EAGER: Hyperdimensional computing with geometric algebra

In the modern era of big data, a crucial challenge is to discover useful information that is buried in highly redundant, seemingly irrelevant, incomplete, or even corrupted data sets. Such information is often contained in certain low-dimensional structures hidden within the high-dimensional space of the data, or may only depend on a small subset of the data.

How to extract this information efficiently and automatically remains an open problem. This project brings together two emerging areas of research — hyperdimensional (HD) computing and geometric algebra (GA) — to tackle this problem from a new stand point by investigating the data representation and the intrinsic geometry of the data. This research is also the first in a systematic quest to uncover the potential of using the high-dimensional generalization of complex numbers in analyzing and discovering patterns in large-scale sensing data.

The success of this research can help advance the capability of other machine learning models, such as deep neural networks, which are mostly based on real numbers today. It also brings a powerful mathematical tool (GA) which is mainly known in the physics community into the machine learning community.

HD computing is a brain-inspired framework for machine learning and artificial intelligence that is based on representing quantities or symbols as high-dimensional vectors and manipulating vectors with simple operations. In recent work by the investigators, it was shown that by using complex-valued vectors in HD computing it is possible to encode images in such a way that patterns can be effectively recognized by a factorization of HD vectors.

To build on this direction, they are exploring the use of geometric algebras which generalize complex numbers to any n-dimensional space. The following thrusts form the core of this research: (1) explore ways of mapping data into the geometric algebra space; (2) investigate how to integrate geometric algebra with the operations of HD computing; (3) apply these methods to real application domains such as multi-microphone speech recognition or distributed sensing to evaluate their efficacy and computational efficiency.

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.