论文标题
Tessellated Wasserstein自动编码器
Tessellated Wasserstein Auto-Encoders
论文作者
论文摘要
非对抗性生成模型，例如变异自动编码器（VAE），Wasserstein自动编码器具有最大平均差异（WAE-MMD），切成薄片 - 瓦斯泰因自动编码器（SWAE）相对易于训练，并且与Wasserstein Auto-Auto-engoder Network相比，训练且模式较小，与生殖器网络（WAESERATIAD EVERVERATIAD GERVERATIAD EVERVERATIAL NETRATIAL（WAEE）相比，它具有较小的模式。但是，它们在近似潜在空间中的目标分布方面并不是很准确，因为它们没有歧视器来检测真实和假货之间的较小差异。为此，我们开发了一个新型的非对抗性框架，称为镶嵌瓦斯坦斯坦自动编码器（TWAE），以将目标分布的支持通过质心Voronoi tessellation（CVT）技术和设计批次的数据置于给定数量的区域中，而不是根据乳胶而不是随机的，而不是随机的变化计算。从理论上讲，我们证明，当样本$ n $和区域$ m $ tessellation的估计误差减少，而$ \ mathcal {o}的速率变得更大$ \ Mathcal {O}（\ frac {1} {\ sqrt {m}}）$。给定固定的$ n $和$ m $，要最小化测量误差的上限的必要条件是镶嵌是由CVT确定的。与Vae，Wae-MMD，SWAE相比，TWAE对不同的非对抗性指标非常灵活，并且可以大大提高其生成性能（FID）。此外，数值结果确实表明，TWAE与对抗性模型Wae-Gan具有竞争力，证明了其强大的生成能力。
Non-adversarial generative models such as variational auto-encoder (VAE), Wasserstein auto-encoders with maximum mean discrepancy (WAE-MMD), sliced-Wasserstein auto-encoder (SWAE) are relatively easy to train and have less mode collapse compared to Wasserstein auto-encoder with generative adversarial network (WAE-GAN). However, they are not very accurate in approximating the target distribution in the latent space because they don't have a discriminator to detect the minor difference between real and fake. To this end, we develop a novel non-adversarial framework called Tessellated Wasserstein Auto-encoders (TWAE) to tessellate the support of the target distribution into a given number of regions by the centroidal Voronoi tessellation (CVT) technique and design batches of data according to the tessellation instead of random shuffling for accurate computation of discrepancy. Theoretically, we demonstrate that the error of estimate to the discrepancy decreases when the numbers of samples $n$ and regions $m$ of the tessellation become larger with rates of $\mathcal{O}(\frac{1}{\sqrt{n}})$ and $\mathcal{O}(\frac{1}{\sqrt{m}})$, respectively. Given fixed $n$ and $m$, a necessary condition for the upper bound of measurement error to be minimized is that the tessellation is the one determined by CVT. TWAE is very flexible to different non-adversarial metrics and can substantially enhance their generative performance in terms of Fréchet inception distance (FID) compared to VAE, WAE-MMD, SWAE. Moreover, numerical results indeed demonstrate that TWAE is competitive to the adversarial model WAE-GAN, demonstrating its powerful generative ability.
