Information-theoretic Generalization Analysis for VQ-VAEs: A Role of Latent Variables

2025-05-26

AI Summary

Variational Quantized Autoencoders (VQ-VAEs) lack theoretical grounding for generalization due to the discrete nature of their latent variables. Method: We extend information-theoretic generalization bounds to discrete latent spaces, introducing a data-dependent prior and deriving a reconstruction error upper bound dependent solely on the latent variables and encoder. We further establish the first explicit upper bound on the 2-Wasserstein distance between the generated and true data distributions, revealing how latent regularization constrains generative fidelity. Contribution/Results: Our analysis uncovers a fundamental trade-off between latent compressibility and reconstruction/generation performance. We propose the first unified information-theoretic framework jointly characterizing generalization and generative quality for discrete representation learning, providing rigorous theoretical foundations for VQ-VAEs and related models. This work bridges theoretical generalization analysis with empirical generative performance evaluation in discrete latent variable models.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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.

Problem

• Analyzing generalization in VQ-VAEs with discrete latent spaces
• Deriving error bounds for reconstruction loss in VQ-VAEs
• Linking latent variable regularization to data generation performance

Innovation

• Extends information-theoretic analysis to VQ-VAEs
• Introduces data-dependent prior for latent variables
• Derives generalization bound independent of decoder