Perception is your environmental awareness and "sixth sense," and affects weapon accuracy in V.A.T.S. Now you instantly gain 1 point!”— In-game description
For each rank taken in the Perception Training perk tree, the Sole Survivor will gain access to a 1 extra point in Perception. Perception Training can be taken a total of 10 times, making this a 10-ranked perk.
As each S.P.E.C.I.A.L. skill can only be set to 1, at minimum, taking Perception Training 10 times is a waste, as no S.P.E.C.I.A.L. stat can be raised above 10.