Related papers: Some Fundamental Aspects about Lipschitz Continuit…
Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence. Yet, despite these advances, critical challenges remain -- most notably,…
In binary classification and regression problems, it is well understood that Lipschitz continuity and smoothness of the loss function play key roles in governing generalization error bounds for empirical risk minimization algorithms. In…
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…
Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class…
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…
Deep Networks have been shown to provide state-of-the-art performance in many machine learning challenges. Unfortunately, they are susceptible to various types of noise, including adversarial attacks and corrupted inputs. In this work we…
Ensuring neural network robustness is essential for the safe and reliable operation of robotic learning systems, especially in perception and decision-making tasks within real-world environments. This paper investigates the robustness of…
Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…
Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…
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…
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…
Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we…
The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…
We present knowledge continuity, a novel definition inspired by Lipschitz continuity which aims to certify the robustness of neural networks across input domains (such as continuous and discrete domains in vision and language,…
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…
Designing neural networks with bounded Lipschitz constant is a promising way to obtain certifiably robust classifiers against adversarial examples. However, the relevant progress for the important $\ell_\infty$ perturbation setting is…
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…
Lipschitz continuity characterizes the worst-case sensitivity of neural networks to small input perturbations; yet its dynamics (i.e. temporal evolution) during training remains under-explored. We present a rigorous mathematical framework…
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…
Deriving sharp and computable upper bounds of the Lipschitz constant of deep neural networks is crucial to formally guarantee the robustness of neural-network based models. We analyse three existing upper bounds written for the $l^2$ norm.…