A relevant question for the paper you linked is what happens if instead of repeating the input prompt you repeat a filler character the same number of times.
replyThis is tested in the paper (see the "padding" ablation)
replyCan you elaborate on that more? Why just a filler character?
replyBecause padding the output in such a manner (which keep in mind is immediately fed back as input) has been shown to increase model performance. It's one of the many reasons to question what "thinking" traces are really doing.
replyIf you consider how the attention mechanism works then a very hand wavey intuition is that despite being entirely arbitrary additional tokens should still provide the opportunity for additional information processing.