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i was reading this https://arxiv.org/pdf/2303.14535v1.pdf paper when i came across this: enter image description here

What is this F? Initially i assumed this was a standard L2 distance but i'm not so sure anymore.

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The subscript F is used to denote the Frobenius norm, see also the section on the Frobenius norm on this wikipedia page to see an example of the notation (including one with a superscript 2 as is the cass for the loss function shown).

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