The Greek mathematician Euclid is renowned for laying the groundwork of geometry more than 2,000 years ago. In present times, Justin Solomon, an Associate Professor at MIT’s Department of Electrical Engineering and Computer Science, is deriving inspiration from Euclid’s fundamental theories and using modern geometric techniques to solve complex problems. Remarkably, these issues frequently bear little resemblance to shapes. One instance of this could be when a statistician wants to compare two datasets to discern how using one for training and the other for testing might affect a machine-learning model’s efficacy.
Solomon mentions that these datasets could share some geometric structure depending on how the data is organized in high-dimensional space. Employing geometric tools to compare them could provide insight into whether the same model will be effective on both datasets, he argues.
Around half of Solomon’s team focuses on problems involving the processing of two- and three-dimensional geometric data, like aligning 3D organ scans in medical imaging, or enabling autonomous vehicles to identify pedestrians in spatial data acquired by LiDAR sensors. The rest of his team conducts high-dimensional statistical research using geometric tools to construct better generative AI models. Solomon states that the algorithms they created for applications in computer animation also have direct relevance to generative AI and other current trending probability tasks.
As a child, Solomon had an interest in computer graphics, sparking his journey towards becoming a professor at MIT. After an internship at a research lab outside Washington where he helped develop algorithms for 3D face recognition, he opted to major in math and computer science at Stanford University. He recalls chatting his way into an internship at Pixar Animation Studios during a career fair during his first year at Stanford. At Pixar, he focused on physical simulation of cloth and fluids to enhance the realism of animated films and rendering techniques to alter the visual style of animated content.
After earning his computer science PhD at Stanford with a focus on optimal transport, Solomon took a faculty position at MIT. Solomon emphasizes the importance of diversifying the field of geometric research and thus founded the Summer Geometry Initiative – a six-week paid research program for undergraduates, mainly from underrepresented backgrounds.
In the future, Solomon anticipates applying geometric techniques to enhance unsupervised machine learning models, which are crucial since the vast majority of 3D data are not labeled, and labeling objects in 3D scenes is often prohibitively expensive.
In his spare time, Solomon indulges in his passion for music, enjoying playing classical tunes on the piano or cello, particularly pieces by Dmitri Shostakovich. He says that the analytical nature of music and research in computer graphics mutually nourish each other.
