Mathematics is the bedrock of AI. Every impactful AI application is built on the numerical foundations that were laid by trailblazers such as Alan Turing. But the mathematics of AI is far from fully understood. There are many open challenges, and these were explored at the Samsung Global Research Symposium which I contributed to in Seoul, South Korea, last week.
Take generative AI, for instance. We now have AI-powered tools such as ChatGPT and Midjourney that can create incredibly sophisticated text, images and videos. But we have only a basic grasp of the mathematics behind how such tools work. The theory lags behind the application. This isn’t especially unusual when it comes to innovation – we can fly planes, for example, but we still don’t fully understand the mathematics describing the physics that keeps them aloft. A better mathematical theory of generative AI would help us to understand not only how generative AI works, but also how and why it can fail – a crucial step towards building trust in this technology.
Generative AI was a frequent talking point at the symposium, which is held annually by the Samsung Science and Technology Foundation (a non-profit organisation that funds pioneering basic research across mathematics, physics, chemistry and biology, founded by Samsung Electronics in 2013). Past event themes have included molecular neuroscience, metamaterials and bioimaging. This year, the focus was on the mathematical theory of AI.
I was invited to represent The Alan Turing Institute and to present my own research, which focuses on improving the accuracy of Monte Carlo algorithms – a type of algorithm that uses random sampling of large, complex datasets to quantify uncertainty in areas as diverse as particle physics, virus transmission, new material characterisation, and computational models of the human heart. In generative AI, these algorithms can help to improve the speed of image generation from text prompts.
The Turing was also represented at the event by Turing Fellow and Oxford mathematician Terry Lyons, who spoke about his mathematical techniques that accurately capture complex sequences of data from multiple sources. His work has a vast array of potential applications, from diagnosing mental health conditions to detecting extreme astronomical events to recognising Chinese handwriting on smartphones. Terry and I work on different mathematical problems, but our work addresses a common, ongoing challenge in AI: how can we improve the accuracy and efficiency of existing algorithms so that they have useful applications across multiple domains and disciplines?
The event in Seoul provided a way for researchers who might not usually cross paths to meet and share ideas. As the only two UK speakers, we were in esteemed company with world-leading mathematicians and computer scientists from institutes including Massachusetts Institute of Technology, Harvard University and Mila - Quebec AI Institute. There was much food for thought. One talk, from Terence Tao at the University of California, Los Angeles, speculated about whether an AI model might one day perform the role of human mathematicians, developing its own proofs and theorems. Maybe it could even explain to humans the maths behind its own functioning.
The symposium underlined the fact that AI is still very much a work in progress. Understanding and developing the fundamental models, techniques and principles that underpin AI is a key focus of the Turing’s new strategy, and our presence at the event demonstrates our growing global influence in this space.
At the Turing, we are committed to changing the world for the better with data science and AI. To do so, we will focus not only on carrying out high-impact research to address grand challenges in the areas of environment, health, and defence and security, but also on reinforcing the mathematical bedrock that will allow our research to reach its full potential.
Top image: SeanPavonePhoto
