相关论文: Controlling the Complexity and Lipschitz Constant …

Deep neural networks are considered to be state of the art models in many offline machine learning tasks. However, their performance and generalization abilities in online learning tasks are much less understood. Therefore, we focus on…

This paper proposes that Lipschitz continuity is a natural outcome of regularized least squares in kernel-based learning. Lipschitz continuity is an important proxy for robustness of input-output operators. It is also instrumental for…

Optimization-based controllers often lack regularity guarantees, such as Lipschitz continuity, when multiple constraints are present. When used to control a dynamical system, these conditions are essential to ensure the existence and…

Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs, including the scattering networks, the AlexNet and the…

Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems. In line with approaches from robust…

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…

In this work we propose a graph-based learning framework to train models with provable robustness to adversarial perturbations. In contrast to regularization-based approaches, we formulate the adversarially robust learning problem as one of…

We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone…

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…

Certifiable robustness gives the guarantee that small perturbations around an input to a classifier will not change the prediction. There are two approaches to provide certifiable robustness to adversarial examples: a) explicitly training…

Lipschitz constraints under L2 norm on deep neural networks are useful for provable adversarial robustness bounds, stable training, and Wasserstein distance estimation. While heuristic approaches such as the gradient penalty have seen much…

This paper presents several novel generalization bounds for the problem of learning kernels based on the analysis of the Rademacher complexity of the corresponding hypothesis sets. Our bound for learning kernels with a convex combination of…

We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output…

Understanding and controlling the informational complexity of neural networks is a central challenge in machine learning, with implications for generalization, optimization, and model capacity. While most approaches rely on entropy-based…

This paper addresses explainability of the operator-regularization approach under the use of monotone Lipschitz-gradient (MoL-Grad) denoiser -- an operator that can be expressed as the Lipschitz continuous gradient of a differentiable…

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…

We systematically explore regularizing neural networks by penalizing low entropy output distributions. We show that penalizing low entropy output distributions, which has been shown to improve exploration in reinforcement learning, acts as…

Using weight decay to penalize the L2 norms of weights in neural networks has been a standard training practice to regularize the complexity of networks. In this paper, we show that a family of regularizers, including weight decay, is…

Neural Lyapunov and barrier certificates have recently been used as powerful tools for verifying the safety and stability properties of deep reinforcement learning (RL) controllers. However, existing methods offer guarantees only under…