Related papers: Adversarial Barrier in Uniform Class Separation
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…
Traditional classification algorithms assume that training and test data come from similar distributions. This assumption is violated in adversarial settings, where malicious actors modify instances to evade detection. A number of custom…
In the univariate case, we show that by comparing the individual complexities of univariate cause and effect, one can identify the cause and the effect, without considering their interaction at all. In our framework, complexities are…
Machine learning models are vulnerable to adversarial perturbations, that when added to an input, can cause high confidence misclassifications. The adversarial learning research community has made remarkable progress in the understanding of…
In this article we prove in the main theorem that, there is a bijection between the isomorphism classes of a certain type of real hyperplane arrangements on the one hand, and the antipodal pairs of convex cones of an associated…
Neural networks are prone to misclassify slightly modified input images. Recently, many defences have been proposed, but none have improved the robustness of neural networks consistently. Here, we propose to use adversarial attacks as a…
Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we…
We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the…
We theoretically analyse the limits of robustness to test-time adversarial and noisy examples in classification. Our work focuses on deriving bounds which uniformly apply to all classifiers (i.e all measurable functions from features to…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
We identify properties of universal adversarial perturbations (UAPs) that distinguish them from standard adversarial perturbations. Specifically, we show that targeted UAPs generated by projected gradient descent exhibit two human-aligned…
We have widely observed that neural networks are vulnerable to small additive perturbations to the input causing misclassification. In this paper, we focus on the $\ell_0$-bounded adversarial attacks, and aim to theoretically characterize…
Abstraction is key to human and artificial intelligence as it allows one to see common structure in otherwise distinct objects or situations and as such it is a key element for generality in AI. Anti-unification (or generalization) is…
The recent years have been marked by extended research on adversarial attacks, especially on deep neural networks. With this work we intend on posing and investigating the question of whether the phenomenon might be more general in nature,…
Convolutional Neural Networks and Deep Learning classification systems in general have been shown to be vulnerable to attack by specially crafted data samples that appear to belong to one class but are instead classified as another,…
Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial…
Neural networks are known to be vulnerable to adversarial examples, inputs that have been intentionally perturbed to remain visually similar to the source input, but cause a misclassification. It was recently shown that given a dataset and…
Adversarial or test time robustness measures the susceptibility of a classifier to perturbations to the test input. While there has been a flurry of recent work on designing defenses against such perturbations, the theory of adversarial…
A main property of support vector machines consists in the fact that only a small portion of the training data is significant to determine the maximum margin separating hyperplane in the feature space, the so called support vectors. In a…
Adversarial examples are input examples that are specifically crafted to deceive machine learning classifiers. State-of-the-art adversarial example detection methods characterize an input example as adversarial either by quantifying the…