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Evgeny Smirnov

Publications and source records attributed to Evgeny Smirnov.

At least 19 recordsLinked to original sources
arXiv2026

Set-valued tableaux and cells of Gelfand-Zetlin polytopes

Two combinatorial rules are known for the Grassmannian Grothendieck polynomial $G^{(β)}_λ$: a sum over set-valued tableaux of shape $λ$, due to Buch, and a sum over the efficient cells of a cellular decomposition of the Gelfand-Zetlin polytope $GZ(λ)$, due to E. Presnova and the author. All coefficients in both sums equal $1$. We construct an explicit bijection between the two indexing sets which matches the summands term by term, carrying the number of excess entries of a tableau to the dimension of the corresponding cell; in particular the two rules are equivalent, either being deducible from the other. The efficiency condition on cells turns out to be the column-strictness of tableaux. We then transport Yu's square-root crystal operators to the cells and find that they respect dimension, along a double $i$-string the cells alternate between two consecutive dimensions, but not incidence: consecutive cells of such a string need not share a point, already for $λ=(2,1,0)$.

math.CO↗
arXiv2026

Polyhedral models for K-theory of toric and flag varieties

In 1992, Pukhlikov and Khovanskii provided a description of the cohomology ring of toric variety as a quotient of the ring of differential operators on spaces of virtual polytopes. Later Kaveh generalized this construction to the case of cohomology rings for full flag varieties. In this paper we extend Pukhlikov-Khovanskii type presentation to the case of K-theory of toric and flag varieties. First, we study the Frobenius algebras obtained as quotients of the group algebra of free abelian group (possibly of infinite rank). Then we apply this construction to define a K-ring associated to a linear family of (virtual) polytopes. We study in detail two examples of such families: the family of integer (virtual) polytopes with a fixed normal fan and the family of (virtual) Gelfand-Zetlin polytopes. We show that the K-theory of toric and flag varieties can be realized as K-rings of the above families and use this to get natural set of relations in the above K-rings. Further, we describe the classes of structure sheaves of toric orbit closures and Schubert varieties in type A flag varieties. Finally, we show that our results also hold true in T-equivariant setting.

math.AG↗
arXiv2025

Quality-Aware Prototype Memory for Face Representation Learning

Prototype Memory is a powerful model for face representation learning. It enables training face recognition models on datasets of any size by generating prototypes (classifier weights) on the fly and efficiently utilizing them. Prototype Memory demonstrated strong results in many face recognition benchmarks. However, the algorithm of prototype generation, used in it, is prone to the problems of imperfectly calculated prototypes in case of low-quality or poorly recognizable faces in the images, selected for the prototype creation. All images of the same person presented in the mini-batch are used with equal weights, and the resulting averaged prototype can be contaminated by imperfect embeddings of low-quality face images. This may lead to misleading training signals and degrade the performance of the trained models. In this paper, we propose a simple and effective way to improve Prototype Memory with quality-aware prototype generation. Quality-Aware Prototype Memory uses different weights for images of different quality in the process of prototype generation. With this improvement, prototypes receive more informative signals from high-quality images and are less affected by low-quality ones. We propose and compare several methods of quality estimation and usage, perform extensive experiments on the different face recognition benchmarks and demonstrate the advantages of the proposed model compared to the basic version of Prototype Memory.

cs.CV↗
arXiv2025

Friezes and continued fractions

We explore basic properties of number friezes, due to Conway and Coxeter, and their relations to decompositions of rational numbers into continued fractions, Farey sequences, and the modular group acting on the hyperbolic plane. These are notes from a mini-course for undergraduate students given at the 19th Summer School ``Modern Mathematics'', Dubna, Russia, July 18-29, 2019.

math.NT↗
arXiv2025

Second FRCSyn-onGoing: Winning Solutions and Post-Challenge Analysis to Improve Face Recognition with Synthetic Data

Synthetic data is gaining increasing popularity for face recognition technologies, mainly due to the privacy concerns and challenges associated with obtaining real data, including diverse scenarios, quality, and demographic groups, among others. It also offers some advantages over real data, such as the large amount of data that can be generated or the ability to customize it to adapt to specific problem-solving needs. To effectively use such data, face recognition models should also be specifically designed to exploit synthetic data to its fullest potential. In order to promote the proposal of novel Generative AI methods and synthetic data, and investigate the application of synthetic data to better train face recognition systems, we introduce the 2nd FRCSyn-onGoing challenge, based on the 2nd Face Recognition Challenge in the Era of Synthetic Data (FRCSyn), originally launched at CVPR 2024. This is an ongoing challenge that provides researchers with an accessible platform to benchmark i) the proposal of novel Generative AI methods and synthetic data, and ii) novel face recognition systems that are specifically proposed to take advantage of synthetic data. We focus on exploring the use of synthetic data both individually and in combination with real data to solve current challenges in face recognition such as demographic bias, domain adaptation, and performance constraints in demanding situations, such as age disparities between training and testing, changes in the pose, or occlusions. Very interesting findings are obtained in this second edition, including a direct comparison with the first one, in which synthetic databases were restricted to DCFace and GANDiffFace.

cs.CV↗
arXiv2024

Lascoux polynomials and subdivisions of Gelfand-Zetlin polytopes

We give a new combinatorial description for stable Grothendieck polynomials in terms of subdivisions of Gelfand-Zetlin polytopes. Moreover, these subdivisions also provide a description of Lascoux polynomials. This generalizes a similar result on key polynomials by Kiritchenko, Smirnov, and Timorin.

math.CO↗
arXiv2024

Partial order on involutive permutations and double Schubert cells

As shown by A. Melnikov, the orbits of a Borel subgroup acting by conjugation on upper-triangular matrices with square zero are indexed by involutions in the symmetric group. The inclusion relation among the orbit closures defines a partial order on involutions. We observe that the same order on involutive permutations also arises while describing the inclusion order on B-orbit closures in the direct product of two Grassmannians. We establish a geometric relation between these two settings.

math.CO↗
arXiv2024

Second Edition FRCSyn Challenge at CVPR 2024: Face Recognition Challenge in the Era of Synthetic Data

Synthetic data is gaining increasing relevance for training machine learning models. This is mainly motivated due to several factors such as the lack of real data and intra-class variability, time and errors produced in manual labeling, and in some cases privacy concerns, among others. This paper presents an overview of the 2nd edition of the Face Recognition Challenge in the Era of Synthetic Data (FRCSyn) organized at CVPR 2024. FRCSyn aims to investigate the use of synthetic data in face recognition to address current technological limitations, including data privacy concerns, demographic biases, generalization to novel scenarios, and performance constraints in challenging situations such as aging, pose variations, and occlusions. Unlike the 1st edition, in which synthetic data from DCFace and GANDiffFace methods was only allowed to train face recognition systems, in this 2nd edition we propose new sub-tasks that allow participants to explore novel face generative methods. The outcomes of the 2nd FRCSyn Challenge, along with the proposed experimental protocol and benchmarking contribute significantly to the application of synthetic data to face recognition.

cs.CV↗
arXiv2022

Pipe dreams for Schubert polynomials of the classical groups

Schubert polynomials for the classical groups were defined by S.Billey and M.Haiman in 1995; they are polynomial representatives of Schubert classes in a full flag variety of a classical group. We provide a combinatorial description for these polynomials, as well as their double versions, by introducing analogues of pipe dreams, or RC-graphs, for the Weyl groups of the classical types.

math.CO↗
arXiv2022

Prototype Memory for Large-scale Face Representation Learning

Face representation learning using datasets with a massive number of identities requires appropriate training methods. Softmax-based approach, currently the state-of-the-art in face recognition, in its usual "full softmax" form is not suitable for datasets with millions of persons. Several methods, based on the "sampled softmax" approach, were proposed to remove this limitation. These methods, however, have a set of disadvantages. One of them is a problem of "prototype obsolescence": classifier weights (prototypes) of the rarely sampled classes receive too scarce gradients and become outdated and detached from the current encoder state, resulting in incorrect training signals. This problem is especially serious in ultra-large-scale datasets. In this paper, we propose a novel face representation learning model called Prototype Memory, which alleviates this problem and allows training on a dataset of any size. Prototype Memory consists of the limited-size memory module for storing recent class prototypes and employs a set of algorithms to update it in appropriate way. New class prototypes are generated on the fly using exemplar embeddings in the current mini-batch. These prototypes are enqueued to the memory and used in a role of classifier weights for softmax classification-based training. To prevent obsolescence and keep the memory in close connection with the encoder, prototypes are regularly refreshed, and oldest ones are dequeued and disposed of. Prototype Memory is computationally efficient and independent of dataset size. It can be used with various loss functions, hard example mining algorithms and encoder architectures. We prove the effectiveness of the proposed model by extensive experiments on popular face recognition benchmarks.

cs.CV↗
arXiv2021

STC speaker recognition systems for the NIST SRE 2021

This paper presents a description of STC Ltd. systems submitted to the NIST 2021 Speaker Recognition Evaluation for both fixed and open training conditions. These systems consists of a number of diverse subsystems based on using deep neural networks as feature extractors. During the NIST 2021 SRE challenge we focused on the training of the state-of-the-art deep speaker embeddings extractors like ResNets and ECAPA networks by using additive angular margin based loss functions. Additionally, inspired by the recent success of the wav2vec 2.0 features in automatic speech recognition we explored the effectiveness of this approach for the speaker verification filed. According to our observation the fine-tuning of the pretrained large wav2vec 2.0 model provides our best performing systems for open track condition. Our experiments with wav2vec 2.0 based extractors for the fixed condition showed that unsupervised autoregressive pretraining with Contrastive Predictive Coding loss opens the door to training powerful transformer-based extractors from raw speech signals. For video modality we developed our best solution with RetinaFace face detector and deep ResNet face embeddings extractor trained on large face image datasets. The final results for primary systems were obtained by different configurations of subsystems fusion on the score level followed by score calibration.

cs.SD↗
arXiv2021

Slide polynomials and subword complexes

Subword complexes were defined by A.Knutson and E.Miller in 2004 for describing Gröbner degenerations of matrix Schubert varieties. The facets of such a complex are indexed by pipe dreams, or, equivalently, by the monomials in the corresponding Schubert polynomial. In 2017 S.Assaf and D.Searles defined a basis of slide polynomials, generalizing Stanley symmetric functions, and described a combinatorial rule for expanding Schubert polynomials in this basis. We describe a decomposition of subword complexes into strata called slide complexes, that correspond to slide polynomials. The slide complexes are shown to be homeomorphic to balls or spheres.

math.CO↗
arXiv2016

Ribbon graphs and bialgebra of Lagrangian subspaces

To each ribbon graph we assign a so-called L-space, which is a Lagrangian subspace in an even-dimensional vector space with the standard symplectic form. This invariant generalizes the notion of the intersection matrix of a chord diagram. Moreover, the actions of Morse perestroikas (or taking a partial dual) and Vassiliev moves on ribbon graphs are reinterpreted nicely in the language of L-spaces, becoming changes of bases in this vector space. Finally, we define a bialgebra structure on the span of L-spaces, which is analogous to the 4-bialgebra structure on chord diagrams.

math.GT↗
arXiv2015

Grassmannians, flag varieties, and Gelfand-Zetlin polytopes

These are extended notes of a talk given at Maurice Auslander Distinguished Lectures and International Conference (Woods Hole, MA) in April 2013. Their aim is to give an introduction into Schubert calculus on Grassmannians and flag varieties. We discuss various aspects of Schubert calculus, such as applications to enumerative geometry, structure of the cohomology rings of Grassmannians and flag varieties, Schur and Schubert polynomials. We conclude with a survey of results of V.Kiritchenko, V.Timorin and the author on a new approach to Schubert calculus on full flag varieties via combinatorics of Gelfand-Zetlin polytopes.

math.AG↗
arXiv2011

Schubert calculus and Gelfand-Zetlin polytopes

We describe a new approach to the Schubert calculus on complete flag varieties using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach allows us to compute the intersection products of Schubert cycles by intersecting faces of a polytope.

math.AG↗
arXiv2010

Springer fiber components in the two columns case for types A and D are normal

We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N^2=0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen-Macaulay, and have rational singularities.

math.AG↗