Related papers: Constructing Sequences One Step at a Time

This paper studies when a sequence of probability measures on a metric space admit subsequential weak limits. A sufficient condition called sequential tightness is formulated, which relaxes some assumptions for asymptotic tightness used in…

A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…

Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide…

The novel idea of weak Galerkin (WG) finite element methods is on the use of weak functions and their weak derivatives defined as distributions. Weak functions and weak derivatives can be approximated by polynomials with various degrees.…

In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is $\Delta^0_1$-definable relative…

We introduce a notion of "weak model category" which is a weakening of the notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions, Quillen equivalences and most of the usual construction of…

Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…

Methods for combining predictions from different models in a supervised learning setting must somehow estimate/predict the quality of a model's predictions at unknown future inputs. Many of these methods (often implicitly) make the…

Wannier tight-binding models are effective models constructed from first-principles calculations. As such, they bridge a gap between the accuracy of first-principles calculations and the computational simplicity of effective models. In this…

This paper presents a solution to the challenges faced by contrastive learning in sequential recommendation systems. In particular, it addresses the issue of false negative, which limits the effectiveness of recommendation algorithms. By…

Concurrent Constraint Programming (CCP) is a simple and powerful model for concurrency where agents interact by telling and asking constraints. Since their inception, CCP-languages have been designed for having a strong connection to logic.…

Bayesian methods provide an elegant framework for estimating parameter posteriors and quantification of uncertainty associated with probabilistic models. However, they often suffer from slow inference times. To address this challenge,…

In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.

In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: "object A is more similar to object B than it is to C", where comparisons are given by humans. Existing solutions…

Recently, contrastive learning has risen to be a promising approach for large-scale self-supervised learning. However, theoretical understanding of how it works is still unclear. In this paper, we propose a new guarantee on the downstream…

Two objects are independent if they do not affect each other. Independence is well-understood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper…

A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt-Picard group of such an order is a certain group of ideal classes that is closely related to the "minus part" of the class group. We present…

Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…

Confident prediction is highly relevant in machine learning; for example, in applications such as medical diagnoses, wrong prediction can be fatal. For classification, there already exist procedures that allow to not classify data when the…

Contrastive learning is an efficient approach to self-supervised representation learning. Although recent studies have made progress in the theoretical understanding of contrastive learning, the investigation of how to characterize the…