sergueibarannikov

Serguei Barannikov

Leading Research Scientist
Research Center in Artificial Intelligence in the Direction of Optimization of Management Decisions to Reduce Carbon Footprint

Serguei Barannikov earned his Ph.D. from UC Berkeley and has made contributions to algebraic topology, algebraic geometry, mathematical physics, and machine learning. His work, prior to his Ph.D., introduced canonical forms of filtered complexes, now known as persistence barcodes, which have become fundamental in topological data analysis. More recently, he has applied topological methods to machine learning, particularly in the study of large language models, with results published in leading ML conferences: NeurIPS, ICML,  ICLR, effectively bridging pure mathematics and advanced AI research.

  1. N.Balabin, D.Voronkova, I.Trofimov, E.Burnaev, S.Barannikov, “Disentanglement Learning via Topology”, [ PDF: English, arXiv: 2308.12696], Proceedings of the 41st International Conference on Machine Learning, ICML 2024
  2. E.Tulchinskii, D.Voronkova, I.Trofimov, E.Burnaev, S.Barannikov, “RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks”,  [PDF: English, arXiv:2503.11910] the 28th International Conference on Artificial Intelligence and Statistics, AISTATS 2025
  3.  I.Trofimov, D.Voronkova, E.Tulchinskii, E.Burnaev, S.Barannikov, “Scalar Function Topology Divergence: Comparing Topology of 3D Objects”, [ PDF:English, arXiv:2407.08364] , European Conference on Computer Vision, ECCV 2024
  4. K.Kuznetsov, E.Tulchinskii, L.Kushnareva, G.Magai, S.Barannikov, S.Nikolenko, I.Piontkovskaya, “Robust AI-Generated Text Detection by Restricted Embeddings”,  [ PDF:English, arXiv:2410.08113]  EMNLP 2024
  5. L.Kushnareva, T.Gaintseva, G.Magai, D.Abulkhanov, K.Kuznetsov, E. Tulchinskii, S.Nikolenko, S.Barannikov, I.Piontkovskaya,  [ PDF: English, arXiv:2311.08349] “Artificial Text Boundary Detection with Topological Data Analysis and Sliding Window Techniques”, Conference on Language Modeling, outstanding paper award, COLM 2024
  6. E. Tulchinskii, K. Kuznetsov, L. Kushnareva, D. Cherniavskii, S. Nikolenko, E. Burnaev, S. Barannikov, I. Piontkovskaya, “Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts” [ PDF: English, arXiv: 2306.04723], Advances in Neural Information Processing Systems 36, NeurIPS 2023
  7. I. Trofimov, D. Cherniavskii, E. Tulchinskii, N. Balabin, E. Burnaev, S. Barannikov, “Learning Topology-Preserving Data Representations” [ PDF: English, arXiv: 2302.00136], 11th International Conference on Learning Representations, ICLR 2023
  8. E. Tulchinskii, K. Kuznetsov, L. Kushnareva, D. Cherniavskii, S. Barannikov, I. Piontkovskaya, S. Nikolenko, E. Burnaev, “Topological Data Analysis for Speech Processing”, doi.org/10.21437/Interspeech.2023-1861 [ PDF: English, arXiv: 2211.17223],  Proceedings  of the 24th Conference of the International Speech Communication Association, 311-315,  INTERSPEECH 2023
  9. S. Barannikov, A. Korotin, D. Oganesyan, D. Emtsev, E. Burnaev, “Barcodes as summary of loss function’s topology”, [ PDF: English, arXiv: 1912.00043], Doklady Mathematics, vol 108  (5), 2023
  10. D.Voronkova, S.Barannikov, E.Burnaev, “One-dimensional Topological Invariants to Estimate Loss Surface Non-Convexity”, Doklady Mathematics, vol 108 (5), 2023
  11. D. Cherniavskii, E. Tulchinskii, V. Mikhailov, I. Proskurina, L. Kushnareva, E. Artemova, S. Barannikov, I. Piontkovskaya, D. Piontkovski, E. Burnaev, “Acceptability Judgements via Examining the Topology of Attention Maps”,  doi.org/10.18653/v1/2022.findings-emnlp.7 [ PDF: English, arXiv: 2205.096303], Findings of the Association for Computational Linguistics: EMNLP 2022, 88-107
  12. S. Barannikov, I. Trofimov, N. Balabin, E. Burnaev, “Representation Topology Divergence: A Method for Comparing Neural Network Representations” [ PDF: English, arXiv: 2201.00058] 39th International Conference on Machine Learning, Proceedings of Machine Learning Research, 162, 1607-1626, ICML 2022
  13. S Barannikov, I Trofimov, E Trimbach, J Wang, E Burnaev, “Homological assessment of data representations”,
    14th International Conference on Machine Vision (ICMV 2021), Proceedings of SPIE, the International Society for Optical Engineering, 2022, vol 12084, 86-90
  14. L. Kushnareva, D. Cherniavskii, V. Mikhailov, E. Artemova, S. Barannikov, A. Bernstein, I. Piontkovskaya, D. Piontkovski, E. Burnaev, “Artificial Text Detection via Examining the Topology of Attention Maps”, Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, 635-649, doi.org/10.18653/v1/2021.emnlp-main.50 [ PDF: English, arXiv: 2109.04825], EMNLP 2021
  15. S. Barannikov, I. Trofimov, G. Sotnikov, E. Trimbach, A. Korotin, A. Filippov, E. Burnaev, “Manifold Topology Divergence: a Framework for Comparing Data Manifolds” [ PDF: English, arXiv: 2106.04024],  Advances in Neural Information Processing Systems 34, 7294-7305, NeurIPS 2021
  16. S. Barannikov, D. Voronkova, I. Trofimov, A. Korotin, G. Sotnikov, E. Burnaev, “Topological obstructions in neural networks learning” [ PDF: English, arXiv: 2012.15834]
  17. S. Barannikov, “Supersymmetry and cohomology of graph complexes”, Lett Math Phys 109, 699–724 (2019) doi.org/10.1007/s11005-018-1123-7 [ PDF: English, arXiv: 1803.11549]
  18. S. Barannikov, “EA-Matrix integrals of associative algebras and equivariant localization”, Arnold Math J. 5, 97–104 (2019) doi.org/10.1007/s40598-019-00111-0 [ PDF: English, arXiv: 1710.08499]
  19. S. Barannikov, “Matrix De Rham Complex and Quantum A-infinity algebras”, Lett Math Phys 104, 373–395 (2014), doi.org/10.1007/s11005-013-0677-7 [ PDF: English, arXiv: 1001.5264]
  20. S. Barannikov, “Solving the noncommutative Batalin–Vilkovisky equation”, Lett Math Phys 103, 605–628 (2013) doi.org/10.1007/s11005-013-0615-8
  21. S Barannikov, “Noncommutative Batalin–Vilkovisky geometry and matrix integrals”, Comptes Rendus Mathematique, v.348(7–8), 2010, 359-362, doi.org/10.1016/j.crma.2010.02.002 [ PDF: English, arXiv: 0912.5484]
  22. S. Barannikov, “Modular operads and Batalin-Vilkovisky geometry”, International Mathematics Research Notices, v.2007, 2007, rnm075, https://doi.org/10.1093/imrn/rnm075 [ PDF: English, arXiv: 1710.08442]
  23. S. Barannikov, “Semi-infinite variations of Hodge structures and integrable hierarchies of KdV type”, International Mathematics Research Notices, v.2002(19) 2002, 973–990, doi.org/10.1155/S1073792802108129 [ PDF: English, arXiv: math/0108148]
  24. S. Barannikov, “Non-Commutative Periods and Mirror Symmetry in Higher Dimensions”, Commun. Math. Phys. 228, 281–325 (2002) https://doi.org/10.1007/s002200200656
  25. S. Barannikov, “Quantum periods, I: Semi-infinite variations of Hodge structures”, Intern. Math. Research Notices 2001 (23), 1243-1264,  doi.org/10.1155/S1073792801000599 [ PDF: English, arXiv: math/0006193]
  26. S. Barannikov, “Semi-infinite Hodge structures and mirror symmetry for projective spaces”, [ PDF: English, arXiv: math/0010157]
  27. S. Barannikov, “Extended moduli spaces and mirror symmetry in dimensions n> 3″, PhD Thesis. Univ. of California, Berkeley, 47p. 1999
  28. S. Barannikov, M. Kontsevich, “Frobenius manifolds and formality of Lie algebras of polyvector fields”, Int. Math. Research Notices, v.1998 (4), 1998, 201–215, doi.org/10.1155/S1073792898000166 [PDF: English, arXiv: alg-geom/9710032]
  29. S. Barannikov, “The framed Morse complex and its invariants”, Advances in Soviet Mathematics, 1994, Singularities and Bifurcations, 21, pp.93-116, doi.org/10.1090/advsov/021/03
  30. S. Barannikov, “The Complements of Resultant and Discriminant Sets in C^n Are M-Manifolds”, Funct Analysis and Its Appl 27 (3), 1-4 (1993) doi.org/10.1007/BF01087532
  31. S. Barannikov, “On the space of real polynomials without multiple critical values”, Funct Analysis and Its Appl 26, 84–90 (1992) doi.org/10.1007/BF01075267

Ph.D. in Mathematics, University of California – Berkeley.