Related papers: Model theoretic forcing in analysis
Linear response theory has developed into a formidable set of tools for studying the forced behaviour of a large variety of systems - including out of equilibrium ones. In this paper we provide a new angle on the problem, by studying under…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
For which (first-order complete, usually countable) $T$ do there exist non-isomorphic models of $T$ which become isomorphic after forcing with a forcing notion $\mathbb{P}$? Necessarily, $\mathbb{P}$ is non-trivial; i.e.~it adds some new…
Turning rich neuroimaging data into mechanistic insight remains challenging. Statistical models capture associations but remain largely agnostic to underlying mechanisms. Biophysical models embody candidate mechanisms but remain difficult…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…
We present three syntactic forcing models for coherent logic. These are based on sites whose underlying category only depends on the signature of the coherent theory, and they do not presuppose that the logic has equality. As an application…
We extend the framework of variational autoencoders to represent transformations explicitly in the latent space. In the family of hierarchical graphical models that emerges, the latent space is populated by higher order objects that are…
Adversarial examples --- perturbations to the input of a model that elicit large changes in the output --- have been shown to be an effective way of assessing the robustness of sequence-to-sequence (seq2seq) models. However, these…
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the…
We study the evolution of latent space in fine-tuned NLP models. Different from the commonly used probing-framework, we opt for an unsupervised method to analyze representations. More specifically, we discover latent concepts in the…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Our basic element is a $C^1$ mapping $f:X\to Y$, with $X,Y$ Banach spaces, and with derivative everywhere invertible. So $f$ is a local diffeomorphism at every point. The aim of this paper is to find a sufficient condition for $f$ to be…
In-context learning is a surprising and important phenomenon that emerged when modern language models were scaled to billions of learned parameters. Without modifying a large language model's weights, it can be tuned to perform various…
As machine learning models are increasingly used in critical decision-making settings (e.g., healthcare, finance), there has been a growing emphasis on developing methods to explain model predictions. Such \textit{explanations} are used to…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
We present a framework to calculate large deviations for nonlinear functions of independent random variables supported on compact sets in Banach spaces, by extending the result in Chatterjee and Dembo [6]. Previous research on nonlinear…
First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…
We deal with an iteration theorem of forcing notion with a kind of countable support of nice enough forcing notion which is proper aleph_2-c.c. forcing notions. We then look at some special cases (Q_D 's preceded by random forcing).
We present a brief introduction to a flexible, general network inference framework which models data as a network space, sampled to optimize network structure to a particular task. We introduce a formal problem statement related to…
Let $M$ be a transitive model of $ZFC$ and let ${\bf B}$ be a $M$-complete Boolean algebra in $M.$ (In general a proper class.) We define a generalized notion of forcing with such Boolean algebras, $^*$forcing. (A $^*$ forcing extension of…