Related papers: Tropical Bisectors and Carlini-Wagner Attacks

Deep neural networks have achieved a great success in solving many machine learning and computer vision problems. The main contribution of this paper is to develop a deep network based on Tucker tensor decomposition, and analyze its…

Despite being effective in many application areas, Deep Neural Networks (DNNs) are vulnerable to being attacked. In object recognition, the attack takes the form of a small perturbation added to an image, that causes the DNN to misclassify,…

Weighted Finite State Transducers (WFSTs) are versatile data structures that can model a great number of problems, ranging from Automatic Speech Recognition to DNA sequencing. Traditional computer science algorithms are employed when…

In this paper, we study the interplay between tropical and analytic geometry for closed subschemes of toric varieties. Let $K$ be a complete non-Archimedean field, and let $X$ be a closed subscheme of a toric variety over $K$. We define the…

Direct computer simulation of intense tropical cyclones (TCs) in weather models is limited by computational expense. Intense TCs are rare and have small-scale structures, making it difficult to produce large ensembles of storms at high…

Recent work has highlighted several advantages of enforcing orthogonality in the weight layers of deep networks, such as maintaining the stability of activations, preserving gradient norms, and enhancing adversarial robustness by enforcing…

Designing microwave absorbers with customized spectrums is an attractive topic in both scientific and engineering communities. However, due to the massive number of design parameters involved, the design process is typically time-consuming…

We find a relation between mixed volumes of several polytopes and the convex hull of their union, deducing it from the following fact: the mixed volume of a collection of polytopes only depends on the product of their support functions…

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, training deep learning models robust to…

This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little…

Our research aims to unify existing works' diverging opinions on how architectural components affect the adversarial robustness of CNNs. To accomplish our goal, we synthesize a suite of three generalizable robust architectural design…

Deep Neural Networks (DNNs) are widely used for computer vision tasks. However, it has been shown that deep models are vulnerable to adversarial attacks, i.e., their performances drop when imperceptible perturbations are made to the…

Efficient CNN designs like ResNets and DenseNet were proposed to improve accuracy vs efficiency trade-offs. They essentially increased the connectivity, allowing efficient information flow across layers. Inspired by these techniques, we…

Recent research studies revealed that neural networks are vulnerable to adversarial attacks. State-of-the-art defensive techniques add various adversarial examples in training to improve models' adversarial robustness. However, these…

It is well known that rapid changes in tropical cyclone motion occur during interaction with extratropical waves. While the translation speed has received much attention in the published literature, acceleration has not. Using a large data…

Model-based control methods for robotic systems such as quadrotors, autonomous driving vehicles and flexible manipulators require motion models that generate accurate predictions of complex nonlinear system dynamics over long periods of…

Annual North Atlantic tropical cyclone (TC) counts are frequently modeled as a Poisson process with a state-dependent rate. We provide a lower bound on the forecasting error of this class of models. Remarkably we find that this bound is…

The main result of this paper is a formula for the limit cycle of a 1-parameter family of subvarieties of a tropical compactification, expressed in terms of tropical intersections. Our theorem generalizes results of…

There is currently a debate within the neuroscience community over the likelihood of the brain performing backpropagation (BP). To better mimic the brain, training a network $\textit{one layer at a time}$ with only a "single forward pass"…

The robustness of neural network classifiers is important in the safety-critical domain and can be quantified by robustness verification. At present, efficient and scalable verification techniques are always sound but incomplete, and thus,…