DOI: https://doi.org/10.36719/2789-6919/56/116-120
Nurana Ismayilova
Azerbaijan State Pedagogical University
https://orcid.org/0009-0007-5795-4605
nurana.smaylova@gmail.com
The Role of Functions in Artificial Intelligence and Machine Learning: Theoretical Foundations and Applications
Abstract
The concept of mathematical function underlies every core component of modern artificial intelligence (AI) systems. From activation functions that enable nonlinear capability in neural networks to loss functions that define the objective of optimization, every architectural decision amounts to a functional choice. This paper systematically examines the historical development of the function concept, its mathematical foundations, and its concrete applications in deep learning, transformer architectures, diffusion models, and quantum machine learning.
The research demonstrates that the properties of functions – particularly differentiability, nonlinearity, and computational efficiency – directly determine the quality of model learning. The choice of activation function affects the learning rate of a neural network, the loss function defines the mathematical objective of learning, and the gradient computation is based on the concept of derivatives.
Keywords: function, activation function, machine learning, artificial intelligence, neural network, loss function, optimization, transformer, diffusion model