Category: News

In this Erlangen Hub Q&A we spoke to Marika Taylor, Co-Investigator and Theme C Deputy Lead. Marika is a Professor of Mathematics, Physics and AI at the University of Southampton. She trained in theoretical physics under Stephen Hawking, and is currently interested in geometric ML for fundamental physics applications and physics-inspired methods for ML. Marika was a Turing Institute Fellow and recipient of the “Dutch ERC” Vidi. She has a long track record with start-ups, including in encryption and fintech.  

Can you share a bit about your background and your current research focus?

My main research background is in mathematical and theoretical physics – particularly string theory, quantum theory and gravity. In parallel with this work in fundamental science, I have always been involved in mathematical modeling for real world problems, particularly finance, and have used neural nets for many years in that context. In recent years I’ve seen a convergence between my fundamental science research and my applied work: concepts from my areas of physics are being used within AI, while AI is increasingly being applied within fundamental physics too. A nice example would be graph neural networks in non-Euclidean geometry. Non-Euclidean geometry underpins our understanding of Einstein’s theory of general relativity (gravity). Many of the physical insights obtained from studying particularly geometries for gravity lead to insights into GNNs embedded into such geometries. Another example would be around symmetries. Physicists always build in their understanding of the underlying symmetries (exact or approximate) into their modelling of a system. One can similarly build symmetry equivariance into neural networks – for example, if you are classifying images of 3d objects and are agnostic about the orientation of the objects, then a network with rotational equivariance built into it will be more efficient in classification. My group is currently exploring more general symmetry equivariant networks, drawing from physics insights; this enables us to reduce substantially the number of parameters that need to be learned, and also to understand conceptually patterns found in previous algorithms. We are also interested in using physics understanding of time dependent systems to develop spiking neural networks; the latter are nature inspired, in that neurons only fire when a threshold is met, making them much more energy efficient.

What inspired you to pursue this area?

Throughout my career I have always worked on the frontiers of fundamental science. String theory is a “theory of everything”. It uses concepts from right across mathematics and also leads to new insights and ideas in mathematics – topological quantum field theory, for which Ed Witten won the Fields Medal, is a notable example. In parallel I’ve always enjoyed using the breadth of my knowledge in mathematical sciences for real world applications and I’ve often found that I get new insights into fundamental science from the applied work I’ve done. Over the last few years I’ve gradually moved more and more into AI, for both fundamental science and applied work, because there are so many exciting developments.

Which themes are you connected to within the Erlangen AI Hub and how does your work within the hub intersect with your research background?

The main theme that I am connected with is “Understanding Learning”, but I link with all the themes. Much of what I do relates to understanding conceptually hidden structures in data, and how geometry and topology can be used to characterize these. My physics insights into geometry also facilitate relating geometric and topological insights to real world phenomena.

What attracted you to the Erlangen AI Hub and what do you hope to see it achieve?

The hub is exploring the mathematical foundations of intelligence – this is essential to develop better, more efficient and safer models, which in turn will allow us to use AI in more contexts.

What’s been the most surprising or exciting finding in your work so far?

I don’t think that I would have predicted ten years ago that my two parallel streams of research would become so closely connected, with physics giving insights into developing AI and AI started to be used more in physics. (For AI to really be adopted more widely in physics, we will need robustness and accuracy.)

What challenges have you faced in your research, and how did you overcome them?

I like to take on research problems that are quite open ended and conceptually challenging. Inevitably that means that at times I get stuck or can’t quite see where to go next! Then I take a break, think about something else, and also talk to others, to get new ideas on where to go next.

What advice would you give to someone just starting out in your field?

I would advise somebody to follow their interests, and see where these take them!

In this Erlangen Hub Q&A we spoke to Yue Ren, Co-Investigator and Theme B lead at Durham University. Yue is a UKRI Future Leaders Fellow and leading expert in tropical geometry, mathematical software, and the application of both to neural networks and problems in industry and sciences. He is a core developer of the computer algebra systems Polymake, Singular, and OSCAR. 

What is your name?

Yue Ren

Can you share a bit about your background and your current research focus?

My background is in algebraic and tropical geometry.  I did my PhD in Germany, and spent some time in the US, South Africa, Israel, and Sweden before moving to the UK. My current focus is on applications of the latter to polynomial system solving and machine learning.

What inspired you to pursue this area?

Mathematically, I’ve always been fascinated by the concrete interplay between algebra, geometry, and combinatorics in tropical geometry.  However, I was always prone to making mistakes in hand calculations, so I decided to specialize in teaching a computer to do them for me instead.  Professionally, I wanted a path that combined my mathematical interests with practical skills like software development.

Which themes are you connected to within the Erlangen AI Hub and how does your work within the hub intersect with your research background?

I am mainly connected to Theme B, though my research touches upon other themes as well.  My work within the hub revolves around taking theoretical techniques from pure mathematics and turning them into practical algorithms. It’s a way to expand the machine learning toolbox with some interesting new tools.

What attracted you to the Erlangen AI Hub and what do you hope to see it achieve?

The Erlangen AI Hub brings together researchers from a wide range of backgrounds who are all pursuing a common goal. I’m really looking forward to the mathematical theories and practical tools that will come out of this unique mix of expertise.

What’s been the most surprising or exciting finding in your work so far?

I’ve found it really surprising that p-adic numbers, an abstract number system developed by pure mathematicians for number theory, can be so useful for data analysis. Their distance prioritizes structural relationships over physical proximity, which is perfect for hierarchical data.

What challenges have you faced in your research, and how did you overcome them?

Most researchers face the same problems: getting stuck on a proof, getting unstuck only to realize you’ve built a suspiciously complicated proof for a simple statement, and Reviewer 2.  Research is an endless chain of challenges, and the best strategy for overcoming them is to ask for advice, ask for feedback, and act on it.  Not only are advice and feedback valuable, but asking for and acting on them is also a valuable skill that needs to be trained.

What advice would you give to someone just starting out in your field?

Don’t just focus on doing things, reflect on how you do them. Finding better work habits will help you spend more time on the things you enjoy and less time on the things you don’t.

What’s something people might be surprised to learn about you outside of research?

I’ve participated in the Cape Argus Cycle Tour, a 110 km race around the Cape of Good Hope with 35k entrants. I finished in the middle of my age group while taking 300 pictures along the way. I was beaten by a group dressed up as the Power Rangers under the ruthless South African sun, but at least I managed to beat that one bloke who rode a unicycle.