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.

在现代大数据时代，一个关键的挑战是发现隐藏在高度冗余、看似无关、不完整甚至损坏的数据集中的有用信息。这些信息通常包含在隐藏在数据的高维空间中的某些低维结构中，或者可能只依赖于数据的一个小子集。如何有效地自动提取这些信息仍然是一个悬而未决的问题。该项目汇集了两个新兴的研究领域-超维（HD）计算和几何代数（GA）-通过调查数据表示和数据的内在几何结构，从一个新的角度来解决这个问题。这项研究也是首次系统地探索使用复数的高维泛化来分析和发现大规模传感数据中的模式的潜力。这项研究的成功可以帮助提高其他机器学习模型的能力，例如深度神经网络，这些模型目前主要基于真实的数字。 它还将一个强大的数学工具（GA）引入了机器学习领域。HD计算是一个受大脑启发的机器学习和人工智能框架，基于将数量或符号表示为高维向量，并通过简单的操作操纵向量。在最近的研究工作中，研究人员表明，通过在HD计算中使用复值向量，可以以这样一种方式对图像进行编码，即可以通过HD向量的因式分解来有效地识别模式。为了建立在这个方向上，他们正在探索使用几何代数将复数推广到任何n维空间。本研究的核心是：（1）探索数据到几何代数空间的映射方法：（2）研究如何将几何代数与HD计算的操作相结合;（3）将这些方法应用到真实的应用领域，如多麦克风语音识别或分布式传感，以评估其功效和计算效率。该奖项反映了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。