Related papers: Logarithmic Width Suffices for Robust Memorization

Neural networks are prone to misclassify slightly modified input images. Recently, many defences have been proposed, but none have improved the robustness of neural networks consistently. Here, we propose to use adversarial attacks as a…

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

We study the sample complexity of learning ReLU neural networks from the point of view of generalization. Given norm constraints on the weight matrices, a common approach is to estimate the Rademacher complexity of the associated function…

Neural networks are an indispensable model class for many complex learning tasks. Despite the popularity and importance of neural networks and many different established techniques from literature for stabilization and robustification of…

Adversarial training is a widely-applied approach to training deep neural networks to be robust against adversarial perturbation. However, although adversarial training has achieved empirical success in practice, it still remains unclear…

Adversarial robustness has proven to be a required property of machine learning algorithms. A key and often overlooked aspect of this problem is to try to make the adversarial noise magnitude as large as possible to enhance the benefits of…

There has been a large amount of interest, both in the past and particularly recently, into the power of different families of universal approximators, e.g. ReLU networks, polynomials, rational functions. However, current research has…

In a neural network with ReLU activations, the number of piecewise linear regions in the output can grow exponentially with depth. However, this is highly unlikely to happen when the initial parameters are sampled randomly, which therefore…

We propose a method to learn deep ReLU-based classifiers that are provably robust against norm-bounded adversarial perturbations on the training data. For previously unseen examples, the approach is guaranteed to detect all adversarial…

We consider the computational complexity of training depth-2 neural networks composed of rectified linear units (ReLUs). We show that, even for the case of a single ReLU, finding a set of weights that minimizes the squared error (even…

The threat of adversarial examples has motivated work on training certifiably robust neural networks to facilitate efficient verification of local robustness at inference time. We formalize a notion of global robustness, which captures the…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

Reason and inference require process as well as memory skills by humans. Neural networks are able to process tasks like image recognition (better than humans) but in memory aspects are still limited (by attention mechanism, size). Recurrent…

Recent studies on the adversarial vulnerability of neural networks have shown that models trained to be more robust to adversarial attacks exhibit more interpretable saliency maps than their non-robust counterparts. We aim to quantify this…

The possibility for one to recover the parameters-weights and biases-of a neural network thanks to the knowledge of its function on a subset of the input space can be, depending on the situation, a curse or a blessing. On one hand,…

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

Compression is a key step to deploy large neural networks on resource-constrained platforms. As a popular compression technique, quantization constrains the number of distinct weight values and thus reducing the number of bits required to…

Adversarial or test time robustness measures the susceptibility of a classifier to perturbations to the test input. While there has been a flurry of recent work on designing defenses against such perturbations, the theory of adversarial…

As humans, we inherently perceive images based on their predominant features, and ignore noise embedded within lower bit planes. On the contrary, Deep Neural Networks are known to confidently misclassify images corrupted with meticulously…