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The advent of advanced neural network models has revolutionized the field of machine learning, enabling breakthroughs in various domains such as computer vision, natural language processing, and predictive analytics. This paper introduces three pivotal neural network architectures: Artificial Neural Networks (ANN), Back-Propagation Neural Networks (BPNN), and Generative Adversarial Networks (GAN). We explore the theoretical underpinnings, practical applications, and the significance of these models in the broader context of artificial intelligence research and industry.