbolica:

https://twitter.com/symbolica

https://www.symbolica.ai/

Dr. Paul Lessard (Principal Scientist - Symbolica)

https://www.linkedin.com/in/paul-roy-lessard/

Interviewer: Dr. Tim Scarfe

TOC:

00:00:00 - Intro

00:05:07 - What is the category paper all about

00:07:19 - Composition

00:10:42 - Abstract Algebra

00:23:01 - DSLs for machine learning

00:24:10 - Inscrutibility

00:29:04 - Limitations with current NNs

00:30:41 - Generative code / NNs don't recurse

00:34:34 - NNs are not Turing machines (special edition)

00:53:09 - Abstraction

00:55:11 - Category theory objects

00:58:06 - Cat theory vs number theory

00:59:43 - Data and Code are one in the same

01:08:05 - Syntax and semantics

01:14:32 - Category DL elevator pitch

01:17:05 - Abstraction again

01:20:25 - Lego set for the universe

01:23:04 - Reasoning

01:28:05 - Category theory 101

01:37:42 - Monads

01:45:59 - Where to learn more cat theory