It is proposed that a cognitive map encoding the relationships between entities in the world supports flexible behavior, but the majority of the neural evidence for such a system comes from studies of spatial navigation. Recent work describing neuronal parallels between spatial and non-spatial behaviors has rekindled the notion of a systematic organization of knowledge across multiple domains. We review experimental evidence and theoretical frameworks that point to principles unifying these apparently disparate functions. These principles describe how to learn and use abstract, generalizable knowledge and suggest that map-like representations observed in a spatial context may be an instance of general coding mechanisms capable of organizing knowledge of all kinds. We highlight how artificial agents endowed with such principles exhibit flexible behavior and learn map-like representations observed in the brain. Finally, we speculate on how these principles may offer insight into the extreme generalizations, abstractions, and inferences that characterize human cognition.

Summary The hippocampal-entorhinal system is important for spatial and relational memory tasks. We formally link these domains, provide a mechanistic understanding of the hippocampal role in generalization, and offer unifying principles underlying many entorhinal and hippocampal cell types. We propose medial entorhinal cells form a basis describing structural knowledge, and hippocampal cells link this basis with sensory representations. Adopting these principles, we introduce the Tolman-Eichenbaum machine (TEM). After learning, TEM entorhinal cells display diverse properties resembling apparently bespoke spatial responses, such as grid, band, border, and object-vector cells. TEM hippocampal cells include place and landmark cells that remap between environments. Crucially, TEM also aligns with empirically recorded representations in complex non-spatial tasks. TEM also generates predictions that hippocampal remapping is not random as previously believed; rather, structural knowledge is preserved across environments. We confirm this structural transfer over remapping in simultaneously recorded place and grid cells.

Collective cell migration is of great significance in many biological processes. The goal of this work is to give a physical model for the dynamics of cell migration during the wound healing response. Experiments demonstrate that an initially uniform cell-culture monolayer expands in a nonuniform manner, developing fingerlike shapes. These fingerlike shapes of the cell culture front are composed of columns of cells that move collectively. We propose a physical model to explain this phenomenon, based on the notion of dynamic instability. In this model, we treat the first layers of cells at the front of the moving cell culture as a continuous one-dimensional membrane (contour), with the usual elasticity of a membrane: curvature and surface-tension. This membrane is active, due to the forces of cellular motility of the cells, and we propose that this motility is related to the local curvature of the culture interface; larger convex curvature correlates with a stronger cellular motility force. This shape-force relation gives rise to a dynamic instability, which we then compare to the patterns observed in the wound healing experiments.