Related papers: Sorting out Lipschitz function approximation
Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz constant. However, approximation-theoretic guarantees for…
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…
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…
It is a highly desirable property for deep networks to be robust against small input changes. One popular way to achieve this property is by designing networks with a small Lipschitz constant. In this work, we propose a new technique for…
Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_{2}$ norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing…
Despite significant advances, deep networks remain highly susceptible to adversarial attack. One fundamental challenge is that small input perturbations can often produce large movements in the network's final-layer feature space. In this…
This paper is motivated by structured sparsity for deep neural network training. We study a weighted group L0-norm constraint, and present the projection and normal cone of this set. Using randomized smoothing, we develop zeroth and…
In this paper, we investigate the underlying factor that leads to failure and success in the training of GANs. We study the property of the optimal discriminative function and show that in many GANs, the gradient from the optimal…
A crucial property for achieving secure, trustworthy and interpretable deep learning systems is their robustness: small changes to a system's inputs should not result in large changes to its outputs. Mathematically, this means one strives…
This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The…
Adversarial examples have pointed out Deep Neural Networks vulnerability to small local noise. It has been shown that constraining their Lipschitz constant should enhance robustness, but make them harder to learn with classical loss…
We consider approximations of 1D Lipschitz functions by deep ReLU networks of a fixed width. We prove that without the assumption of continuous weight selection the uniform approximation error is lower than with this assumption at least by…
In this paper, we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction on the…
We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…
Wasserstein-GANs have been introduced to address the deficiencies of generative adversarial networks (GANs) regarding the problems of vanishing gradients and mode collapse during the training, leading to improved convergence behaviour and…
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…
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…
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…
The Lipschitz constant of a neural network is connected to several important properties of the network such as its robustness and generalization. It is thus useful in many settings to estimate the Lipschitz constant of a model. Prior work…
We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (B\"olcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a…