相关论文: A Dynamical System Perspective for Lipschitz Neura…

As deep neural networks (DNNs) are increasingly deployed in sensitive applications, ensuring their security and robustness has become critical. A major threat to DNNs arises from adversarial attacks, where small input perturbations can lead…

We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…

In this paper we discuss the stability properties of convolutional neural networks. Convolutional neural networks are widely used in machine learning. In classification they are mainly used as feature extractors. Ideally, we expect similar…

Deep neural networks have shown remarkable performance across a wide range of vision-based tasks, particularly due to the availability of large-scale datasets for training and better architectures. However, data seen in the real world are…

The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…

Neural networks have gained much interest because of their effectiveness in many applications. However, their mathematical properties are generally not well understood. If there is some underlying geometric structure inherent to the data or…

Empirical studies have widely demonstrated that neural networks are highly sensitive to small, adversarial perturbations of the input. The worst-case robustness against these so-called adversarial examples can be quantified by the Lipschitz…

Relying on the premise that the performance of a binary neural network can be largely restored with eliminated quantization error between full-precision weight vectors and their corresponding binary vectors, existing works of network…

Despite the promise of Lipschitz-based methods for provably-robust deep learning with deterministic guarantees, current state-of-the-art results are limited to feed-forward Convolutional Networks (ConvNets) on low-dimensional data, such as…

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…

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…

Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and…

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,…

In this work we propose lifted regression/reconstruction networks (LRRNs), which combine lifted neural networks with a guaranteed Lipschitz continuity property for the output layer. Lifted neural networks explicitly optimize an energy model…

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only…

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both…

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…

Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so…

Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…

The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…