相关论文: An Analytic Solution to Covariance Propagation in …

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…

We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the…

We address the problem of estimating statistics of hidden units in a neural network using a method of analytic moment propagation. These statistics are useful for approximate whitening of the inputs in front of saturating non-linearities…

We study the problem of propagating the mean and covariance of a general multivariate Gaussian distribution through a deep (residual) neural network using layer-by-layer moment matching. We close a longstanding gap by deriving exact moment…

Bayesian neural networks (BNNs) have been an important framework in the study of uncertainty quantification. Deterministic variational inference, one of the inference methods, utilizes moment propagation to compute the predictive…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Understanding when neural networks can be learned efficiently is a fundamental question in learning theory. Existing hardness results suggest that assumptions on both the input distribution and the network's weights are necessary for…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

In this technical report we study the problem of propagation of uncertainty (in terms of variances of given uni-variate normal random variables) through typical building blocks of a Convolutional Neural Network (CNN). These include layers…

A novel method to propagate uncertainty through the soft-thresholding nonlinearity is proposed in this paper. At every layer the current distribution of the target vector is represented as a spike and slab distribution, which represents the…

Bayesian Neural Networks (BNNs) extend traditional neural networks to provide uncertainties associated with their outputs. On the forward pass through a BNN, predictions (and their uncertainties) are made either by Monte Carlo sampling…

We consider the problem of estimating the parameters of a $d$-dimensional rectified Gaussian distribution from i.i.d. samples. A rectified Gaussian distribution is defined by passing a standard Gaussian distribution through a one-layer ReLU…

Reproducibility of a deep-learning fully convolutional neural network is evaluated by training several times the same network on identical conditions (database, hyperparameters, hardware) with non-deterministic Graphics Processings Unit…

Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty…

Machine learning (ML) models are increasingly being used in metrology applications. However, for ML models to be credible in a metrology context they should be accompanied by principled uncertainty quantification. This paper addresses the…

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…

Predictive uncertainty estimation remains a challenging problem precluding the use of deep neural networks as subsystems within safety-critical applications. Aleatoric uncertainty is a component of predictive uncertainty that cannot be…

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which…