Today, artificial intelligence must see billions of images to learn how to differentiate them. The machine sifts through vast amounts of potential patterns and characteristics before having enough information to recognize images on its own.
"We are working to study the mathematics behind image analysis and to develop new ways of studying characteristic features of images. We want to better understand how a computer can, for example, distinguish between an image of a dog and an image of a cat. In the long run, we hope that this mathematical knowledge can make artificial intelligence much more efficient, needing fewer resources for training," says Fabian Harang, Professor of Mathematics at the Department of Economics at BI Norwegian Business School.
Professor of mathematics at BI Fabian Harang (photo: Alexander Eriksson / BI Norwegian Business School).
It also opens new horizons for application.
"There are many areas where one would want to train computers but lacks enough images, such as some types of medical imaging diagnostics," Harang continues.
Together with researchers from across the world, he has just spent a year at the Centre for Advanced Study in Oslo. He and Professor Kurusch Ebrahimi-Fard from NTNU Trondheim he led the research project Signatures for Images. A groundbreaking project to develop a new algebraic and analytical foundation for understanding mathematical structures in two-dimensional data, such as images.
"An image consists of two axes so that each pixel or coordinate can have a color. In this sense, an image is a mathematical function of two variables, and given a collection of such functions, or images, we can study abstract characteristics to better understand what the functions represent and how they change when examined in detail."
Curiosity-driven research
"What characterizes basic research is that it is curiosity driven. It is not something we do to solve practical problems today. Nevertheless, basic research has historically proven to be a cornerstone in innovation and technological development. Although our research primarily focuses on developing abstract mathematical research, it may have relevance for modern applications in data security and image recognition."
Illustration of pixels with different colour values (image: Getty Images).
A team in the UK is already using the research to improve artificial intelligence for image recognition, making it more resistant to attacks from hackers.
"Imagine your car is driving, and a little girl is standing in the road. The car’s camera sees what’s happening and helps you brake faster so that no one is hurt. However, the car's camera systems and image recognition algorithms are susceptible to manipulation that could potentially alter the input images, so the car does not recognize the girl in the road. You might react more slowly, meaning the car doesn’t brake in time. Our research could potentially be used to make camera systems better at detecting and countering such manipulation."
The Centre for Advanced Study plays an important role in facilitating such groundbreaking and curiosity-driven basic research, where there is no pressure for immediate practical applications but rather an expansion of human knowledge.
"They have a team whose sole purpose is to ensure that researchers have as efficient a working environment as possible so that we can spend our time on research and nothing else. They also provide a generous budget that allows us to invite the best researchers from around the world to Oslo. It’s fantastic."
A leading mathematical research environment at BI
Advanced mathematics is important for several fields at BI, including finance, economics, and data science.
"The mathematics and statistics environment at BI is strong and consists of people from several interesting fields. I hope we can strengthen it even more going forward by applying for funding from the Research Council and the EU to further develop both the field and the academic environment."
Harang’s research covers several topics, and he is also active in interdisciplinary research related to finance and economics. This fall, he is organizing a series of research seminars in collaboration with UiO and Simula, dedicated to mathematical economics. The goal is to create a meeting place for researchers from both mathematics and economics to discuss new ideas and inspire collaborations across disciplines.
"We hope that mathematicians will be inspired to discover new mathematical problems and equations to study, while economists may be inspired to find new ways to solve their challenges. I currently work at the Department of Economics at BI, but as a mathematician. I find the intersection of these two fields very exciting," concludes Harang.
For 2024-2025, another BI researcher has been invited by the Centre for Advanced Study. Professor of finance Paul Ehling will investigate the behavior of different types of investors and how this affects wealth distribution.