Related papers: Signature-Based Gr\"obner Basis Algorithms --- Ext…
This survey provides a comparative overview of code-based signature schemes with respect to security and performance. Furthermore, we explicitly describe serveral code-based signature schemes with additional properties such as…
This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals…
Adversarial attacks make their success in DNNs, and among them, gradient-based algorithms become one of the mainstreams. Based on the linearity hypothesis, under $\ell_\infty$ constraint, $sign$ operation applied to the gradients is a good…
The structure of the F5 algorithm to compute Gr\"obner bases makes it very efficient. However, while it is believed to terminate for so-called regular sequences, it is not clear whether it terminates for all inputs. This paper has two major…
Experiences with the implementation of strong Gr\"obner bases respectively standard bases for polynomial rings over principal ideal rings are explained: different strategies for creating the pair set, methods to avoid coefficient growth and…
The application of machine learning (ML) algorithms in the intelligent diagnosis of three-phase engines has the potential to significantly enhance diagnostic performance and accuracy. Traditional methods largely rely on signature analysis,…
We provide an introduction to the signature method, focusing on its theoretical properties and machine learning applications. Our presentation is divided into two parts. In the first part, we present the definition and fundamental…
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a…
Gradient Boosting Machine (GBM) introduced by Friedman is a powerful supervised learning algorithm that is very widely used in practice---it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the…
Suppose that $\gamma$ and $\sigma$ are two continuous bounded variation paths which take values in a finite-dimensional inner product space $V$. Recent papers have introduced the truncated and the untruncated signature kernel of $\gamma$…
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gr\"obner bases. We present several linear algebra algorithms for computing Gr\"obner…
This paper uses Support Vector Machines (SVM) to fuse multiple classifiers for an offline signature system. From the signature images, global and local features are extracted and the signatures are verified with the help of Gaussian…
Machine Learning (ML) is increasingly used to implement advanced applications with non-deterministic behavior, which operate on the cloud-edge continuum. The pervasive adoption of ML is urgently calling for assurance solutions assessing…
It is known that for binary codes one can use Gr\"obner bases to obtain a subset of codewords of minimal support that can be used to determine the second generalized Hamming weight of the code. In this paper we establish conditions on a…
Modular algorithm are widely used in computer algebra systems (CAS), for example to compute efficiently the gcd of multivariate polynomials. It is known to work to compute Groebner basis over $\Q$, but it does not seem to be popular among…
The area of Handwritten Signature Verification has been broadly researched in the last decades, but remains an open research problem. The objective of signature verification systems is to discriminate if a given signature is genuine…
Non-convex optimization is ubiquitous in machine learning. Majorization-Minimization (MM) is a powerful iterative procedure for optimizing non-convex functions that works by optimizing a sequence of bounds on the function. In MM, the bound…
Numerical Association Rule Mining is a popular variant of Association Rule Mining, where numerical attributes are handled without discretization. This means that the algorithms for dealing with this problem can operate directly, not only…
In this paper we present the first-ever computer formalization of the theory of Gr\"obner bases in reduction rings, which is an important theory in computational commutative algebra, in Theorema. Not only the formalization, but also the…
Two models were recently proposed to explore the robust hardness of Gr\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for…