I am trying to fully understand neural network regularization that is performed in the Neural Network Toolbox. On https://www.mathworks.com/help/nnet/ref/trainautoencoder.html , there is a bit of theory behind L2 regularization used in stacked autoencoders. However, the definition of L2 regularization in the related equation is not clear to me. First, why is the sum running through all hidden layers l = 1..L but not through all neurons in each hidden layer? Second, I do not understand "k is the number of variables in the training data". Does it mean that k corresponds to the dimensionality of feature vectors?

Thanks for any clarification.

Regards, Lukas Vareka