Question

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?

Accepted Answer

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 average of past squared gradients, the weight decay term is also unfairly scaled, causing it to lose its intended strength and consistency. AdamW fixes this by decoupling weight decay from the gradient update process. In AdamW, weight decay is applied directly to the weights after the adaptive learning rate update has been calculated, rather than including it in the loss function or the gradient calculation. Specifically, the weight update rule for AdamW takes the form of subtracting a fraction of the current weight from the weight itself, independent of the adaptive gradient steps that account for momentum and variance. By separating weight decay from the adaptive gradient, AdamW ensures that the regularization strength remains constant and independent of the scaling applied by the optimizer, leading to more effective weight shrinkage and significantly better generalization performance on deep neural networks.

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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?