Related papers: R3Net: Random Weights, Rectifier Linear Units and …
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…
Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years,…
This study explores the number of neurons required for a Rectified Linear Unit (ReLU) neural network to approximate multivariate monomials. We establish an exponential lower bound on the complexity of any shallow network approximating the…
For sensitive problems, such as medical imaging or fraud detection, Neural Network (NN) adoption has been slow due to concerns about their reliability, leading to a number of algorithms for explaining their decisions. NNs have also been…
Despite the promise of Lipschitz-based methods for provably-robust deep learning with deterministic guarantees, current state-of-the-art results are limited to feed-forward Convolutional Networks (ConvNets) on low-dimensional data, such as…
This paper proposes a class of well-conditioned neural networks in which a unit amount of change in the inputs causes at most a unit amount of change in the outputs or any of the internal layers. We develop the known methodology of…
We consider the problem of engineering robust direct perception neural networks with output being regression. Such networks take high dimensional input image data, and they produce affordances such as the curvature of the upcoming road…
Recently, recurrent neural networks have become state-of-the-art in acoustic modeling for automatic speech recognition. The long short-term memory (LSTM) units are the most popular ones. However, alternative units like gated recurrent unit…
Local robustness verification can verify that a neural network is robust wrt. any perturbation to a specific input within a certain distance. We call this distance Robustness Radius. We observe that the robustness radii of correctly…
The vulnerability to adversarial attacks has been a critical issue for deep neural networks. Addressing this issue requires a reliable way to evaluate the robustness of a network. Recently, several methods have been developed to compute…
Recent works have introduced input-convex neural networks (ICNNs) as learning models with advantageous training, inference, and generalization properties linked to their convex structure. In this paper, we propose a novel feature-convex…
While generalizing well over natural inputs, neural networks are vulnerable to adversarial inputs. Existing defenses against adversarial inputs have largely been detached from the real world. These defenses also come at a cost to accuracy.…
In this work we propose lifted regression/reconstruction networks (LRRNs), which combine lifted neural networks with a guaranteed Lipschitz continuity property for the output layer. Lifted neural networks explicitly optimize an energy model…
We consider functions from the real numbers to the real numbers, output by a neural network with 1 hidden activation layer, arbitrary width, and ReLU activation function. We assume that the parameters of the neural network are chosen…
We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However,…
Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat…
Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…
We explore the concept of co-design in the context of neural network verification. Specifically, we aim to train deep neural networks that not only are robust to adversarial perturbations but also whose robustness can be verified more…
We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions in input space, and the piecewise multilinear structure in…
Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…