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In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP)…

This paper presents a novel structure-preserving, Kron-based reduction framework for unbalanced distribution feeders. The method aggregates electrically similar nodes within a mixed-integer optimization (MIP) problem to produce reduced…

A big, diverse and balanced training data is the key to the success of deep neural network training. However, existing publicly available datasets used in facial landmark localization are usually much smaller than those for other computer…

We perform theoretical and algorithmic studies for the problem of clustering and semi-supervised classification on graphs with both pairwise relational information and single-point feature information, upon a joint stochastic block model…

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 input uncertainty, but researchers…

Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness…

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…

As a new programming paradigm, deep neural networks (DNNs) have been increasingly deployed in practice, but the lack of robustness hinders their applications in safety-critical domains. While there are techniques for verifying DNNs with…

Graph neural networks are recognized for their strong performance across various applications, with the backpropagation algorithm playing a central role in the development of most GNN models. However, despite its effectiveness, BP has…

Biological membranes are one of the most basic structures and regions of interest in cell biology. In the study of membranes, segment extraction is a well-known and difficult problem because of impeding noise, directional and thickness…

In the previous article, we introduced a neural network framework based on symmetric differential equations. This novel framework exhibits complete symmetry, endowing it with perfect mathematical properties. While we have examined some of…

We consider the problem of certifying the robustness of deep neural networks against real-world distribution shifts. To do so, we bridge the gap between hand-crafted specifications and realistic deployment settings by proposing a novel…

Recent works have shown that exploiting unlabeled data through label propagation can substantially reduce the labeling cost, which has been a critical issue in developing visual recognition models. Yet, how to propagate labels reliably,…

Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for…

Widely used traditional pipelines for subcortical brain segmentation are often inefficient and slow, particularly when processing large datasets. Furthermore, deep learning models face challenges due to the high resolution of MRI images and…

Verification of neural networks enables us to gauge their robustness against adversarial attacks. Verification algorithms fall into two categories: exact verifiers that run in exponential time and relaxed verifiers that are efficient but…

In this paper, we derive for the first time the exact Cramer-Rao bounds (CRBs) on semi-blind channel estimation for amplify-and-forward two-way relay networks. The bounds cover a wide range of modulation schemes that satisfy a certain…

We describe a method for verifying the output of a deep neural network for medical image segmentation that is robust to several classes of random as well as worst-case perturbations i.e. adversarial attacks. This method is based on a…

Bounded model checking is among the most efficient techniques for the automatic verification of concurrent programs. However, encoding all possible interleavings often requires a huge and complex formula, which significantly limits the…

Sparse training is a natural idea to accelerate the training speed of deep neural networks and save the memory usage, especially since large modern neural networks are significantly over-parameterized. However, most of the existing methods…