This article explores the implementation of gradient descent algorithms for minimizing global loss functions in neural networks, particularly in problems governed by Rankine-Hugoniot conditions. While gradient descent reliably converges, scalability issues arise when handling large domains with many coupled networks. To address this, a domain decomposition method (DDM) is introduced, enabling parallel optimization of local loss functions. The result is faster convergence, improved scalability, and a more efficient framework for training complex AI models.

Mathematical theorem and credit transaction prediction using Stochastic / Batch GD

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