Related papers: Generalized Ideals and Co-Granular Rough Sets

Neural Combinatorial Optimization approaches have recently leveraged the expressiveness and flexibility of deep neural networks to learn efficient heuristics for hard Combinatorial Optimization (CO) problems. However, most of the current…

Deep learning models for semantics are generally evaluated using naturalistic corpora. Adversarial methods, in which models are evaluated on new examples with known semantic properties, have begun to reveal that good performance at these…

This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…

In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…

There are many structures (algebras, categories, etc) with natural gradings such that the degree 0 components are not semisimple. Particular examples include tensor algebras with non-semisimple degree 0 parts, extension algebras of standard…

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

The use of semantic descriptions in data intensive domains require a systematic model for linking semantic descriptions with their manifestations in fragments of heterogeneous information and data objects. Such information heterogeneity…

Considering smooth mappings from input vectors to continuous targets, our goal is to characterise subspaces of the input domain, which are invariant under such mappings. Thus, we want to characterise manifolds implicitly defined by level…

Parametric Gr\"obner bases have been studied for more than 15 years and are now a further developed subject. Here we propose a general study of parametric standard bases, that is with local orders. We mainly focus on the commutative case…

In his seminal Inventiones paper from 1972 Grauert proved the existence of a semiuniversal deformation of an arbitrary complex analytic isolated singularity. For the proof he invented an approximation theorem for solving a system of…

Granular media surround us, comprising everything from the ground we walk on to the foods we eat. Owing to their ubiquity our ability to understand and predict the mechanical evolution of grains is not only of key scientific importance, but…

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…

Local nonlinear approximations to the growth of cosmic perturbations are developed, resulting in relations, at a given epoch, between the peculiar velocity and gravity fields and their gradients. Only the equation of motion is approximated,…

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…

It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…

Recurrent neural networks have recently been used for learning to describe images using natural language. However, it has been observed that these models generalize poorly to scenes that were not observed during training, possibly depending…

The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algebra. We are hoping to convey a firm grasp of three ideas: (1)…

This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…

Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are…

We describe a general framework for probabilistic modeling of complex scenes and inference from ambiguous observations. The approach is motivated by applications in image analysis and is based on the use of priors defined by stochastic…