Adversarial training methods typically align distributions by solving two-player games. However, in most current formulations, even if the generator aligns perfectly with data, a sub-optimal discriminator can still drive the two apart. Absent additional regularization, the instability can manifest itself as a never-ending game. In this paper, we introduce a family of objectives by leveraging pairwise discriminators, and show that only the generator needs to converge. The alignment, if achieved, would be preserved with any discriminator. We provide sufficient conditions for local convergence; characterize the capacity balance that should guide the discriminator and generator choices; and construct examples of minimally sufficient discriminators. Empirically, we illustrate the theory and the effectiveness of our approach on synthetic examples. Moreover, we show that practical methods derived from our approach can better generate higher-resolution images.

In this paper, we propose a method for obtaining sentence-level embeddings. While the problem of securing word-level embeddings is very well studied, we propose a novel method for obtaining sentence-level embeddings. This is obtained by a simple method in the context of solving the paraphrase generation task. If we use a sequential encoder-decoder model for generating paraphrase, we would like the generated paraphrase to be semantically close to the original sentence. One way to ensure this is by adding constraints for true paraphrase embeddings to be close and unrelated paraphrase candidate sentence embeddings to be far. This is ensured by using a sequential pair-wise discriminator that shares weights with the encoder that is trained with a suitable loss function. Our loss function penalizes paraphrase sentence embedding distances from being too large. This loss is used in combination with a sequential encoder-decoder network. We also validated our method by evaluating the obtained embeddings for a sentiment analysis task. The proposed method results in semantic embeddings and outperforms the state-of-the-art on the paraphrase generation and sentiment analysis task on standard datasets. These results are also shown to be statistically significant.

Existing Markov Chain Monte Carlo (MCMC) methods are either based on general-purpose and domain-agnostic schemes which can lead to slow convergence, or hand-crafting of problem-specific proposals by an expert. We propose A-NICE-MC, a novel method to train flexible parametric Markov chain kernels to produce samples with desired properties. First, we propose an efficient likelihood-free adversarial training method to train a Markov chain and mimic a given data distribution. Then, we leverage flexible volume preserving flows to obtain parametric kernels for MCMC. Using a bootstrap approach, we show how to train efficient Markov chains to sample from a prescribed posterior distribution by iteratively improving the quality of both the model and the samples. A-NICE-MC provides the first framework to automatically design efficient domain-specific MCMC proposals. Empirical results demonstrate that A-NICE-MC combines the strong guarantees of MCMC with the expressiveness of deep neural networks, and is able to significantly outperform competing methods such as Hamiltonian Monte Carlo.