Weight decay, also known as L2 regularization or ridge regularization, is a technique used in machine learning to prevent overfitting and improve the generalization performance of a model.
In machine learning models, this technique is applied by adding a regularization term to the loss function during training. This regularization term penalizes the model for having large weights and encourages it to have smaller weights. The idea behind weight decay is that by reducing the magnitude of the weights, the model becomes less sensitive to small variations in the input data and is less likely to overfit.
Mathematically, it is achieved by adding a regularization term to the loss function that is proportional to the sum of the squared values of the model’s weights. The loss function with weight decay can be written as:
where Loss_without_decay is the original loss function without regularization, λ is the weight decay coefficient (a hyperparameter that controls the strength of the regularization), and ||w||^2 is the squared L2 norm of the model’s weights.
During training, the model aims to minimize the loss function with weight decay. The regularization term encourages the optimization algorithm to find weight values that are not only able to fit the training data but also have smaller magnitudes. This helps prevent the model from relying too heavily on any particular feature or overemphasizing noisy or irrelevant patterns in the data.
The weight decay coefficient (λ) is a hyperparameter that needs to be tuned to achieve the right balance between fitting the training data and preventing overfitting. Higher values of λ increase the strength of the regularization, leading to smaller weights but potentially sacrificing some model performance on the training data. On the other hand, lower values of λ may result in less regularization and a higher risk of overfitting.
This technique is commonly used in various machine learning models, including linear regression, logistic regression, neural networks, and support vector machines. It is a simple yet effective technique to control model complexity and improve generalization by preventing excessive reliance on individual weights.
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