Розмір шрифта:
ALGORITHMIC COMPLEXITY AND ADVANCED MATHEMATICS: OPTIMIZING NEURAL NETWORKS THROUGH LOW-LEVEL IMPLEMENTATIONS
Остання редакція: 2026-05-22
Анотація
The efficiency of neural networks directly depends on the mathematical optimization and speed of computational algorithms at the processor architecture level. The combination of higher mathematics with low-level programming allows to minimize computational costs when implementing complex matrix arithmetic and gradient descent operations. The paper analyzes how direct memory management and vectorization of calculations in system-level languages can significantly accelerate the training of deep models compared to high-level interpreted languages. Special attention is paid to algorithmic complexity and methods of function approximation, which require maximum accuracy and optimization at the hardware level to ensure the operation of artificial intelligence systems in real time.
Ключові слова
algorithmic complexity, higher mathematics, neural networks, low-level optimization, matrix arithmetic, memory management, computational efficiency, C++
Посилання
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2. Heaton, J. Goodfellow, I., Bengio, Y., Courville, A. (2018). Deep learning. Genet Program Evolvable Mach 19, 305–307. DOI: https://doi.org/10.1007/s10710-017-9314-z.
3. Knuth, D. E. (1997). The Art of Computer Programming, Volume 1: Fundamental Algorithms. Addison-Wesley. URL: https://seriouscomputerist.atariverse.com/media/pdf/book/Art%20of%20Computer%20Programming%20-%20Volume%201%20(Fundamental%20Algorithms).pdf.
4. Gereron, A. (2019). Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow. O'Reilly Media. URL: https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632.
5. Kravchenko, K., Ketsyk-Zinchenko, U., Suduk, I., Nykyporets, S., & Cherednychenko, V. (2025). Effectiveness of online platforms in developing language skills of higher education students. Revista Eduweb, 19(3), 303-314. DOI: https://doi.org/10.46502/issn.1856-7576/2025.19.03.19.
6. Sachaniuk-Kavets’ka, N. V., & Nykyporets, S. S. (2026). LLM-based automation for translating mathematical formulae and symbols: Challenges and perspectives for technical communication. Scientific Innovations and Advanced Technologies. Series "Education/Pedagogy", 3(55), 660-677. DOI: https://doi.org/10.52058/2786-5274-2026-3(55)-660-677.
7. Sachaniuk-Kavets’ka, N. V., & Nykyporets, S. S. (2025). Developing critical thinking in students of technical specialties through the mathematics of uncertainty and educational debates in English: An integrated experimental-methodological model. Bulletin of Science and Education. Series "Pedagogy", 11(41), 1524-1541. DOI: https://doi.org/10.52058/2786-6165-2025-11(41)-1524-1541.
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