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1121450通过噪声稳定生成对抗训练0Simon Jenni Paolo Favaro伯尔尼大学0{ simon.jenni,paolo.favaro } @inf.unibe.ch0摘要0我们提出了一种新的方法和分析,以稳定的方式训练生成对抗网络(GAN)。如最近的分析所示,训练往往受到数据概率分布在数据空间的邻域上为零的影响。我们注意到,即使在经过相同滤波的情况下,真实数据和生成数据的分布也应该匹配。因此,为了解决有限支持的问题,我们提出使用真实数据和生成数据分布的不同滤波版本来训练GAN。这样,滤波不会阻止数据分布的精确匹配,同时通过扩展两个分布的支持来帮助训练。作为滤波,我们考虑将来自任意分布的样本添加到数据中,这相当于将数据分布与任意分布进行卷积。我们还建议学习生成这些样本,以挑战鉴别器的对抗训练。我们证明了我们的方法可以稳定和良好地训练甚至原始的极小极大GAN公式。此外,我们的技术可以纳入大多数现代GAN公式,并在几个常见数据集上得到一致的改进。01. 引言0自从[6]的开创性工作以来,生成对抗网络(GAN)因其产生的样本质量而被广泛使用和分析,特别是在自然图像领域的应用。不幸的是,GAN的训练仍然很困难。事实上,普通的实现不能收敛到高质量的样本生成器,用于改进生成器的启发式方法经常表现出不稳定的行为。这导致了大量的工作来更好地理解GAN(参见[23,19,1])。特别是,[1]指出GAN的不稳定训练是由于数据和模型分布的(有限和低维)支持的限制。在原始的GAN公式中,生成器在极小极大优化问题中针对鉴别器进行训练。鉴别器学习区分真实样本和伪造样本,而生成器学习生成可以欺骗鉴别器的伪造样本。当数据和模型分布的支持不重叠时,生成器在鉴别器实现完美分类后停止改进,因为这阻止了通过梯度下降向生成器传播有用信息(见图1a)。0(a)0(b)0(c)0图1:(a) 当真实数据的概率密度函数pd和生成数据的概率密度函数pg不重叠时,鉴别器可以轻松区分样本。鉴别器对其输入的梯度在这些区域为零,这阻止了生成器的进一步改进。(b)将来自任意分布p �的样本添加到真实数据和生成数据中会得到滤波后的版本pd � p � 和p g � p�。由于滤波后的分布的支持重叠,鉴别器的梯度不为零,生成器可以改进。然而,原始分布的高频内容丢失了。(c)通过变化p�,生成器可以准确地学习匹配数据分布,这要归功于扩展的支持。0以区分真实样本和伪造样本,而生成器学习生成可以欺骗鉴别器的伪造样本。当数据和模型分布的支持不重叠时,生成器在鉴别器实现完美分类后停止改进,因为这阻止了通过梯度下降向生成器传播有用信息(见图1a)。0最近的工作[1]提出了在将生成的和真实的图像输入鉴别器之前,向它们添加噪声来扩展分布的支持。这个过程导致了数据的平滑。minG maxDD(x) =AAAB8HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzEOSJcxOZpMh81hmZoWw5Cu8eFDEq5/jzb9xNtmDJhY0FFXddHdFCWfG+v63V1pb39jcKm9Xdnb39g+qh0dto1JNaIsornQ3woZyJmnLMstpN9EUi4jTTjS5zf3OE9WGKflgpwkNBR5JFjOCrZMe+zQxjCtZGVRrft2fA62SoCA1KNAcVL/6Q0VSQaUlHBvTC/zEhhnWlhFOZ5V+amiCyQSPaM9RiQU1YTY/eIbOnDJEsdKupEVz9fdEhoUxUxG5ToHt2Cx7ufif10ttfB1mTCappZIsFsUpR1ah/Hs0ZJoSy6eOYKKZuxWRMdaYWJdRHkKw/PIqaV/UA78e3F/WGjdFHGU4gVM4hwCuoAF30IQWEBDwDK/w5mnvxXv3PhatJa+YOYY/8D5/AIRBkDQ= 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p�已经丢失了pd的高频内容。一种直接的解决方案是使用噪声退火的形式,其中噪声方差最初很高,然后在迭代过程中逐渐减小,以便最终匹配原始分布,而不是平滑的分布。这导致了改进的训练,但随着噪声方差趋近于零,优化问题收敛到原始公式,算法可能出现通常的不稳定行为。在这项工作中,我们设计了一种新的对抗训练过程,它是稳定的并且产生准确的结果。我们证明,在一些一般假设下,可以在不影响原始无噪声公式的最优性条件的情况下,修改数据和生成的概率密度,添加额外的噪声。作为原始公式的替代方案,使用z�N(0,Id)和x�p d,0min G max D E_x [log D ( x )] + E_z [log(1 - D ( G ( z )))],(1)0其中D表示鉴别器,我们建议通过解决以下优化问题来训练生成模型G0p_� ∈S E_� � p_� [ E_x � p_d [log D ( x + � )]] + 0E_� � p_� � E_z �N (0 ,I d ) [log(1 - D ( G ( z ) + 0在这里,我们引入了一个概率密度函数集合S。如果我们解决问题(2)中最内层的优化问题,那么我们就得到了最优鉴别器0p_0p_� ∈S p_d,� ( x ) + p_g,� ( x ),(3)0在这里,我们将p_g定义为G ( z )的概率密度,其中z � N (0 ,I d )。如果我们将其代入0鉴别器 D0生成器 G0生成器 N ϵ0G ( z ) + ϵ0x + ϵ0真实的0伪造的0噪声样本0噪声样本0真实图像样本0图2:所提出的GAN训练的简化方案。我们还展示了一个噪声生成器N,详细说明见第3.1节。鉴别器D需要区分无噪声和有噪声的真实样本与伪造样本。0上述问题并简化,我们有0p_� ∈S p_d,�|S| �0p_� ∈S p_g,� � ,(4)0其中JSD是Jensen-Shannon散度。我们证明,在适当的假设下,问题(4)的最优解是唯一的,p_g =p_d。此外,由于1 / |S| �0p_� ∈Sp_d,�比p_d具有更大的支撑集,通过基于梯度下降的迭代方法进行优化更有可能达到全局最小值,而不受p_d的支撑集的影响。因此,我们的公式具有以下特点:1)它定义了一种概率密度的拟合,不受其支撑集的影响;2)它保证了数据概率密度函数的精确匹配;3)它可以轻松应用于其他GAN公式。所提出方法的简化方案如图2所示。0在接下来的几节中,我们详细介绍了我们的分析,然后设计了一个计算上可行的问题形式的近似解决方案(2)。我们对CIFAR-10 [12]、STL-10 [5]和CelebA[15]进行了定量评估,并对ImageNet[20]和LSUN卧室[24]进行了定性评估。02. 相关工作0GAN
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