Understanding and Applying Non-Euclidean Geometry in Machine Learning
Abstract
Analysts work with large amounts of data and require performant tools to perform analysis and prediction. Machine learning (ML) models are a powerful way to accomplish these objectives but require translating available information and knowledge into ML-friendly representations. The fidelity of this translation directly impacts the performance of the ML models. We address the problem of understanding key aspects of these representations: their geometric properties and the downstream impact. We propose a technical approach to improving the quality of representations based on mathematical tools from the area of non-Euclidean geometry. Our research groups past theoretical and applied work into these non-Euclidean geometric approaches has enabled improved representations for a variety of network embeddings along with better performance on powerful ML models such as graph neural networks. We focus on two aspects: understanding the fundamental theory underlying the choice of geometric space to be used and converting existing ML models to work in a broad variety of geometric spaces. If successful, the proposed research will enable users to build more performant models that extract the maximum amount of signal from available data.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 08, 2020
- Source ID
- N000142012480
Entities
People
- Christopher Ré
Organizations
- Office of Naval Research
- Stanford University
- United States Navy