Discrete Variational Autoencoders (1609.02200v2)

Abstract: Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We present a novel method to train a class of probabilistic models with discrete latent variables using the variational autoencoder framework, including backpropagation through the discrete latent variables. The associated class of probabilistic models comprises an undirected discrete component and a directed hierarchical continuous component. The discrete component captures the distribution over the disconnected smooth manifolds induced by the continuous component. As a result, this class of models efficiently learns both the class of objects in an image, and their specific realization in pixels, from unsupervised data, and outperforms state-of-the-art methods on the permutation-invariant MNIST, Omniglot, and Caltech-101 Silhouettes datasets.

• The paper integrates discrete latent variables with continuous layers into a hybrid VAE framework for enhanced modeling of data with distinct classes.
• It introduces an efficient gradient estimation method by expanding discrete variables into a continuous space for backpropagation.
• The model achieves competitive log-likelihood scores on benchmarks such as MNIST, Omniglot, and Caltech-101, setting a new performance standard.

Discrete Variational Autoencoders: A Technical Overview

The paper presents a novel approach to training probabilistic models with discrete latent variables using the Variational Autoencoder (VAE) framework. Discrete latent variables are naturally suitable for datasets consisting of distinct classes, yet their training involves significant complexities, primarily due to the incompatibility of conventional backpropagation techniques with discrete values. This paper addresses this difficulty by integrating discrete variables with continuous latent variables, creating what the author terms discrete variational autoencoders (discrete VAEs).

Core Contributions

1. Hybrid Latent Structures: The proposed model amalgamates an undirected graphical component defined over discrete latent variables with directed continuous latent layers. The continuous layers model smooth manifold transformations, typical in natural data changes, whereas the discrete component efficiently handles distinct data classes.
2. Efficient Gradient Estimation: A significant contribution of this work is devising a method to allow backpropagation through discrete variables, albeit indirectly. The solution involves expanding into a continuous space via additional latent variables, enabling the use of the reparameterization trick—well-suited for continuous distributions—and thus allowing efficient training using the VAE methodology.
3. Hierarchical Approximating Posterior: The paper introduces a hierarchical structure within the approximating posterior to capture strong correlations in the posterior distribution induced by observing dataset elements. This complexity allows for a more robust and flexible model that can represent intricate data derivations, such as explaining-away effects.
4. Benchmark Performance: Discrete VAEs deliver competitive performance, outperforming many state-of-the-art methods on datasets like permutation-invariant MNIST, Omniglot, and Caltech-101 Silhouettes. The framework's efficacy is demonstrated through improved log-likelihood scores compared to various models, including deep belief networks and ladder variational autoencoders.

Numerical Results

On dynamically binarized MNIST, the discrete VAE achieves a test set log-likelihood of -80.15, markedly better than previous results like -82.90 (IWAE) and -81.74 (Ladder VAE). In the context of the static binarization, it attains -81.01, surpassing the Variational Gaussian Process's -81.32. These results substantiate the versatility and effectiveness of the hybrid approach in modeling datasets with inherent discrete class structures.

Theoretical and Practical Implications

The advancement here challenges the conventional boundary between discrete and continuous models, providing a framework where both can coexist harmoniously, leveraging the strengths of each to model complex data distributions. Practically, this could mean improved unsupervised learning capabilities in image processing, natural language processing, and beyond where data classes tend to involve discrete distinctions.

Theoretically, the paper invites further exploration of, and improvement upon, the integration of discrete and continuous systems within machine learning frameworks. Upcoming research could expand this methodology to more complex models and larger datasets, enhancing the scope of variational inference techniques.

Future Developments

Looking forward, the challenges of scalability and model complexity management will be crucial as discrete VAEs are applied to more diverse and larger datasets. Possible advancements include more sophisticated sampling methods to decrease convergence times further and implementing more efficient parameter-sharing techniques to handle extensive data types and classes.

In conclusion, this paper provides a methodically sound and numerically validated approach to incorporating discrete latent variables into the VAE framework, setting a foundation for future research into hybrid probabilistic models. This work aids in bridging a significant methodological gap, allowing discrete variables to be part of the highly effective VAE framework, paving the way for richer probabilistic models.