Университет Лобачевского

Alexander N. Gorban

The DAMDID–2026 conference is dedicated to the memory of our colleague, friend, and teacher, Alexander Nikolaevich Gorban (1952–2025), who passed away unexpectedly on September 21, 2025.

Doctor of Physical and Mathematical Sciences, Professor at Central University, Leading Researcher at AIRI and Lobachevsky University. An expert in interdisciplinary research and one of the world’s leading scientists. He has worked at universities in the Russia, US, UK, Switzerland, and France.

In 1967, Alexander N. Gorban entered the Physics Department at Novosibirsk State University. He decided to pursue a different education and graduated from the Mathematics Department of Omsk State Pedagogical Institute in 1973. He also received his Doctor of Physical and Mathematical Sciences (Biophysics) degree from there in 1990, and then the title of Professor in Mathematical Modeling, Numerical Methods, and Software Systems in 1993. He has published over 20 books and 250 articles in scientific journals. He has over 30 students with PhDs, seven of whom are Doctors of Science and Professors.

He has worked at nearly all the world’s leading mathematical centers, each leading its own research program:

  • Kleey Mathematical Institute, Cambridge, USA
  • Isaac Newton Mathematical Institute, Cambridge
  • Institute for Higher Scientific Studies (IHES), UK
  • Bures-sur-Yvette near Paris
  • Courant Mathematical Institute, New York

The professor has also worked at other institutions, including ETH Zurich, the University of Leicester, and King’s College London.

Memberships in Scientific Societies and Honorary Titles

  • Board Member of the International Neural Network Society (INNS)
  • Member of the Society for Industrial and Applied Mathematics (SIAM)
  • Member of the London Mathematical Society (LMS)
  • Member of the Higher Education Academy (HEA)
  • Member of the Sber Scientific Prize Selection Committee
  • Board Member of the Russian Association of Neuroinformatics
  • Honorary Doctor of Lobachevsky University
  • Ivan Prigogine Medal for Work on Nonequilibrium Thermodynamics

Key scientific achievements

Corrector of AI Errors and Vulnerabilities

The problem of AI errors is becoming increasingly pressing. Errors inevitably accompany AI, but completely retraining large systems to correct each error is virtually impossible. Therefore, a probabilistic framework for rapid and non-destructive error correction in AI systems was developed.

The proposed new theorems provide tools for rapid, non-iterative error correction in existing systems. Together with I. Yu. Tyukin, approaches effective for high-dimensional problems were developed, enabling the correction of multivariate systems in a multivariate environment.

Research has shown that the maintainability of AI is often linked to its vulnerability to malicious attacks. New types of attacks have been developed and analyzed that allow attackers to control the decisions of general-purpose AI systems, including deep learning neural networks. Simultaneously, work is underway on strategies that minimize the risk of exploiting such vulnerabilities.

Some of these results were presented by A. N. Gorban in an invited plenary talk at the IEEE World Congress on Computational Intelligence (Glasgow, 2020). Patents have been obtained, so the work is actively developing, including expanding the scope of application and creating reliable and robust AI. Particular attention is paid to the development of multi-agent systems with heterogeneous agent populations. Artificial Intelligence Error and Vulnerability Corrector

Training neural networks

Between 1987 and 1999, a system of methods was developed for accelerated training of neural networks and extracting explicit knowledge from data. Software implementing these methods found widespread use in Russia, particularly in the field of medical neuroinformatics.

In collaboration with D. A. Rossiev (later a Doctor of Medical Sciences and Vice-Rector of the Krasnoyarsk Medical University) and a team of physicians, systems were created to address key problems:

  • assessing the risk of complications after myocardial infarction;
  • differential diagnosis of acute abdomen syndrome;
  • selecting a treatment strategy for patients with thromboangiitis obliterans;
  • predicting pregnancy and childbirth complications.

These developments were also applied to the creation of security systems, demonstrating the versatility of the approaches. The results of the work were published in a number of books and articles and were supported by grants from federal target programs and the Ministry of Science and Technology. For this cycle of research, the Russian Association of Neuroinformatics, together with the organizing committee of the 19th annual international conference “Neuroinformatics-1999-2017”, awarded A. N. Gorban the honorary title “Pioneer of Russian Neuroinformatics”.

  • Gorban A. N., Mirkes E. M. & Tyukin I. Y. (2019) How deep should be the depth of convolutional neural networks: a backyard dog case study. Cognitive Computation
  • Горбань А. Н. и Росиев Д. А. (1996) Нейронные сети на персональном компьютере. Новосибирск: Наука
  • Горбань А. Н. (1990) Обучение нейронных сетей. СССР-США СП «Параграф»

Hilbert’s Sixth Problem and Slow Manifolds

Hilbert’s famous sixth problem, related to the limit transition from kinetics to continuum mechanics, has been solved in a narrow sense. This problem was investigated in a series of papers from 1989 to 2014, carried out jointly with his student I.V. Karlin (now a professor at ETH Zurich). These studies demonstrated that such a limit transition is not always possible.

A review of the results was published by special request in the journal where Hilbert’s problems were originally presented:

  • A. N. Gorban, I. Karlin (2014) Hilbert’s 6th Problem: Exact and Approximate Hydrodynamic Manifolds for Kinetic Equations, Bulletin of the American Mathematical Society, 51(2), 186–246

These papers have received recognition in the scientific community. Their description for a general audience has appeared in various publications, including the popular journal Quanta Magazine:
Wolchover N. (2015) Famous fluid equations are incomplete: a 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer. Quanta Magazine.

In the process of solving Hilbert’s sixth problem, a system of methods for solving multidimensional problems of nonequilibrium kinetics and thermodynamics was developed. Research in this area continues. One goal is to move toward a broader understanding of Hilbert’s sixth problem. This includes exploring the possibilities of creating provable models in physics and applying artificial intelligence methods to search for such models.

  • Gorban A. N. (2019) Hilbert’s sixth problem: the path to mathematical rigor in science. London Mathematical Society’s Newsletter, 481, 16-20
  • Gorban A. N., Karlin I. (2014) Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations, Bulletin of the American Mathematical Society 51 (2), 186-246
  • Gorban A. N., Karlin I. V. (1994) Method of invariant manifolds and regularization of acoustic spectrum. Transport Theory and Stat. Phys., 23, 559-632

Theory of Slow Transient Processes in Dynamic Systems and Its Applications to Chemical and Physical Kinetics

From 1978 to 2005, a systematic analysis of transient singularities in dynamic systems was conducted, taking into account their dependence on parameters. This research examined general dynamic systems, including relaxation time features as functions of initial conditions and parameters.

A classification of bifurcations (explosions) of limit sets was developed, and the relationship between these bifurcations and relaxation time features was studied. The resulting theory responded to the challenges associated with observed slow transient processes in heterogeneous catalytic reactions and was subsequently applied to various subject areas, such as physics, ecology, and physiology.

One of the most recent applications of these developments has been the theory of cellular intelligence, demonstrating the versatility and broad potential of this approach.

  • Gorban A. N. (2004) Singularities of transition processes in dynamical systems: qualitative theory of critical delays. Electron. J. Diff. Eqns., Monograph No. 05 (55 pages)
  • Gorban A. N., Cherezis V. M. (1981) Slow relaxations of dynamical systems and bifurcations of ω-limit sets. Doklad A N SSSR, 261 (5), 1050–1054

Dynamics of the Correlation Graph under Stress and Adaptation

Based on long-term observations and comparative analysis of populations and groups living in the Far North and mid-latitudes of Siberia, a group of students from Krasnoyarsk and I reached an important conclusion. Correlations between physiological parameters provide the most information about the degree of a population’s adaptation to extreme or changing conditions.

The research developed a hierarchy of stress indicators and dynamic models of adaptation. These models allow us to predict phenomena such as fluctuating mortality and fluctuating remission.

A review of the results of the work from 1987 to 2020 was published in Physics of Life Review (Volume 37, July 2021, Pages 17-64), one of the world’s most cited journals in the field of biophysics. The review was co-authored by a group of students. Volumes 37 and 38 of the same journal published extensive discussions of these results by leading global experts.

  • Gorban N., Tyukina T. A., Pokidysheva L. I. & Smirnova E. V. (2021) Dynamic and thermodynamic models of adaptation. Physics of Life Reviews, 37, 17-64
  • Gorban A. N., Pokidysheva L. I., Smirnova E. V. & Tyukina T. A. (2011) Law of the minimum paradoxes. Bulletin of Mathematical Biology, 73 (9), 2013-2044
  • Sedov K. R., Gorban A. N., Petushkova E. V., Manchuk V. T. & Shalamova E. N. (1988) Correlation adaptometry as a method of population clinical examination, Bulletin of the USSR Academy of Medical Sciences. No. 10, 69-75

Topological Grammars, Principal Manifolds, and Graphs for Complex Data Analysis

From 2003 to 2023, constructive methods using elastic principal manifolds and graphs were developed for exploratory analysis of multivariate data. This work was completed jointly with my student, A. Yu. Zinoviev, who currently holds an interdisciplinary chair at the Paris Institute for Artificial Intelligence and leads the Cancer Systems Biology Group at the Institut Curie (Paris).

Data approximation methods using principal graphs, based on innovative topological grammar technology, have proven particularly effective in processing modern single-cell data (single-cell omics). In collaboration with the Institut Curie, Harvard University, Harvard Medical School, MIT, and other partners, software was developed that is actively used by research groups to analyze such data.

One of the key applications of this work was a semi-supervised dynamic phenotyping methodology for large clinical datasets. This approach enables the construction of patient development trajectories (pathological scenarios) with a qualitative assessment of prognostic uncertainty.

  • Chen H., Albergante L., Hsu J. Y., Lareau C. A., Bosco G. Lo., Guan J., Zhou S., Gorban A. N., Bauer D. E., Aryee M. J., Langenau D. M., Zinovyev A., Buenrostro J. D., Yuan G. C. & Pinello L. (2019) Single-cell trajectories reconstruction exploration and mapping of omics data with STREAM. Nat Commun., 10, 1903
  • Gorban A. N. & Zinovyev A. (2019) Principal manifolds and graphs in practice: from molecular biology to dynamical systems. International Journal of Neural Systems
  • Gorban A. N., Sumner N. R. & Zinovyev A. Y. (2007) Topological grammars for data approximation. Applied Mathematics Letters, 20(4), 382-386

A New Neuromorphic Computational Model of Short-Term Memory Based on the Situation in Neuronal-Astrocyte Networks

From 2018 to 2023, the following tasks were completed:

Neural Mechanisms of Working Memory

  • Approaches to retaining a relatively small number of entities (“patterns”) in working memory were developed
  • Methods for managing working memory content were studied
  • The organization of such processes in neuronal-astrocytic networks was proposed

Network Functions of Large Cells—Astrocytes

  • The mechanisms of “calcium events,” in which large astrocytes release calcium, stimulating interneuronal connections, were deciphered
  • The functional roles of these events in network interactions were established

Co-author of these works, Susanna Gordleeva, was awarded the Russian Presidential Prize in Science and Innovation for Young Scientists in 2023.

  • Gordleeva S., Tsybina Y. A., Krivonosov M. I., Tyukin I. Y., Kazantsev V. B., Zaikin A. A. & Gorban A. N. (2023) Situation-based neuromorphic memory in spiking neuron-astrocyte network. IEEE Transactions on Neural Networks and Learning Systems
  • Tsybina Y., Kastalskiy I., Krivonosov M., Zaikin A., Kazantsev V., Gorban A. & Gordleeva S. (2022) Astrocytes mediate analogous memory in a multi-layer neuron-astrocytic network. Neural Comput & Applic.
  • Gordleeva S. Y., Tsybina Y. A., Krivonosov M. I., Ivanchenko M. V., Zaikin A. A., Kazantsev V. B. & Gorban A. N. (2021) Modeling working memory in spiking neuron network accompanied by astrocytes. Frontiers in Cellular Neuroscience, 15, 86