Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is accurate.

We show additional image synthesis in Fig.2. For reported numbers in main text, we adopt the network structure that contains Residue Blocks (see implementation details in Tab.5). We then test our model for the task of image inpainting. As shown in Fig.1, our This is the marginal version of Eqn.8 shown in the main text. 2 2.3 Learning Algorithm Three models are trained in an alternative and iterative manner based on the current model parameters. Compared to Eqn.3 and Eqn.6 in the main text, Eqn.5 and Eqn.6 start with initial points initialized We present the learning algorithm in Alg.1.

This paper studies the fundamental learning problem of the energy-based model (EBM).

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We study the problem of combining neural networks with symbolic reasoning.

This view of the data generating process is also adopted and promoted by popular existing works.

The variational autoencoder (VAE) is a popular model for density estimation and representation learning. Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is accurate. However, it is often overlooked that an overly-expressive inference model can be detrimental to the test set performance of both the amortized posterior approximator and, more importantly, the generative density estimator. In this paper, we leverage the fact that VAEs rely on amortized inference and propose techniques for amortized inference regularization (AIR) that control the smoothness of the inference model. We demonstrate that, by applying AIR, it is possible to improve VAE generalization on both inference and generative performance. Our paper challenges the belief that amortized inference is simply a mechanism for approximating maximum likelihood training and illustrates that regularization of the amortization family provides a new direction for understanding and improving generalization in VAEs.

We present a novel introspective variational autoencoder (IntroVAE) model for synthesizing high-resolution photographic images. IntroVAE is capable of self-evaluating the quality of its generated samples and improving itself accordingly. Its inference and generator models are jointly trained in an introspective way. On one hand, the generator is required to reconstruct the input images from the noisy outputs of the inference model as normal VAEs. On the other hand, the inference model is encouraged to classify between the generated and real samples while the generator tries to fool it as GANs. These two famous generative frameworks are integrated in a simple yet efficient single-stream architecture that can be trained in a single stage. IntroVAE preserves the advantages of VAEs, such as stable training and nice latent manifold. Unlike most other hybrid models of VAEs and GANs, IntroVAE requires no extra discriminators, because the inference model itself serves as a discriminator to distinguish between the generated and real samples. Experiments demonstrate that our method produces high-resolution photo-realistic images (e.g., CELEBA images at (1024^{2})), which are comparable to or better than the state-of-the-art GANs.

Partial label learning (PLL) is a typical weakly supervised learning problem, where each training example is associated with a set of candidate labels among which only one is true. Most existing PLL approaches assume that the incorrect labels in each training example are randomly picked as the candidate labels. However, this assumption is not realistic since the candidate labels are always instance-dependent. In this paper, we consider instance-dependent PLL and assume that each example is associated with a latent label distribution constituted by the real number of each label, representing the degree to each label describing the feature. The incorrect label with a high degree is more likely to be annotated as the candidate label.