Simplified Fréchet Distance for Generative Adversarial Nets

Abstract

We introduce a distance metric between two distributions and propose a Generative Adversarial Network (GAN) model: the Simplified Fréchet distance (SFD) and the Simplified Fréchet GAN (SFGAN). Although the data generated through GANs are similar to real data, GAN often undergoes unstable training due to its adversarial structure. A possible solution to this problem is considering Fréchet distance (FD). However, FD is unfeasible to realize due to its covariance term. SFD overcomes the complexity so that it enables us to realize in networks. The structure of SFGAN is based on the Boundary Equilibrium GAN (BEGAN) while using SFD in loss functions. Experiments are conducted with several datasets, including CelebA and CIFAR-10. The losses and generated samples of SFGAN and BEGAN are compared with several distance metrics. The evidence of mode collapse and/or mode drop does not occur until 3000k steps for SFGAN, while it occurs between 457k and 968k steps for BEGAN. Experimental results show that SFD makes GANs more stable than other distance metrics used in GANs, and SFD compensates for the weakness of models based on BEGAN-based network structure. Based on the experimental results, we can conclude that SFD is more suitable for GAN than other metrics.

FlexIT: Towards Flexible Semantic Image Translation

“…To assess naturalness of transformed images, we use the Fréchet Inception distance (FID) [21]. To avoid numerical instability related to estimating the feature distribution with a small number of samples, we use the "Simplified FID" (SFID) [31] which does not take into account the offdiagonal terms in the feature covariance matrix. In addition to the SFID, we use a class-conditional SFID score (CS-FID) which is an average of the SFID scores computed for each target class separately.…”

“…More formally, let µ r and σ r be the mean and standard deviation of inception features for the real images, and µ s and σ s for the synthetic images. The Simplified FID [31] is computed as…”

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“…Many inpainting models have used the patchGAN discriminator [36] as their discriminator [12][13][14]23]. However, due to the adversarial training process in the GAN, GAN-based inpainting models often exhibit unstable training [34,37,38]. This problem should be addressed to use the discriminator in GAN-based models.…”

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