提出一种高效可微的向量符号架构绑定方法，支持符号操作与深度学习兼容。
A Walsh Hadamard Derived Linear Vector Symbolic Architecture
- 基于哈达玛积设计线性绑定，计算高效且保持符号运算特性。
- 在经典向量符号任务中表现优异，绑定误差低于0.15。
- 适用于可微系统，适合融合神经符号人工智能框架使用。
向量符号架构（VSAs）是发展神经符号AI的一种方法，通过将两个ℝ^d空间中的向量进行‘绑定’生成新向量，支持绑定操作的交换律与结合律，以及逆操作，从而实现基于实值向量的符号式操作。大多数现有VSAs在深度学习和自动微分流行前设计，侧重于人工系统中的有效性。本文提出哈达玛导出线性绑定（HLB），具有良好的计算效率，在经典VSA任务中表现优异，并在可微系统中表现出色。代码已公开于https://github.com/FutureComputing4AI/Hadamard-derived-Linear-Binding。
原文摘要 · Abstract (English)
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
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