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In the paper (1), there is a description of a deconvolutional network.

The loss function (with only one layer) compares the colour channels of the orignal image with the colour channels of the generated image. To increase the sparsity of the feature maps there is also added a regularization term.

Intuitively, one can say that the loss function tries to create feature maps and filters to reconstruct the original image.

Image of loss function and deconvolutional network for the last layer

What does the dark green marked term mean?

(1) Link to paper: https://www.matthewzeiler.com/mattzeiler/deconvolutionalnetworks.pdf

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Then green term indicates that they are taking the L2 norm of the difference between the orange and the pink terms (indicated by the lower 2), and taking the square of that L2 norm (indicated by the upper 2). See also this answer on the statistics stackexchange.

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