Related papers: Signature-Based Gr\"obner Basis Algorithms --- Ext…

Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…

State-of-the-art methods for solving smooth optimization problems are nonlinear conjugate gradient, low memory BFGS, and Majorize-Minimize (MM) subspace algorithms. The MM subspace algorithm which has been introduced more recently has shown…

Graph self-supervised learning (SSL) is now a go-to method for pre-training graph foundation models (GFMs). There is a wide variety of knowledge patterns embedded in the graph data, such as node properties and clusters, which are crucial to…

Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital documents. In the post-quantum era, classical public key-based signature schemes become vulnerable to brute-force and…

In this paper we present a new efficient variant to compute strong Gr\"obner basis over quotients of principal ideal domains. We show an easy lifting process which allows us to reduce one computation over the quotient $R/nR$ to two…

Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models…

This paper deals with offline handwriting signature verification.We propose a planar neuronal model of signature image. Planarmodelsare generally based on delimiting homogenous zones ofimages; we propose in this paper an automatic…

In this paper we present the formal, computer-supported verification of a functional implementation of Buchberger's critical-pair/completion algorithm for computing Gr\"obner bases in reduction rings. We describe how the algorithm can be…

Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…

Classic control techniques typically rely on a model of the system's response to external inputs, which is difficult to obtain from first principles especially if the unknown dynamics are nonlinear. In this paper, we address this issue by…

We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges…

A Generalized Numeration Base is defined in this paper, and then particular cases are presented, such as Prime Base, Square Base, m-Power Base, Factorial Base, and operations in these bases. These bases are important for partitions of…

Recommender systems (RS) serve as a fundamental tool for navigating the vast expanse of online information, with deep learning advancements playing an increasingly important role in improving ranking accuracy. Among these, graph neural…

The augmented usage of deep learning-based models for various AI related problems are as a result of modern architectures of deeper length and the availability of voluminous interpreted datasets. The models based on these architectures…

Signed networks are such social networks having both positive and negative links. A lot of theories and algorithms have been developed to model such networks (e.g., balance theory). However, previous work mainly focuses on the unipartite…

Identity verification based on authenticity assessment of a handwritten signature is an important issue in biometrics. There are many effective methods for signature verification taking into account dynamics of a signing process. Methods…

Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered.…

Gestures are a topic of increasing interest in authentication and successful implementation as a security layer requires reliable gesture recognition. So far much work focuses on new ways to recognize gestures, leaving discussion on the…

In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [Hur\'e-Pham-Warin. Mathematics of Computation 89, no. 324 (2020)] for state-dependent FBSDEs with reflections to…

Due to the widespread use of complex machine learning models in real-world applications, it is becoming critical to explain model predictions. However, these models are typically black-box deep neural networks, explained post-hoc via…