Studying biological learning in order to advance artificial intelligence
Johannes Schmidt-Hieber, Professor of Statistics at the University of Twente, develops and applies mathematical statistics to enhance our understanding of both artificial and biological neural networks. “By better understanding the statistical properties that underlie learning in the brain, we can address the current limitations of artificial networks.”
Trained as a mathematician analysing the theoretical properties of statistical methods, Johannes Schmidt-Hieber has contributed to various topics within mathematical statistics over the years. He is particularly recognized for his work on the theoretical understanding of artificial intelligence (AI).
“I was amazed by the rapid progress and the society-changing successes of AI,” he says. “AI develops very quickly, but we still cannot completely explain how it works. Thousands of data scientists apply it, but we do not understand why it works so well.”
That is the gap that Johannes Schmidt-Hieber has been addressing. The UT professor quickly recognized that the statistical theory that has been developed over the past century could be leveraged to gain a deeper understanding of artificial neural networks, which are at the heart of the AI revolution.
“If you think of AI as a collection of statistical procedures, you can build on a range of sophisticated techniques to analyse artificial neural networks,” explains Schmidt-Hieber. However, this is extremely challenging. “Artificial neural networks are non-linear and highly complex objects with typically millions of parameters learned from data. In public media, they are often portrayed as black-box machines that cannot be understood theoretically anymore. While this view is overly pessimistic, the complexity of neural networks puts them far beyond the scope of classical statistical theory with its focus on interpretable statistical models and linear structures. Yet, statistics offers a completely new perspective on understanding artificial neural networks.”
The scientist’s goal is to ensure that theoretical insights have a tangible impact on the development of AI technology. “Currently, AI progress is largely driven by trial and error. Mathematicians often step in after new advancements are made to explain them, meaning theory follows practice in computer science. A significant drawback of this approach is that we end up creating machines that we don’t fully understand.”
Ideally, theoretical insights should precede and guide practical developments, stresses Schmidt-Hieber. “This motivation drives my research,” he says, adding that the current situation is even more concerning. “Artificial networks excel in scenarios where classical theory suggests no method should perform well, revealing gaps between existing theory and practical outcomes. Our work aims to bridge these gaps.”
Now, the professor has shifted his research focus to a related, yet distinct area—biological learning. Or in other words, studying how our brain learns. “One can think of the brain as a statistical method,” says the UT scientist. “By better understanding the statistical properties that underlie learning in the brain, we can address the current limitations of artificial networks.”
While artificial neural networks are inspired by the brain, they differ in many critical ways. In his project funded by an ERC Consolidator Grant, Johannes Schmidt-Hieber applies statistical methods to understand biologically inspired learning rules. “After interpreting AI methods as statistical procedures, we are now viewing learning in the brain as a statistical process,” he explains. “By extending the theory we previously developed, I aim to gain deeper insights into how the brain processes signals and how we learn. With this understanding, we hope to explain why the brain requires much less data to learn, insights that could lead to the development of more efficient algorithms for training artificial neural networks.”
Education
Johannes Schmidt-Hieber particularly enjoys supervising students, with his primary goal being to help them become independent researchers. “Universities today resemble schools more than ever, offering little room for independence and flexibility,” he says. “However, at some point, students need to develop autonomy. They should learn to formulate their own concepts and research questions and master time management. I try to help them with that because I believe that gaining independence is the key to success.”
About Johannes Schmidt-Hieber
Johannes Schmidt-Hieber is the Professor of Statistics at the Department of Applied Mathematics of the University of Twente. He studied mathematics with a minor in theoretical physics at the Universität Freiburg and the Universität Göttingen, followed by PhD research at the Universität Göttingen and the Universität Bern (2007- 2010). He then held Postdoc positions at Vrije Universiteit Amsterdam and ENSAE Paris before becoming an assistant professor at Leiden University (2014-2018). In 2018, he was appointed as a full professor at the University of Twente, making him the youngest professor at the university at the time.
Johannes Schmidt-Hieber is a recipient of several prestigious personal grants, including a VIDI grant (2019-2024) and an ERC Consolidator Grant (2024). In 2024, he was named an IMS (Institute of Mathematical Statistics) Fellow, an honour reserved for experts who have demonstrated distinction in research in statistics or probability or have demonstrated leadership that has profoundly influenced the field.
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