(48-4) 17 * << * >> * Russian * English * Content * All Issues

Multigrammatical modelling of neural networks
I.A. Sheremet 1

1 Geophysical Center of Russian Academy of Sciences,
119296, Russia, Moscow, Molodezhnaya St. 3

 PDF, 925 kB

DOI: 10.18287/2412-6179-CO-1436

Pages: 619-632.

Full text of article: English language.

Abstract:
This paper is dedicated to the proposed techniques of modelling artificial neural networks (NNs) by application of the multigrammatical framework. Multigrammatical representations of feed-forward and recurrent NNs are described. Application of multiset metagrammars to modelling deep learning of NNs of the aforementioned classes is considered. Possible developments of the announced approach are discussed.

Keywords:
neural networks, multiset grammars, multiset metagrammars, deep learning.

Citation:
Sheremet IA. Multigrammatical Modelling of Neural Networks. Computer Optics 2024; 48(4): 619-632. DOI: 10.18287/2412-6179-CO-1436.

References:
  1. Sheremet IA. Recursive multisets and their applications [In Russian]. Moscow: "Nauka" Publisher; 2010.
  2. Sheremet I.A. Recursive multisets and their applications. European Academy of Natural Sciences; 2011. ISBN: 9783942944120.
  3. Sheremet IA. Multigrammatical framework for knowledge-based digital economy. Cham: Springer Nature Switzerland AG; 2022. ISBN: 978-3-031-13857-7.
  4. Petrovskiy AB. Theory of measured sets and multisets [In Russian]. Moscow: "Nauka" Publisher; 2018.
  5. Ben-Ari M. Mathematical logic for computer science.  London: Springer-Verlag; 2012.
  6. Kowalski R.A. Algorithm = Logic + Control. Comm ACM 1979; 22(7): 424-436.
  7. Lee KD. Foundations of programming languages. 2nd ed. Cham: Springer International Publishing AG; 2017.
  8. Davis MD, Sigal R, Weyuker EJ. Computability, complexity, and languages: Fundamentals of theoretical computer science. 2nd ed. Boston: Academic Press; 1994.
  9. Chomsky N. Syntactic Structures. The Hague: Mouton de Gruyter; 2005.
  10. Post EL. Formal reductions of the general combinatorial problem. Am J Math 1943; 65: 197-215.
  11. Sheremet IA. Intelligent software environments for information processing systems [In Russian]. Moscow: "Nauka" Publisher; 1994.
  12. Sheremet IA. Augmented post systems: The mathematical framework for data and knowledge engineering in network-centric environment. Berlin: EANS; 2013.
  13. Sheremet I. Augmented post systems: Syntax, semantics, and applications. In Book: Sud K, Erdogmus P, Kadry S, eds. Introduction to data science and machine learning. Ch 11. London: IntechOpen; 2020. DOI: 10.5772/intechopen.86207.
  14. Hopcroft JE, Motwani R, Ullman JD. Introduction to automata theory, languages, and computation. 2nd ed. Boston: Addison–Wesley; 2001.
  15. David R, Alla H. Discrete, continuous, and hybrid Petri Nets. Berlin, Heidelberg: Springer-Verlag; 2010.
  16. Ullman JD. Computational aspects of VLSI. New York, NY: W H Freeman & Co; 1984.
  17. Schiff JL. Cellular automata: A discrete view of the world. Hoboken, NJ: John Wiley & Sons Inc; 2011.
  18. McCulloch W, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bull Math Biol 1943; 7: 115-133.
  19. Rosenblatt F. The perceptron: a probabilistic model for information storage and organization in the brain. Psychol Rev 1958; 65(6): 386.
  20. Siegelmann HT, Sontag ED. Analog computation via neural networks. Theor Comput Sci 1994; 131(2): 331-360.
  21. Bragin AD, Spitsyn VG. Motor imagery recognition in electroencephalograms using convolutional neural networks. Computer Optics 2020; 44(3): 482-487. DOI: 10.18287/2412-6179-CO-669.
  22. Kalinina MO, Nikolaev PL. Book spine recognition with the use of deep neural networks. Computer Optics 2020; 44(6): 968-977. DOI: 10.18287/2412-6179-CO-731.
  23. Firsov N, Podlipnov V, Ivliev N, Nikolaev P, Mashkov S, Ishkin P, Skidanov R, Nikonorov A. Neural network-aided classification of hyperspectral vegetation images with a training sample generated using an adaptive vegetation index. Computer Optics 2021; 45(6): 887-896. DOI: 10.18287/2412-6179-CO-1038.
  24. Acemoglu D. Redesigning AI. MIT Press; 2021.
  25. Andriyanov NA, Dementiev VE, Tashlinskiy AG. Detection of objects in the images: from likelihood relationships towards scalable and efficient neural networks. Computer Optics 2022; 46(1): 139-159. DOI: 10.18287/2412-6179-CO-922.
  26. Arlazarov VV, Andreeva EI, Bulatov KB, Nikolaev DP, Petrova OO, Savelev BI, Slavin OA. Document image analysis and recognition: a survey. Computer Optics 2022; 46(4): 567-589. DOI: 10.18287/2412-6179-CO-1020.
  27. Agafonova YD, Gaidel AV, Zelter PM, Kapishnikov AV, Kuznetsov AV, Surovtsev EN, Nikonorov AV. Joint analysis of radiological reports and CT images for automatic validation of pathological brain conditions. Computer Optics 2023; 47(1): 152-159. DOI: 10.18287/2412- 6179-CO-1201.
  28. Sallans B, Hinton G. Reinforcement learning with factored states and actions. J Mach Learn Res 2004; 5: 1063-1088.
  29. Salakhutdinov R, Hinton G. Semantic hashing. Int J Approx Reasoning 2009; 50(7): 969-978.
  30. LeCun Y, Bengio Y, Hinton G. Deep learning. Nature 2015; 521: 436-444.
  31. Goodfellow I, Bengio Y, Courville A. Deep learning. MIT Press; 2016.
  32. Nielsen M. Neural networks and deep learning. Determination Press; 2019.
  33. Aggarwal CC. Neural networks and deep learning. Cham: Springer International Publishing AG; 2018.
  34. Bommasani R, Hudson DA, Adeli E, et al. On the opportunities and risks of foundation models. arXiv Preprint. 2022. Source: <https://arxiv.org/abs/2108.07258>.
  35. Metz C. “The Godfather of A.I.” leaves google and warns of danger ahead. The New York Times 2023, 1 May.
  36. Graves A, Wayne G, Danihelka I. Neural turing machines. arXiv Preprint. 2014. Source: <https://arxiv.org/abs/1410.5401>.
  37. Ackerman J, Cybenko G. A survey of neural networks and formal languages. arXiv Preprint. 2020. Source: <https://arxiv.org/abs/2006.01338>.
  38. Sheremet I. Application of the multigrammatical framework to the assessment of resilience and recoverability of large-scale industrial systems. In Book: Roberts FS, Sheremet IA, eds. Resilience in the digital age. Ch 2. Cham: Springer Nature Switzerland AG; 2021: 16-34. DOI: 10.1007/978-3-030-70370-7_2.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20