Related papers: Tropical Bisectors and Carlini-Wagner Attacks

Shift invariance is a critical property of CNNs that improves performance on classification. However, we show that invariance to circular shifts can also lead to greater sensitivity to adversarial attacks. We first characterize the margin…

The fact that deep neural networks are susceptible to crafted perturbations severely impacts the use of deep learning in certain domains of application. Among many developed defense models against such attacks, adversarial training emerges…

The tropical semiring is an algebraic system with addition ``$\max$'' and multiplication ``$+$''. As well as in conventional algebra, linear programming in the tropical semiring has been developed. In this study, we introduce a new type of…

Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_{2}$ norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing…

Recent works have introduced input-convex neural networks (ICNNs) as learning models with advantageous training, inference, and generalization properties linked to their convex structure. In this paper, we propose a novel feature-convex…

Capsule Networks preserve the hierarchical spatial relationships between objects, and thereby bears a potential to surpass the performance of traditional Convolutional Neural Networks (CNNs) in performing tasks like image classification. A…

The convolutional layers are core building blocks of neural network architectures. In general, a convolutional filter applies to the entire frequency spectrum of the input data. We explore artificially constraining the frequency spectra of…

Building on our earlier results on tropical independence and shapes of divisors in tropical linear series, we give a tropical proof of the maximal rank conjecture for quadrics. We also prove a tropical analogue of Max Noether's theorem on…

This paper addresses the robustness of a network to sustain its connectivity and controllability against malicious attacks. This kind of network robustness is typically measured by the time-consuming attack simulation, which returns a…

We study tropical degree bounds, stable tropical intersections, and tropical B\'ezout-type estimates through the geometry of Newton polytopes, mixed subdivisions, and lattice indices. We establish an upper bound for the tropical degree of a…

Recent work suggests that changing Convolutional Neural Network (CNN) architecture by introducing a bottleneck in the second layer can yield changes in learned function. To understand this relationship fully requires a way of quantitatively…

Adapters are widely popular parameter-efficient transfer learning approaches in natural language processing that insert trainable modules in between layers of a pre-trained language model. Apart from several heuristics, however, there has…

CNNs achieve remarkable performance by leveraging deep, over-parametrized architectures, trained on large datasets. However, they have limited generalization ability to data outside the training domain, and a lack of robustness to noise and…

We perform accurate numerical experiments with fully-connected (FC) one-hidden layer neural networks trained with a discretized Langevin dynamics on the MNIST and CIFAR10 datasets. Our goal is to empirically determine the regimes of…

Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical…

Extreme value statistics is the max analogue of classical statistics, while tropical geometry is the max analogue of classical geometry. In this paper, we review recent work where insights from tropical geometry were used to develop new,…

We study cascading failures in smart grids, where an attacker selectively compromises the nodes with probabilities proportional to their degrees, betweenness, or clustering coefficient. This implies that nodes with high degrees,…

We examine the incidence geometry of lines in the tropical plane. We prove tropical analogs of the Sylvester-Gallai and Motzkin-Rabin theorems in classical incidence geometry. This study leads naturally to a discussion of the realizability…

The problem where a tropical cyclone intensifies dramatically within a short period of time is known as rapid intensification. This has been one of the major challenges for tropical weather forecasting. Recurrent neural networks have been…

The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it…