Generative Adversarial Nets (GANs) are currently the dominant model for high fidelity image synthesis. GANs suffer from two major drawbacks: complicated dynamics and the requirement for an auxiliary network for training (discriminator). However, if we train a decoder-only network we circumvent both drawbacks. To achieve that, the decoder should capture high-order correlations that exist between the variables. We demonstrate this is possible by designing a high-order polynomial generator using tensorial factors. We implement two variants of the model, which we call NAPS. We experiment with both MNIST and CelebA and showcase that our model captures the data distribution and synthesizes new images with significantly less parameters than the corresponding baseline.

生成对抗网络（GANs）当前是高保真图像合成的主要模型。GAN具有两个主要缺点：复杂的动力学以及对训练的辅助网络（区分器）的需求。但是，如果我们训练仅解码器的网络，则会避免这两个缺点。为此，解码器应捕获变量之间存在的高阶相关性。我们通过使用张量因子设计一个高阶多项式生成器来证明这是可能的。我们实现了模型的两个变体，我们称之为NAPS。我们对MNIST和CelebA进行了实验，展示了我们的模型可以捕获数据分布并以比相应基线少得多的参数来合成新图像。