Glossary of mathematical symbols.

Hippocampal remapping, in which place cells form distinct activity maps across different environments, is a well-established phenomenon with a range of theoretical interpretations. Some theories propose that remapping helps to minimize interference between competing spatial memories, whereas others link it to shifts in an underlying latent state representation. However, how these interpretations of remapping relate to one another, and what types of activity changes they are compatible with, remains unclear. To unify and elucidate the mechanisms behind remapping, we here adopt a neural coding and population geometry perspective. Assuming that hippocampal population activity can be understood through a linearly-decodable latent space, we show that there are three possible mechanisms to induce remapping: (i) a true change in the mapping between neural and latent space, (ii) modulation of activity due to non-spatial mixed selectivity of place cells, or (iii) neural variability in the null space of the latent space that reflects a redundant code. We simulate and visualize examples of these remapping types in a network model, and relate the resultant remapping behavior to various models and experimental findings in the literature. Overall, our work serves as a unifying framework with which to visualize, understand, and compare the wide array of theories and experimental observations about remapping, and may serve as a testbed for understanding neural response variability under various experimental conditions.