Spectral Normalization is a technique used for Generative Adversarial Networks (GANs). Its purpose is to stabilize the training of the discriminator. It does this by controlling the Lipschitz constant of the discriminator through the spectral norm of each layer. Spectral normalization has the advantage that the only hyper-parameter that is needed to be tuned is the Lipschitz constant.
What is Lipschitz Norm?
Lipschitz norm of a function is a property that is used in mathematical analysis to describe the smoothness of the function. In other words, it measures how much a function can vary when its input varies.
What is Spectral Norm?
Spectral norm is a mathematical concept used to measure the magnitude of matrix operators. For a matrix A, the spectral norm is defined as the maximum eigenvalue of A^TA, where eigenvalue is a scalar value that characterizes the properties of eigenvectors.
How does Spectral Normalization work?
For a linear layer, the Lipschitz norm of the layer is given by the maximum singular value of the weight matrix W. Spectral normalization normalizes this maximum singular value to 1. This is done by dividing the weight matrix by its maximum singular value, thereby forcing the Lipschitz norm of the layer to be equal to 1.
Spectral normalization constrains the spectral norm of each layer in the discriminator network. Thus, it ensures that the discriminator network is not too sensitive to small input changes. By not allowing the discriminator network to be overly sensitive to input changes, the generative adversarial network becomes more stable during training.
Spectral normalization is not limited to only linear layers. It can be used in any layer that has weight parameters.
Advantages of Spectral Normalization
The primary advantage of spectral normalization is that it is a simple and effective technique to stabilize the training of GANs. Furthermore, the only hyper-parameter that is needed to be tuned is the Lipschitz constant.
Spectral normalization helps to prevent mode collapse during training. Mode collapse occurs when the generator in a GAN learns to produce only a few outputs, rather than producing a variety of different possible outputs. With spectral normalization, the generator is less likely to collapse in this manner.
Another advantage of spectral normalization is that it smooths the discriminator decision boundary. This means that the discriminator is less likely to classify samples as either real or fake when the samples are actually on the boundary between real and fake.
Spectral normalization is a simple and effective technique to stabilize the training of GANs. Its primary purpose is to control the Lipschitz constant of the discriminator. By normalizing the Lipschitz norm, spectral normalization ensures that the discriminator network is not too sensitive to small input changes. Overall, spectral normalization provides several advantages, including prevention of mode collapse, smoothing the discriminator decision boundary, and requiring only one hyper-parameter to be tuned.
