Providing feedback is an integral part of teaching. Most open online courses on programming make use of automated grading systems to support programming assignments and give real-time feedback. These systems usually rely on test results to quantify the programs' functional correctness. They return failing tests to the students as feedback. However, students may find it difficult to debug their programs if they receive no hints about where the bug is and how to fix it.

We propose a novel confidence metric, namely, attribution-based confidence (ABC) for deep neural networks (DNNs). ABC metric characterizes whether the output of a DNN on an input can be trusted. DNNs are known to be brittle on inputs outside the training distribution and are, hence, susceptible to adversarial attacks. This fragility is compounded by a lack of effectively computable measures of model confidence that correlate well with the accuracy of DNNs. These factors have impeded the adoption of DNNs in high-assurance systems.

Aimed at explaining the surprisingly good generalization behavior of overparameterized deep networks, recent works have developed a variety of generalization bounds for deep learning, all based on the fundamental learning-theoretic technique of uniform convergence. While it is well-known that many of these existing bounds are numerically large, through numerous experiments, we bring to light a more concerning aspect of these bounds: in practice, these bounds can {\em increase} with the training dataset size. Guided by our observations, we then present examples of overparameterized linear classifiers and neural networks trained by gradient descent (GD) where uniform convergence provably cannot explain generalization'' -- even if we take into account the implicit bias of GD {\em to the fullest extent possible}. More precisely, even if we consider only the set of classifiers output by GD, which have test errors less than some small $\epsilon$ in our settings, we show that applying (two-sided) uniform convergence on this set of classifiers will yield only a vacuous generalization guarantee larger than $1-\epsilon$. Through these findings, we cast doubt on the power of uniform convergence-based generalization bounds to provide a complete picture of why overparameterized deep networks generalize well.

We study a deep learning inspired formulation for the blind demodulation problem, which is the task of recovering two unknown vectors from their entrywise multiplication. In the case when the networks corresponding to the generative models are expansive, the weight matrices are random and the dimension of the unknown vectors satisfy $\ell \Omega(n 2 p 2)$, up to log factors, we show that the empirical risk objective has a favorable landscape for optimization. That is, the objective function has a descent direction at every point outside of a small neighborhood around four hyperbolic curves. We also characterize the local maximizers of the empirical risk objective and, hence, show that there does not exist any other stationary points outside of these neighborhood around four hyperbolic curves and the set of local maximizers. We also implement a gradient descent scheme inspired by the geometry of the landscape of the objective function.

We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variational evidence lower bound (ELBO) while remaining as broadly applicable. We provide a computationally efficient gradient estimator for the TVO that applies to continuous, discrete, and non-reparameterizable distributions and show that the objective functions used in variational inference, variational autoencoders, wake sleep, and inference compilation are all special cases of the TVO. We use the TVO to learn both discrete and continuous deep generative models and empirically demonstrate state of the art model and inference network learning. Papers published at the Neural Information Processing Systems Conference.

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning controllers. Existing methods in the literature for estimating the Lipschitz constant suffer from either lack of accuracy or poor scalability. In this paper, we present a convex optimization framework to compute guaranteed upper bounds on the Lipschitz constant of DNNs both accurately and efficiently. Our main idea is to interpret activation functions as gradients of convex potential functions. Hence, they satisfy certain properties that can be described by quadratic constraints.

Recent works have shown the effectiveness of randomized smoothing as a scalable technique for building neural network-based classifiers that are provably robust to $\ell_2$-norm adversarial perturbations. In this paper, we employ adversarial training to improve the performance of randomized smoothing. We design an adapted attack for smoothed classifiers, and we show how this attack can be used in an adversarial training setting to boost the provable robustness of smoothed classifiers. We demonstrate through extensive experimentation that our method consistently outperforms all existing provably $\ell_2$-robust classifiers by a significant margin on ImageNet and CIFAR-10, establishing the state-of-the-art for provable $\ell_2$-defenses. Moreover, we find that pre-training and semi-supervised learning boost adversarially trained smoothed classifiers even further.

Missing value imputation is a fundamental problem in spatiotemporal modeling, from motion tracking to the dynamics of physical systems. Deep autoregressive models suffer from error propagation which becomes catastrophic for imputing long-range sequences. In this paper, we take a non-autoregressive approach and propose a novel deep generative model: Non-AutOregressive Multiresolution Imputation (NAOMI) to impute long-range sequences given arbitrary missing patterns. NAOMI exploits the multiresolution structure of spatiotemporal data and decodes recursively from coarse to fine-grained resolutions using a divide-and-conquer strategy. We further enhance our model with adversarial training.

Convolutional neural networks (CNNs) contain local pooling to effectively downsize feature maps for increasing computation efficiency as well as robustness to input variations. The local pooling methods are generally formulated in a form of convex combination of local neuron activations for retaining the characteristics of an input feature map in a manner similar to image downscaling. In this paper, to improve performance of CNNs, we propose a novel local pooling method based on the Gaussian-based probabilistic model over local neuron activations for flexibly pooling (extracting) features, in contrast to the previous model restricting the output within the convex hull of local neurons. In the proposed method, the local neuron activations are aggregated into the statistics of mean and standard deviation in a Gaussian distribution, and then on the basis of those statistics, we construct the probabilistic model suitable for the pooling in accordance with the knowledge about local pooling in CNNs. Through the probabilistic model equipped with trainable parameters, the proposed method naturally integrates two schemes of adaptively training the pooling form based on input feature maps and stochastically performing the pooling throughout the end-to-end learning.

A learned generative model often produces biased statistics relative to the underlying data distribution. A standard technique to correct this bias is importance sampling, where samples from the model are weighted by the likelihood ratio under model and true distributions. When the likelihood ratio is unknown, it can be estimated by training a probabilistic classifier to distinguish samples from the two distributions. We employ this likelihood-free importance weighting method to correct for the bias in generative models. We find that this technique consistently improves standard goodness-of-fit metrics for evaluating the sample quality of state-of-the-art deep generative models, suggesting reduced bias.