Processing of sensory information depends on the interactions between hierarchically connected neocortical regions, but it remains unclear how the activity in one area causally influences the activity dynamics in another and how rapidly such interactions change with time. Here, we show that the communication between the primary visual cortex (V1) and high-order visual area LM is context-dependent and surprisingly dynamic over time. By momentarily silencing one area while recording activity in the other, we find that both areas reliably affected changing subpopulations of target neurons within one hundred milliseconds while mice observed a visual stimulus. The influence of LM feedback on V1 responses became even more dynamic when the visual stimuli predicted a reward, causing fast changes in the geometry of V1 population activity and affecting stimulus coding in a context-dependent manner. Therefore, the functional interactions between cortical areas are not static but unfold through rapidly shifting communication subspaces whose dynamics depend on context when processing sensory information.