Related papers: An Improvement over the GVW Algorithm for Inhomoge…
Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gr{\"o}bner bases taking into account the valuation of K. Because of the use of the valuation, the theory of tropical Gr{\"o}bner bases…
Graph Neural Networks (GNNs) exploit signals from node features and the input graph topology to improve node classification task performance. However, these models tend to perform poorly on heterophilic graphs, where connected nodes have…
Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be…
Various privacy-preserving frameworks that respect the individual's privacy in the analysis of data have been developed in recent years. However, available model classes such as simple statistics or generalized linear models lack the…
A general fuzzy min-max (GFMM) neural network is one of the efficient neuro-fuzzy systems for classification problems. However, a disadvantage of most of the current learning algorithms for GFMM is that they can handle effectively numerical…
Grammar-Guided Genetic Programming (GGGP) employs a variety of insights from evolutionary theory to autonomously design solutions for a given task. Recent insights from evolutionary biology can lead to further improvements in GGGP…
We define Macaulay bases of modules, which are a common generalization of Groebner bases and Macaulay $H$-bases to suitably graded modules over a commutative graded $\mathbf{k}$-algebra, where the index sets of the two gradings may differ.…
Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence…
Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…
In this paper, an original reduction algorithm for solving simultaneous multivariate polynomial equations is presented. The algorithm is exponential in complexity, but the well-known algorithms, such as the extended Euclidean algorithm and…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
Grover adaptive search (GAS) is a quantum exhaustive search algorithm designed to solve binary optimization problems. In this paper, we propose higher-order binary formulations that can simultaneously reduce the numbers of qubits and gates…
Imbalanced Learning is an important learning algorithm for the classification models, which have enjoyed much popularity on many applications. Typically, imbalanced learning algorithms can be partitioned into two types, i.e., data level…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
We apply machine learning methods to build a time-domain model for gravitational waveforms from binary black hole mergers, called mlgw. The dimensionality of the problem is handled by representing the waveform's amplitude and phase using a…
The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
Systems of polynomial equations arise frequently in computer vision, especially in multiview geometry problems. Traditional methods for solving these systems typically aim to eliminate variables to reach a univariate polynomial, e.g., a…
$GW$ is an accurate method for computing electron addition and removal energies of molecules and solids. In a conventional $GW$ implementation, however, its computational cost is $O(N^4)$ in the system size $N$, which prohibits its…
We consider the problem of computing critical points of the restriction of a polynomial map to an algebraic variety. This is of first importance since the global minimum of such a map is reached at a critical point. Thus, these points…