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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:

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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):

enter image description here

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

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