The practice of multiplying the weights by a factor slightly less than 1 after each gradient update is a form of weight decay, often referred to as "weight decay with momentum" or "weight decay with rescaling." This technique is used in neural network training as a form of regularization, and it serves several useful purposes:
Regularization: Weight decay is primarily used to prevent overfitting. By reducing the magnitude of the weights after each update, it encourages the model to have smaller weight values, effectively penalizing large weight magnitudes. This regularization helps the model generalize better to unseen data and reduces the risk of fitting noise in the training data.
Stability: Weight decay can enhance the stability of the training process. When neural networks have large weights, they can be more sensitive to small changes in the input data or the optimization process itself. Smaller weights make the network less prone to numerical issues like exploding gradients, vanishing gradients, or loss function oscillations.
Convergence Acceleration: While weight decay acts as a regularization term, it doesn't necessarily slow down convergence. In some cases, it can even accelerate convergence by encouraging the optimization process to explore a broader range of weight configurations early in training. This exploration can help the model escape poor local minima and converge faster to a better solution.
Parameter Scaling: Weight decay helps ensure that the scale of the model parameters (weights) remains appropriate throughout training. It prevents weight values from growing excessively large, which can lead to numerical instability during training.
Interplay with Learning Rate Scheduling: Weight decay is often used in conjunction with learning rate schedules. The reduction in weight magnitude caused by weight decay can be offset by appropriately adjusting the learning rate. This interplay allows for fine-tuning of the regularization effect during training.
Consistency with Weight Initialization: Weight decay aligns with weight initialization techniques like Xavier/Glorot or He initialization, which are designed with regularization in mind. These initialization methods aim to set weights close to zero, and weight decay helps maintain this initialization philosophy during training.
It's important to note that the factor by which the weights are multiplied (often referred to as the weight decay coefficient or the regularization strength, denoted as λ) is a hyperparameter that needs to be tuned based on the specific problem and dataset. Too much weight decay can lead to underfitting, while too little may not provide sufficient regularization. Cross-validation or validation set performance is typically used to find an appropriate value for λ.
In summary, weight decay, implemented as a multiplicative factor slightly less than 1 applied to weights, is a valuable regularization technique in neural network training. It promotes regularization, stability, and convergence acceleration, ultimately leading to improved generalization performance.