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Wasserstein Distance
Metric measuring the distance between two probability distributions by quantifying the minimum cost to transform one distribution into another, particularly effective for distributions with low or disjoint support.
Earth Mover's Distance (EMD)
Geometric interpretation of the Wasserstein distance conceptualized as the minimum work required to move earth mass from one distribution to another, providing a continuous and smooth measure.
Critic Network
Neural network replacing the discriminator in WGANs, evaluating real and generated samples to produce a scalar score rather than a probability, allowing better correlation with sample quality.
Lipschitz Continuity
Mathematical property ensuring that the critic function does not vary too rapidly, essential for guaranteeing that the Wasserstein distance remains finite and that training is stable.
Discriminator vs Critic
Fundamental distinction where the classical discriminator produces classification probabilities while the WGAN critic provides an unbounded continuous score to evaluate sample quality.
Training Dynamics
Specific learning behavior in WGANs characterized by more constant gradients, progressive convergence, and a linear relationship between loss and generated sample quality.
Sample Quality Metrics
Evaluation measures where the WGAN loss itself serves as a reliable indicator of generated sample quality, unlike traditional GANs where the loss is not informative.
WGAN Generator Loss
Generator objective function in WGANs seeking to minimize the Wasserstein distance, providing always informative gradients and avoiding the problem of gradient saturation.
Critic Loss
Objective function of the critic trained to maximize the difference between scores of real and generated samples under Lipschitz constraint, approximating the exact Wasserstein distance.