Learning Holographic Reduced Representations with Clifford Variational Autoencoders
Clifford-VAE learns torus embeddings that beat Gaussian VAEs on vector-symbolic binding and capacity tests.
Clifford-VAE is a variational autoencoder that projects unstructured data onto a Clifford torus so perceptual inputs can enter vector symbolic algebras. Experiments on MNIST, FashionMNIST, and CIFAR-10 show semi-supervised classification competitive with Gaussian and hyperspherical VAEs. It outperforms those baselines on self-binding and unbinding, role-filler recovery, and bundle capacity. The authors present it as a way to ground perceptual data in a symbolic reasoning framework.
- Clifford-VAE maps data onto a Clifford torus in arbitrary dimensions.
- Tests use MNIST, FashionMNIST, and CIFAR-10.
- Classification performance matches Gaussian and hyperspherical VAEs.
- It outperforms those VAEs on binding, unbinding, role-filler recovery, and bundle capacity.
Full article130 words · extracted from arxiv.org · click to collapse
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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.28409