Related papers: Solving Probabilistic Verification Problems of Neu…
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
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…
Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…
Neural networks have emerged as a tool for solving differential equations in many branches of engineering and science. But their progress in frequency domain acoustics is limited by the vanishing gradient problem that occurs at higher…
Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…
With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to…
Verifying the input-output relationships of a neural network so as to achieve some desired performance specification is a difficult, yet important, problem due to the growing ubiquity of neural nets in many engineering applications. We use…
With the rapid development of deep learning, the sizes of neural networks become larger and larger so that the training and inference often overwhelm the hardware resources. Given the fact that neural networks are often over-parameterized,…
Various problems in Engineering and Statistics require the computation of the likelihood ratio function of two probability densities. In classical approaches the two densities are assumed known or to belong to some known parametric family.…
We study the problem of formal verification of Binarized Neural Networks (BNN), which have recently been proposed as a energy-efficient alternative to traditional learning networks. The verification of BNNs, using the reduction to hardware…
Neural network verification aims to provide provable bounds for the output of a neural network for a given input range. Notable prior works in this domain have either generated bounds using abstract domains, which preserve some dependency…
Researchers have developed neural network verification algorithms motivated by the need to characterize the robustness of deep neural networks. The verifiers aspire to answer whether a neural network guarantees certain properties with…
State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial or worst-case inputs, but researchers…
Binarized neural networks (BNNs) are feedforward neural networks with binary weights and activation functions. In the context of using a BNN for classification, the verification problem seeks to determine whether a small perturbation of a…
We introduce two algorithms for computing tight guarantees on the probabilistic robustness of Bayesian Neural Networks (BNNs). Computing robustness guarantees for BNNs is a significantly more challenging task than verifying the robustness…
We study the {\em verification} problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would like to verify whether $H$ has some…