相关论文: Tropical Bisectors and Carlini-Wagner Attacks

Standard Convolutional Neural Networks (CNNs) can be easily fooled by images with small quasi-imperceptible artificial perturbations. As alternatives to CNNs, the recently proposed Capsule Networks (CapsNets) are shown to be more robust to…

We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks ($G$-CNNs), which we call the $G$-triple-correlation ($G$-TC) layer. The approach leverages the theory of the…

We investigate the robustness of random networks reinforced by adding hidden edges against targeted attacks. This study focuses on two types of reinforcement: uniform reinforcement, where edges are randomly added to all nodes, and selective…

Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…

For the task of subdecimeter aerial imagery segmentation, fine-grained semantic segmentation results are usually difficult to obtain because of complex remote sensing content and optical conditions. Recently, convolutional neural networks…

State-of-the-art convolutional neural network models for object detection and image classification are vulnerable to physically realizable adversarial perturbations, such as patch attacks. Existing defenses have focused, implicitly or…

Convolutional neural networks (CNNs) are commonly used for image classification. Saliency methods are examples of approaches that can be used to interpret CNNs post hoc, identifying the most relevant pixels for a prediction following the…

The use of deep neural networks in edge computing devices hinges on the balance between accuracy and complexity of computations. Ternary Connect (TC) \cite{lin2015neural} addresses this issue by restricting the parameters to three levels…

We define tropical analogues of the notions of linear space and Plucker coordinate and study their combinatorics. We introduce tropical analogues of intersection and dualization and define a tropical linear space built by repeated…

Deep learning-based tropical cyclone (TC) forecasting methods have demonstrated significant potential and application advantages, as they feature much lower computational cost and faster operation speed than numerical weather prediction…

Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical…

Neural networks are susceptible to artificially designed adversarial perturbations. Recent efforts have shown that imposing certain modifications on classification layer can improve the robustness of the neural networks. In this paper, we…

Anthropogenic influences have been linked to tropical cyclone (TC) poleward migration, TC extreme precipitation, and an increased proportion of major hurricanes [1, 2, 3, 4]. Understanding past TC trends and variability is critical for…

Building on recent research for prediction of hurricane trajectories using recurrent neural networks (RNNs), we have developed improved methods and generalized the approach to predict Bayesian intervals in addition to simple point…

In this paper, we propose Code-Bridged Classifier (CBC), a framework for making a Convolutional Neural Network (CNNs) robust against adversarial attacks without increasing or even by decreasing the overall models' computational complexity.…

Network robustness is critical for various societal and industrial networks again malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness…

We establish a layer-wise parameterization for 1D convolutional neural networks (CNNs) with built-in end-to-end robustness guarantees. In doing so, we use the Lipschitz constant of the input-output mapping characterized by a CNN as a…

For certain tropical quartic curves the existing techniques could not predict the lifting behavior of their bitangents over the real numbers. We close this gap by using patchworking techniques. Further, this paper provides an analysis of…

We propose a definition of tropical linear series that isolates some of the essential combinatorial properties of tropicalizations of not-necessarily-complete linear series on algebraic curves. The definition combines the Baker-Norine…

Tropical cyclone wind-intensity prediction is a challenging task considering drastic changes climate patterns over the last few decades. In order to develop robust prediction models, one needs to consider different characteristics of…