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Learning Holographic Reduced Representations with Clifford Variational Autoencoders

2026-09-23 17:10:56
Mohamed Malek Abid, P. Michael Furlong
arXiv_AI
       
Abstract

Vector Symbolic Algebras project data structures into a hyperdimensional vector space through the application of their vector algebras to randomly generated atomic vector symbols and fractional power encodings of real-valued data. Embedding unstructured data remains an open question. We present \textit{Clifford-VAE}, a variational autoencoder that learns to project data onto a Clifford torus in arbitrary dimensions. Experiments using the MNIST, FashionMNIST, and CIFAR-10 datasets demonstrate that Clifford-VAE produces representations that are competitive with those produced by Gaussian and Hyperspherical VAEs for semi-supervised classification tasks while outperforming Gaussian and Hyperspherical counterparts in the VSA benchmark tests of self-binding and unbinding, role-filler recovery, and bundle capacity. Clifford-VAE provides a principled technique for grounding perceptual data into a symbolic reasoning framework, providing a new approach to a long-standing problem in the VSA literature.

Abstract (translated)

URL

https://arxiv.org/abs/2609.28409

PDF

https://arxiv.org/pdf/2609.28409.pdf

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