A Walsh Hadamard Derived Linear Vector Symbolic Architecture

Mohammad Mahmudul Alam, Alexander Oberle, Edward Raff, Stella Biderman, Tim Oates +1 more
10/1/2024

No official code found. Best implementation: FutureComputing4AI/Hadamard-derived-Linear-Binding (13 stars, Apache-2.0, last commit 2026-01-30).

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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Code Implementations(1)

FutureComputing4AI/Hadamard-derived-Linear-BindingCommunity61%
Apache-2.0

A Walsh Hadamard Derived Linear Vector Symbolic Architecture :fire:

133PythonOct 14, 20248 months agoApache-2.0
fourier-transformhadamardhadamard-derived-linear-bindinghadamard-transformshlb+4 more

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Cite this paper

@article{alam2024walsh,
  title  = {A Walsh Hadamard Derived Linear Vector Symbolic Architecture},
  author = {Mohammad Mahmudul Alam and Alexander Oberle and Edward Raff and Stella Biderman and Tim Oates and James Holt},
  year   = {2024},
  eprint = {2410.22669},
  archivePrefix = {arXiv},
  doi    = {10.48550/arXiv.2410.22669},
  url    = {https://arxiv.org/abs/2410.22669},
  journal = {NEURIPS 2024 2024}
}

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