Related papers: Transfer Principle for the Fundamental Lemma
We show that any finite set S in a characteristic zero integral domain can be mapped to the finite field of order p, for infinitely many primes p, preserving all algebraic incidences in S. This can be seen as a generalization of the…
Transfer learning has emerged as a powerful methodology for adapting pre-trained deep neural networks on image recognition tasks to new domains. This process consists of taking a neural network pre-trained on a large feature-rich source…
This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…
We relate the recognition principle for infinite $\mathbf P^1$-loop spaces to the theory of motivic fundamental classes of D\'eglise, Jin, and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories…
We present an application of elimination theory to the study of singularities over arbitrary fields, particularly to the open problem of resolution. A partial extension of a function, defining resolution of singularities over fields of…
We build a bridge from density combinatorics to dimension theory of continued fractions. We establish a fractal transference principle that transfers common properties of subsets of $\mathbb N$ with positive upper density to properties of…
Transfer learning refers to the promising idea of initializing model fits based on pre-training on other data. We particularly consider regression modeling settings where parameter estimates from previous data can be used as anchoring…
Let $F$ be a global field, $A$ a central simple algebra over $F$ and $K$ a finite (separable or not) field extension of $F$ with degree $[K:F]$ dividing the degree of $A$ over $F$. An embedding of $K$ in $A$ over $F$ exists implies an…
In many business settings, task-specific labeled data are scarce or costly to obtain, limiting supervised learning on a target task. A classical response is transfer learning (TL). Many TL works study how to transfer information from…
Motivated by the notion of a set of uniqueness in a locally compact group $G$, we introduce and study ideals of uniqueness in the Fourier algebra $A(G)$ of $G$, and their accompanying operator version, masa-bimodules of uniqueness. We…
We show that the category of motivic spaces with transfers along finite flat morphisms, over a perfect field, satisfies all the properties we have come to expect of good categories of motives. In particular we establish the analog of…
In this paper we explore the possibility of defining p-local finite groups in terms of transfer properties of their classifying spaces. More precisely, we consider the question posed by Haynes Miller, whether an equivalent theory can be…
Transfer Learning (TL) aims to transfer knowledge acquired in one problem, the source problem, onto another problem, the target problem, dispensing with the bottom-up construction of the target model. Due to its relevance, TL has gained…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…
This review article provides the basics and discusses some important applications of thermal field theory, namely the combination of statistical mechanics and relativistic quantum field theory. In a first part the fundamentals are covered:…
Neural Style Transfer has recently demonstrated very exciting results which catches eyes in both academia and industry. Despite the amazing results, the principle of neural style transfer, especially why the Gram matrices could represent…
We use the dictionary between general field theories and strongly homotopy algebras to provide an algebraic formulation of the procedure of integrating out of degrees of freedom in terms of homotopy transfer. This includes more general…
The Fundamental Lemma is a somewhat obscure combinatorial identity introduced by Robert P. Langlands as an ingredient in the theory of automorphic representations. After many years of deep contributions by mathematicians working in…
Parameters in deep neural networks which are trained on large-scale databases can generalize across multiple domains, which is referred as "transferability". Unfortunately, the transferability is usually defined as discrete states and it…