分析离散潜变量如何影响VQ-VAE的泛化与生成性能
Information-theoretic Generalization Analysis for VQ-VAEs: A Role of Latent Variables
- 引入数据相关先验，建立潜变量与模型泛化的信息论关联
- 推导出仅依赖潜变量和编码器复杂度的重构误差上界
- 揭示潜变量正则化对生成数据分布质量的提升机制
潜变量在编码器-解码器模型中起关键作用，支持高效的数据压缩、预测与生成。尽管其理论性质（如泛化能力）在监督学习中已广泛研究，但在无监督模型如变分自编码器（VAEs）中的分析仍不足。本文将信息论泛化分析拓展至具有离散潜空间的向量量化（VQ）VAE，提出一种新型数据相关先验，严格分析潜变量、泛化能力与数据生成之间的关系。我们推导出VQ-VAE重构损失的全新泛化误差上界，该上界仅依赖于潜变量的复杂度和编码器，与解码器无关。此外，我们给出了真实数据分布与生成数据分布之间2-Wasserstein距离的上界，解释了潜变量正则化如何促进生成性能。
原文摘要 · Abstract (English)
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.
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