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.
From the original article
1 min read at arxiv.orgVector 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.
By Mohamed Malek Abid · arxiv.org
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