arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1809.05964cs.LGstat.ML
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生成模型的潜空间最优迁移

Latent Space Optimal Transport for Generative Models

Stony Brook University(石溪大学);Dalian University of Technology(大连理工大学);Harvard University(哈佛大学)

Huidong Liu, Yang Guo, Na Lei, Zhixin Shu, Shing-Tung Yau, Dimitris Samaras, Xianfeng Gu

摘要:

变分自动编码器将其学习的中间潜在空间数据分布强制为简单分布,例如各向同性高斯分布。然而,这会导致后验崩溃问题,并失去流形结构,这对面部图像等数据集很重要。GAN可以将简单分布转换为潜在空间数据分布,从而保留流形结构,但优化GAN涉及解决Min-Max优化问题,这是困难的,迄今为止还没有很好地理解。因此,我们提出了一种类似GAN的方法,通过仅解决最小化问题将简单分布转换为潜在空间中的数据分布。这个最小化问题来自于训练一个简单分布和潜在空间数据分布之间的映射。然后,我们可以明确地制定一个最优运输(OT)问题,计算两个分布之间的期望映射。这意味着我们可以在不解决困难的Min-Max优化问题的情况下转换分布。在八高斯数据集上的实验结果表明,该算法能够处理多类分布的数据。在MNIST和CelebA数据集上的实验结果验证了该方法的有效性。

英文摘要:

Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which can be important for datasets such as facial images. A GAN can transform a simple distribution to a latent-space data distribution and thus preserve the manifold structure, but optimizing a GAN involves solving a Min-Max optimization problem, which is difficult and not well understood so far. Therefore, we propose a GAN-like method to transform a simple distribution to a data distribution in the latent space by solving only a minimization problem. This minimization problem comes from training a discriminator between a simple distribution and a latent-space data distribution. Then, we can explicitly formulate an Optimal Transport (OT) problem that computes the desired mapping between the two distributions. This means that we can transform a distribution without solving the difficult Min-Max optimization problem. Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions. Results on the MNIST and the CelebA datasets validate the effectiveness of the proposed method.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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