相关论文: Levels of Distribution and the Affine Sieve

These are the notes for the lectures that I was giving during Fall 2020 at the Moscow Institute of Physics and Technology (MIPT) and at the Yandex School of Data Analysis (YSDA). The notes cover some aspects of initialization, loss…

The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant…

The proposed method extends upon the representational output of semantic instance segmentation by explicitly including both visible and occluded parts. A fully convolutional network is trained to produce consistent pixel-level embedding…

Automated semantic segmentation of cell nuclei in microscopic images is crucial for disease diagnosis and tissue microenvironment analysis. Nonetheless, this task presents challenges due to the complexity and heterogeneity of cells. While…

In this work we discuss an elementary self-contained presentation of the notion of a semiabelian category, introduced by Raikov and Palamodov. Fundamental examples of (non-abelian) semiabelian categories occuring in Functional Analysis and…

Deep learning methods show promising results for overlapping cervical cell instance segmentation. However, in order to train a model with good generalization ability, voluminous pixel-level annotations are demanded which is quite expensive…

The goal of this paper is to make a surprising connection between several central conjectures in algebraic geometry: the Nonvanishing Conjecture, the Abundance Conjecture, and the Semiampleness Conjecture for nef line bundles on K-trivial…

These lecture notes cover four topics. There is a proof of the fact that the functors represented by the motivic Eilenberg-Maclane spaces on the motivic homotopy category coincide with the motivic cohomology defined in terms of the motivic…

Over the past years, semantic segmentation, as many other tasks in computer vision, benefited from the progress in deep neural networks, resulting in significantly improved performance. However, deep architectures trained with…

A complete classification of the WZNW modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of SU(2), and level 1 of all simple algebras. In this paper we solve the…

Graph-based learning is a cornerstone for analyzing structured data, with node classification as a central task. However, in many real-world graphs, nodes lack informative feature vectors, leaving only neighborhood connectivity and class…

Recent works have made great progress in semantic segmentation by exploiting richer context, most of which are designed from a spatial perspective. In contrast to previous works, we present the concept of class center which extracts the…

I describe extended gradings of open topological field theories in two dimensions in terms of skew categories, proving a result which alows one to translate between the formalism of graded open 2d TFTs and equivariant cyclic categories. As…

Knowledge distillation involves transferring the predictive capabilities of large, high-performing AI models (teachers) to smaller models (students) that can operate in environments with limited computing power. In this paper, we address…

Recent research has found that knowledge distillation can be effective in reducing the size of a network and in increasing generalization. A pre-trained, large teacher network, for example, was shown to be able to bootstrap a student model…

This is an expended and revised version of the preprint "Schematization of homotopy types". The purpose of this work is to introduce a notion of \emph{affine stacks}, which is a homotopy version of the notion of affine schemes, and to give…

These brief lecture notes are intended mainly for undergraduate students in engineering or physics or mathematics who have met or will soon be meeting the Dirac delta function and some other objects related to it. These students might have…

Knowledge distillation as a broad class of methods has led to the development of lightweight and memory efficient models, using a pre-trained model with a large capacity (teacher network) to train a smaller model (student network).…

In recent years, deep neural networks have achieved high ac-curacy in the field of image recognition. By inspired from human learning method, we propose a semantic segmentation method using cooperative learning which shares the information…

Essentials of sheaves are briefly presented, followed by related comments on presheaves, bundles, manifolds and singularities, aiming to point to their differences not only in their different formal mathematical structures, but also in the…