More than 2000 years after Greek mathematician Euclid revolutionized the understanding of shapes, MIT associate professor Justin Solomon uses modern geometric techniques to resolve complex problems that seemingly have little to do with shapes. Adopting these techniques to compare two datasets for machine learning model performance, Solomon argues that geometric tools can reveal whether the model will work on both datasets. The datasets may share geometric structure based on their arrangement in high-dimensional space.
The Geometric Data Processing Group led by Solomon uses these techniques for a broad range of problems. Half of his team focuses on processing two- and three-dimensional geometric data, such as aligning 3D organ scans in medical imaging, or helping autonomous vehicles identify pedestrians using spatial data from LiDAR sensors. The other half conduct high-dimensional statistical research using geometric tools, such as constructing improved generative AI models.
Solomon was inspired to work with computer graphics while interning at a research lab and working at Pixar during his education at Stanford, where he double-majored in math and computer science. He stayed at Stanford for his computer science PhD and researched a problem, known as optimal transport. It involves finding the most efficient way to move a distribution from one place to another, such as shipping bags of flour from various manufacturers to bakeries distributed throughout a city.
To make the field of geometric research more accessible, especially to underserved students, Solomon initiated the Summer Geometry Initiative, a six-week paid research program for undergraduates, mainly from underrepresented backgrounds. The program has seen an impact on the composition of the incoming classes of PhD students, not just at MIT but at other institutions as well.
Solomon plans to apply geometry to unlabelled 3D data to improve unsupervised machine learning, helping computers decode complex, unlabeled 3D scenes.
Apart from his work, Solomon is enthusiastic about classical music and regularly plays cello with the New Philharmonia Orchestra. He understands music as analytical and finds it mutually beneficial to his research in computer graphics, closely linked to artistic practice.
