InfoGAN-CR: Disentangling Generative Adversarial Networks with Contrastive Regularizers

Training disentangled representations with generative adversarial networks (GANs) remains challenging, with leading implementations failing to achieve comparable performance to Variational Autoencoder (VAE)-based methods. After $\beta$-VAE and FactorVAE discovered that regularizing the total correlation of the latent vectors promotes disentanglement, numerous VAE-based methods emerged. Such a discovery has yet to be made for GANs, and reported disentanglement scores of GAN-based methods are significantly inferior to VAE-based methods on benchmark datasets. To this end, we propose a novel regularizer that achieves higher disentanglement scores than state-of-the-art VAE- and GAN-based approaches. The proposed contrastive regularizer is inspired by a natural notion of disentanglement: latent traversal. Latent traversal refers to generating images by varying one latent code while fixing the rest. We turn this intuition into a regularizer by adding a discriminator that detects how the latent codes are coupled together, in paired examples. Numerical experiments show that this approach improves upon competing state-of-the-art approaches on benchmark datasets.

Robust conditional GANs under missing or uncertain labels

Matching the performance of conditional Generative Adversarial Networks with little supervision is an important task, especially in venturing into new domains. We design a new training algorithm, which is robust to missing or ambiguous labels. The main idea is to intentionally corrupt the labels of generated examples to match the statistics of the real data, and have a discriminator process the real and generated examples with corrupted labels. We showcase the robustness of this proposed approach both theoretically and empirically. We show that minimizing the proposed loss is equivalent to minimizing true divergence between real and generated data up to a multiplicative factor, and characterize this multiplicative factor as a function of the statistics of the uncertain labels. Experiments on MNIST dataset demonstrates that proposed architecture is able to achieve high accuracy in generating examples faithful to the class even with only a few examples per class.

Learning in Gated Neural Networks

Gating is a key feature in modern neural networks including LSTMs, GRUs and sparsely-gated deep neural networks. The backbone of such gated networks is a mixture-of-experts layer, where several experts make regression decisions and gating controls how to weigh the decisions in an input-dependent manner. Despite having such a prominent role in both modern and classical machine learning, very little is understood about parameter recovery of mixture-of-experts since gradient descent and EM algorithms are known to be stuck in local optima in such models. In this paper, we perform a careful analysis of the optimization landscape and show that with appropriately designed loss functions, gradient descent can indeed learn the parameters accurately. A key idea underpinning our results is the design of two {\em distinct} loss functions, one for recovering the expert parameters and another for recovering the gating parameters. We demonstrate the first sample complexity results for parameter recovery in this model for any algorithm and demonstrate significant performance gains over standard loss functions in numerical experiments.

Number of Connected Components in a Graph: Estimation via Counting Patterns

Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that have been surveyed. Inferring a global property of the original graph from such a sampled subgraph is of a fundamental interest. In this work, we focus on estimating the number of connected components. It is a challenging problem and, for general graphs, little is known about the connection between the observed subgraph and the number of connected components of the original graph. In order to make this connection, we propose a highly redundant and large-dimensional representation of the subgraph, which at first glance seems counter-intuitive. A subgraph is represented by the counts of patterns, known as network motifs. This representation is crucial in introducing a novel estimator for the number of connected components for general graphs, under the knowledge of the spectral gap of the original graph. The connection is made precise via the Schatten $k$-norms of the graph Laplacian and the spectral representation of the number of connected components. We provide a guarantee on the resulting mean squared error that characterizes the bias variance tradeoff. Experiments on synthetic and real-world graphs suggest that we improve upon competing algorithms for graphs with spectral gaps bounded away from zero.

LEARN Codes: Inventing Low-latency Codes via Recurrent Neural Networks

Designing channel codes under low latency constraints is one of the most demanding requirements in 5G standards. However, sharp characterizations of the performances of traditional codes are only available in the large block-length limit. Code designs are guided by those asymptotic analyses and require large block lengths and long latency to achieve the desired error rate. Furthermore, when the codes designed for one channel (e.g. Additive White Gaussian Noise (AWGN) channel) are used for another (e.g. non-AWGN channels), heuristics are necessary to achieve any nontrivial performance -thereby severely lacking in robustness as well as adaptivity. Obtained by jointly designing Recurrent Neural Network (RNN) based encoder and decoder, we propose an end-to-end learned neural code which outperforms canonical convolutional code under block settings. With this gained experience of designing a novel neural block code, we propose a new class of codes under low latency constraint - Low-latency Efficient Adaptive Robust Neural (LEARN) codes, which outperforms the state-of-the-art low latency codes as well as exhibits robustness and adaptivity properties. LEARN codes show the potential of designing new versatile and universal codes for future communications via tools of modern deep learning coupled with communication engineering insights.

Robustness of Conditional GANs to Noisy Labels

We study the problem of learning conditional generators from noisy labeled samples, where the labels are corrupted by random noise. A standard training of conditional GANs will not only produce samples with wrong labels, but also generate poor quality samples. We consider two scenarios, depending on whether the noise model is known or not. When the distribution of the noise is known, we introduce a novel architecture which we call Robust Conditional GAN (RCGAN). The main idea is to corrupt the label of the generated sample before feeding to the adversarial discriminator, forcing the generator to produce samples with clean labels. This approach of passing through a matching noisy channel is justified by corresponding multiplicative approximation bounds between the loss of the RCGAN and the distance between the clean real distribution and the generator distribution. This shows that the proposed approach is robust, when used with a carefully chosen discriminator architecture, known as projection discriminator. When the distribution of the noise is not known, we provide an extension of our architecture, which we call RCGAN-U, that learns the noise model simultaneously while training the generator. We show experimentally on MNIST and CIFAR-10 datasets that both the approaches consistently improve upon baseline approaches, and RCGAN-U closely matches the performance of RCGAN.

PacGAN: The power of two samples in generative adversarial networks

Generative adversarial networks (GANs) are innovative techniques for learning generative models of complex data distributions from samples. Despite remarkable recent improvements in generating realistic images, one of their major shortcomings is the fact that in practice, they tend to produce samples with little diversity, even when trained on diverse datasets. This phenomenon, known as mode collapse, has been the main focus of several recent advances in GANs. Yet there is little understanding of why mode collapse happens and why existing approaches are able to mitigate mode collapse. We propose a principled approach to handling mode collapse, which we call packing. The main idea is to modify the discriminator to make decisions based on multiple samples from the same class, either real or artificially generated. We borrow analysis tools from binary hypothesis testing---in particular the seminal result of Blackwell [Bla53]---to prove a fundamental connection between packing and mode collapse. We show that packing naturally penalizes generators with mode collapse, thereby favoring generator distributions with less mode collapse during the training process. Numerical experiments on benchmark datasets suggests that packing provides significant improvements in practice as well.

Rate Distortion For Model Compression: From Theory To Practice

As the size of neural network models increases dramatically today, study of model compression algorithms becomes important. Despite many practically successful compression methods, the fundamental limit of model compression remains unknown. In this paper, we study the fundamental limit for model compression via rate distortion theory. We bring the rate distortion function from data compression to model compression to quantify the fundamental limit. We prove a lower bound for the rate distortion function and prove its achievability for linear models. Motivated by our theory, we further present a pruning algorithm which takes consideration of the structure of neural networks and demonstrate its good performance for both synthetic and real neural network models.

Estimating Mutual Information for Discrete-Continuous Mixtures

Estimating mutual information from observed samples is a basic primitive, useful in several machine learning tasks including correlation mining, information bottleneck clustering, learning a Chow-Liu tree, and conditional independence testing in (causal) graphical models. While mutual information is a well-defined quantity in general probability spaces, existing estimators can only handle two special cases of purely discrete or purely continuous pairs of random variables. The main challenge is that these methods first estimate the (differential) entropies of X, Y and the pair (X;Y) and add them up with appropriate signs to get an estimate of the mutual information. These 3H-estimators cannot be applied in general mixture spaces, where entropy is not well-defined. In this paper, we design a novel estimator for mutual information of discrete-continuous mixtures. We prove that the proposed estimator is consistent. We provide numerical experiments suggesting superiority of the proposed estimator compared to other heuristics of adding small continuous noise to all the samples and applying standard estimators tailored for purely continuous variables, and quantizing the samples and applying standard estimators tailored for purely discrete variables. This significantly widens the applicability of mutual information estimation in real-world applications, where some variables are discrete, some continuous, and others are a mixture between continuous and discrete components.

Learning One-hidden-layer Neural Networks under General Input Distributions

Significant advances have been made recently on training neural networks, where the main challenge is in solving an optimization problem with abundant critical points. However, existing approaches to address this issue crucially rely on a restrictive assumption: the training data is drawn from a Gaussian distribution. In this paper, we provide a novel unified framework to design loss functions with desirable landscape properties for a wide range of general input distributions. On these loss functions, remarkably, stochastic gradient descent theoretically recovers the true parameters with global initializations and empirically outperforms the existing approaches. Our loss function design bridges the notion of score functions with the topic of neural network optimization. Central to our approach is the task of estimating the score function from samples, which is of basic and independent interest to theoretical statistics. Traditional estimation methods (example: kernel based) fail right at the outset; we bring statistical methods of local likelihood to design a novel estimator of score functions, that provably adapts to the local geometry of the unknown density.