Variational Autoencoders (VAEs) have been a pioneering force in the realm of deep generative models. Amongst its legions of progenies, Wasserstein Autoencoders (WAEs) stand out in particular due to the dual offering of heightened generative quality and a strong theoretical backbone. WAEs consist of an encoding and a decoding network forming a bottleneck with the prime objective of generating new samples resembling the ones it was catered to. In the process, they aim to achieve a target latent representation of the encoded data. Our work is an attempt to offer a theoretical understanding of the machinery behind WAEs. From a statistical viewpoint, we pose the problem as concurrent density estimation tasks based on neural network-induced transformations. This allows us to establish deterministic upper bounds on the realized errors WAEs commit. We also analyze the propagation of these stochastic errors in the presence of adversaries. As a result, both the large sample properties of the reconstructed distribution and the resilience of WAE models are explored.

翻译：变分自编码器（VAEs）是深度生成模型领域的先驱力量。在其众多衍生模型中，Wasserstein自编码器（WAEs）尤为突出，因其兼具卓越的生成质量和坚实的理论基础。WAEs由编码网络和解码网络构成瓶颈结构，核心目标是生成与训练数据相似的新样本。在此过程中，它们致力于实现编码数据的目标潜在表示。本文试图为WAEs背后的机理提供理论理解。从统计学视角出发，我们将该问题建模为基于神经网络诱导变换的联合密度估计任务。这使我们得以建立WAEs所产生误差的确定性上界。我们还分析了这些随机误差在对抗环境下的传播特性。由此，本文探究了重构分布的大样本性质以及WAE模型的鲁棒性。