L2 and L1 regularization are both techniques used to prevent overfitting in deep neural networks. The choice between L2 and L1 regularization depends on the specific problem being solved and the characteristics of the data.

L2 regularization is the most commonly used regularization method and adds a penalty term to the loss function equal to the sum of the squares of the weights. This has the effect of reducing the magnitude of the weights and encouraging the network to use small weights. L2 regularization is often used when the data is normally distributed, as the penalty term is sensitive to large weights and less sensitive to small weights.

L1 regularization, on the other hand, adds a penalty term to the loss function equal to the sum of the absolute values of the weights. This has the effect of encouraging the network to use sparse weights, with many weights being set to zero. L1 regularization is often used when the data is sparse or contains many irrelevant features, as it encourages the network to use only a small subset of the features.

In general, L2 regularization is preferred when the goal is to reduce overfitting, while L1 regularization is preferred when the goal is to promote sparse representations and feature selection. The choice between L2 and L1 regularization will also depend on the specific requirements of the problem, such as computational time, model size, and accuracy, among others.
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