  The dimensionality of the embedding and the number of available embeddings (
also called codebook size) are critical factors influencing the performance of
Vector Quantization(VQ), a discretization process used in many models such as
the Vector Quantized Variational Autoencoder (VQ-VAE) architecture. This study
examines the balance between the codebook sizes and dimensions of embeddings in
VQ, while maintaining their product constant. Traditionally, these hyper
parameters are static during training; however, our findings indicate that
augmenting the codebook size while simultaneously reducing the embedding
dimension can significantly boost the effectiveness of the VQ-VAE. As a result,
the strategic selection of codebook size and embedding dimensions, while
preserving the capacity of the discrete codebook space, is critically
important. To address this, we propose a novel adaptive dynamic quantization
approach, underpinned by the Gumbel-Softmax mechanism, which allows the model
to autonomously determine the optimal codebook configuration for each data
instance. This dynamic discretizer gives the VQ-VAE remarkable flexibility.
Thorough empirical evaluations across multiple benchmark datasets validate the
notable performance enhancements achieved by our approach, highlighting the
significant potential of adaptive dynamic quantization to improve model
performance.
