Related papers: Rethinking Lipschitz Neural Networks and Certified…
We initiate the study of the inherent tradeoffs between the size of a neural network and its robustness, as measured by its Lipschitz constant. We make a precise conjecture that, for any Lipschitz activation function and for most datasets,…
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…
Datasets can be biased due to societal inequities, human biases, under-representation of minorities, etc. Our goal is to certify that models produced by a learning algorithm are pointwise-robust to potential dataset biases. This is a…
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…
The Lipschitz constant of neural networks has been established as a key quantity to enforce the robustness to adversarial examples. In this paper, we tackle the problem of building $1$-Lipschitz Neural Networks. By studying Residual…
This paper analyzes regularization terms proposed recently for improving the adversarial robustness of deep neural networks (DNNs), from a theoretical point of view. Specifically, we study possible connections between several effective…
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…
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…
The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers. Obtaining…
Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded…
We study the invertibility of nonlinear dynamical systems from the perspective of contraction and incremental stability analysis and propose a new invertible recurrent neural model: the BiLipREN. In particular, we consider a nonlinear state…
This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed $\ell^2$ Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are…
Graph neural networks (GNNs) have recently been demonstrated to perform well on a variety of network-based tasks such as decentralized control and resource allocation, and provide computationally efficient methods for these tasks which have…
We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity --- a transducer is K-(Lipschitz) robust if the…
Reinforcement learning (RL) policies deployed in real-world environments must remain reliable under adversarial perturbations. At the same time, modern deep RL agents are heavily over-parameterized, raising costs and fragility concerns.…
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…
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…
Recent works have shown the effectiveness of randomized smoothing as a scalable technique for building neural network-based classifiers that are provably robust to $\ell_2$-norm adversarial perturbations. In this paper, we employ…
It has been observed that certain loss functions can render deep-learning pipelines robust against flaws in the data. In this paper, we support these empirical findings with statistical theory. We especially show that empirical-risk…
Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the…