Abstract:

Spatial navigation is crucial for the survival of humans and other animals living in complex environments, and efficient spatial navigation requires effective mental representation of spatial information, which is functionally similar to maps in geography and is therefore referred to as cognitive maps. Previous behavioral and modeling studies have shown that cognitive maps have several typical properties. First, selectivity and distortion. Cognitive maps do not faithfully represent all information but selectively represent task-critical information, thereby enhancing the economy of cognition. However, this also implies that there is no completely accurate cognitive map, and cognitive maps serving specific functions are accompanied by distortion. Second, flexibility and redundancy. One of the important manifestations of efficient navigation is the ability to cope with dynamic changes in environmental clues and structures. The flexibility of cognitive maps may be the basis for this ability, but behind the flexibility may be the redundancy of spatial representational format, i.e., the same spatial information may be organized and stored in multiple forms at the same time and invoked under specific conditions. Third, hierarchy and coherence. Navigable space is often nested environments, in which information from different local regions may be organized hierarchically. However, different local regions are gradually integrated with learning, forming a coherent cognitive map eventually.

The brain regions involved in forming cognitive maps include the hippocampus-entorhinal system and the neocortex. The hippocampus-entorhinal system is vital for representing Euclidean metric information, where the place cells in the hippocampus can represent specific locations, and the grid cells in the entorhinal cortex provide background scaling. This system can also represent topological relationships. The scene selection regions which consists of the parahippocampal gyrus, the occipital place area, and the retrosplenial complex, mainly participate in "stitching together" multiple discrete vistas, promoting the formation of a global coherent cognitive map. Different regions of the prefrontal cortex play roles in different stages of spatial navigation, mainly as users and operators of the cognitive map, receiving spatial information from the hippocampus and flexibly applying it to spatial navigation. Besides, the cooperation between the hippocampus and the neocortex may serve as the basis of the selectivity and hierarchy of the cognitive map, but the relationship between the hippocampus and neocortex is still controversial.

The theoretical controversy regarding the representational format of cognitive maps is mainly divided into two schools: Euclidean map and topological graph. The Euclidean map hypothesis assumes that cognitive maps adopt an absolute, globally consistent Euclidean metric structure based on an allocentric reference frame, while the topological graph hypothesis assumes that cognitive maps only encode rough topological structures, representing location nodes and the connection relationships between them. Neither of these two assumptions can fully account for the characteristics observed in navigation behavior, so some researchers have attempted to combine them, proposing hybrid theories such as the labeled graph hypothesis and the reference frame network theory. Other researchers have also attempted to integrate them using a unified mechanism, proposing the Tolman-Eichenbaum machine and the successor representation models. However, these theories overlook the hierarchical nature of spatial representation. Early researchers proposed the hierarchical representation theory of nested spaces, which suggests that different regions of an environment are stored in different branches of a tree-like structure. More detailed spatial knowledge is stored or represented at lower levels, while more abstract and generalized spatial knowledge corresponds to higher levels.

Neither the Euclidean map nor the topological map contains hierarchical information. Hierarchy is closely related to spatial scales. The hierarchical nature of cognitive maps emerges when navigators represent the large-scale environments or nested spaces, while both Euclidean and topological representation exist within a relatively smaller scale. However, since the construction of cognitive maps is a dynamic process, the large-scale space is not fixed. As the cognitive map gradually expands, the boundaries of different regions in the initial large-scale space may gradually overlap, resulting in a fusion of spatial representation. The hierarchical nature of the initial large-scale space representation may gradually decrease or even disappear in this process, forming a global and homogeneous cognitive map that contains both Euclidean and topological information. New relationship connecting sub-regions belonging to different upper levels would develop correspondingly as well. Hierarchical representations in different-scale environments may be organized in a "back-to-front" order from the hippocampus to the prefrontal cortex. The prefrontal cortex have a larger predictive field, while the hippocampus has a relatively smaller counterpart. Therefore, the prefrontal cortex may be at a higher level of the hierarchical representation. The scene selection area weaves local areas into a whole, which may fill the gap in the representation content between the hippocampal-entorhinal system and the prefrontal cortex.

Key words: cognitive map, Euclidean map, topological graph, hierarchy, spatial representation