Hybrid Analytical-Numerical Techniques for Machine Learning Optimization: Integrating Laplace Transform and Runge-Kutta Fourth-Order Methods
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Abstract
Machine learning (ML) optimization often employs gradient-based approaches, which may encounter issues with sluggish convergence, trapping of local minima, and expensive computing expenses. Optimizing ML loss functions is made easier using a new hybrid technique that combines analytical smoothing with numerical accuracy via Runge-Kutta Fourth-Order (RK4) and Laplace Transform (LT). The suggested approach makes use of LT to simplify gradient calculations by transforming the differential equations controlling optimization dynamics into an algebraic domain. Subsequently, RK4 is used to achieve numerical integration with great precision in weight updates. Comparing it to more conventional optimizers like SGD and Adam, experiments on benchmark datasets (MNIST, CIFAR-10) show that it converges quicker and has better generalization. Stability and computing efficiency have been verified by theoretical analysis, which points to a potential path for hybrid optimization in deep learning.
In this research, we provide a new technique for improving machine learning algorithms that combines analytical and numerical approaches. It combines the Laplace Transform with the Runge-Kutta Fourth-Order (RK4) method. In an effort to improve learning efficiency, convergence stability, and computing performance, the work combines deterministic system modeling and numerical analysis with machine learning's stochastic character. By combining theoretical analysis with practical testing, we show that the hybrid approach enhances the training of certain ML models.