How can we change the geometry of a neuromanifold by varying the architecture of its neural network?

Kathlén Kohn, WASP AI/Math Assistant Professor at the Department of Mathematics at KTH Royal Institute of Technology in Sweden, has recently published a news journal article in SIAM NEWS. The article, called The Geometry of the Neuromanifold, gives an overview of her research on neural network theory for a broad mathematical audience.

“At heart, I’m an algebraic geometer, and since I joined KTH and WASP, I use algebra to investigate the underlying geometry of neural networks in machine learning and of 3D reconstruction in computer vision.”

What is the news article The Geometry of the Neuromanifold about?
“It gives an overview of my research on neural network theory for a broad mathematical audience.”

Can you share some results from your research?
“In my group’s research on neural network theory, we advocate to study the training of a neural network in function space instead of parameter space. We aim to understand the geometry of that function space and how it varies when changing the network architecture. We then analyse how these varying geometric features affect the optimization problem of training the network. This line of research will lead to a better understanding of the capabilities and limitations of different network architectures, and hopefully to better informed network design choices in the future.”

How is it to be a part of WASP?
“Being part of WASP is great. Not only is the funding landscape for Math in AI superior, but also the networking opportunities: I have integrated much faster in the Swedish research landscape and could establish contacts much easier with computer scientists and engineers outside my own discipline.”