Weight Standardization is a normalization technique used in machine learning that standardizes the weights in convolutional layers. This technique focuses on the smoothing effects of weights more than just length-direction decoupling, unlike previous normalization methods that focused solely on activations. This technique aims to reduce the Lipschitz constants of the loss and the gradients, which ultimately smooths the loss landscape and improves training.
Reparameterizing the Weights in Weight Standardization
In Weight Standardization, the original weights $\hat{W}$ are reparameterized as a function of $W$ in order to optimize the loss $\mathcal{L}$ on $W$ using stochastic gradient descent (SGD). The reparameterized weights $\hat{W}$ are defined as:
$$ \hat{W} = \Big[ \hat{W}\_{i,j}~\big|~ \hat{W}\_{i,j} = \dfrac{W\_{i,j} - \mu\_{W\_{i,\cdot}}}{\sigma\_{W\_{i,\cdot}+\epsilon}}\Big] $$
This reparameterization of weights normalizes the weights using the means and standard deviations of each output channel individually in convolutional layers. The constant $\epsilon$ is added to the denominator of the equation to avoid dividing by zero.
The means and standard deviations of each output channel individually are defined as:
$$ \mu_{W\_{i,\cdot}} = \dfrac{1}{I}\sum\_{j=1}^{I}W\_{i, j},~~\sigma\_{W\_{i,\cdot}}=\sqrt{\dfrac{1}{I}\sum\_{i=1}^I(W\_{i,j} - \mu\_{W\_{i,\cdot}})^2} $$
Comparison to Batch Normalization
Weight Standardization is similar to Batch Normalization in that both techniques aim to control the first and second moments of the weights in convolutional layers. However, Weight Standardization standardizes the weights in a differentiable way that aims to normalize gradients during back-propagation.
Unlike Batch Normalization, Weight Standardization does not have any affine transformation on $\hat{W}$. This is because normalization layers such as Batch Normalization or Group Normalization are assumed to normalize the convolutional layer in Weight Standardization again.
Benefits of Weight Standardization
The main benefit of Weight Standardization is that it smooths the loss landscape and improves training by reducing the Lipschitz constants of the loss and gradients. This technique also reduces memory usage during training compared to other normalization techniques due to its lower dependence on memory and computation.
Weight Standardization can also work well with low batch sizes, which means that it can be used effectively in small datasets. This technique can also improve the results of transfer learning by making the convolutional layers more adaptable to new tasks.
Weight Standardization is a powerful normalization technique used in machine learning that standardizes the weights in convolutional layers. It focuses on the smoothing effects of weights more than just length-direction decoupling and reduces the Lipschitz constants of the loss and gradients. This technique can improve training, reduce memory usage, and work effectively with low batch sizes. With its numerous benefits, Weight Standardization is an essential technique for those working in the field of machine learning.
