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This research delves into the innovative application of group theory, particularly symmetric groups, in the realm of artificial intelligence algorithms for image identification. It also explores the distinctive architectures of Convolutional Neural Networks (CNNs) in the context of computer vision. CNNs have brought about a paradigm shift in computer vision, playing a central role in image classification, object detection, and diverse visual recognition tasks. Among these architectures, AlexNet, VGG16, and VGG32 have garnered significant attention for their impactful contributions and architectural innovations. In this study, our objective is to explore and compare these three CNN architectures, elucidating their design principles, performance, and suitability for various computer vision tasks.

The core aim is to develop advanced techniques that enhance the robustness of image recognition by accounting for image rotations and sub-image transformations. Traditional image recognition systems often falter when confronted with rotated or transformed images, constraining their practical utility. To surmount this challenge, we harness the principles of symmetric group theory to devise innovative algorithms adept at handling these variations. This research systematically evaluates and compares the image recognition performance of the three networks (AlexNet, VGG16, and VGG32).

The research is bifurcated into two primary aspects: image rotations and sub-image transformations. To address rotations, we delve into the mathematical underpinnings of symmetric groups and their ability to model various rotation angles. We employ these group-based representations to devise AI algorithms that proficiently identify images, irrespective of their orientation. The study encompasses a diverse range of datasets, underlining the effectiveness of the proposed algorithms. Our results show substantial enhancements in image identification accuracy, especially in scenarios involving image rotations and sub-image transformations. The integration of symmetric group theory in artificial intelligence holds the promise of broadening the capabilities of image recognition systems, rendering them more adaptable to real-world applications in fields such as computer vision, robotics, and autonomous systems. This research serves as a bridge between theoretical group theory and pragmatic AI applications, showcasing the potential of interdisciplinary approaches in propelling image recognition technologies.