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Invited researcher Gorban Alexander Nikolaevich
Contract number
Time span of the project

As of 15.02.2021

Number of staff members
scientific publications
Objects of intellectual property
General information

Name of the project: Scalable networks of AI systems for analysis of data of increasing dimensionality

Strategy for Scientific and Technological Development Priority Level: а, в

Goals and objectives

Research directions: Computer and information sciences

Project objective: Developing prospective methods of intellectual high dimensional data analysis optimized for working with high dimensional (tens and hundreds) to very high dimensional (thousands, tens of thousands) dimensions

The practical value of the study

A mathematical theory of high-dimensional data analysis methods based on geometric functional analysis is developed. The problem of errors in artificial intelligence (AI) systems and their rapid correction was analysed. A methodology for correcting of high-dimensional AI systems has been elaborated, based on new results in geometric functional analysis and stochastic separability theory developed in the course of the project. The phenomenon of stochastic separability in high-dimensional spaces has been identified and used in machine learning to correct AI system errors and analyze AI instabilities. Various corrector schemes have been invented and their effectiveness on benchmarks and real-world problems has been demonstrated.

The idea of a competitive game with an AI supervisor, combined with a new theory of stochastic separability and technology of correctors, allowed us to analyze two classes of malicious actions in relation to universal AI systems. The first class of attacks consists in small adversarial perturbations of the input data, which lead to errors. The second class, described for the first time and called stealth attacks, involves small perturbations of the AI system itself. Here, the perturbed system produces any result desired by the attacker on a certain small “trigger” data set, but works as usual on a large test set that is unknown to the attacker. In the case of a stealth attack, the dimension of the AI's decision space is a major factor in the AI's vulnerability. Conditions that generate vulnerabilities to attacks are found and ways to avoid attacks are formulated.

51 papers were published in scientific publications indexed in the Web of Science database, Core collection, including 20 paper in scientific publications included in the first quartile (Q1) of scientific journals in the Web of Science database, Science Citation Index, seven patent applications were filled.

Implemented results of research:

New effective algorithms for geometric data analysis have been developed and implemented. The software is used for processing transcriptomics data of individual cells, biomedical and other data of complex structure. These algorithms and programs are now intensively used as the main core ElPiGraph (ELastic Principal Graph) of an integrated analytical tool for analyzing collections of data from various fields of knowledge, from biology, where it is used to analyze data of single cell transcriptomics and revealing of dynamic phenotypes of diseases, to astronomy, where it can be used to study complex structures in galaxies and their distributions. The software is in the public domain. The work is carried out within the framework of an international consortium, including the University. Lobachevsky (Nizhny Novgorod), Curie Institute (Paris), Harvard Medical School, Harvard University, Massachusetts Central Hospital and other Institutes of Russia, Europe, USA and China.

Education and career development:

  • Organization of scientific schools and conferences:

Seven scientific schools and conferences were organized, of which three sections within the framework of the international conference on neural networks IJCNN (2018 Brazil, 2019 Hungary, 2020 Great Britain), a section within the framework of the international conference Volga Neuroscince meeting (2018 Russia), a section within the framework of the All-Russian conferences Neuroinformatics (2019 Russia), international conference "Neural networks the day after tomorrow: problems and prospects" (2019 Russia) and a section within the XX international conference and youth school "Mathematical modeling and supercomputer technologies".

  • Master-classes and seminars for students, postgraduates and young scientists, provided by A. N. Gorban.

Under the leadership of A.N. Gorban a series of introductory seminars and master classes were held for the project participants, where the development of scientific research of the project participants were discussed, the plans of individual and group work were prepared and the results presented (the list of seminars is given on the website dalab.unn.ru).

  • A.N. Gorban actively participated in public events and expertise, in particular:
  1. Conducted a master class for young scientists - participants of the III International Conference "Science of the Future", Sochi on May 13 - 18, 2019 (together with Professor Oganov from Skoltech).
  2. Delivered a popular lecture on the project for a wide audience of students, graduate students and researchers at the IAP RAS. The lecture was devoted to the developments that are currently underway in the field of neural artificial intelligence, about the existing limitations and problems that can lead to a delay in the development of artificial intelligence applications.
  3. Conducted a course of lectures "Intelligent data processing" for senior students, graduate students and young scientists. As a result of the course, students received certificates and certificates of professional development. The course of lectures was recorded and posted on the youtube portal https://www.youtube.com/playlist?list=PLcDrEDOQaVTQBVXIkks0F_y5Oahn7Ia1o.
  4. Conducted public lectures for students (at UNN) and schoolchildren (Lyceum "Second School", Moscow). A.N. Gorban's lecture "The Artistic Intelligence of the Day After Tomorrow" was recorded and posted in the public domain: https://www.youtube.com/watch?v=YkP-lJlt2UM
  5. Delivered an invited lecture: “Front-line engineering problems with examples from the development of artificial intelligence” "at the conference “Modern education of engineers.” June 22-23, 2020, based on NTI SPbPU.https://www.youtube.com/watch?v=j9VVPHlyw0w&list=PLPKLknfMAcyvBD6ZjJ8yL01ImC2bODKjI&...
  6. Was an invited expert for discussions with members of the "Artificial Intelligence" group on the strategy for the development of LETI in this direction. May 28, 2020, on the basis of the Education Transformation Center of the Moscow School of Management SKOLKOVO.
  7. Gave an invited lecture: "Errors of AI and geometry of big data" at the world conference of Russian-speaking scientists, organized by RASA (RASA-America, Russian-American Science Association) from 5 to 6 December 2020 of the year. (https://www.youtube.com/watch?v=Ba7blrEhZD4&feature=youtu.be).
  8. Delivered an invited lecture: "Man and Artificial Intelligence - the Birth of a Centaur" on August 22, 2020 as part of the NTI month from the NTI Circle movement in the "Big Change" channel and preparation for the "Strong Ideas for a New Time" forum. (https://vk.com/video-193258751_456257154) More than 320 thousand views.
  9. Participated in the business program on the topic "Scenarios of modernization of vocational education of the region and WorldSkills practice" on December 3-5 in the framework of the VIII Regional WorldSkills championship "Young professionals" in the Krasnoyarsk region. Lecture: "New professions born of the development of artificial intelligence."
  10. Gave a plenary talk "Correction and vulnerability of data-driven AI and multidimensional geometry" at the 1st National Congress on Cognitive Research, Artificial Intelligence and Neuroinformatics, Russia October 10-16, 2020.

  • Organization of internships for students, graduate students and laboratory researchers in leading Russian and international scientific and educational centres in the direction of scientific research: Complutense University of Madrid (Spain, Madrid), University of Leicester (UK, Leicester),SPbSU (Russia, Saint Petersburg), German Center for Neurodegenerative Diseases (Germany, Magdeburg), Moscow State University, Skoltech (Russia, Moscow).

  • In the framework of the laboratory in the spring of 2020, two master projects were successfully finalised by members of the research team Alexandra Koneva ("Methods of preprocessing the electrocardiogram signal") and Sergey Alekseev ("Neural network method for detecting artifacts on electrocardiograms") in the MSc program in Applied mathematics and computer science.


Bioinformatics of Cancer department, Institut Curie, Paris (France), Department of Mathematics, University of Leicester, Leicester (UK), Molecular Pathology Unit & Cancer Center, Massachusetts General Hospital Research Institute and Harvard Medical School, Boston, MA, (USA), Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, MA (USA), Department of Computer Science and Technology, Tongji University, Shanghai 201804 (China), Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA (USA), Department of Mathematics and Computer Science, University of Palermo, Palermo (Italy), Department of Sciences for technological innovation, Euro-Mediterranean Institute of Science and Technology, Palermo (Italy), Shanghai Key Lab of Intelligent Information Processing, and School of Computer Science, Fudan University, Shanghai (China), Harvard Stem Cell Institute, Cambridge, MA (USA): joint research to create and develop a technology for processing biological data of a new type - a transcript of a large number of single cells.

German Center for Neurodegenerative Diseases (Germany), Complutense University of Madrid (Spain), Federal State Budgetary Educational Institution of Higher Education "St. Petersburg State University"(Russia), Skolkovo Institute of Science and Technology (Russia), Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences (Russia): joint research in the field of mathematical modeling and development of neural networks.

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B. Grechuk, A.N. Gorban, & I.Y.Tyukin
General stochastic separation theorems with optimal bounds. Neural Networks, 2021 (138).
A.N. Gorban, A. Golubkov, B. Grechuk, E.M. Mirkes, I.Y. Tyukin
Correction of AI systems by linear discriminants: Probabilistic foundations, Information Sciences, 2018 (466).
A. Naldi, C. Hernandez, N. Levy, G. Stoll, P.T. Monteiro, C. Chaouiya, T. Helikar, A. Zinovyev, L. Calzone, S. Cohen-Boulakia, D. Thieffry, L Paulevé.
The CoLoMoTo Interactive Notebook: Accessible and Reproducible Computational Analyses for Qualitative Biological Networks, Front. Physiol., June 2018 (9).
IY Tyukin, AN Gorban, S Green, D Prokhorov
Fast Construction of Correcting Ensembles for Legacy Artificial Intelligence Systems: Algorithms and a Case Study, Information Sciences, 2019 (485).
H Chen, L Albergante, JY Hsu, CA Lareau, GL Bosco, J Guan, S Zhou, AN Gorban, DE Bauer, MJ Aryee, DM Langenau, A Zinovyev, JD Buenrostro, G-C Yuan, L Pinello
Single-cell trajectories reconstruction, exploration and mapping of omics data with STREAM, Nature Communications, 2019 (10, 1).
AN Gorban, VA Makarov, IY Tyukin
The unreasonable effectiveness of small neural ensembles in high-dimensional brain, Physics of Life Reviews, 2019 (29).
A.N. Gorban, E. M. Mirkes, I.Y. Tyukin
(2020). How Deep Should be the Depth of Convolutional Neural Networks: a Backyard Dog Case Study. Cognitive Computation, 2020 (12),
EV Pankratova, AI Kalyakulina, SV Stasenko, SY Gordleeva, IA Lazarevich, VB Kazantsev
Neuronal synchronization enhanced by neuron–astrocyte interaction. Nonlinear Dynamics, 2019 (97).
S.E. Golovenkin, J. Bac, A. Chervov, E.M. Mirkes, Y.V. Orlova, E. Barillot, A.N. Gorban, A. Zinovyev
Trajectories, bifurcations and pseudotime in large clinical datasets: applications to myocardial infarction and diabetes data, GigaScience, 2020 (9,11).
A. N. Gorban, T. A. Tyukina, L. I. Pokidysheva, & E. V. Smirnova
Dynamic and thermodynamic models of adaptation. Physics of Life Reviews, 2021 (37).
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