Riemannian Normalizing Flow on Variational Wasserstein Autoencoder for Text Modeling

Recurrent Variational Autoencoder has been widely used for language modeling and text generation tasks. These models often face a difficult optimization problem, also known as the Kullback-Leibler (KL) term vanishing issue, where the posterior easily collapses to the prior, and the model will ignore latent codes in generative tasks. To address this problem, we introduce an improved Wasserstein Variational Autoencoder (WAE) with Riemannian Normalizing Flow (RNF) for text modeling. The RNF transforms a latent variable into a space that respects the geometric characteristics of input space, which makes posterior impossible to collapse to the non-informative prior. The Wasserstein objective minimizes the distance between the marginal distribution and the prior directly and therefore does not force the posterior to match the prior. Empirical experiments show that our model avoids KL vanishing over a range of datasets and has better performances in tasks such as language modeling, likelihood approximation, and text generation. Through a series of experiments and analysis over latent space, we show that our model learns latent distributions that respect latent space geometry and is able to generate sentences that are more diverse.Comment: NAACL 2019 (oral

Conditional Flow Variational Autoencoders for Structured Sequence Prediction

Prediction of future states of the environment and interacting agents is a key competence required for autonomous agents to operate successfully in the real world. Prior work for structured sequence prediction based on latent variable models imposes a uni-modal standard Gaussian prior on the latent variables. This induces a strong model bias which makes it challenging to fully capture the multi-modality of the distribution of the future states. In this work, we introduce Conditional Flow Variational Autoencoders (CF-VAE) using our novel conditional normalizing flow based prior to capture complex multi-modal conditional distributions for effective structured sequence prediction. Moreover, we propose two novel regularization schemes which stabilizes training and deals with posterior collapse for stable training and better fit to the target data distribution. Our experiments on three multi-modal structured sequence prediction datasets -- MNIST Sequences, Stanford Drone and HighD -- show that the proposed method obtains state of art results across different evaluation metrics.Comment: To appear at Bayesian Deep Learning and Machine Learning for Autonomous Driving @NeurIPS 201

Normalizing Flows on Tori and Spheres

Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles, are defined on spaces with more complex geometries, such as tori or spheres. In this paper, we propose and compare expressive and numerically stable flows on such spaces. Our flows are built recursively on the dimension of the space, starting from flows on circles, closed intervals or spheres.Comment: Accepted to the International Conference on Machine Learning (ICML) 202

Neural Manifold Ordinary Differential Equations

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for specific cases; however, these advancements hand craft layers on a manifold-by-manifold basis, restricting generality and inducing cumbersome design constraints. We overcome these issues by introducing Neural Manifold Ordinary Differential Equations, a manifold generalization of Neural ODEs, which enables the construction of Manifold Continuous Normalizing Flows (MCNFs). MCNFs require only local geometry (therefore generalizing to arbitrary manifolds) and compute probabilities with continuous change of variables (allowing for a simple and expressive flow construction). We find that leveraging continuous manifold dynamics produces a marked improvement for both density estimation and downstream tasks.Comment: Submitted to NeurIPS 202