Dr. Christos Thrampoulidis Awarded the 2024 PIMS/UBC Early Career Prize

PIMS is thrilled to announce the Dr. Christos Thrampoulidis, Associate Professor in the Department of Electrical and Computer Engineering at UBC, has been awarded the 2024 PIMS/UBC Mathematical Sciences Early Career Award.

This award recognizes UBC researchers for their innovative contributions to mathematics or its applications in the sciences. Notably, Dr. Thrampoulidis is the first recipient of this honour from outside the Mathematics or Statistics Department.

Dr. Thrampoulidis' research lies at the intersection of statistical signal-processing, machine learning, high-dimensional statistics, and optimization. Before joining UBC, he served as an Assistant Professor at the ECE Department of the University of California, Santa Barbara. 
 

Congratulations to Dr. Thrampoulidis on this well-deserved recognition!
 

PIMS had the chance to talk to Dr. Thrampoulidis about his current research and what winning the PIMS/UBC Early Career Prize means to him.

Can you tell us a little bit about your current research?

My research lies at the intersection of statistical signal processing and machine learning theory.

Initially, I focused on compressive sensing - a framework that revolutionized how we acquire and process signals, particularly in medical and computational imaging. Building on the work of prominent mathematicians, my contributions helped develop a mathematical framework for determining fundamental limits and predicting the performance of compressive sensing algorithms.

Around 2018, my research took an exciting turn when we discovered that this mathematical framework could help explain puzzling phenomena observed in deep learning, such as 'benign overfitting' and 'double descent' - where neural networks perform well on unseen data despite memorizing their training data, challenging classical machine learning principles about overfitting.

Most recently, my group has focused on developing mathematical models to understand the geometry of deep-learning representations. We're particularly interested in how neural networks organize information in their embedding space and in linking this structure to the data they were trained on. We aim not only  to understand these systems but to reverse-engineer this geometry by designing improved optimization algorithms and architectural modifications to create more robust learning models. This research is particularly exciting because our mathematical models, beyond presenting fundamental questions about optimization dynamics, generate testable predictions about real deep learning systems and datasets, bringing our mathematical understanding closer to their practical applications.

We have also begun extending these insights to large language models, working step by step to understand how they process and represent text data. These models are trained simply to predict the next word given the preceding context, yet they demonstrate a remarkable ability to capture complex meaning. Developing mathematical models to understand how models acquire such sophisticated semantic understanding is one of the fascinating questions we are working to address.

How will winning the PIMS/UBC Mathematical Sciences Early Career Award will affect your work?

I am especially honoured and humbled to receive this award, particularly as someone who comes from an engineering rather than a mathematical background. Even during my undergraduate engineering studies, mathematics was what excited me most and what I found myself naturally drawn to. During my PhD, I had the wonderful opportunity to learn from brilliant applied mathematicians, and mathematics has continued to be not only the foundation of my research but often the most enjoyable part of my work.

This recognition is particularly meaningful because of UBC's exceptional strength in mathematics, which spans across departments. Since arriving on campus, I've benefited tremendously and have been inspired by this collaborative mathematical environment, and I look forward to strengthening these connections moving forward.

As an Assistant Professor at the Department of Electrical and Computer Engineering (ECE) at UBC, can you please speak to the importance of the mathematical sciences in the work you do?

Mathematical sciences are essential to almost every research area in ECE. Traditionally, fields like signal processing, control systems, and information theory have been particularly mathematics-intensive, and the boundaries between these engineering disciplines and applied mathematics have become increasingly fluid over the years.

In my research experience, this close connection is very clear. In compressive sensing, while the core engineering question was practical - how to recover noisy structured signals from minimal measurements - the solutions required deep mathematical insights that attracted some of the most prominent mathematicians of our time. Similarly, in my current work on understanding deep learning systems, mathematics plays a crucial role. The engineering challenge often lies in finding the right mathematical abstractions to model these complex systems and identifying the fundamental questions that will advance our understanding. After all, as I often tell my engineering students, mathematics is more than just a tool - it's a language, a way of thinking and a way of conveying your ideas clearly.