Related papers: Majorization framework for balanced lattice design…

In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on moment matrices (if criteria depend on designs via moment matrices) or with respect to the designs…

A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…

In recent years, the scaling laws of recommendation models have attracted increasing attention, which govern the relationship between performance and parameters/FLOPs of recommenders. Currently, there are three mainstream architectures for…

Evaluation of large language models (LLMs) is increasingly critical, yet standard benchmarking methods rely on average accuracy, overlooking both the inherent stochasticity of LLM outputs and the heterogeneity of benchmark items. Item…

We construct the universal realized limit sketch associated to a given limit sketch. The construction uses factorization systems to organize the classical argument of [2], yielding a streamlined and conceptually unified formulation of the…

A unified approach to parametrization of the mixing matrix for $N$ generations is developed. This approach not only has a clear geometrical underpinning but also has the advantage of being economical and recursive and leads in a natural way…

In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. We define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is…

As compared to using randomly generated sensing matrices, optimizing the sensing matrix w.r.t. a carefully designed criterion is known to lead to better quality signal recovery given a set of compressive measurements. In this paper, we…

Probabilistic predictions can be evaluated through comparisons with observed label frequencies, that is, through the lens of calibration. Recent scholarship on algorithmic fairness has started to look at a growing variety of…

We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals, the standard determinantal ideals, and the ideals…

Matrix factorization models are the core of current commercial collaborative filtering Recommender Systems. This paper tested six representative matrix factorization models, using four collaborative filtering datasets. Experiments have…

For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic polynomial-time algorithm to accomplish…

Although being a crucial question for the development of machine learning algorithms, there is still no consensus on how to compare classifiers over multiple data sets with respect to several criteria. Every comparison framework is…

This work investigates the factorization of finite lattices to implode selected intervals while preserving the remaining order structure. We examine how complete congruence relations and complete tolerance relations can be utilized for this…

Inferring from inconsistency and making decisions are two problems which have always been treated separately by researchers in Artificial Intelligence. Consequently, different models have been proposed for each category. Different…

In odd dimensions the lattice overlap formalism is simpler than in even dimensions. Masslessness of fermions can still be preserved without fine tuning and gauge invariance without gauge averaging can be maintained, although, sometimes,…

We analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of…

A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…

We first obtain the most general and compact parametrization of the unitary transformation diagonalizing any 3 by 3 hermitian matrix H, as a function of its elements and eigenvalues. We then study a special class of fermion mass matrices,…

Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…