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Konstantinos Spiliopoulos believes that applied mathematics\u2014the use of math in a variety of other fields\u2014could address both problems. \u201cArtificial intelligence is a marriage between applied mathematics, statistics, computer science, and engineering,\u201d says the professor of math and statistics and director of statistics.<\/p>\n
A model like ChatGPT is trained with a massive amount of data from books, websites, articles, and other sources. When we ask it a question, the response is based on patterns learned during its training. But what if it can\u2019t find an answer to our question, or if it finds conflicting information? Those conflicts can lead to errors, or \u201cAI hallucinations.\u201d Sometimes those mistakes are innocent, but the consequences grow as we ask AI to perform more important tasks.<\/p>\n
And that process also uses a lot of energy. The International Energy Agency estimates the energy consumption of data centers, which we rely on for AI as well as data storage and cryptocurrency production, will double by 2030, to approximately 945 terawatt-hours annually\u2014nearly equivalent to the annual electricity consumption of Japan.<\/p>\n
The most popular AI models have billions or even trillions of interconnected parameters guiding its actions. Spiliopoulos\u2019 big idea is to bypass their superfluous parameters and to quantify and minimize uncertainty. \u201cIt turns out that not all of these connections are important,\u201d he says.<\/p>\n
To improve an AI model\u2019s efficiency and reliability, Spiliopoulos tweaks the underlying algorithms, experimenting with more direct routes to an answer while isolating the components that matter. These incremental changes make the model faster and cheaper while maintaining\u2014or improving\u2014its accuracy and reliability.<\/p>\n
Arts<\/em> x Sciences<\/em> spoke with Spiliopoulos about how and why he got into AI research\u2014and where he hopes his work will lead.<\/p>\n Konstantinos Spiliopoulos:<\/strong> More than 10 years ago, I started being interested in how to make better sense of these methods and algorithms. Not as many people as today were focused on it, so I felt there was a lot of room to grow in that area and to do something that will probably be meaningful and impactful for the years to come.<\/p>\n I had realized there were many problems that we were not able to do, or that we were not able to do in a satisfactory way. For example, I was one of the first to look at solving things like partial differential equations\u2014which govern dynamical systems like how airplanes fly. Deep learning and machine learning have now enabled us to go beyond the standard numerical methods we had been using forever.<\/p>\n I\u2019m trying to solve problems in a way that will be robust and as computationally efficient as possible. Let\u2019s say there are two extremes. One extreme is that you may have something that works very well, but is computationally inefficient\u2014it consumes a lot of energy, many hours, and a lot of work. And you may have something that works very quickly, but it gives you nonsensical results. My work is in the space of trying to provide both statistical and computational guarantees\u2014being able to say that if you use this algorithm, or if you tune things this way, you are guaranteed to get to the right answer with high probability in a way that will not be computationally inefficient. Finding that sweet spot is very hard.<\/p>\n Deep neural networks [a complex AI technology] have thousands, millions, or billions of parameters. I think ChatGPT now has the order of trillions of parameters. When we train these models, we typically train all of the connections between parameters\u2014but maybe some of them can be switched off. It\u2019s like having a house with 50 doors but you only use 10 of them. The other 40 could be kept open or closed. The work we\u2019re trying to do is to find some methodological way to say, \u201cThese are the doors you need and these are the doors you don\u2019t need.\u201d<\/p>\n The goal of the book is to help undergraduate and graduate students and practitioners to think about how to effectively approach these models\u2014to understand the mathematics behind them instead of just coding them. So the book is targeted at computer scientists, data scientists, engineers, statisticians, and mathematicians. I think it will become clear in the future that we need more of this training for our students and for ourselves and it will be important for the younger generation of scientists to be trained mathematically on this topic. Scientific breakthrough and innovation is more likely to come from people who know how things work, who are capable of leading well into the future, and who are far more than just AI-users.<\/p>\n This interview has been edited for brevity and clarity.<\/p>\nArts<\/em> x Sciences<\/em>: What led you to study AI algorithms?<\/h6>\n
What were you seeing as the areas where your work could have a meaningful impact?<\/h6>\n
And where are the potential areas to improve on how AI handles complex questions?<\/h6>\n
What are you experimenting with as you try to strike that balance?<\/h6>\n
You recently published a book\u2014Mathematical Foundations of Deep Learning Models and Algorithms<\/em> (American Mathematical Society, 2025). Who is this for?<\/h6>\n
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