Georgios Arvanitidis

Project title

GADL: Geometric Analysis of Deep Learning

What is your project about?

Artificial intelligence (AI) technology progresses rapidly, finding applications in every aspect of our lives, from minor decisions like recommending a video to more complex tasks such as driving a car and even important problems such as disease diagnostic systems. The main cause of this progress is the advances in the deep learning field, where both the models and the optimization processes used to train them with the given data are particularly complex. Despite practical achievements, a key research question persists: How do these models exhibit high performance on new, unseen data? The goal of GADL is to analyze this concept, known as generalization, and explain the behavior of deep learning methods relying on differential geometry. We can explore and study several aspects of deep learning from the geometric perspective, which enables the development of new learning theories for the associated models.

How did you become interested in your particular field of research?

I have always been interested in mathematics because, with creativity and imagination, someone can model and analyze potentially any type of problem in a rigorous way. I particularly enjoy geometry, as it naturally facilitates the intuitive visualization of abstract concepts. During my undergraduate studies, I discovered the field of machine learning, where mathematical models are developed and trained to solve certain tasks given relevant data, forming the foundation of modern AI. As a PhD student, I combined these two interests by working at the intersection of geometry and machine learning, with a focus on developing models. Lately, I have been fascinated by the intriguing concept of generalization in deep learning, where the inherent geometric information provides many possibilities for analysis.

What are the scientific challenges and perspectives in your project?

The long-existing learning theories are not capable of explaining the generalization in deep learning. While modern approaches have been proposed, they typically rely on conflicting and unrealistic assumptions, hence the absence of a unified and convincing theory. The main reason is the inherent complexity of deep learning models, which makes it particularly challenging to understand how they learn and analyze the actual behavior of the associated optimization process. Differential geometry appears to be a promising mathematical framework for studying the static properties of models and the dynamics of the learning process, as it approaches the problem from a different and under-explored perspective.

What is your estimate of the impact, which your project may have to society in the long term?

Artificial intelligence is integrated and utilized extensively in all aspects of our lives, and it is therefore essential to know how the associated models behave. We need the ability to assess the generalization capabilities and specific behaviors of the models we employ. This becomes crucial in many applications, for instance, in disease diagnosis systems, autonomous driving, or even in climate models, on which we may depend for designing policies. Our research community focuses on providing convincing answers to the fundamental question of generalization, and we anticipate this project to significantly contribute to making AI trustworthy.

Which impact do you expect the Sapere Aude programme will have on your career as a researcher?

I am grateful to have received the prestigious Sapere Aude grant, which provides a unique opportunity to initiate my research group, establish my research niche, and start new collaborations with notable international groups. This significantly enhances my development as a researcher and group leader, enables the pursuit of many interesting ideas, and sets the ground for further expanding my research agenda in the future.

Background and personal life

I come from a small town in northern Greece. After completing my undergraduate studies, I continued my academic journey abroad, in Germany and Denmark. Outside of work, I like spending time with friends, cooking, reading, occasionally fishing during the summer, and trekking. My daughter consistently consumes my energy but in return she makes me laugh all the time. In general, I maintain an optimistic attitude and positive vibe, enjoying every aspect of my life.