Over two thousand years ago, Greek mathematician Euclid revolutionized the world with his groundbreaking work in geometry. Today, MIT Associate Professor Justin Solomon is using contemporary geometric techniques to solve intricate problems, which often don’t appear to be related to shapes, albeit heavily correlate with data arrangement in a high-dimensional space.
Solomon, who is also a member of the Computer Science and Artificial Intelligence Laboratory (CSAIL), uses geometry to compare datasets used for training and testing to evaluate the performance of machine learning models. The data within these sets might share some geometric structure which can reveal insight into whether the same model will work on both datasets. Solomon and his team are using these principles to contribute to complex issues in data science.
Solomon named his group the Geometric Data Processing Group and uses geometric techniques for a variety of problems. For instance, half of his team focuses on processing two- and three-dimensional geometric data, like aligning 3D organ scans in medical imaging or using spatial data gathered by LiDAR sensors to help autonomous vehicles identify pedestrians. The other half of his team uses geometric tools to conduct high-dimensional statistical research and enhance generative AI models that create new images from different parts of an image-rich dataset. This mapping process is essentially a geometric one.
Before becoming an MIT professor, Solomon was primarily interested in computer graphics, an enthusiasm that started when he interned at a research lab during high school to learn algorithm development for 3D face recognition. This motivated him to major in math and computer science at Stanford University where his research interests broadened.
Upon deciding to transition into academia, Solomon stayed at Stanford to get a computer science PhD and focused on a problem known as optimal transport – seeking the most efficient way to move a distribution from one place to another. His journey allowed him to apply his knowledge in different areas, which greatly influences his research at MIT today.
As an MIT professor, Solomon is committed to making geometric research accessible to all, especially underserved students who may not have exposure to such opportunities. He established the Summer Geometry Initiative, a six-week paid research program that introduces geometry research to undergraduates, mostly coming from underrepresented backgrounds. Since initiation, this scheme has seen positive results, including changes in the composition of incoming PhD students at various institutions.
Solomon anticipates using geometric tools to enhance unsupervised machine learning models, which learn to recognize patterns without labeled training data. By fostering improved understanding of complex, unlabeled 3D scenes, he believes these models can learn more effectively.
In his spare time, Solomon enjoys playing classical music on the piano or cello. A fervent musician, he makes it a point to join a symphony in any city he lives in, currently playing with the New Philharmonia Orchestra in Newton, Massachusetts. For Solomon, music and graphics form a harmonious combination, mutually benefiting his research field and artistic practice.
