Rodents and primates exhibit trade-offs between exploitation and exploration. Understanding how different behavioral states modulate neural activities remains a critical question. Previous research has demonstrated that high and low head pitch in rats correlate with distinct head-movement frequencies, which are coupled with breathing frequency, suggesting a potential connection between pitch states and exploration/exploitation behaviors. Additionally, place cells exhibit remapping across low/high-pitch states. In our study using a path-integration paradigm with rats, we found that parameters of rat locomotion trajectories reflect exploratory and goal-directed phases of the task. Specifically, low-pitch walking is associated with exploratory behavior, while high-pitch walking is related to goal-directed movement. Furthermore, we observed similar correlations in mice, where pitch and rhythmic head movements were linked to behavioral states. We found that head-direction cells in the Postsubiculum showing rate remapping across these states. The alternation between states corresponded to transitions between two ring manifolds in a low-dimensional embedding.