Weight Decay

Weight decay, also known as L2 regularization, is a technique used to prevent overfitting by adding a penalty term to the loss function based on the magnitude of the model's weights.

Adjusting the weight decay during fine-tuning can help maintain the balance between fitting the task-specific data and retaining the general knowledge learned during pre-training.

Weight decay is implemented by subtracting a fraction of the weights at each update during the training process, leading to a gradual decrease in their values.

This technique differs from L2 regularization in its direct modification of the weight update step, as opposed to altering the loss function. Mathematically, weight decay adjusts the weights by subtracting a scaled version, controlled by a regularization parameter.

Weight decay prevents overfitting by reducing the complexity of the model. When the weights are too large, the model can fit the training data too closely and not generalize well to new, unseen data. By adding a penalty term to the loss function, the model is encouraged to use smaller weights, which can reduce the complexity of the model and help it generalize better.

What levels of weight decay should you use in training a model?

The optimal level of weight decay for a particular model depends on several factors, including the complexity of the model, the size and diversity of the training data, and the specific task or problem being addressed.

Here are some general guidelines to consider when selecting a weight decay value:

Start with a small value: It is typically best to start with a small weight decay value, such as 0.0001 or 0.001, and then gradually increase it as needed. This can help to prevent the model from over-regularizing and sacrificing too much accuracy on the training data.

Adjust based on model complexity: More complex models generally require higher levels of weight decay to prevent overfitting. If the model has many layers or a large number of parameters, it may be necessary to increase the weight decay value to ensure that the model generalizes well to new data.

Use cross-validation: Cross-validation is a useful technique for selecting hyperparameters such as weight decay. By dividing the training data into multiple folds and training the model on each fold while evaluating on the remaining folds, you can get a more accurate estimate of the model's performance for different values of weight decay.

Balance weight decay with other regularization techniques: Weight decay is just one of many regularization techniques that can be used to prevent overfitting. It is often used in combination with other techniques, such as dropout, early stopping, or batch normalization, to further improve the model's generalization performance.

In general, the optimal value of weight decay depends on the specific characteristics of the model and the data, and it may require some trial and error to find the best value.

However, starting with a small value and adjusting based on the complexity of the model and the performance on the validation data is a good strategy to begin with.

L2 Regularization: Incorporating a Penalty Term

Often referred to interchangeably with weight decay, L2 regularization introduces an additional term to the loss function that penalizes the square of the weights. This penalty term is a function of the squared weights, multiplied by a regularization constant. The objective remains consistent with weight decay: to promote smaller weights and reduce overfitting. In the weight update process, this leads to a subtraction of a fraction of the weight parameters, similar to weight decay.