SUN’IY INTELLEKTNI O‘RGATISHDA FOYDALANILADIGAN MATEMATIK ASOSLAR. GRADIENT TUSHISH, KONVEKS FUNKSIYALAR VA NEYRON TARMOQLAR
Keywords:
convex functions, gradient descent, neural networks, Adam, SGD, optimization, artificial intelligence.Abstract
This article presents a scientific analysis of the mathematical
foundations used in artificial intelligence algorithms, with a particular focus on gradient
descent methods and the role of convex functions. Through practical experiments, the
study demonstrates how convexity properties impact accuracy, stability, and learning
efficiency in the optimization of neural networks. Moreover, several modern variations of
the gradient descent algorithm (Stochastic Gradient Descent – SGD, Momentum, and
Adam) are compared, and their effects on learning speed and loss function values are
discussed. The research emphasizes the importance of mathematically grounded
algorithmic approaches for the development of artificial intelligence in Uzbekistan.
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