I am trying to learn about regularity structure. In the mini course part 1 and part 2 https://www.youtube.com/watch?v=RgLW6dxl0IU Dr. Martin Hairer has mentioned several times about lifting noise. May I ask what does lifting noise mean? How it is done? I understand lift as mentioned in https://mathworld.wolfram.com/Lift.html
Can anyone please expalin a bit?