A Walsh Hadamard Derived Linear Vector Symbolic Architecture

Alexander Oberle; Edward Raff; James Holt; Mohammad Mahmudul Alam; Stella Biderman; Tim Oates

A Walsh Hadamard Derived Linear Vector Symbolic Architecture

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arxiv 2410.22669 v1 pith:MRLDGG6Q submitted 2024-10-30 cs.AI cs.LG

Mohammad Mahmudul Alam , Alexander Oberle , Edward Raff , Stella Biderman , Tim Oates , James Holt This is my paper

classification cs.AIcs.LG

keywords vectorvsasbindingefficacylinearoperationsymbolicsystems

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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

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