Information-theoretic Generalization Analysis for VQ-VAEs: A Role of Latent Variables
This work addresses a theoretical gap for researchers in unsupervised learning, specifically for VQ-VAEs, by providing rigorous generalization bounds, though it is incremental as it builds on existing information-theoretic frameworks.
The authors tackled the problem of insufficient theoretical generalization analysis for unsupervised models like VAEs by extending information-theoretic analysis to VQ-VAEs with discrete latent spaces, deriving a generalization error bound for reconstruction loss that depends only on latent variable and encoder complexity, and providing an upper bound for the 2-Wasserstein distance between true and generated data distributions.
Latent variables (LVs) play a crucial role in encoder-decoder models by enabling effective data compression, prediction, and generation. Although their theoretical properties, such as generalization, have been extensively studied in supervised learning, similar analyses for unsupervised models such as variational autoencoders (VAEs) remain insufficiently underexplored. In this work, we extend information-theoretic generalization analysis to vector-quantized (VQ) VAEs with discrete latent spaces, introducing a novel data-dependent prior to rigorously analyze the relationship among LVs, generalization, and data generation. We derive a novel generalization error bound of the reconstruction loss of VQ-VAEs, which depends solely on the complexity of LVs and the encoder, independent of the decoder. Additionally, we provide the upper bound of the 2-Wasserstein distance between the distributions of the true data and the generated data, explaining how the regularization of the LVs contributes to the data generation performance.