Parameter Norm Penalties

# L1 Regularization

$L_{1}$ Regularization is a regularization technique applied to the weights of a neural network. We minimize a loss function compromising both the primary loss function and a penalty on the $L_{1}$ Norm of the weights:

$$L_{new}\left(w\right) = L_{original}\left(w\right) + \lambda{||w||}_{1}$$

where $\lambda$ is a value determining the strength of the penalty. In contrast to weight decay, $L_{1}$ regularization promotes sparsity; i.e. some parameters have an optimal value of zero.

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