Orchard Jeff, Furlong P Michael, Simone Kathryn
Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Systems Design Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Neural Comput. 2024 Aug 19;36(9):1886-1911. doi: 10.1162/neco_a_01693.
Hyperdimensional (HD) computing (also referred to as vector symbolic architectures, VSAs) offers a method for encoding symbols into vectors, allowing for those symbols to be combined in different ways to form other vectors in the same vector space. The vectors and operators form a compositional algebra, such that composite vectors can be decomposed back to their constituent vectors. Many useful algorithms have implementations in HD computing, such as classification, spatial navigation, language modeling, and logic. In this letter, we propose a spiking implementation of Fourier holographic reduced representation (FHRR), one of the most versatile VSAs. The phase of each complex number of an FHRR vector is encoded as a spike time within a cycle. Neuron models derived from these spiking phasors can perform the requisite vector operations to implement an FHRR. We demonstrate the power and versatility of our spiking networks in a number of foundational problem domains, including symbol binding and unbinding, spatial representation, function representation, function integration, and memory (i.e., signal delay).
超维（HD）计算（也称为向量符号架构，VSAs）提供了一种将符号编码为向量的方法，使这些符号能够以不同方式组合，在同一向量空间中形成其他向量。向量和运算符构成一种组合代数，使得复合向量能够分解回其组成向量。许多有用的算法都有在HD计算中的实现，如分类、空间导航、语言建模和逻辑。在这封信中，我们提出了傅里叶全息降维表示（FHRR）的脉冲实现，FHRR是最通用的VSAs之一。FHRR向量的每个复数的相位被编码为一个周期内的脉冲时间。从这些脉冲相位器派生的神经元模型可以执行必要的向量运算以实现FHRR。我们在一些基础问题领域展示了我们的脉冲网络的能力和通用性，包括符号绑定和解绑、空间表示、函数表示、函数积分和记忆（即信号延迟）。
