Gradient Equilibrium Loss: A Novel Loss Function for Stable Deep Learning

I introduce Gradient Equilibrium Loss (GEL), a novel loss function that combines task-specific loss with gradient equilibrium regularization. GEL aims to maintain an optimal gradient norm during training, addressing the vanishing and exploding gradient problems in deep neural networks. My method adds an equilibrium regularization term that encourages the gradient magnitude to stay near a target value (tau), providing implicit gradient stabilization without explicit gradient manipulation. Experimental results on MNIST and CIFAR-10 datasets demonstrate that GEL achieves comparable performance on simple tasks and provides up to 2.4% improvement on more complex datasets. The proposed loss function is simple to implement, requires no additional hyperparameters beyond tau and the equilibrium weight, and can be combined with any base loss function. My approach provides a new perspective on loss function design for deep learning.