Do lower-difficulty Lockpicking perks have any effect on higher-difficulty locks?

Do the Novice Locks/Apprentice Locks perks have any impact on higher locks? I'm wondering if I should put any perks into Lockpicking at all, as Quick Hands is the only iteresting one of all. But seeing how Novice locks are trivially easy to pick and Apprentice locks are easy enough, perking those seems pointless.

Only Master locks are a challenge, so if perking low-lvl locks does have an impact on them, it certiantly would be worth it. The only question: Does it?

The descriptions of the perks only refer to one level of lock, so I am certain that the lower level perks do not have any effect on the higher level locks. Even if they did, I don't think that it would be worth it to get the lower level perks just to have higher level locks be easier to pick.

They low level perks won't affect high level locks, but the perks for high level locks require you to take the low level perks as a prerequisite. Thus, to get perks to make Master locks easier to pick, you need to spend (waste?) perks on the easier locks.