  In this work, we propose an Implicit Regularization Enhancement (IRE)
framework to accelerate the discovery of flat solutions in deep learning,
thereby improving generalization and convergence. Specifically, IRE decouples
the dynamics of flat and sharp directions, which boosts the sharpness reduction
along flat directions while maintaining the training stability in sharp
directions. We show that IRE can be practically incorporated with {\em generic
base optimizers} without introducing significant computational overload.
Experiments show that IRE consistently improves the generalization performance
for image classification tasks across a variety of benchmark datasets
(CIFAR-10/100, ImageNet) and models (ResNets and ViTs). Surprisingly, IRE also
achieves a $2\times$ {\em speed-up} compared to AdamW in the pre-training of
Llama models (of sizes ranging from 60M to 229M) on datasets including
Wikitext-103, Minipile, and Openwebtext. Moreover, we provide theoretical
guarantees, showing that IRE can substantially accelerate the convergence
towards flat minima in Sharpness-aware Minimization (SAM).
