Learning Hierarchical Features from Generative Models

Abstract: Deep neural networks have been shown to be very successful at learning feature hierarchies in supervised learning tasks. Generative models, on the other hand, have benefited less from hierarchical models with multiple layers of latent variables. In this paper, we prove that hierarchical latent variable models do not take advantage of the hierarchical structure when trained with existing variational methods, and provide some limitations on the kind of features existing models can learn. Finally we propose an alternative architecture that do not suffer from these limitations. Our model is able to learn highly interpretable and disentangled hierarchical features on several natural image datasets with no task specific regularization or prior knowledge.

• The paper introduces VLAE, a novel architecture that bypasses redundancy in traditional hierarchical generative models.
• It demonstrates that conventional HVAEs struggle to learn disentangled hierarchies due to limitations in unimodal conditional distributions.
• Empirical results on MNIST, SVHN, and CelebA confirm VLAE’s superior capability to organize features by complexity.

Learning Hierarchical Features from Generative Models

Introduction

The paper "Learning Hierarchical Features from Generative Models" (1702.08396) investigates the challenge of hierarchical feature learning within the context of deep generative models. While deep neural networks have demonstrated prowess in supervised learning by developing hierarchical feature representations, generative models have not exhibited similar success. Specifically, hierarchical models with multiple layers of latent variables do not effectively utilize the hierarchical structure when trained with existing variational methods. The paper identifies limitations in the types of features these models can learn and proposes an alternative architecture, the Variational Ladder Autoencoder (VLAE), which bypasses these shortcomings.

Limitations of Hierarchical Generative Models

Representational Efficiency

Contrary to the anticipated representational efficiency of hierarchical architectures, the paper demonstrates that hierarchical variational autoencoders (HVAEs) do not achieve improved representational power. In a well-optimized HVAE, the generative process's bottom layer alone can accurately reconstruct the data distribution, rendering subsequent layers redundant. This insight challenges the expectation that deep networks offer exponential gains in parameter efficiency. Through both theoretical propositions and empirical observations, the paper substantiates that optimal HVAE models reflect redundancy rather than enhanced representation capability.

Feature Learning

Traditional HVAE models fail to learn rich, disentangled hierarchies of features. Despite variational inference techniques aimed at training hierarchical models, conditional distributions in most HVAEs are limited to simple unimodal families, such as Gaussians. Such programming limits the ability to capture the complex, multimodal characteristics necessary for the rich feature hierarchies observed in feed-forward networks. Through controlled experiments, the paper highlights that higher-level features tend to compress into the topmost layer, undermining the notion of progressive abstraction across model layers.

Variational Ladder Autoencoders

To address these limitations, the paper introduces the Variational Ladder Autoencoder (VLAE). Unlike stacked HVAEs, the VLAE architecture emphasizes disentangled feature representations by utilizing varying network depths for different latent code layers. This model does not rely on multiple hierarchical layers but instead organizes the latent code into subparts with deliberate architectural expressiveness. VLAE prioritizes a flat latent hierarchy designed to distribute features according to complexity, facilitating the learning of structured and disentangled representations without the pitfalls of traditional model stacking.

Architecture and Comparison

VLAE diverges from conventional ladder variational autoencoders (LVAE) by employing a flat hierarchical structure for the latent code. This approach leverages the expressive power of neural networks to separate features with varying levels of abstraction. Unlike LVAE, which uses hierarchical stacking, VLAE successfully isolates abstract features through architectural sophistication rather than multi-layer encoding.

Experiments

The paper presents empirical evaluations of VLAE across datasets including MNIST, SVHN, and CelebA, demonstrating the model's ability to capture and disentangle hierarchical features such as stroke width, color schemes, and facial attributes. These results underscore VLAE's capacity to organize features hierarchically through architecture alone, showcasing disentangled representations and robust feature abstractions across complex datasets.

Conclusion

The research articulates the limitations inherent in traditional hierarchical generative modeling concerning feature learning and representation efficiency. The Variational Ladder Autoencoder emerges as a compelling alternative, offering innovative architectural strategies that effectively disentangle hierarchical features. Future work may expand upon VLAE to explore architectures facilitating complex feature structures beyond hierarchical disentanglement. The insights from this paper shape the understanding of hierarchical generative models and propose functional architectural principles for advanced feature learning.