EAGER: Hyperdimensional computing with geometric algebra

EAGER：几何代数的超维计算

• 批准号: 2147640
• 负责人: Bruno Olshausen
• 金额: $ 25万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2147640&HistoricalAwards=false
• 关键词: EAGER; Hyperdimensional; computing; 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.

在大数据的现代时代，一个至关重要的挑战是发现有用的信息，这些信息掩埋在高度冗余的E，甚至是损坏的数据集中。数据，或可能仅取决于一小部分数据。代表和数据的固有几何形状。 s，例如当今主要基于实际数字的深神经网络智力代表数量或符号作为简单的高度矢量和操纵器。通过识别HD矢量的分解。高清计算； TED感知他们的评估和计算。该奖项反映了NSF'SF'Stutrory Mission，并通过评估Usindation的智力优点和更广泛的影响来审查标准。