A Walsh Hadamard Derived Linear Vector Symbolic Architecture

TL;DR

This paper introduces a new Hadamard-derived linear binding method for Vector Symbolic Architectures that enhances computational efficiency and integrates well with differentiable systems, advancing neuro-symbolic AI capabilities.

Contribution

The paper presents the Hadamard-derived linear Binding (HLB), a novel VSA operation optimized for efficiency and compatibility with deep learning frameworks.

Findings

HLB improves computational efficiency in VSA tasks.

HLB performs well in differentiable systems.

Code availability facilitates adoption and testing.

Abstract

Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in $\mathbb{R}^d$ are `bound' together to produce a new vector in the same space. VSAs support the commutativity and associativity of this binding operation, along with an inverse operation, allowing one to construct symbolic-style manipulations over real-valued vectors. Most VSAs were developed before deep learning and automatic differentiation became popular and instead focused on efficacy in hand-designed systems. In this work, we introduce the Hadamard-derived linear Binding (HLB), which is designed to have favorable computational efficiency, and efficacy in classic VSA tasks, and perform well in differentiable systems. Code is available at https://github.com/FutureComputing4AI/Hadamard-derived-Linear-Binding