2019
DOI: 10.1109/tpami.2018.2872043
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On the Effectiveness of Least Squares Generative Adversarial Networks

Abstract: Unsupervised learning with generative adversarial networks (GANs) has proven to be hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process. To overcome such a problem, we propose in this paper the Least Squares Generative Adversarial Networks (LSGANs) which adopt the least squares loss for both the discriminator and the generator. … Show more

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Cited by 172 publications
(115 citation statements)
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“…Let false‖vfalse‖p denote the Lp‐norm of a vector v . Our loss function for the discriminators is based on LSGAN . LossD=λDxCBfalse‖DP(GCPfalse(xfalse))-bold0false‖2+false‖DC(x)-bold1false‖2+λDyPlanfalse‖DC(GPCfalse(yfalse))-bold0false‖2+false‖DP(y)-bold1false‖2. The loss function forces DP (and, respectively, DC) to be trained to distinguish the distributions of real PlanCT (and, respectively, CBCT) images from synthesized ones.…”
Section: Methodsmentioning
confidence: 99%
“…Let false‖vfalse‖p denote the Lp‐norm of a vector v . Our loss function for the discriminators is based on LSGAN . LossD=λDxCBfalse‖DP(GCPfalse(xfalse))-bold0false‖2+false‖DC(x)-bold1false‖2+λDyPlanfalse‖DC(GPCfalse(yfalse))-bold0false‖2+false‖DP(y)-bold1false‖2. The loss function forces DP (and, respectively, DC) to be trained to distinguish the distributions of real PlanCT (and, respectively, CBCT) images from synthesized ones.…”
Section: Methodsmentioning
confidence: 99%
“…By maximizing the mutual information between the reconstruction and z, we prevented posterior collapse and constrained the decoder g(·) to effectively use the modality factors. L ADV is the adversarial loss of a Least-Squares GAN [11], used to discriminate ground truth from predicted segmentations in the unsupervised setting. L T R is the loss associated to the self-supervised signal, computed as the differentiable Dice loss betweens t+dt and s t+dt .…”
Section: Cost Function and Trainingmentioning
confidence: 99%
“…In general, the resulting DSMs from our cGAN model revealed the same or slightly worse results compared even to the normal stereo DSM. The reason for this lies in the fact that the cGAN model uses the sigmoid cross entropy loss function for the discriminator [33] that leads to the vanishing gradient problem when updating the generator using the created samples that are on the correct side of the decision boundary but are still far from the real data [49]. As a result, the discriminator believes that the created images come from real samples and causes almost no error by updating the generator as the images are on the correct side of the decision boundary.…”
Section: Cgan Vs Clsganmentioning
confidence: 99%
“…The results obtained by the cLSGAN model on both datasets quantitatively outperforms the stereo DSM and the DSMs generated by the cGAN model as they are much smoother, able to reconstruct even small parts of buildings, and do not contain any artifacts. Mao et al [49] explained that as a powerful feature of the least squares loss function that moves the created samples toward the decision boundary and penalizes samples that lie in a long way on the correct side of the decision boundary. As a result, this allows the generation of more realistic samples.…”
Section: Cgan Vs Clsganmentioning
confidence: 99%