Discrete Flows: Invertible Generative Models of Discrete Data

While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. In this paper, we show that flows can in fact be extended to discrete events---and under a simple change-of-variables formula not requiring log-determinant-Jacobian computations. Discrete flows have numerous applications. We consider two flow architectures: discrete autoregressive flows that enable bidirectionality, allowing, for example, tokens in text to depend on both left-to-right and right-to-left contexts in an exact language model; and discrete bipartite flows that enable efficient non-autoregressive generation as in RealNVP. Empirically, we find that discrete autoregressive flows outperform autoregressive baselines on synthetic discrete distributions, an addition task, and Potts models; and bipartite flows can obtain competitive performance with autoregressive baselines on character-level language modeling for Penn Tree Bank and text8.

On Variational Bounds of Mutual Information

Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational bounds parameterized by neural networks, but the relationships and tradeoffs between these bounds remains unclear. In this work, we unify these recent developments in a single framework. We find that the existing variational lower bounds degrade when the MI is large, exhibiting either high bias or high variance. To address this problem, we introduce a continuum of lower bounds that encompasses previous bounds and flexibly trades off bias and variance. On high-dimensional, controlled problems, we empirically characterize the bias and variance of the bounds and their gradients and demonstrate the effectiveness of our new bounds for estimation and representation learning.

Preventing Posterior Collapse with delta-VAEs

Due to the phenomenon of "posterior collapse," current latent variable generative models pose a challenging design choice that either weakens the capacity of the decoder or requires augmenting the objective so it does not only maximize the likelihood of the data. In this paper, we propose an alternative that utilizes the most powerful generative models as decoders, whilst optimising the variational lower bound all while ensuring that the latent variables preserve and encode useful information. Our proposed $\delta$-VAEs achieve this by constraining the variational family for the posterior to have a minimum distance to the prior. For sequential latent variable models, our approach resembles the classic representation learning approach of slow feature analysis. We demonstrate the efficacy of our approach at modeling text on LM1B and modeling images: learning representations, improving sample quality, and achieving state of the art log-likelihood on CIFAR-10 and ImageNet $32\times 32$.

Fixing a Broken ELBO

Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation is to maximize the evidence lower bound (ELBO) instead. However, maximum likelihood training (whether exact or approximate) does not necessarily result in a good latent representation, as we demonstrate both theoretically and empirically. In particular, we derive variational lower and upper bounds on the mutual information between the input and the latent variable, and use these bounds to derive a rate-distortion curve that characterizes the tradeoff between compression and reconstruction accuracy. Using this framework, we demonstrate that there is a family of models with identical ELBO, but different quantitative and qualitative characteristics. Our framework also suggests a simple new method to ensure that latent variable models with powerful stochastic decoders do not ignore their latent code.

Categorical Reparameterization with Gumbel-Softmax

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a novel Gumbel-Softmax distribution. This distribution has the essential property that it can be smoothly annealed into a categorical distribution. We show that our Gumbel-Softmax estimator outperforms state-of-the-art gradient estimators on structured output prediction and unsupervised generative modeling tasks with categorical latent variables, and enables large speedups on semi-supervised classification.

On the Expressive Power of Deep Neural Networks

We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated set of measures of expressivity, unified by the novel notion of trajectory length, which measures how the output of a network changes as the input sweeps along a one-dimensional path. Our findings can be summarized as follows: (1) The complexity of the computed function grows exponentially with depth. (2) All weights are not equal: trained networks are more sensitive to their lower (initial) layer weights. (3) Regularizing on trajectory length (trajectory regularization) is a simpler alternative to batch normalization, with the same performance.

Continual Learning Through Synaptic Intelligence

While deep learning has led to remarkable advances across diverse applications, it struggles in domains where the data distribution changes over the course of learning. In stark contrast, biological neural networks continually adapt to changing domains, possibly by leveraging complex molecular machinery to solve many tasks simultaneously. In this study, we introduce intelligent synapses that bring some of this biological complexity into artificial neural networks. Each synapse accumulates task relevant information over time, and exploits this information to rapidly store new memories without forgetting old ones. We evaluate our approach on continual learning of classification tasks, and show that it dramatically reduces forgetting while maintaining computational efficiency.

Unrolled Generative Adversarial Networks

We introduce a method to stabilize Generative Adversarial Networks (GANs) by defining the generator objective with respect to an unrolled optimization of the discriminator. This allows training to be adjusted between using the optimal discriminator in the generator's objective, which is ideal but infeasible in practice, and using the current value of the discriminator, which is often unstable and leads to poor solutions. We show how this technique solves the common problem of mode collapse, stabilizes training of GANs with complex recurrent generators, and increases diversity and coverage of the data distribution by the generator.

Adversarially Learned Inference

We introduce the adversarially learned inference (ALI) model, which jointly learns a generation network and an inference network using an adversarial process. The generation network maps samples from stochastic latent variables to the data space while the inference network maps training examples in data space to the space of latent variables. An adversarial game is cast between these two networks and a discriminative network is trained to distinguish between joint latent/data-space samples from the generative network and joint samples from the inference network. We illustrate the ability of the model to learn mutually coherent inference and generation networks through the inspections of model samples and reconstructions and confirm the usefulness of the learned representations by obtaining a performance competitive with state-of-the-art on the semi-supervised SVHN and CIFAR10 tasks.

Improved generator objectives for GANs

We present a framework to understand GAN training as alternating density ratio estimation and approximate divergence minimization. This provides an interpretation for the mismatched GAN generator and discriminator objectives often used in practice, and explains the problem of poor sample diversity. We also derive a family of generator objectives that target arbitrary $f$-divergences without minimizing a lower bound, and use them to train generative image models that target either improved sample quality or greater sample diversity.