Related papers: Training robust neural networks using Lipschitz bo…
The neural network with $1$-Lipschitz property based on $\ell_\infty$-dist neuron has a theoretical guarantee in certified $\ell_\infty$ robustness. However, due to the inherent difficulties in the training of the network, the certified…
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…
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…
Deep neural networks are notorious for being sensitive to small well-chosen perturbations, and estimating the regularity of such architectures is of utmost importance for safe and robust practical applications. In this paper, we investigate…
The fact that deep neural networks are susceptible to crafted perturbations severely impacts the use of deep learning in certain domains of application. Among many developed defense models against such attacks, adversarial training emerges…
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…
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…
Neural Ordinary Differential Equations (NODEs) probed the usage of numerical solvers to solve the differential equation characterized by a Neural Network (NN), therefore initiating a new paradigm of deep learning models with infinite depth.…
This work explores the Benevolent Training Hypothesis (BTH) which argues that the complexity of the function a deep neural network (NN) is learning can be deduced by its training dynamics. Our analysis provides evidence for BTH by relating…
Training convolutional neural networks (CNNs) with a strict Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients and stable training. While $1$-Lipschitz CNNs can be designed by…
We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of…
Making neural networks robust against adversarial inputs has resulted in an arms race between new defenses and attacks. The most promising defenses, adversarially robust training and verifiably robust training, have limitations that…
For the past few years, Deep Neural Network (DNN) robustness has become a question of paramount importance. As a matter of fact, in sensitive settings misclassification can lead to dramatic consequences. Such misclassifications are likely…
With the development of neural networks based machine learning and their usage in mission critical applications, voices are rising against the \textit{black box} aspect of neural networks as it becomes crucial to understand their limits and…
This paper is concerned with the computation of the local Lipschitz constant of feedforward neural networks (FNNs) with activation functions being rectified linear units (ReLUs). The local Lipschitz constant of an FNN for a target input is…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
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 study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating $n$ noisy training data points in…
This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…
Effective hyper-parameter tuning is essential to guarantee the performance that neural networks have come to be known for. In this work, a principled approach to choosing the learning rate is proposed for shallow feedforward neural…