Related papers: BERN-NN: Tight Bound Propagation For Neural Networ…

We introduce a method to train Binarized Neural Networks (BNNs) - neural networks with binary weights and activations at run-time. At training-time the binary weights and activations are used for computing the parameters gradients. During…

We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

In material science, image segmentation is of great significance for quantitative analysis of microstructures. Here, we propose a novel Weighted Propagation Convolution Neural Network based on U-Net (WPU-Net) to detect boundary in…

In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper…

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature…

Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…

This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…

Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs, including the scattering networks, the AlexNet and the…

Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization…

Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap,…

Recurrent Neural Networks (RNNs) produce state-of-art performance on many machine learning tasks but their demand on resources in terms of memory and computational power are often high. Therefore, there is a great interest in optimizing the…

Nearest neighbor (kNN) methods have been gaining popularity in recent years in light of advances in hardware and efficiency of algorithms. There is a plethora of methods to choose from today, each with their own advantages and…

We introduce a method to train Binarized Neural Networks (BNNs) - neural networks with binary weights and activations at run-time and when computing the parameters' gradient at train-time. We conduct two sets of experiments, each based on a…

A neural network is essentially a high-dimensional complex mapping model by adjusting network weights for feature fitting. However, the spectral bias in network training leads to unbearable training epochs for fitting the high-frequency…

The recent rapid growth in mobile data traffic entails a pressing demand for improving the throughput of the underlying wireless communication networks. Network node deployment has been considered as an effective approach for throughput…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Logic-based methods for explaining neural network decisions offer formal guarantees of correctness and non-redundancy, but they often suffer from high computational costs, especially for large networks. In this work, we improve the…