Related papers: Attaque algebrique de NTRU a l'aide des vecteurs d…
Admissible vectors lead to frames or coherent states under the action of a group by means of square integrable representations. This work shows that admissible vectors can be seen as weights with central support on the (left) group von…
Vision Transformers (ViTs) are becoming a very popular paradigm for vision tasks as they achieve state-of-the-art performance on image classification. However, although early works implied that this network structure had increased…
With the rapid development of artificial intelligence, a number of machine learning algorithms, such as graph neural networks have been proposed to facilitate network analysis or graph data mining. Although effective, recent studies show…
We give a $K$-theoretic account of the basic properties of Witt vectors. Along the way we re-prove basic properties of the little-known Witt vector norm, give a characterization of Witt vectors in terms of algebraic $K$-theory, and a…
We extend the big and $p$-typical Witt vector functors from commutative rings to commutative semirings. In the case of the big Witt vectors, this is a repackaging of some standard facts about monomial and Schur positivity in the…
We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…
The purpose of this note is to demonstrate the advantages of Y.-Z.~Huang's definition of the Zhu algebra (Comm.\ Contemp.\ Math., 7 (2005), no.~5, 649--706) for an arbitrary vertex algebra, not necessarily equipped with a Hamiltonian…
We adapt a continuous logic axiomatization of tracial von Neumann algebras due to Farah, Hart and Sherman in order to prove a metatheorem for this class of structures in the style of proof mining, a research program that aims to obtain the…
Backdoor attacks are an insidious security threat against machine learning models. Adversaries can manipulate the predictions of compromised models by inserting triggers into the training phase. Various backdoor attacks have been devised…
We report on experience with an investigation of the analytic structure of the solution of certain algebraic complex equations. In particular the behavior of their series expansions around the origin is discussed. The investigation imposes…
This is the first part of a 2 part survey on the functor of the big and p-adic Witt vectors.
Recently, the pre-trained language model, BERT (and its robustly optimized version RoBERTa), has attracted a lot of attention in natural language understanding (NLU), and achieved state-of-the-art accuracy in various NLU tasks, such as…
In recent years, deep neural networks demonstrated state-of-the-art performance in a large variety of tasks and therefore have been adopted in many applications. On the other hand, the latest studies revealed that neural networks are…
Deep neural networks (DNNs) are vulnerable to adversarial examples obtained by adding small perturbations to original examples. The added perturbations in existing attacks are mainly determined by the gradient of the loss function with…
Deep neural networks are susceptible to small-but-specific adversarial perturbations capable of deceiving the network. This vulnerability can lead to potentially harmful consequences in security-critical applications. To address this…
Adversarial attacks on explainability models have drastic consequences when explanations are used to understand the reasoning of neural networks in safety critical systems. Path methods are one such class of attribution methods susceptible…
It is shown that the ternary Virasoro-Witt algebra of Curtright, Fairlie and Zachos can be constructed by applying the Nambu commutator to the vect(1) realization on scalar densities. This construction is generalized to vect(d), but the…
A subtraction-free definition of the big Witt vector construction was recently given by the first author. This allows one to define the big Witt vectors of any semiring. Here we give an explicit combinatorial description of the big Witt…
This paper is the first of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we present an elementary, progressive and self-contained approch to vertex operator superalgebra.…
We provide a robust defence to adversarial attacks on discriminative algorithms. Neural networks are naturally vulnerable to small, tailored perturbations in the input data that lead to wrong predictions. On the contrary, generative models…