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 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.