Variational autoencoders (VAEs) are one of the deep generative models that have experienced enormous success over the past decades. However, in practice, they suffer from a problem called posterior collapse, which occurs when the encoder coincides, or collapses, with the prior taking no information from the latent structure of the input data into consideration. In this work, we introduce an inverse Lipschitz neural network into the decoder and, based on this architecture, provide a new method that can control in a simple and clear manner the degree of posterior collapse for a wide range of VAE models equipped with a concrete theoretical guarantee. We also illustrate the effectiveness of our method through several numerical experiments.

翻译：变分自编码器（Variational Autoencoders, VAEs）是过去几十年取得巨大成功的深度生成模型之一。然而在实际应用中，它们会面临一个称为后验坍塌（posterior collapse）的问题，即编码器与先验分布重合或坍塌，未能考虑输入数据潜在结构中的任何信息。本文在解码器中引入一种逆Lipschitz神经网络，并基于该架构提出一种新方法，能够以简洁清晰的方式控制多种VAE模型的后验坍塌程度，同时提供具体的理论保证。我们还通过多项数值实验验证了该方法的有效性。