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Related papers: Model theoretic forcing in analysis

200 papers

We take inspiration from the study of human explanation to inform the design and evaluation of interpretability methods in machine learning. First, we survey the literature on human explanation in philosophy, cognitive science, and the…

Artificial Intelligence · Computer Science 2021-09-21 David Alvarez-Melis , Harmanpreet Kaur , Hal Daumé , Hanna Wallach , Jennifer Wortman Vaughan

We present a version with non-definable forcing notions of Shelah's theory of iterated forcing along a template. Our main result, as an application, is that, if $\kappa$ is a measurable cardinal and $\theta<\kappa<\mu<\lambda$ are…

Logic · Mathematics 2015-06-23 Diego Alejandro Mejía

We draw the connection between the model theoretic notions of internality and the binding group on one hand, and the Tannakian formalism on the other. More precisely, we deduce the fundamental results of the Tannakian formalism by…

Logic · Mathematics 2010-12-17 Moshe Kamensky

To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…

Computation and Language · Computer Science 2018-07-17 Joseph Corneli , Ursula Martin , Dave Murray-Rust , Gabriela Rino Nesin , Alison Pease

We propose a framework that leverages foundation models as teachers, guiding a reinforcement learning agent to acquire semantically meaningful behavior without human feedback. In our framework, the agent receives task instructions grounded…

Machine Learning · Computer Science 2023-12-15 Taewook Nam , Juyong Lee , Jesse Zhang , Sung Ju Hwang , Joseph J. Lim , Karl Pertsch

This paper aims to extend the framework of causal modelling to teleological explanations. It conceives final models as second-order models produced by interventions on first-order causal models. It shows why such formalisation permits us to…

Methodology · Statistics 2023-10-05 Dario Compagno

We provide sufficient conditions for a mapping between two Banach spaces to be a diffeomorphism using the approach of an auxiliary functional and also by the aid of a duality mapping corresponding to a normalization function. We simplify…

Functional Analysis · Mathematics 2018-09-17 Marek Galewski , Dušan Repovš

In this article, we present a new approach to averaging in non-Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In fact, we show that our averaging method fits into an…

Dynamical Systems · Mathematics 2010-06-15 Mickaël D. Chekroun , Michael Ghil , Jean Roux , Ferenc Varadi

This thesis explores how deep learning models learn over time, using ideas inspired by force analysis. Specifically, we zoom in on the model's training procedure to see how one training example affects another during learning, like…

Machine Learning · Computer Science 2025-09-25 Yi Ren

In this paper, methods of second order and higher order reverse mathematics are applied to versions of a theorem of Banach that extends the Schroeder-Bernstein theorem. Some additional results address statements in higher order arithmetic…

Logic · Mathematics 2023-11-15 Jeffry L. Hirst , Carl Mummert

The aim of this paper is to present the technique (and its linkage with physics) of overcoming problems connected to modeling social structures, which are typically hierarchical. Hierarchical Linear Models provide a conceptual and…

Physics and Society · Physics 2007-05-23 Magdalena Jelonek

Reinforcement learning methods are increasingly used to optimise dialogue policies from experience. Most current techniques are model-free: they directly estimate the utility of various actions, without explicit model of the interaction…

Artificial Intelligence · Computer Science 2013-04-09 Pierre Lison

Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are…

Functional Analysis · Mathematics 2015-05-13 P. G. Casazza , S. J. Dilworth , E. Odell , Th. Schlumprecht , Andras Zsak

In spite of its fundamental importance, inference has not been an inherent function of multidimensional models and analytical applications. These models are mainly aimed at numeric (quantitative) analysis where the notions of inference and…

Databases · Computer Science 2014-09-12 Alexandr Savinov

In this paper, a force-based beam finite element model based on a modified higher-order shear deformation theory is proposed for the accurate analysis of functionally graded beams. In the modified higher-order shear deformation theory, the…

Computational Engineering, Finance, and Science · Computer Science 2025-07-15 Wenxiong Li , Huiyi Chen , Suiyin Chen , Zhiwei Liu

We extend the classical Brunel-Sucheston definition of the spreading model by introducing the $\mathcal{F}$-sequences $(x_s)_{s\in\mathcal{F}}$ in a Banach space and the plegma families in $\mathcal{F}$ where $\mathcal{F}$ is a regular thin…

Functional Analysis · Mathematics 2014-04-18 S. A. Argyros , V. Kanellopoulos , K. Tyros

We introduce an efficient algorithmic framework for model selection in online learning, also known as parameter-free online learning. Departing from previous work, which has focused on highly structured function classes such as nested balls…

Machine Learning · Computer Science 2018-01-08 Dylan J. Foster , Satyen Kale , Mehryar Mohri , Karthik Sridharan

This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…

Machine Learning · Statistics 2021-10-12 K. P. Chowdhury

We now have a rich and growing set of modeling tools and algorithms for inducing linguistic structure from text that is less than fully annotated. In this paper, we discuss some of the weaknesses of our current methodology. We present a new…

Computation and Language · Computer Science 2012-07-17 Noah A. Smith

We survey the developments in the model theory of tracial von Neumann algebras that have taken place in the last fifteen years. We discuss the appropriate first-order language for axiomatizing this class as well as the subclass of II$_1$…

Logic · Mathematics 2022-10-28 Isaac Goldbring , Bradd Hart