Geodesic
Machine learning of the well-known things
Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 3, pp. 517-528
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Machine learning (ML) in its current form implies that the answer to any problem can be well approximated by a function of a very peculiar form: a specially adjusted iteration of Heaviside theta-functions. It is natural to ask whether the answers to questions that we already know can be naturally represented in this form. We provide elementary and yet nonevident examples showing that this is indeed possible, and suggest to look for a systematic reformulation of existing knowledge in an ML-consistent way. The success or failure of these attempts can shed light on a variety of problems, both scientific and epistemological.
Keywords: exact approaches to QFT, nonlinear algebra, machine learning, steepest descent method. 
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V. V. Dolotin; A. Yu. Morozov; A. V. Popolitov. Machine learning of the well-known things. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 3, pp. 517-528. http://geodesic.mathdoc.fr/item/TMF_2023_214_3_a8/

[1] D. Guest, K. Cranmer, D. Whiteson, “Deep learning and its application to lhc physics”, Ann. Rev. Nucl. Part. Sci., 68 (2018), 161–181 | DOI

[2] J. Craven, M. Hughes, V. Jejjala, A. Kar, Illuminating new and known relations between knot invariants, arXiv: 2211.01404

[3] J. Craven, M. Hughes, V. Jejjala, A. Kar, Learning knot invariants across dimensions, arXiv: 2112.00016 | DOI

[4] E. Lanina, A. Morozov, “Defect and degree of the Alexander polynomial”, Eur. Phys. J. C, 82:11 (2022), 1022, 16 pp. | DOI

[5] E. Lanina, A. Sleptsov, N. Tselousov, “Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure”, Nucl. Phys. B, 974 (2022), 115644, 30 pp. | DOI | MR

[6] V. Mishnyakov, A. Sleptsov, N. Tselousov, “A novel symmetry of colored HOMFLY Polynomials Coming from $\mathfrak{sl}(N|M)$ Superalgebras”, Comm. Math. Phys., 384:2 (2021), 955–969 | DOI | MR

[7] S. Chen, O. Savchuk, S. Zheng, B. Chen, H. Stoecker, L. Wang, K. Zhou, Fourier-flow model generating Feynman paths, arXiv: 2211.03470

[8] K. Hornik, M. Stinchcombe, H. White, “Multilayer feedforward networks are universal approximators”, Neural Networks, 2:5 (1989), 359–366 | DOI

[9] I. M. Gel'fand, M. M. Kapranov, A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston, MA, 1994 | DOI | MR

[10] V. Dolotin, A. Morozov, Introduction to Non-Linear Algebra, World Sci., Sungapore, 2007, arXiv: hep-th/0609022 | DOI | MR

[11] Y. LeCun, Y. Bengio, G. Hinton, “Deep learning”, Nature, 521:7553 (2015), 436–444 | DOI

[12] A. Grothendieck, “Sketch of a programme”, Geometric Galois Actions. I. Around Grothendieck's Esquisse d'un Programme, Proceedings of the Conference on Geometry and Arithmetic of Moduli Spaces (Luminy, France, August, 1995), London Mathematical Society Lecture Note Series, 242, eds. L. Schneps, P. Lochak, Cambridge Univ. Press, Cambridge, 1997, 243–283 | MR | Zbl

[13] R. P. Langlands, “Problems in the theory of automorphic forms to Salomon Bochner in gratitude. Modern Harmonic Analysis and Applications”, Lectures in Modern Analysis and Applications III, Lecture Notes in Mathematics, 170, ed. T. C. Taam, Springer, Berlin, Heidelberg, 2006, 18–61 | DOI | MR

[14] M. B. Green, J. H. Schwarz, E. Witten, Superstring Theory, v. 1–3, Cambridge Univ. Press, Cambridge, 2012 | MR

[15] A. Yu. Morozov, “Teoriya strun – chto eto takoe?”, UFN, 162:8 (1992), 83–175 | DOI | DOI

[16] G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, L. Zdeborova, “Machine learning and the physical sciences”, Rev. Modern Phys., 91:4 (2019), 045002, 39 pp., arXiv: 1903.10563 | DOI

[17] H. Erbin, R. Finotello, “Machine learning for complete intersection Calabi–Yau manifolds: a methodological study”, Phys. Rev. D, 103:12 (2021), 126014, 40 pp., arXiv: 2007.15706 | DOI | MR

[18] H. Chen, Y. He, S. Lal, S. Majumder, “Machine learning Lie structures applications to physics”, Phys. Lett. B, 817 (2021), 136297, 5 pp., arXiv: 2011.00871 | MR

[19] Y.-H. He, K.-H. Lee, T. Oliver, A. Pozdnyakov, Murmurations of elliptic curves, arXiv: 2204.10140

[20] J. Bao, Y.-H. He, E. Heyes, E. Hirst, Machine learning algebraic geometry for physics, arXiv: 2204.10334

[21] A. Levin, A. Morozov, “On the foundations of the random lattices approach to quantum gravity”, Phys. Lett. B, 243:3 (1990), 207–214 | DOI | MR

[22] V. Dolotin, A. Morozov, Algebraic geometry of discrete dynamics. The case of one variable, arXiv: ; “Introduction to Khovanov homologies. III. A new and simple tensor-algebra construction of Khovanov–Rozansky invariants”, Nucl. Phys. B, 878 (2014), 12–81, arXiv: hep-th/05012351308.5759 | DOI | MR

[23] A. Yu. Morozov, Sh. R. Shakirov, “Novye i starye rezultaty v teorii rezultantov”, TMF, 163:2 (2010), 222–257, arXiv: 0911.5278 | DOI | DOI

[24] A. Mironov, A. Morozov, Sh. Shakirov, A. Sleptsov, “Interplay between MacDonald and Hall–Littlewood expansions of extended torus superpolynomials”, JHEP, 05 (2012), 070, 11 pp., arXiv: 1201.3339 | DOI | MR

[25] and references therein http://wwwth.itep.ru/knotebook/

[26] A. Mironov, A. Morozov, An. Morozov, A. Sleptsov, “Gaussian distribution of LMOV numbers”, Nucl. Phys. B, 924 (2017), 1–32, arXiv: 1706.00761 | DOI | MR

[27] A. Anokhina, A. Morozov, A. Popolitov, “Nimble evolution for pretzel Khovanov polynomials”, Eur. Phys. J. C, 79 (2019), 867, 18 pp., arXiv: ; “Khovanov polynomials for satellites and asymptotic adjoint polynomials”, Internat. J. Modern Phys. A, 36:34–35 (2021), 2150243, 24 pp., arXiv: 1904.102772104.14491 | DOI | DOI

[28] A. Anokhina, Talk at StringMath-2019 https://www.stringmath2019.se/wp-content/uploads/sites/39/2019/07/Gong_Show_StringMath2019.pdf

[29] A. Mironov, A. Morozov, “Superintegrability summary”, Phys. Lett. B, 835 (2022), 137573, 10 pp., arXiv: 2201.12917 | DOI | MR