Model outline. A, Two-ring attractor for HD. The thickness of the black lines within the rings schematically illustrates the strength of inhibitory connections, originating from the filled black cell in the LMNcw ring, to the other neurons in both rings (empty circles). Gray dashed lines and filled gray cell indicate connections from the corresponding cell in the LMNccw ring. B, The network structure supporting learning. A spatially modulated mapping between visual input and the LMN HD rings is established by associating visual information (Vis) with sheets of cells in RSC that are modulated by place cells and in turn connect back to LMN via PrS. Plasticity acts on the set of connections from Vis to RSC. ADN projects to RSC, creating an activity bump in RSC that is the target for plasticity. C, RSC representation: Lateral inhibition within RSC silences all sheets not currently targeted by a place cell (CA1 in B). This allows for the association of different egocentric landmark bearing in Vis (at different positions, e.g., at x1 and x5) to the same allocentric HD (in RSC, driven by ADN). D, Simple visual feedback model for HD. Top, Topographic (one-to-one) connections from a ring of visual cells (filled circles) to HD neurons (empty circles). Bottom, The effect of simple visual feedback on HD tuning when the visual cue card (black bar) is proximal (left) versus the experimentally observed parallelism of HD tuning across the arena (right).