Сергей Баранников

ведущий научный сотрудник / Сколковский институт науки и технологий

Профессиональные интересы
машинное обучение, алгебраическая топология, алгебраическая геометрия, математическая физика

Образование, учёные степени
1994 / Московский государственный университет / механико-математический факультет / специальность “математика”
1999 / Ph.D. по математике / Калифорнийский университет в Беркли / тема диссертации “Расширенные пространства модулей и зеркальная симметрия в измерениях n> 3″ / “Extended moduli spaces and mirror symmetry in dimensions n> 3″

Публикации

  1. E. Tulchinskii, K. Kuznetsov, L. Kushnareva, D. Cherniavskii, S. Barannikov, I. Piontkovskaya, S. Nikolenko, E. Burnaev, “Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts” [ PDF: English, arXiv: 2306.04723]
  2. 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)
  3. E. Tulchinskii, K. Kuznetsov, L. Kushnareva, D. Cherniavskii, S. Barannikov, I. Piontkovskaya, S. Nikolenko, E. Burnaev, “Topological Data Analysis for Speech Processing” [ PDF: English, arXiv: 2211.17223],  INTERSPEECH 2023
  4. 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” [ PDF: English, arXiv: 2205.096303], Findings of the Association for Computational Linguistics: EMNLP 2022
  5. 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)
  6. 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’21)
  7. 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)
  8. S. Barannikov, D. Voronkova, I. Trofimov, A. Korotin, G. Sotnikov, E. Burnaev, “Topological obstructions in neural networks learning” [ PDF: English, arXiv: 2012.15834]
  9. S. Barannikov, A. Korotin, D. Oganesyan, D. Emtsev, E. Burnaev, “Barcodes as summary of objective function’s topology” [ PDF: English, arXiv: 1912.00043]
  10. 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]
  11. 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]
  12. 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]
  13. S. Barannikov, “Solving the noncommutative Batalin–Vilkovisky equation”, Lett Math Phys 103, 605–628 (2013) doi.org/10.1007/s11005-013-0615-8
  14. 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]
  15. 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]
  16. 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]
  17. S. Barannikov, “Non-Commutative Periods and Mirror Symmetry in Higher Dimensions”, Commun. Math. Phys. 228, 281–325 (2002) https://doi.org/10.1007/s002200200656
  18. 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]
  19. S. Barannikov, “Semi-infinite Hodge structures and mirror symmetry for projective spaces”, [ PDF: English, arXiv: math/0010157]
  20. S. Barannikov, “Generalized periods and mirror symmetry in dimensions n> 3″, [ PDF: English, arXiv: math/9903124]
  21. 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]
  22. S. Barannikov, “Extended moduli spaces and mirror symmetry in dimensions n> 3″, PhD Thesis. Univ. of California, Berkeley, 47p. 1998
  23. 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
  24. 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
  25. 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