Do place cells dream of conditional probabilities? Learning Neural Nyström representations
This provides a computational framework for neuroscience to model place cell activity, with potential applications in navigation systems and supervised learning tasks.
The paper tackles the problem of understanding hippocampal place cell function by proposing they encode future location probabilities under transition distributions, and demonstrates that a biologically-inspired neural network derived from Nyström approximations successfully approximates these distributions while producing sparse, localized receptive fields similar to place cells.
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 Nyström 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.