The cross or soft anomalous dimension matrix describes the renormalization of Wilson loops with a self-intersection and is an important object in the study of infrared divergences of scattering amplitudes. I will discuss it for the case of the Maldacena--Wilson loop in N=4 supersymmetric Yang--Mills theory, considering both the strong-coupling description in terms of minimal surfaces in AdS5 as well as the weak-coupling side up to the two-loop level. In either case, the coefficients of the cross anomalous dimension matrix can be expressed in terms of the cusp anomalous dimension. The strong-coupling description displays a Gross--Ooguri phase transition and I will argue that the cross anomalous dimension is an interesting object to study in an integrability-based approach.