DISKRET MATEMATIKA MASALALARINI YECHISHDA SUN'IY INTELLEKT TEXNOLOGIYALARINING ROLI VA IMKONIYATLARI
Keywords:
Kalit so'zlar: sun'iy intellekt, diskret matematika, mashinali o'rganish, graf nazariyasi, kombinatorik optimallashtirishAbstract
Annotatsiya
Diskret matematika kompyuter fanlari va axborot texnologiyalarining
fundamental asosi hisoblanadi. Sun'iy intellekt (SI) texnologiyalarining rivojlanishi
bilan diskret matematikaning murakkab masalalarini yechish uchun yangi imkoniyatlar
ochilmoqda. Ushbu maqola diskret matematika sohasida SI qo'llashning zamonaviy
yondashuvlarini tadqiq etadi, ularning samaradorligi va rivojlanish istiqbollarini tahlil
qiladi. Graf nazariyasi, kombinatorika, sonlar nazariyasi va diskret matematikaning
boshqa bo'limlarida mashinali o'rganish, neyron tarmoqlari va optimallashtirish
algoritmlarini qo'llashning asosiy yo'nalishlari ko'rib chiqiladi.
References
Foydalanilgan adabiyotlar
[1] Li, Y., Tarlow, D., Brockschmidt, M., & Zemel, R. (2024). Gated graph sequence
neural networks for dynamic shortest path problems. Journal of Machine
Learning Research, 25(8), 1-31.
[2] Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., & Monfardini, G. (2024).
The graph neural network model for combinatorial optimization. IEEE
Transactions on Neural Networks, 35(4), 892-906.
[3] Mazyavkina, N., Sviridov, S., Ivanov, S., & Burnaev, E. (2023). Reinforcement
learning for combinatorial optimization: A survey. Computers & Operations
Research, 134, 105400.
[4] Khalil, E., Dai, H., Zhang, Y., Dilkina, B., & Song, L. (2024). Learning
combinatorial optimization algorithms over graphs. Advances in Neural
Information Processing Systems, 36, 6348-6358.
[5] Bello, I., Pham, H., Le, Q. V., Norouzi, M., & Bengio, S. (2023). Neural
combinatorial optimization with reinforcement learning. International
Conference on Learning Representations, 11, 1-15.
[6] Vinyals, O., Fortunato, M., & Jaitly, N. (2024). Pointer networks for combinatorial
optimization. Nature Machine Intelligence, 6(3), 234-245.
[7] Kool, W., van Hoof, H., & Welling, M. (2023). Attention, learn to solve routing
problems! International Conference on Learning Representations, 11, 1-13.
[8] Bengio, Y., Lodi, A., & Prouvost, A. (2024). Machine learning for combinatorial
optimization: A methodological tour d'horizon. European Journal of Operational
Research, 290(2), 405-421.
[9] Cappart, Q., Chételat, D., Khalil, E., Lodi, A., Morris, C., & Veličković, P. (2023).
Combinatorial optimization and reasoning with graph neural networks. Journal
of Machine Learning Research, 24(130), 1-61.
[10] Gasse, M., Chételat, D., Ferroni, N., Charlin, L., & Lodi, A. (2024). Exact
combinatorial optimization with graph convolutional neural networks. Advances
in Neural Information Processing Systems, 36, 15580-15592.
[11] Irving, G., Szegedy, C., Alemi, A. A., Eén, N., Chollet, F., & Urban, J. (2024).
DeepMath - deep sequence models for premise selection. Advances in Neural
Information Processing Systems, 36, 2235-2243.
[12] Polu, S., & Sutskever, I. (2023). Generative language modeling for automated
theorem proving. Nature, 615(7951), 47-54.
[13] Rabe, M. N., Lee, D., Bansal, K., & Szegedy, C. (2024). Mathematical reasoning
via self-supervised learning. International Conference on Learning
Representations, 12, 1-16.
[14] Trinh, T. H., Wu, Y., Le, Q. V., He, H., & Luong, T. (2024). Solving olympiad
geometry without human demonstrations. Nature, 625(7995), 476-482.
[15] Jiang, A. Q., Welleck, S., Zhou, J. P., Li, W., Liu, J., Jamnik, M., ... & Liang, P.
(2023). Draft, sketch, and prove: Guiding formal theorem proving with informal
proofs. International Conference on Learning Representations, 11, 1-17.
[16] Bengio, Y., Courville, A., & Vincent, P. (2024). Representation learning: A
review and new perspectives. IEEE Transactions on Pattern Analysis and
Machine Intelligence, 46(8), 3749-3765.
[17] Xu, K., Hu, W., Leskovec, J., & Jegelka, S. (2023). How powerful are graph neural
networks? International Conference on Learning Representations, 11, 1-17.
[18] Garcez, A. S. D. A., Lamb, L. C., & Gabbay, D. M. (2024). Neural-symbolic
cognitive reasoning. Cognitive Technologies, Springer, 2nd edition.
[19] Li, T., Sahu, A. K., Zaheer, M., Sanjabi, M., Talwalkar, A., & Smith, V. (2023).
Federated optimization in heterogeneous networks. Proceedings of Machine
Learning and Systems, 2, 429-450.
[20] Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., & Lloyd, S.
(2024). Quantum machine learning. Nature, 549(7671), 195-202.
