Generative Adversarial Networks (GANs) are performant generative methods yielding high-quality samples. However, under certain circumstances, the training of GANs can lead to mode collapse or mode dropping, i.e. the generative models not being able to sample from the entire probability distribution. To address this problem, we use the last layer of the discriminator as a feature map to study the distribution of the real and the fake data. During training, we propose to match the real batch diversity to the fake batch diversity by using the Bures distance between covariance matrices in feature space. The computation of the Bures distance can be conveniently done in either feature space or kernel space in terms of the covariance and kernel matrix respectively. We observe that diversity matching reduces mode collapse substantially and has a positive effect on the sample quality. On the practical side, a very simple training procedure, that does not require additional hyperparameter tuning, is proposed and assessed on several datasets.

翻译：生成自变网络(GANs)是产生高质量样品的基因化方法,但在某些情况下,GANs的培训可能导致模式崩溃或模式下降,即基因模型无法从整个概率分布中取样。为解决这一问题,我们用歧视者最后一层作为特征图,研究真实数据和假数据的分布。在培训期间,我们提议利用地物空间共变矩阵之间的布雷斯距离,将真实的批量多样性与虚假的批量多样性相匹配。对于地物空间或内核空间,可以分别以共变和内核矩阵来方便地进行布雷斯距离的计算。我们观察到,多样性匹配极大地减少了模式崩溃,并对样本质量产生了积极影响。在实际操作方面,一个不需要额外超参数调整的非常简单的培训程序是在若干数据集上提出和评估的。