Collaborative Research: ATD: Principled machine learning and packing subspaces for improved spatiotemporal data processing

For national security, it is imperative that US government agencies detect and classify potential threats as rapidly and accurately as possible. The project will contribute to this cause by delivering mathematical innovations that offer reliable predictions from machine learning algorithms, superior time resolution for surveillance data, and optimal sensor arrangements for robust dataset assembly. In the context of basic research, these contributions will further develop the mathematics of how machines sense and learn. The project will focus on the following three objectives: (1) Develop theory and algorithms for transfer learning and neural networks. (2) Design optimal or nearly optimal line packings for extremely sparse signals. (3) Design optimal ensembles of equal-rank operators for dataset assembly. To this end, the research aims to solve various open problems from metric geometry and machine learning: (a) to develop new algorithms for transfer learning; (b) to explain emergent phenomena in neural networks using gradient descent trajectories; (c) to construct new line packings that achieve equality in the second Levenshtein bound; (d) to construct incoherent line packings from finite field objects; and (e) to construct highly symmetric subspace packings that are optimal with respect to spectral distance. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.