Parallax error indicates simple cue-anchoring in the head-direction system

The rodent head-direction (HD) system provides an allocentric orientation signal for spatial navigation through integration of self-motion inputs and visual landmarks ('cues'). Inferring HD from nearby visual cues faces a fundamental challenge: the direction towards the cue shifts with the animal's position. If left uncorrected, this introduces a position-dependent parallax error. Here, we show that the HD signal in freely moving mice indeed exhibits a position-dependent bias consistent with parallax in a single-cue environment. This bias is smaller than predicted by geometric parallax and is further reduced in more natural multi-cue settings. Computational modeling revealed that this reduction of parallactic error can be explained by two averaging operations: multi-view averaging - temporal integration of the same cue viewed from different locations, and multi-cue averaging - concurrent weighting of multiple cues. Thus, averaging without explicit position-dependent correction provides a fast and robust heuristic that the HD system seems to employ for the maintenance of the internal compass. Our findings have broader implications for biological and artificial navigation systems. First, accurate allocentric reference frames are a key component of the cognitive map postulated in the extended hippocampal circuit and used for spatial cognition as well as abstract mental manipulation. Second, the employment of a fast heuristic in the HD system echoes heuristic strategies observed in other behaviors, such as decision making. More broadly, these findings highlight a trade-off in neural coding between computational efficiency and positional accuracy.