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

arXiv: https://arxiv.org/abs/2505.19470 · HTML: https://mlsanity.com/paper/2505.19470/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 81 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 30 of 44)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Emergence of Invariance and Disentanglement in Deep Representations](https://mlsanity.com/paper/1706.01350/) (2017)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Reasoning About Generalization via Conditional Mutual Information](https://mlsanity.com/paper/2001.09122/) (2020)
- [Information Dropout: Learning Optimal Representations Through Noisy Computation](https://mlsanity.com/paper/1611.01353/) (2016)
- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates](https://mlsanity.com/paper/1911.02151/) (2019)
- [How Does Information Bottleneck Help Deep Learning?](https://mlsanity.com/paper/2305.18887/) (2023)
- [Information-Theoretic Generalization Bounds for Stochastic Gradient Descent](https://mlsanity.com/paper/2102.00931/) (2021)
- [Generalization Bounds of SGLD for Non-convex Learning: Two Theoretical Viewpoints](https://mlsanity.com/paper/1707.05947/) (2017)
- [Generalization Error Bounds for Noisy, Iterative Algorithms](https://mlsanity.com/paper/1801.04295/) (2018)
- [SQ-VAE: Variational Bayes on Discrete Representation with Self-annealed Stochastic Quantization](https://mlsanity.com/paper/2205.07547/) (2022)
- [On Generalization Error Bounds of Noisy Gradient Methods for Non-Convex Learning](https://mlsanity.com/paper/1902.00621/) (2019)
- [Hierarchical Quantized Autoencoders](https://mlsanity.com/paper/2002.08111/) (2020)
- [Theory and Experiments on Vector Quantized Autoencoders](https://mlsanity.com/paper/1805.11063/) (2018)
- [Information-theoretic generalization bounds for black-box learning algorithms](https://mlsanity.com/paper/2110.01584/) (2021)
- [On the Generalization of Models Trained with SGD: Information-Theoretic Bounds and Implications](https://mlsanity.com/paper/2110.03128/) (2021)
- [PAC-Bayes Information Bottleneck](https://mlsanity.com/paper/2109.14509/) (2021)
- [A New Family of Generalization Bounds Using Samplewise Evaluated CMI](https://mlsanity.com/paper/2210.06422/) (2022)
- [Tighter Information-Theoretic Generalization Bounds from Supersamples](https://mlsanity.com/paper/2302.02432/) (2023)
- [On PAC-Bayesian reconstruction guarantees for VAEs](https://mlsanity.com/paper/2202.11455/) (2022)

## Abstract (arXiv)

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.