# Tikhonov Regularization in continuous probability density functions

Can anyone helps me understand Bishop's Training with Noise is Equivalent to Tikhonov Regularization?

In the paper, Bishop first defined the cost function (Equation 1) as:

where $$x$$ stands for features, $$t$$ stands for the labels, and $$y$$ stands for the output of the model.

Then he introduced that the Tikhonov regularizer takes the form (Equation 6):

but he seems to forget to define what $$h_r$$ is. So what is $$h_r$$?