Geometric GAN

By Jae Hyun Lim, Jong Chul Ye. 2017

581 citations recorded by the source corpus.

Generative Adversarial Nets (GANs) represent an important milestone for effective generative models, which has inspired numerous variants seemingly different from each other. One of the main contributions of this paper is to reveal a unified geometric structure in GAN and its variants. Specifically, we show that the adversarial generative model training can be decomposed into three geometric steps: separating hyperplane search, discriminator parameter update away from the separating hyperplane, and the generator update along the normal vector direction of the separating hyperplane. This geometric intuition reveals the limitations of the existing approaches and leads us to propose a new formulation called geometric GAN using SVM separating hyperplane that maximizes the margin. Our theoretical analysis shows that the geometric GAN converges to a Nash equilibrium between the discriminator and generator. In addition, extensive numerical results show that the superior performance of geometric GAN.

Subfields: Computer Vision and Pattern Recognition, Generative Models, Signal Processing

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Citations in the corpus

Large Scale GAN Training for High Fidelity Natural Image Synthesis (2018, methodology): “One line of work is focused on changing the objective function (Arjovsky et al., 2017; Mao et al., 2016; Lim & Ye, 2017; Bellemare et al., 2017; Salimans et al., 2018) to encourage convergence.”
Spectral Normalization for Generative Adversarial Networks (2018, methodology): “This type of loss has been already proposed and used in Lim & Ye (2017); Tran et al. (2017).”
Projected GANs Converge Faster (2021, methodology): “Using a hinge loss [33], we train with a batch size of 64 until 1 million real images have been shown to the discriminator, a sufficient amount for G to reach values close to convergence.”
Learning Layout and Style Reconfigurable GANs for Controllable Image Synthesis (2020, methodology): “For the discriminator, we utilize the hinge version [27], [28] of the standard adversarial loss [1],”
Object-Centric Image Generation from Layouts (2020, methodology): “Generator and Discriminator losses We train the generator and patch discriminators using the adversarial hinge loss (Lim and Ye 2017):”
Semantic Image Synthesis With Spatially-Adaptive Normalization (2019, methodology): “We train the generator with the same multi-scale discrim inator and loss function used in pix2pixHD except that we replace the least squared loss term [33] with the hinge loss term [30,35,51].”
Large Scale Adversarial Representation Learning (2019, neutral): “Concretely, the discriminator loss LD and the encoder-generator loss LEG are defined as follows, based on scalar discriminator “score” functions s∗ and the corresponding per-sample losses `∗: sx(x) = θ T xFΘ(x) sz(z) = θ T zHΘ(z) sxz(x, z) = θ T xzJΘ(FΘ(x), HΘ(z)) `EG(x, z, y) = y (sx(x) + sz(z) + s”
Coulomb GANs: Provably Optimal Nash Equilibria via Potential Fields (2017, methodology): “ + WD Figure 2: Scatter plots of generated samples from different GAN variants for the mixture of 25 Gaussians and the true data distribution. “WD” indicates weight decay and “proj.” means projection [31]. Results and images for all methods except the Coulomb GAN are taken from Lim et al. [31]. 3 Ex”
Self-Attention Generative Adversarial Networks (2018, methodology): “task. In SAGAN, the proposed attention module has been applied to both generator and discriminator, which are trained in an alternating fashion by minimizing the hinge version of the adversarial loss [13, 30, 16], L D = E (x;y)˘p data [min(0; 1 + D(x;y))] E z˘p z;y˘p [min(0; 1 D(G(z);y))]; L G = E z”
cGANs with Projection Discriminator (2018, methodology): “For the objective function, we used the following hinge version of the standard adversarial loss (1) (Lim & Ye, 2017; Tran et al., 2017) where the last activation function A of D is identity function. p ( z ) is standard Gaussian distribution and G ( z , y ) is the generator network.”
High-Fidelity Audio Compression with Improved RVQGAN (2023, methodology): “We use the HingeGAN [22] adversarial loss formulation, and apply the L1 feature matching loss [19].”
MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis (2019, methodology): “To train the GAN, we use the hinge loss version of the GAN objective (Lim & Ye, 2017; Miyato et al., 2018).”
High Fidelity Speech Synthesis with Adversarial Networks (2019, neutral): “We use the hinge loss (Lim & Ye, 2017), a batch size of 1024 and the Adam optimizer (Kingma & Ba, 2015) with hyperparameters β 1 = 0 , β 2 = 0 .”
End-to-End Adversarial Text-to-Speech (2020, positive): “The loss function we use to train the generator is as follows: where L G, adv is the adversarial loss, linear in the discriminators’ outputs, paired with the hinge loss [35, 57] used as the discriminators’ objective, as used in GAN-TTS [8].”
Adversarial score matching and improved sampling for image generation (2020, background): “LSGAN (Mao et al., 2017) yielded the best FID scores among all other loss functions considered, namely the original GAN loss function (Goodfellow et al., 2014), HingeGAN (Lim and Ye, 2017), as well as their relativistic counterparts (Jolicoeur-Martineau, 2018; 2019).”
Consistency Regularization for Generative Adversarial Networks (2019, methodology): “Speciﬁcally, we evaluate regularization methods using three loss functions: the non-saturating loss (NS) (Goodfellow et al., 2014), the Wasserstein loss (WAS) (Arjovsky et al., 2017), and the hinge loss (Hinge) (Lim & Ye, 2017; Tran et al., 2017).”
Discriminator Rejection Sampling (2018, methodology): “Finally, this whole model is trained using a special hinge version of the adversarial loss (Lim & Ye, 2017; Miyato & Koyama, 2018; Tran et al., 2017): (2)”
LOGAN: Latent Optimisation for Generative Adversarial Networks (2019, methodology): “Nevertheless, Appendix C provides a Poisson log-likelihood interpretation for the hinge loss commonly used in GANs (Lim & Ye, 2017; Tran et al., 2017).”