A Walsh Hadamard Derived Linear Vector Symbolic Architecture
This work addresses the problem of integrating neuro-symbolic AI with deep learning frameworks, though it appears incremental as it builds on existing VSA concepts with a new binding method.
The authors tackled the challenge of making Vector Symbolic Architectures (VSAs) more efficient and compatible with modern differentiable systems by introducing the Hadamard-derived linear Binding (HLB) method, which demonstrated favorable computational efficiency and efficacy in classic VSA tasks.
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