Tessellating the Latent Space for Non-Adversarial Generative Auto-Encoders

Area of Science:

• Machine Learning
• Artificial Intelligence
• Computer Vision

Background:

• Non-adversarial generative models offer training ease and reduced mode collapse but lack discriminator accuracy in latent space approximation.
• Existing models struggle with precise target distribution approximation due to inherent limitations.

Purpose of the Study:

• To develop a novel divide-and-conquer generative model, Tessellated Wasserstein Auto-Encoders (TWAE), to minimize statistical error in target distribution approximation.
• To enhance the accuracy and generative performance of non-adversarial models.

Main Methods:

• TWAE utilizes centroidal Voronoi tessellation (CVT) to partition the target distribution's support into regions.
• Data batches are structured based on this tessellation, moving away from random shuffling for precise discrepancy computation.
• The model's theoretical error bounds were analyzed concerning sample size (n) and region count (m).

Main Results:

• Theoretical analysis shows error decreases with increased samples (n) and regions (m) at specific rates.
• TWAE significantly improves generative performance, as measured by Fréchet Inception Distance (FID), over existing non-adversarial models.
• Numerical results indicate TWAE is competitive with adversarial models, demonstrating strong generative capabilities.

Conclusions:

• Tessellated Wasserstein Auto-Encoders (TWAE) offer a significant advancement in non-adversarial generative modeling.
• The tessellation approach enhances statistical accuracy and generative performance, providing a powerful alternative to traditional methods.
• TWAE demonstrates competitive performance against adversarial models, highlighting its potential for complex generative tasks.