Related papers: Higher Order Differentiation over Finite Fields wi…

Graph Neural Network-based methods face privacy leakage risks due to the introduction of topological structures about the targets, which allows attackers to bypass the target's prior knowledge of the sensitive attributes and realize…

Differential cryptanalysis is one of the most popular methods in attacking block ciphers. However, there still some limitations in traditional differential cryptanalysis. On the other hand, researches of quantum algorithms have made great…

To explore the vulnerability of deep neural networks (DNNs), many attack paradigms have been well studied, such as the poisoning-based backdoor attack in the training stage and the adversarial attack in the inference stage. In this paper,…

We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…

Many works have investigated the adversarial attacks or defenses under the settings where a bounded and imperceptible perturbation can be added to the input. However in the real-world, the attacker does not need to comply with this…

In $1801$, Gauss found an explicit description, in the language of binary quadratic forms, for the $2$-torsion of the narrow class group and dual narrow class group of a quadratic number field. This is now known as Gauss's genus theory. In…

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

We consider cubic number fields ordered by their discriminants, and show that there exist arbitrarily long sequences that contain only fields with class numbers greater than a given bound.

Graph Neural Networks (GNNs) are a class of deep learning-based methods for processing graph domain information. GNNs have recently become a widely used graph analysis method due to their superior ability to learn representations for…

Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…

Our work targets at searching feasible adversarial perturbation to attack a classifier with high-dimensional categorical inputs in a domain-agnostic setting. This is intrinsically an NP-hard knapsack problem where the exploration space…

We present theory for general partial derivatives of matrix functions on the form $f(A(x))$ where $A(x)$ is a matrix path of several variables ($x=(x_1,\dots,x_j)$). Building on results by Mathias [SIAM J. Matrix Anal. Appl., 17 (1996), pp.…

Binary code similarity detection (BCSD) serves as a fundamental technique for various software engineering tasks, e.g., vulnerability detection and classification. Attacks against such models have therefore drawn extensive attention, aiming…

We propose to utilize gradients for detecting adversarial and out-of-distribution samples. We introduce confounding labels -- labels that differ from normal labels seen during training -- in gradient generation to probe the effective…

We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and…

We show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra…

Despite the great success of deep neural networks, the adversarial attack can cheat some well-trained classifiers by small permutations. In this paper, we propose another type of adversarial attack that can cheat classifiers by significant…

Let $\tilde{f}(X)\in\mathbb{Z}[X]$ be a degree-$n$ polynomial such that $f(X):=\tilde{f}(X)\bmod p$ factorizes into $n$ distinct linear factors over $\mathbb{F}_p$. We study the problem of deterministically factoring $f(X)$ over…

Differential categories were introduced by Blute, Cockett, and Seely as categorical models of differential linear logic and have since lead to abstract formulations of many notions involving differentiation such as the directional…

We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this…