  We posit that hippocampal place cells encode information about future
locations under a transition distribution observed as an agent explores a given
(physical or conceptual) space. The encoding of information about the current
location, usually associated with place cells, then emerges as a necessary step
to achieve this broader goal. We formally derive a biologically-inspired neural
network from Nystr\"om kernel approximations and empirically demonstrate that
the network successfully approximates transition distributions. The proposed
network yields representations that, just like place cells, soft-tile the input
space with highly sparse and localized receptive fields. Additionally, we show
that the proposed computational motif can be extended to handle supervised
problems, creating class-specific place cells while exhibiting low sample
complexity.
