Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in Rd 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
Cite
@article{arxiv.2410.22669,
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},
journal= {arXiv preprint arXiv:2410.22669},
year = {2024}
}
Comments
To appear in the 38th Conference on Neural Information Processing Systems (NeurIPS 2024)