Itcomeswiththeadvantages ofVAEs, such asstable training, largesample diversity and aprincipled inference network, while having the flexibility to model a combination of continuous and discrete generative factors.

Paraphrase generation is a longstanding important problem in natural language processing. Recent progress in deep generative models has shown promising results on discrete latent variables for text generation. Inspired by variational autoencoders with discrete latent structures, in this work, we propose a latent bag of words (BOW) model for paraphrase generation. We ground the semantics of a discrete latent variable by the target BOW. We use this latent variable to build a fully differentiable content planning and surface realization pipeline. Specifically, we use source words to predict their neighbors and model the target BOW with a mixture of softmax.

Backpropagation, the cornerstone of deep learning, is limited to computing gradients for continuous variables. This limitation poses challenges for problems involving discrete latent variables. To address this issue, we propose a novel approach to approximate the gradient of parameters involved in generating discrete latent variables. First, we examine the widely used Straight-Through (ST) heuristic and demonstrate that it works as a first-order approximation of the gradient. Guided by our findings, we propose ReinMax, which achieves second-order accuracy by integrating Heun's method, a second-order numerical method for solving ODEs. ReinMax does not require Hessian or other second-order derivatives, thus having negligible computation overheads. Extensive experimental results on various tasks demonstrate the superiority of ReinMax over the state of the art.

Learning useful representations without supervision remains a key challenge in machine learning.

We present a framework for learning disentangled and interpretable jointly continuous and discrete representations in an unsupervised manner.

Boltzmann machines (BMs) are appealing candidates for powerful priors in varia-tional autoencoders (V AEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables.

Deep generative models with discrete latent space, such as the Vector-Quantized Variational Autoencoder (VQ-VAE), offer excellent data generation capabilities, but, due to the large size of their latent space, their probabilistic inference is deemed intractable. We demonstrate that the VQ-VAE can be distilled into a tractable model by selecting a subset of latent variables with high probabilities. This simple strategy is particularly efficient, especially if the VQ-VAE underutilizes its latent space, which is, indeed, very often the case. We frame the distilled model as a probabilistic circuit, and show that it preserves expressiveness of the VQ-VAE while providing tractable probabilistic inference. Experiments illustrate competitive performance in density estimation and conditional generation tasks, challenging the view of the VQ-VAE as an inherently intractable model.