Welcome everybody to our pattern recognition symposium!

My name is Andreas Meyer and I am the host of the symposium and we,

every 6 months, have this workshop where all of our PhD students are presenting on their

research

and give an update what they have been working on over the past half year.

This is also accompanied with invited talks

and on this pattern recognition symposium I'm very proud that we have welcomed

Garou Marcus from Robust AI and Pim de Haan from the University of Amsterdam.

And in this first video on our pattern recognition symposium I want to feature

the presentation by Pim de Haan. He is a second year PhD student of the University

of Amsterdam and a research associate at Qualcomm AI research. Under the

supervision of Max Welling he works on building machine learning methods that

take into account the geometry and symmetries of the domain using

mathematics of groups, representations and categories. Prior to his PhD Pim was

a visiting researcher at UC Berkeley's Robotics and AI lab and obtained a

master's degree in artificial intelligence in Amsterdam and in

theoretical physics at the University of Cambridge. So today Pim will show us a

bit on his latest work on natural graph networks and how to use basic category

theory to make graph networks more expressive. Pim it's a great pleasure to

have you here and I'm very much looking forward to your presentation. So Pim the

stage is yours.

Thanks for the introduction, thanks for the invite. So I'll be talking about

the work we presented at NURBS last year called natural graph networks

and in this talk I'll try to introduce some basic concepts from category

theory and I'll try to show how we can use these to make more expressive graph

neural networks and along the way we'll be using some techniques that have been

used with quite some success to make agrarian neural networks on the images

and we'll see how they can be applied to graphs and this has been a

collaboration with wonderful help from Taka Kohan and Max Benning at the

University of Amsterdam and Qualcomm AI research and during this talk I'll be

first looking into kind of a basic building block for a lot of graph neural

networks that are around these states which are based on message passing, also

called message passing networks and I'll give you an example of where they are

lacking, what are problems that they cannot solve and thus where there may be

room for improvement and then I'll set up a bit of notation about what do we mean

by graphs and what are the symmetries of graphs and then we'll look at prior work

called equivariant graph networks that try to use the symmetries of graphs to

make graph networks more expressive and I'll show you where we can generalize

over these generalizing equivariant to something called a natural

transformation to build a global version of our natural graph networks and

lastly we'll talk about a local version of our natural graph network that is

also scalable to larger graphs which is a property we generally desire.

So as you probably know neural networks on graphs have experienced a massive

boom in popularity in the last five years or so and that's basically I guess

because a lot of problems can be reformulated or are already naturally

formulated in terms of information processing on graphs. So you can think of

friendships and some social network being represented as a graph and think

of molecules being represented by a molecular graph or even 3D shapes being

represented by the graph of vertices and edges of a 3D mesh. So all these

problems if you have good neural networks that process information on