The head direction (HD) system is classically modeled as a ring attractor network which ensures a stable representation of the animal’s head direction. This unidimensional description popularized the view of the HD system as the brain’s internal compass. However, unlike a globally consistent magnetic compass, the orientation of the HD system is dynamic, depends on local cues and exhibits remapping across familiar environments5. Such a system requires mechanisms to remember and align to familiar landmarks, which may not be well described within the classic 1-dimensional framework. To search for these mechanisms, we performed large population recordings of mouse thalamic HD cells using calcium imaging, during controlled manipulations of a visual landmark in a familiar environment. First, we find that realignment of the system was associated with a continuous rotation of the HD network representation. The speed and angular distance of this rotation was predicted by a 2nd dimension to the ring attractor which we refer to as network gain, i.e. the instantaneous population firing rate. Moreover, the 360-degree azimuthal profile of network gain, during darkness, maintained a ‘memory trace’ of a previously displayed visual landmark. In a 2nd experiment, brief presentations of a rotated landmark revealed an attraction of the network back to its initial orientation, suggesting a time-dependent mechanism underlying the formation of these network gain memory traces. Finally, in a 3rd experiment, continuous rotation of a visual landmark induced a similar rotation of the HD representation which persisted following removal of the landmark, demonstrating that HD network orientation is subject to experience-dependent recalibration. Together, these results provide new mechanistic insights into how the neural compass flexibly adapts to environmental cues to maintain a reliable representation of the head direction.