Related papers: Two minicourses on analytic microlocal analysis
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
This textbook is based on lectures given by the authors at MIPT (Moscow), HSE (Moscow), FEFU (Vladivostok), V.I. Vernadsky KFU (Simferopol), ASU (Republic of Adygea), and the University of Grenoble-Alpes (Grenoble, France). First of all,…
These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions…
Large language models are powerful but costly. We ask whether meta-learning can make the pretraining of small language models not only better but also more interpretable. We integrate first-order MAML with subset-masked LM pretraining,…
These are the handouts of an undergraduate minicourse at the Universit\`a di Bari, in the context of the 2017 INdAM Intensive Period "Contemporary Research in elliptic PDEs and related topics". Without any intention to serve as a throughout…
Some early chapters of the upcoming book "Polyfold Constructions: Tools, Techniques, and Functors"
Automatic morphological processing can aid downstream natural language processing applications, especially for low-resource languages, and assist language documentation efforts for endangered languages. Having long been multilingual, the…
We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable…
We refine a recently-proposed class of local entropic loss functions by restricting the smoothening regularization to only a subset of weights. The new loss functions are referred to as partial local entropies. They can adapt to the…
Recent advancements in Large Language Models (LLMs) have revealed new capabilities and opportunities across the technological landscape. However, the practicality of very large LLMs is challenged by their high compute cost, which does not…
Model-agnostic tools for interpreting machine-learning models struggle to summarize the joint effects of strongly dependent features in high-dimensional feature spaces, which play an important role in pattern recognition, for example in…
These notes discuss, in a style intended for physicists, how to average data and fit it to some functional form. I try to make clear what is being calculated, what assumptions are being made, and to give a derivation of results rather than…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…
This volume contains a selection of papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford. Linearity has been a key feature in several lines of research in both…
Let $W$ be a domain in a connected complex manifold $M$ and $w_0\in W$. Let ${\mathcal A}_{w_0}(W,M)$ be the space of all continuous mappings of a closed unit disk $\overline D$ into $M$ that are holomorphic on the interior of $\overline…
We provide a motivated introduction to the theory of categorical actions of groups and the local geometric Langlands program. Along the way we emphasize applications, old and new, to the usual representation theory of reductive and affine…
Artificial Neural Networks of varying architectures are generally paired with affine transformation at the core. However, we find dot product neurons with global influence less interpretable as compared to local influence of euclidean…
In the first of two articles, we present here a novel mesoscopic micromagnetic approach for simulating materials composed of ferromagnetic and antiferromagnetic phases. Starting with the atomistic modeling of quasi one-dimensional systems,…
This work-in-progress research paper explores the efficacy of a small-scale microelectronics debugging education intervention utilizing quasi-experimental design in an introductory microelectronics course for third-year electrical and…