Related papers: Representation Gap of the Motzkin Monoid

We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…

The problem of representative selection amounts to sampling few informative exemplars from large datasets. This paper presents MOSAIC, a novel representative selection approach from high-dimensional data that may exhibit non-linear…

3D action recognition was shown to benefit from a covariance representation of the input data (joint 3D positions). A kernel machine feed with such feature is an effective paradigm for 3D action recognition, yielding state-of-the-art…

Linear diagrams are used to visualize set systems by depicting set memberships as horizontal line segments in a matrix, where each set is represented as a row and each element as a column. Each such line segment of a set is shown in a…

We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the…

Despite significant advances, deep networks remain highly susceptible to adversarial attack. One fundamental challenge is that small input perturbations can often produce large movements in the network's final-layer feature space. In this…

Deep networks are well-known to be fragile to adversarial attacks. We conduct an empirical analysis of deep representations under the state-of-the-art attack method called PGD, and find that the attack causes the internal representation to…

We present a MATLAB/Octave toolbox to decompose finite dimensionial representations of compact groups. Surprisingly, little information about the group and the representation is needed to perform that task. We discuss applications to…

The recent surge in jailbreaking attacks has revealed significant vulnerabilities in Large Language Models (LLMs) when exposed to malicious inputs. While various defense strategies have been proposed to mitigate these threats, there has…

In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…

Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling. In this model, the signal is assumed to be generated as a random linear combination of a few atoms from a…

Reliable identification of encrypted file fragments is a requirement for several security applications, including ransomware detection, digital forensics, and traffic analysis. A popular approach consists of estimating high entropy as a…

In applications like medical imaging, error correction, and sensor networks, one needs to solve large-scale linear systems that may be corrupted by a small number of arbitrarily large corruptions. We consider solving such large-scale…

Network decomposition is a central concept in the study of distributed graph algorithms. We present the first polylogarithmic-round deterministic distributed algorithm with small messages that constructs a strong-diameter network…

Recently, an image block encryption algorithm was proposed based on some well-known chaotic maps. The authors claim that the encryption algorithm achieves enough security level and high encryption speed at the same time. In this paper, we…

Visual analytics have played an increasingly critical role in the Internet of Things, where massive visual signals have to be compressed and fed into machines. But facing such big data and constrained bandwidth capacity, existing…

The matrix rank and its positive versions are robust for small approximations, i.e. they do not decrease under small perturbations. In contrast, the multipartite tensor rank can collapse for arbitrarily small errors, i.e. there may be a gap…

A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…

Compact user representations (such as embeddings) form the backbone of personalization services. In this work, we present a new theoretical framework to measure re-identification risk in such user representations. Our framework, based on…

We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…