Improved Variational Inference in Discrete VAEs using Error Correcting Codes

María Martínez-García, Grace Villacrés, David Mitchell, Pablo M. Olmos

Keywords: deep generative models, variational inference, discrete representations, error correcting codes

TL;DR: This paper presents the first proof-of-concept demonstration that safeguarding latent information with Error Correcting Codes within generative models can enhance Variational Inference.

Abstract: Despite significant advancements in deep probabilistic models, effective learning of low-dimensional discrete latent representations remains challenging. This paper introduces a novel method to improve variational inference in discrete latent variable models by employing Error Correcting Codes (ECCs) to add redundancy to the latent representations, later exploited by the variational approximated posterior to provide more accurate estimates, thereby reducing the variational gap. Drawing inspiration from ECCs used in digital communications and data storage, we demonstrate proof-of-concept using a Discrete Variational Autoencoder (DVAE) with binary latent variables and block repetition codes. We then extend it to a hierarchical structure inspired by polar codes, in which some latent bits are more robustly protected than others. Our approach significantly enhances generation quality, data reconstruction, and uncertainty calibration compared to the uncoded DVAE, even when trained with tighter bounds such as the Importance Weighted Autoencoder (IWAE) objective. In particular, we demonstrate superior performance on MNIST, FMNIST, CIFAR10, and Tiny ImageNet datasets. The general approach of integrating ECCs into variational inference is compatible with existing techniques to boost variational inference, such as importance sampling or Hamiltonian Monte Carlo. We also formulate the properties that ECCs need to possess to be effectively used for improved discrete variational inference.

Primary Area: generative models

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Submission Number: 9465