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We posit that hippocampal place cells encode information about futurelocations under a transition distribution observed as an agent explores a given(physical or conceptual) space. The encoding of information about the currentlocation, usually associated with place cells, then emerges as a necessary stepto achieve this broader goal. We formally derive a biologically-inspired neuralnetwork from Nystr\"om kernel approximations and empirically demonstrate thatthe network successfully approximates transition distributions. The proposednetwork yields representations that, just like place cells, soft-tile the inputspace with highly sparse and localized receptive fields. Additionally, we showthat the proposed computational motif can be extended to handle supervisedproblems, creating class-specific place cells while exhibiting low samplecomplexity.

Do place cells dream of conditional probabilities? Learning Neural Nystr\"om representations