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Differentially Private Stochastic Gradient Descent (DP-SGD) limits the amount of private information deep learning models can memorize during training. This is achieved by clipping and adding noise to the model's gradients, and thus…
Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of perturbations of their inputs. We derive such constants in the context of a general layered network model involving…
Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. This is useful in a variety of applications ranging from reinforcement learning to autonomous systems.…
1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and…
Effectively scaling up deep reinforcement learning models has proven notoriously difficult due to network pathologies during training, motivating various targeted interventions such as periodic reset and architectural advances such as layer…
Existing Rademacher complexity bounds for neural networks rely only on norm control of the weight matrices and depend exponentially on depth via a product of the matrix norms. Lower bounds show that this exponential dependence on depth is…
For sensitive problems, such as medical imaging or fraud detection, Neural Network (NN) adoption has been slow due to concerns about their reliability, leading to a number of algorithms for explaining their decisions. NNs have also been…
Despite having high accuracy, neural nets have been shown to be susceptible to adversarial examples, where a small perturbation to an input can cause it to become mislabeled. We propose metrics for measuring the robustness of a neural net…
Estimating the Lipschitz constant of deep neural networks is of growing interest as it is useful for informing on generalisability and adversarial robustness. Convolutional neural networks (CNNs) in particular, underpin much of the recent…
Deep Neural Networks have achieved extraordinary results on image classification tasks, but have been shown to be vulnerable to attacks with carefully crafted perturbations of the input data. Although most attacks usually change values of…
This paper proposes to learn high-performance deep ConvNets with sparse neural connections, referred to as sparse ConvNets, for face recognition. The sparse ConvNets are learned in an iterative way, each time one additional layer is…
In this work we study the properties of deep neural networks (DNN) with random weights. We formally prove that these networks perform a distance-preserving embedding of the data. Based on this we then draw conclusions on the size of the…
It is well known that adversarial attacks can fool deep neural networks with imperceptible perturbations. Although adversarial training significantly improves model robustness, failure cases of defense still broadly exist. In this work, we…
Deep neural networks continue to awe the world with their remarkable performance. Their predictions, however, are prone to be corrupted by adversarial examples that are imperceptible to humans. Current efforts to improve the robustness of…
Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…
We employ constraints to control the parameter space of deep neural networks throughout training. The use of customized, appropriately designed constraints can reduce the vanishing/exploding gradients problem, improve smoothness of…
Deep neural networks are notorious for being sensitive to small well-chosen perturbations, and estimating the regularity of such architectures is of utmost importance for safe and robust practical applications. In this paper, we investigate…
Effective hyper-parameter tuning is essential to guarantee the performance that neural networks have come to be known for. In this work, a principled approach to choosing the learning rate is proposed for shallow feedforward neural…
Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical…
We consider deep neural networks with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias…