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@article{191374,
        author = {Shikha Sharma},
        title = {Mathematics Behind Artificial Intelligence: From Deterministic Models to Probabilistic Learning},
        journal = {International Journal of Innovative Research in Technology},
        year = {},
        volume = {12},
        number = {no},
        pages = {44-47},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=191374},
        abstract = {The evolution of Artificial Intelligence (AI) represents a significant transformation in computational thinking, shifting from rigid deterministic models to flexible probabilistic learning systems. Early AI systems were built on deterministic mathematical logic and rule-based frameworks, assuming complete information and predictable environments. However, real-world problems are inherently uncertain, noisy, and dynamic, making deterministic approaches insufficient for modern intelligent systems. This limitation prompted a paradigm shift toward probabilistic learning, where uncertainty is explicitly modeled and managed using mathematical tools.
Probabilistic learning integrates concepts from probability theory, statistics, linear algebra, optimization, Bayesian inference, and stochastic processes. These mathematical foundations allow AI systems to learn from data, adapt to changing environments, and make informed decisions under uncertainty. Techniques such as machine learning, neural networks, deep learning, probabilistic graphical models, and reinforcement learning exemplify this transition. Unlike deterministic systems, probabilistic models continuously update their parameters based on experience, enabling self-improvement and generalization.
This paper explores the mathematical journey of Artificial Intelligence, tracing its development from deterministic rule-based models to modern probabilistic learning frameworks. It highlights the mathematical principles underlying both paradigms, examines their strengths and limitations, and demonstrates how probabilistic learning has revolutionized AI applications across domains such as healthcare, finance, robotics, and autonomous systems. By emphasizing adaptability, scalability, and uncertainty handling, probabilistic mathematics has become the backbone of contemporary AI, marking a profound shift in both theory and practice.},
        keywords = {Artificial Intelligence, Deterministic Models, Probabilistic Learning, Mathematics, Machine Learning, Bayesian Inference},
        month = {},
        }