What is the specific mathematical function of the AdamW optimizer that allows it to achieve better generalization than standard Adam when applied to deep neural networks?

Standard Adam attempts to implement weight decay, which is a regularization technique that penalizes large weights to prevent overfitting, by adding a penalty term directly to the loss function. When this loss-based penalty is integrated into Adam, the weight decay component becomes entangled with the adaptive gradient mechanism. Because Adam scales weight updates based on the moving averag....