?
Structure-adaptive Manifold Estimation
Journal of Machine Learning Research. 2022. Vol. 23. No. 40. P. 1–62.
We consider a problem of manifold estimation from noisy observations. Many manifold learning procedures locally approximate a manifold by a weighted average over a small neighborhood. However, in the presence of large noise, the assigned weights become so corrupted that the averaged estimate shows very poor performance. We suggest a structure-adaptive procedure, which simultaneously reconstructs a smooth manifold and estimates projections of the point cloud onto this manifold. The proposed approach iteratively refines the weights on each step, using the structural information obtained at previous steps. After several iterations, we obtain nearly “oracle” weights, so that the final estimates are nearly efficient even in the presence of relatively large noise. In our theoretical study, we establish tight lower and upper bounds proving asymptotic optimality of the method for manifold estimation under the Hausdorff loss, provided that the noise degrades to zero fast enough.
Tyukin I., Tyukina T., van Helden D. P. et al., Information Sciences 2024 Vol. 678 Article 120856
AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...
Added: May 23, 2026
Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84
High-dimensional tabular data are common in biomedical and clinical research, yet conventional machine learning methods often struggle in such settings due to data scarcity, feature redundancy, and limited generalization. In this study, we systematically evaluate Synolitic Graph Neural Networks (SGNNs), a framework that transforms high-dimensional samples into sample-specific graphs by training ensembles of low-dimensional pairwise ...
Added: May 23, 2026
Kibkalo Vladislav, Chertopolokhov V., Mukhamedov A. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...
Added: May 22, 2026
Морозов С. В., Calcolo 2026 Vol. 63 No. 2 Article 23
The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...
Added: May 22, 2026
Loshkareva M. E., Matveeva N., Вестник Томского государственного университета. История 2026 № 100 С. 112–118
This research is an endeavor to apply social network analysis (SNA) to the study of a medieval narrative source. The authors suppose that the use of network analysis may offer new possibilities in the study of the history of regions characterized by some political fragmentation. Authors tried to construct networks of historical interactions from 1193 ...
Added: May 22, 2026
Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 P. 1–16
A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...
Added: May 21, 2026
Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 No. 106192
The Vickrey-Clarke-Groves (VCG) mechanism is one of the most compelling constructs in mechanism design, but the presence of complementary goods creates the possibility of non-core and even zero-revenue outcomes. In this article, we show that joint feasibility constraints on allocations offer a second pathway to ill-behaved outcomes in the VCG mechanism, even when all bidders ...
Added: May 20, 2026
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Rabat: Association for Computational Linguistics, 2026.
Added: May 19, 2026
Bezzubov S., Malikov D., Krasnov L. et al., Scientific data 2026 Vol. 13 Article 727
Solubility is a crucial property of organic compounds, impacting their potential applications in synthetic chemistry, materials science and drug design. Moreover, in technological processes mixtures of solvents are often utilized, making the solubility assessment more complicated. Predicting solubility values in mixtures of solvents from a molecular structure can help to address this issue, although a ...
Added: May 19, 2026
Pikalov V., Meshcheryakov V., Kondratev S. et al., Technologies 2026 Vol. 14 No. 1 P. 1–27
This paper presents Aerokinesis, an IoT-based software–hardware system for intuitive gesture-driven control of quadcopter unmanned aerial vehicles (UAVs), developed within the Robot Operating System 2 (ROS2) framework. The proposed system addresses the challenge of providing an accessible human–drone interaction interface for operators in scenarios where traditional remote controllers are impractical or unavailable. The architecture comprises ...
Added: May 19, 2026
Kondratev S., Yulia Dyrchenkova, Georgiy Nikitin et al., Technologies 2026 Vol. 14 No. 1 Article 69
This paper presents Aerokinesis, an IoT-based software–hardware system for intuitive gesture-driven control of quadcopter unmanned aerial vehicles (UAVs), developed within the Robot Operating System 2 (ROS2) framework. The proposed system addresses the challenge of providing an accessible human–drone interaction interface for operators in scenarios where traditional remote controllers are impractical or unavailable. The architecture comprises ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Springer, 2025.
This book constitutes the refereed proceedings of the 19th International Conference on Parallel Computational Technologies, PCT 2025, held in Moscow, Russia, during April 8–10, 2025.
The 31 full papers included in this volume were carefully reviewed and selected from 122 submissions. These papers were organized under the following topical sections: High Performance Architectures, Tools and Technologies; ...
Added: May 18, 2026
Ronglin Z., Wei L., Jiahong C. et al., Journal of Signal Processing Systems 2026 Vol. 98 P. 1–15
To address the need for lightweight and low-latency protection in massive resource-constrained 5G Internet of Things (IoT) systems, this paper proposes Key-Controlled Modulation Hopping and Constellation Rotation (KMHCR). KMHCR is designed as a physical-layer confidentiality-enhancement mechanism that avoids bit-wise full-payload encryption in the protection pipeline. It uses a shared key derived from channel-reciprocity secret key ...
Added: May 16, 2026
Suvorov N. M., Proceedings of the Institute for System Programming of the RAS 2026 Vol. 38 No. 3(2) P. 49–66
Data Petri Nets (DPNs) extend classical Petri nets to model processes where data directly influences control-flow, enabling a comprehensive view of system behavior and possibility to detect failure points that could otherwise be hidden. Soundness is a correctness criterion that captures such failure points as deadlocks and livelocks as well as model boundedness and absence ...
Added: May 16, 2026
Kachan O., Yanovich Y., Abramov E., Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 2018 Vol. 160 No. 2 P. 300–308
According to the manifold hypothesis, high-dimensional data can be viewed and meaning- fully represented as a lower-dimensional manifold embedded in a higher dimensional feature space. Manifold learning is a part of machine learning where an intrinsic data representation is uncovered based on the manifold hypothesis.
Many manifold learning algorithms were developed. The one called Grassmann&Stiefel eigenmaps ...
Added: January 21, 2026
Nikita Puchkin, Vladimir Spokoiny, Eugene Stepanov et al., ESAIM - Control, Optimisation and Calculus of Variations 2024 Vol. 30 Article 3
We consider the problem of reconstructing an embedding of a compact connected Riemannian manifold in a Euclidean space up to an almost isometry, given the information on intrinsic distances between points from its “sufficiently large” subset. This is one of the classical manifold learning problems. It happens that the most popular methods to deal with ...
Added: February 2, 2024
Puchkin N., Zhivotovskiy N., , in: Proceedings of Machine Learning Research: Volume 195: The Thirty Sixth Annual Conference on Learning Theory, 12-15 July 2023, Bangalore, IndiaVol. 195: The Thirty Sixth Annual Conference on Learning Theory, 12-15 July 2023, Bangalore, India.: PMLR, 2023. P. 1993–2013.
We consider the standard problem of stochastic convex optimization with exp-concave losses using Empirical Risk Minimization in a convex class. Answering a question raised in several prior works, we provide a 𝑂(𝑑/𝑛 + 1/𝑛 log(1/𝛿)) excess risk bound valid for a wide class of bounded exp-concave losses, where 𝑑 is the dimension of the convex reference set, 𝑛 is the sample ...
Added: August 2, 2023
Alanov A., Kochurov M., Volkhonskiy D. et al., , in: Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISAPP 2020)Vol. 4.: SciTePress, 2020. P. 214–221.
We propose a novel multi-texture synthesis model based on generative adversarial networks (GANs) with a user-controllable mechanism. The user control ability allows to explicitly specify the texture which should be generated by the model. This property follows from using an encoder part which learns a latent representation for each texture from the dataset. To ensure ...
Added: November 8, 2020
Kachan O. N., Yanovich Y., Abramov E., Ученые записки Казанского университета. Серия: Физико-математические науки 2018 Vol. 160 No. 2 P. 300–308
According to the manifold hypothesis, high-dimensional data can be viewed and meaningfully represented as a lower-dimensional manifold embedded in a higher dimensional feature space. Manifold learning is a part of machine learning where an intrinsic data representation is uncovered based on the manifold hypothesis.
Many manifold learning algorithms were developed. The one called Grassmann & Stiefel eigenmaps (GSE) ...
Added: October 29, 2020
Abramov E., Yanovich Y., Ученые записки Казанского университета. Серия: Физико-математические науки 2018 Vol. 160 No. 2 P. 220–228
Real data are usually characterized by high dimensionality. However, real data obtained from real sources, due to the presence of various dependencies between data points and limitations on their possible values, form, as a rule, form a small part of the high-dimensional space of observations. The most common model is based on the hypothesis that ...
Added: October 29, 2020
Kuleshov A. P., Bernstein A. V., Yanovich Y., Ученые записки Казанского университета. Серия: Физико-математические науки 2018 Vol. 160 No. 2 P. 327–338
The problem of unknown high-dimensional density estimation has been considered. It has been suggested that the support of its measure is a low-dimensional data manifold. This problem arises in many data mining tasks. The paper proposes a new geometrically motivated solution to the problem in the framework of manifold learning, including estimation of an unknown ...
Added: October 28, 2020