Reciprocal GAN Through Characteristic Functions (RCF-GAN).

Area of Science:

• Artificial Intelligence
• Machine Learning
• Deep Learning

Background:

• Generative Adversarial Nets (GANs) often face training instability and mode collapse.
• Integral Probability Metric (IPM) GANs stabilize training by comparing statistical moments but lack direct distribution comparison.
• Characteristic Functions (CFs) uniquely represent probability distributions.

Purpose of the Study:

• To generalize IPM-GANs by directly comparing probability distributions using CFs.
• To develop a novel GAN architecture for enhanced generation and reconstruction.
• To demonstrate superior performance on diverse data domains.

Main Methods:

• Introduced a novel CF loss for direct probability distribution comparison.
• Proved theoretical properties of CFs, including their phase and amplitude interpretation.
• Developed an optimal sampling strategy for CF calculation.
• Established domain equivalence under reciprocal theory.
• Integrated CFs with an auto-encoder using an advanced anchor architecture to form RCF-GAN.

Main Results:

• Theoretically proved the ability of CF loss to compare probability distributions.
• Established the physical meaning of CF phase and amplitude.
• Demonstrated domain equivalence between embedded and data domains.
• Achieved state-of-the-art bi-directional generation using the RCF-GAN structure.
• Showcased superior performance on both image and graph data.

Conclusions:

• RCF-GAN offers a robust and efficient approach for generative modeling.
• Directly comparing probability distributions via CFs enhances GAN performance.
• The RCF-GAN architecture enables high-quality bi-directional generation and reconstruction.