LL-VQ-VAE: Learnable Lattice Vector-Quantization For Efficient
  Representations
Ahmed Khalil Robert Piechocki Raul Santos-Rodriguez
In this paper we introduce learnable lattice vector quantization and
demonstrate its effectiveness for learning discrete representations. Our
method, termed LL-VQ-VAE, replaces the vector quantization layer in VQ-VAE with
lattice-based discretization. The learnable lattice imposes a structure over
all discrete embeddings, acting as a deterrent against codebook collapse,
leading to high codebook utilization. Compared to VQ-VAE, our method obtains
lower reconstruction errors under the same training conditions, trains in a
fraction of the time, and with a constant number of parameters (equal to the
embedding dimension $D$), making it a very scalable approach. We demonstrate
these results on the FFHQ-1024 dataset and include FashionMNIST and Celeb-A.