Learning Latent Space Energy-Based Prior Model (2006.08205v2)

Abstract: We propose to learn energy-based model (EBM) in the latent space of a generator model, so that the EBM serves as a prior model that stands on the top-down network of the generator model. Both the latent space EBM and the top-down network can be learned jointly by maximum likelihood, which involves short-run MCMC sampling from both the prior and posterior distributions of the latent vector. Due to the low dimensionality of the latent space and the expressiveness of the top-down network, a simple EBM in latent space can capture regularities in the data effectively, and MCMC sampling in latent space is efficient and mixes well. We show that the learned model exhibits strong performances in terms of image and text generation and anomaly detection. The one-page code can be found in supplementary materials.

• The paper introduces a novel framework where an energy‐based prior in latent space significantly enhances the performance of deep generative models.
• It employs maximum likelihood estimation combined with short-run MCMC and Langevin dynamics for efficient joint learning of the prior and generator.
• Experimental results show improved image synthesis (lower FID), text generation (lower perplexity), and anomaly detection (higher AUPRC), validating the model’s efficacy.

Learning Latent Space Energy-Based Prior Model

Introduction

The paper "Learning Latent Space Energy-Based Prior Model" introduces a novel approach to enhancing deep generative models using an energy-based model (EBM) as a prior in the latent space of a generator. The approach leverages the advantages of a generator model by refining its expressive power through an EBM, ultimately capturing more complex data distributions efficiently. This framework targets improvements in image synthesis, text generation, and anomaly detection tasks by jointly learning the latent space EBM and the top-down network using maximum likelihood estimation (MLE) and Markov chain Monte Carlo (MCMC) sampling.

Model and Learning

Model Description

The model proposes a joint framework where both the latent space EBM and the top-down network of the generator are learned. The EBM acts as a prior model that modifies a simple distribution like an isotropic Gaussian to better capture the complexities of the data. The joint distribution of an observed example $x$ and a latent variable $z$ is given by:

$p_{\theta}(x, z) = p_{\alpha}(z) p_\beta(x | z)$

where $p_{\alpha}(z)$ is the energy-based prior and $p_\beta(x | z)$ is the generation network. The prior $p_{\alpha}(z)$ is an exponentially tilted version of a simpler distribution, aiming to enhance the generator's coverage of the data distribution effectively.

Learning Procedure

The model employs MLE with short-run MCMC for training. Specifically, the latent variables are sampled to estimate gradients necessary for updating both the prior model and the generation model. The short-run MCMC is a computationally efficient method that aids in sampling from both the prior and the posterior distributions quickly, using a fixed number of steps starting from a Gaussian noise distribution.

Implementation Considerations

Practical implementation focuses on ensuring efficient sampling and parameter updates through the following:

• MCMC Sampling: Requires careful tuning of step sizes and the number of steps for short-run MCMC to balance exploration and computational efficiency. Langevin dynamics is utilized for this purpose.
• Network Architecture: The energy function is represented by a small multi-layer perceptron, allowing effective computation without incurring prohibitive computational costs.
• Optimization Strategy: The model employs Adam for parameter updates with a learning rate schedule that needs careful tuning based on empirical observations.

Experimental Results

The proposed model demonstrates superior performance in tasks of image and text generation, as well as anomaly detection.

• Image Generation: Outperforms baseline models such as VAEs in terms of Fréchet Inception Distance (FID), demonstrating the effectiveness of the learned EBM prior in generating more realistic images.
• Text Generation: Achieves lower perplexity scores compared to baseline methods, indicating better fluency and diversity in generated text sequences.
• Anomaly Detection: Shows strong results by effectively distinguishing between normal and anomalous data with high area under the precision-recall curve (AUPRC) scores, highlighting the discriminative power of the learned latent space.

Theoretical and Practical Implications

The theoretical implications include a robust framework for integrating EBMs with generator models, providing a solid foundation for further exploration in empirical Bayes methods. Practically, this approach can result in more capable generative models in a variety of applications, potentially influencing advancements in fields requiring complex model distributions such as healthcare diagnostics, automated content creation, and security.

Conclusion

The latent space energy-based prior model offers a potent enhancement to deep generative frameworks by embedding a flexible and expressive EBM as a learned prior. Through efficient joint training, the model effectively captures complex patterns in high-dimensional data, yielding significant improvements over traditional methods. Future works could extend this model with amortized inference and additional applications in diverse generative tasks.