A broad class of unsupervised deep learning methods such as Generative Adversarial Networks (GANs) involve training of overparameterized models where the number of parameters of the model exceeds a certain threshold. Indeed, most successful GANs used in practice are trained using overparameterized generator and discriminator networks, both in terms of depth and width. A large body of work in supervised learning have shown the importance of model overparameterization in the convergence of the gradient descent (GD) to globally optimal solutions. In contrast, the unsupervised setting and GANs in particular involve non-convex concave mini-max optimization problems that are often trained using Gradient Descent/Ascent (GDA). The role and benefits of model overparameterization in the convergence of GDA to a global saddle point in non-convex concave problems is far less understood. In this work, we present a comprehensive analysis of the importance of model overparameterization in GANs both theoretically and empirically. We theoretically show that in an overparameterized GAN model with a 1-layer neural network generator and a linear discriminator, GDA converges to a global saddle point of the underlying non-convex concave min-max problem. To the best of our knowledge, this is the first result for global convergence of GDA in such settings. Our theory is based on a more general result that holds for a broader class of nonlinear generators and discriminators that obey certain assumptions (including deeper generators and random feature discriminators). Our theory utilizes and builds upon a novel connection with the convergence analysis of linear timevarying dynamical systems which may have broader implications for understanding the convergence behavior of GDA for non-convex concave problems involving overparameterized models. We also empirically study the role of model overparameterization in GANs using several large-scale experiments on CIFAR-10 and Celeb-A datasets.

Application of deep neural networks to medical imaging tasks has in some sense become commonplace. Still, a "thorn in the side" of the deep learning movement is the argument that deep networks are somehow prone to overfitting and are thus unable to generalize well when datasets are small. The claim is not baseless and likely stems from the observation that PAC bounds on generalization error are usually so large for deep networks that they are vacuous (i.e., logically meaningless). Contrary to this, recent advances using the PAC-Bayesian framework have instead shown non-vacuous bounds on generalization error for large (stochastic) networks and standard datasets (e.g., MNIST and CIFAR-10). We apply these techniques to a much smaller medical imagining dataset (the ISIC 2018 challenge set). Further, we consider generalization of deep networks on segmentation tasks which has not commonly been done using the PAC-Bayesian framework. Importantly, we observe that the resultant bounds are also non-vacuous despite the sharp reduction in sample size. In total, our results demonstrate the applicability of PAC-Bayesian bounds for deep stochastic networks in the medical imaging domain.

State-of-the-art deep neural networks require large-scale labeled training data that is often expensive to obtain or not available for many tasks. Weak supervision in the form of domain-specific rules has been shown to be useful in such settings to automatically generate weakly labeled training data. However, learning with weak rules is challenging due to their inherent heuristic and noisy nature. An additional challenge is rule coverage and overlap, where prior work on weak supervision only considers instances that are covered by weak rules, thus leaving valuable unlabeled data behind. In this work, we develop a weak supervision framework (ASTRA) that leverages all the available data for a given task. To this end, we leverage task-specific unlabeled data through self-training with a model (student) that considers contextualized representations and predicts pseudo-labels for instances that may not be covered by weak rules. We further develop a rule attention network (teacher) that learns how to aggregate student pseudo-labels with weak rule labels, conditioned on their fidelity and the underlying context of an instance. Finally, we construct a semi-supervised learning objective for end-to-end training with unlabeled data, domain-specific rules, and a small amount of labeled data. Extensive experiments on six benchmark datasets for text classification demonstrate the effectiveness of our approach with significant improvements over state-of-the-art baselines.

Deep Neural Networks are known to be vulnerable to small, adversarially crafted, perturbations. The current most effective defense methods against these adversarial attacks are variants of adversarial training. In this paper, we introduce a radically different defense trained only on clean images: a sparse coding based front end which significantly attenuates adversarial attacks before they reach the classifier. Deep neural networks (DNNs) are known to be vulnerable to small, adversarially designed perturbations (Biggio et al., 2013; Szegedy et al., 2014). Since the discovery of such adversarial attacks, researchers have tried various defense strategies such as adversarial training (Madry et al., 2018; Zhang et al., 2019), constraining Lipschitz constant (Cisse et al., 2017), randomized smoothing (Cohen et al., 2019), and preprocessing methods (Guo et al., 2017; Yang et al., 2019).

Bayes' theorem is used as foundation Autoencoders are a family of unsupervised learning methods for inference in Bayesian neural networks, and Markov that use neural network architectures and learning algorithms chain Monte Carlo (MCMC) sampling methods [25] are used to learn a lower-dimensional representation (encoding) for constructing the posterior distribution. Variational inference of the data, which can then be used to reconstruct a representation [26] is another way to approximate the posterior distribution, close to the original input. They thus facilitate dimensionality which approximates an intractable posterior distribution by a reduction for prediction and classification [1, 2], and have tractable one. This makes it particularly suited to large data been successfully applied to image classification [3, 4], face sets and models, and so it has been popular for autoencoders recognition [5, 6], geoscience and remote sensing [7], speechbased and neural networks [13, 27].

Forecasting graph-based time-dependent data has many practical applications. This task is challenging as models need not only to capture spatial dependency and temporal dependency within the data, but also to leverage useful auxiliary information for accurate predictions. In this paper, we analyze limitations of state-of-the-art models on dealing with temporal dependency. To address this limitation, we propose GSA-Forecaster, a new deep learning model for forecasting graph-based time-dependent data. GSA-Forecaster leverages graph sequence attention (GSA), a new attention mechanism proposed in this paper, for effectively capturing temporal dependency. GSA-Forecaster embeds the graph structure of the data into its architecture to address spatial dependency. GSA-Forecaster also accounts for auxiliary information to further improve predictions. We evaluate GSA-Forecaster with large-scale real-world graph-based time-dependent data and demonstrate its effectiveness over state-of-the-art models with 6.7% RMSE and 5.8% MAPE reduction.

One strategy for adversarially training a robust model is to maximize its certified radius -- the neighborhood around a given training sample for which the model's prediction remains unchanged. The scheme typically involves analyzing a "smoothed" classifier where one estimates the prediction corresponding to Gaussian samples in the neighborhood of each sample in the mini-batch, accomplished in practice by Monte Carlo sampling. In this paper, we investigate the hypothesis that this sampling bottleneck can potentially be mitigated by identifying ways to directly propagate the covariance matrix of the smoothed distribution through the network. To this end, we find that other than certain adjustments to the network, propagating the covariances must also be accompanied by additional accounting that keeps track of how the distributional moments transform and interact at each stage in the network. We show how satisfying these criteria yields an algorithm for maximizing the certified radius on datasets including Cifar-10, ImageNet, and Places365 while offering runtime savings on networks with moderate depth, with a small compromise in overall accuracy. We describe the details of the key modifications that enable practical use. Via various experiments, we evaluate when our simplifications are sensible, and what the key benefits and limitations are.

In this article a surprising result is demonstrated using the neural tangent kernel. This kernel is defined as the inner product of the vector of the gradient of an underlying model evaluated at training points. This kernel is used to perform kernel regression. The surprising thing is that the accuracy of that regression is independent of the accuracy of the underlying network.

Relational knowledge bases (KBs) are established tools for world knowledge representation in machines. While they are advantageous for their precision and interpretability, they usually sacrifice some data modeling flexibility for these advantages because they adhere to a manually engineered schema. In this review, we take a natural language processing perspective to the limitations of KBs, examining how they may be addressed in part by training neural contextual language models (LMs) to internalize and express relational knowledge in free-text form. We propose a novel taxonomy for relational knowledge representation in contextual LMs based on the level of KB supervision provided, considering both works that probe LMs for implicit relational knowledge acquired during self-supervised pretraining on unstructured text alone, and works that explicitly supervise LMs at the level of KB entities and/or relations. We conclude that LMs and KBs are complementary representation tools, as KBs provide a high standard of factual precision which can in turn be flexibly and expressively modeled by LMs, and provide suggestions for future research in this direction.

This paper proposes a question-answering (QA) benchmark for spatial reasoning on natural language text which contains more realistic spatial phenomena not covered by prior work and is challenging for state-of-the-art language models (LM). We propose a distant supervision method to improve on this task. Specifically, we design grammar and reasoning rules to automatically generate a spatial description of visual scenes and corresponding QA pairs. Experiments show that further pretraining LMs on these automatically generated data significantly improves LMs' capability on spatial understanding, which in turn helps to better solve two external datasets, bAbI, and boolQ. We hope that this work can foster investigations into more sophisticated models for spatial reasoning over text.