Over 2,000 years ago, Euclid, a Greek mathematician often referred to as the father of geometry, fundamentally transformed our understanding of shapes. Today, Justin Solomon, a professor at MIT’s Department of Electrical Engineering and Computer Science and a member of the Computer Science and Artificial Intelligence Laboratory (CSAIL), employs contemporary geometric approaches to tackle complex problems that ostensibly bear no relation to shapes.
Solomon explains, for example, that a statistician might wish to evaluate the impacts on a machine-learning model’s performance when different datasets are used for training and testing. Even if the information these datasets contain is not evidently geometric, their underlying geometric structure could yield essential insights when considered in high-dimensional terms. Solomon clarifies that “The language we use to talk about data often involves distances, similarities, curvature, and shape — exactly the kinds of things that we’ve been talking about in geometry forever.”
Solomon’s Geometric Data Processing Group employs geometric techniques, which he observes can be surprisingly diverse in their applications, to process two- and three-dimensional geometric data and conduct high-dimensional statistical research. His team has for instance contributed to improving the realism of animated films by developing algorithms for physical simulation of cloth and fluids, and has advanced the progress of generative AI models by using geometry to map spaces of images.
Solomon’s journey towards his innovative work began with an early fascination with computer graphics in high school. An internship at a Washington research lab developed his interest in 3D face recognition algorithms, and subsequent studies at Stanford University in math and computer science allowed him to further delve into research of this nature. Over his years at Stanford, Solomon spent several summers working at Pixar Animation Studios, where he honed his skills at computer graphics and physical simulation.
While completing his computer science PhD at Stanford, Solomon’s research concentrated on an area known as optimal transport, which involves moving an item’s distribution to another distribution as efficiently as possible. Initially intended for application to computer graphics, this area of research would later expand to include fascinating and diverse fields.
Today at MIT, Solomon is passionate about offering underserved students access to geometric research opportunities. He recently launched a six-week paid research program, the Summer Geometry Initiative, aimed primarily at underrepresented students and dedicated to introducing participants to geometry research. This initiative is Solomon’s active contribution to increased diversity in a field that sees significant application in machine learning and statistics, which he sees as an avenue for introducing fresh perspectives and innovative ideas.
Looking ahead, Solomon is excited about utilizing geometric tools to improve unsupervised machine learning models – an area of machine learning where models learn to recognize patterns without having labeled training data. He believes that advanced models with geometric insight and data inference capabilities can effectively unravel complex, unlabeled 3D scenes, dramatically facilitating machine learning.
When he isn’t immersed in research, Solomon finds joy in playing classical music on the piano or cello. He is part of the New Philharmonia Orchestra in Newton, Massachusetts and sees clear intersections between music, which he describes as analytical, and his computer graphics research that is closely intertwined with artistic practice. For Solomon, his dual passions are “mutually beneficial.”
