Research philosophy

My research is focused on understanding the fundamental principles of intelligence through the lens of category theory. The method and the goal in this case are intertwined: to understand the abstract nature of intelligence - how we structure the thoughts in our heads - it is first necessary to find a better way of structuring these thoughts. Category theory is a tool to do that. This is a strong claim which calls for an explanation. Eventually I hope to get around to writing one.

The notion of intelligence largely overlaps with notions such as life, autopoiesis, philosophy of mind, consciousness, and cybernetics. All of these notions have always had a mythical component assigned to them. But with science and mathematics in the 21st century we are finally starting to have enough context to ask the right questions. At the moment my work is mostly theoretical (see papers), but the plan is to eventually start writing actual code. Even more, for reasons unknown yet, the question of understanding intelligence might itself be nonsensical or ill-phrased. I considering framing the issue and asking the right questions to be progress in itself.

In essence, by investing my resources into this, I am betting that the required ingredient to make progress on these abstract questions of intelligence and consciousness is the study of abstraction itself: category theory. ¹ I’ll eventually write up more thoughts on all of this: how I understand the role of category theory in modern science and how it can be used to understand machine learning.

I am learning how to best express this long-term research philosophy. These are still rough notes that I keep coming back to in order to reflect on and improve them. Please do challenge anything that doesn’t come across as clear and compelling. I’m also trying to scale up these endeavours, so if your goals overlap, feel free to get in touch!

While this is a long-term goal, the work I am currently doing as a part of my PhD is more concrete. I am still using category theory, but now to formalize and distill the essence of information flow in artificial neural networks, with detours into game theory. This allows me to make tangible, measurable progress on the long-term research goal.

I’ve written a number of papers which unpack the building blocks of neural networks into composable pieces: automatic differentiation in terms of reverse derivative categories and lenses, neural network weights in terms of the Para construction, and various neural networks as compositions of parameterized lenses. I am currently working on formalizing specific neural network architectures, especially Generative Adversarial Networks, whose game theoretic properties I am aiming to connect to existing work in compositional game theory.