A Walsh Hadamard Derived Linear Vector Symbolic Architecture

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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

Mohammad Mahmudul Alam, Alexander Oberle, Edward Raff, Stella Biderman, Tim Oates, James Holt · 2024

Related benchmarks

Task	Dataset	Result
Image Classification	MNIST	Accuracy—	417
Image Classification	SVHN	Accuracy94.53	395
Image Clustering	CIFAR-10	NMI—	318
Clustering	MNIST	ARI18.44	37
Clustering	CIFAR-100	NMI—	25
Clustering	SVHN	Accuracy—	18
Image Classification	CIFAR-10 CR10	Top-1 Acc83.81	5
Image Classification	CIFAR-100 CR100	Top-1 Acc58.82	5
Image Classification	Mini-ImageNet (MIN)	Top-1 Acc59.48	5
XML classification	BIBTEX	nDCG61.741	5