  Neuroscientists postulate 3D representations in the brain in a variety of
different coordinate frames (e.g. 'head-centred', 'hand-centred' and
'world-based'). Recent advances in reinforcement learning demonstrate a quite
different approach that may provide a more promising model for biological
representations underlying spatial perception and navigation. In this paper, we
focus on reinforcement learning methods that reward an agent for arriving at a
target image without any attempt to build up a 3D 'map'. We test the ability of
this type of representation to support geometrically consistent spatial tasks
such as interpolating between learned locations using decoding of feature
vectors. We introduce a hand-crafted representation that has, by design, a high
degree of geometric consistency and demonstrate that, in this case, information
about the persistence of features as the camera translates (e.g. distant
features persist) can improve performance on the geometric tasks. These
examples avoid Cartesian (in this case, 2D) representations of space.
Non-Cartesian, learned representations provide an important stimulus in
neuroscience to the search for alternatives to a 'cognitive map'.
