Justin Solomon, an associate professor at the Massachusetts Institute of Technology (MIT), is applying modern geometric techniques to solve complex problems in data science, computer graphics, and artificial intelligence. He draws upon the principles of geometry— the study of shapes—pioneered over 2,000 years ago by Greek mathematician Euclid.
The relevance of geometric principles extends beyond the domain of shapes. Solomon explains how geometric tools could help compare datasets by observing the geometric structure shared by the data, depending upon its positioning in high-dimensional space. The insights gleaned could help determine whether a specific model will work on both datasets.
The applications of geometric tools for problem-solving are broad, leading Solomon to give his Geometric Data Processing Group a “purposefully ambiguous” name. Half of his team works on two- and three-dimensional geometric data problems, such as aligning 3D organ scans or enabling autonomous vehicles to identify pedestrians through LiDAR sensor data. The other half conducts high-dimensional statistical research using geometric techniques, for instance in improving generative AI models.
Solomon’s interest in computer graphics started during his teenage years when he interned at a research lab working on algorithms for 3D face recognition. This early interest inspired him to major in math and computer science at Stanford University, where he worked on improving the realism of animated movies during summer internships at Pixar Animation Studios.
Solomon’s interest in applying geometric principles to computer graphics led him to research on ‘optimal transport’, aiming to move a distribution as efficiently as possible. For instance, it may be used to find the cheapest way to distribute goods from multiple manufacturers to a network of distributors. While originally focused on applying optimal transport to computer graphics, Solomon found it useful across a wide spectrum of applications, influencing the structure of his research group at MIT.
Solomon appreciates the opportunity to work with talented students and colleagues at MIT on complex problems with practical applications. He is passionate about making the world of geometric research accessible to those who may not usually have exposure to the field, with a special emphasis on underserved students. Solomon launched the Summer Geometry Initiative, a six-week paid research program for undergraduate students from underrepresented backgrounds.
Solomon observes a growing list of machine learning and statistical challenges that can be addressed using geometric principles. He plans to use geometry to enhance the efficiency of unsupervised machine learning models, which have to learn to identify patterns without any labeled training data. Despite the complex problems he works on, Solomon finds time to perform classical music on the piano or cello, combining his analytical work with an artistic practice.
