Related papers: Lipschitz regularization for softening material mo…

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…

We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…

Machine learning models suffer from overfitting, which is caused by a lack of labeled data. To tackle this problem, we proposed a framework of regularization methods, called density-fixing, that can be used commonly for supervised and…

Regularization is an effective way to promote the generalization performance of machine learning models. In this paper, we focus on label smoothing, a form of output distribution regularization that prevents overfitting of a neural network…

Principled decision-making in continuous state--action spaces is impossible without some assumptions. A common approach is to assume Lipschitz continuity of the Q-function. We show that, unfortunately, this property fails to hold in many…

Generative models have attracted considerable attention for their ability to produce novel shapes. However, their application in mechanical design remains constrained due to the limited size and variability of available datasets. This study…

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…

In recent years, continual learning, a prediction setting in which the problem environment may evolve over time, has become an increasingly popular research field due to the framework's gearing towards complex, non-stationary objectives.…

Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…

Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization cannot be found explicitly, originating the need of approximating discrete-time models. This note studies the preservation of the Lipschitz…

This paper addresses Lipschitzian stability issues that play an important role in both theoretical and numerical aspects of variational analysis, optimization, and their applications. We particularly concentrate on the so-called relaxed…

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However…

Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified robustness and empirical robustness accuracy. This paper…

Training materials through periodic drive allows to endow materials and structures with complex elastic functions. As a result of the driving, the system explores the high dimensional space of structures, ultimately converging to a…

The local behavior of the lowest order boundary element method on quasi-uniform meshes for Symm's integral equation and the stabilized hyper-singular integral equation on polygonal/polyhedral Lipschitz domains is analyzed. We prove local a…

To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the…

Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…

In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading…

Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency…

Label Smoothing (LS) is an effective regularizer to improve the generalization of state-of-the-art deep models. For each training sample the LS strategy smooths the one-hot encoded training signal by distributing its distribution mass over…