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We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight…
This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…
With the great capabilities of deep classifiers for radar data processing come the risks of learning dataset-specific features that do not generalize well. In this work, the robustness of two deep convolutional architectures, trained and…
Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…
We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…
Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve…
Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…
Neural networks are susceptible to artificially designed adversarial perturbations. Recent efforts have shown that imposing certain modifications on classification layer can improve the robustness of the neural networks. In this paper, we…
Beside the minimization of the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we propose continuous-domain formulations for one-dimensional…
The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…
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…
A residual network (or ResNet) is a standard deep neural net architecture, with state-of-the-art performance across numerous applications. The main premise of ResNets is that they allow the training of each layer to focus on fitting just…
Improving adversarial robustness of neural networks remains a major challenge. Fundamentally, training a neural network via gradient descent is a parameter estimation problem. In adaptive control, maintaining persistency of excitation (PoE)…
Deep Neural Networks are powerful tools to understand complex patterns and making decisions. However, their black-box nature impedes a complete understanding of their inner workings. While online saliency-guided training methods try to…
Recent studies on the adversarial vulnerability of neural networks have shown that models trained with the objective of minimizing an upper bound on the worst-case loss over all possible adversarial perturbations improve robustness against…
It is well-known that deep neural networks (DNNs) have shown remarkable success in many fields. However, when adding an imperceptible magnitude perturbation on the model input, the model performance might get rapid decrease. To address this…
Neural networks have achieved remarkable performance in various application domains. Nevertheless, a large number of weights in pre-trained deep neural networks prohibit them from being deployed on smartphones and embedded systems. It is…
Deep neural networks are vulnerable against adversarial examples. In this paper, we propose to train and test the networks with randomly subsampled images with high drop rates. We show that this approach significantly improves robustness…
Layer-wise learning, as an alternative to global back-propagation, is easy to interpret, analyze, and it is memory efficient. Recent studies demonstrate that layer-wise learning can achieve state-of-the-art performance in image…
Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize…