Grid coding, spatial representation, and navigation: Should we assume an isomorphism?

Abstract

Grid cells provide a compelling example of a link between cellular activity and an abstract and difficult to define concept like space. Accordingly, a representational perspective on grid coding argues that neural grid coding underlies a fundamentally spatial metric. Recently, some theoretical proposals have suggested extending such a framework to nonspatial cognition as well, such as category learning. Here, we provide a critique of the frequently employed assumption of an isomorphism between patterns of neural activity (e.g., grid cells), mental representation, and behavior (e.g., navigation). Specifically, we question the strict isomorphism between these three levels and suggest that human spatial navigation is perhaps best characterized by a wide variety of both metric and nonmetric strategies. We offer an alternative perspective on how grid coding might relate to human spatial navigation, arguing that grid coding is part of a much larger conglomeration of neural activity patterns that dynamically tune to accomplish specific behavioral outputs.

Keywords: entorhinal cortex; grid cells; heuristics; human behavior; spatial navigation.

Figure 1:

Navigation in everyday situations: Getting from the Psychology Building to the Student Union at University of Arizona based on the representation and dynamical systems perspectives (a) Representational perspective: Grid cells, which arise as a result of input from other neural systems, represent the Euclidean coordinates of the environment and provide a direct relationship with behavior. Note, for convenience, only one grid cell is shown, but we assume multiple grid cells of different scales, orientations, and phases are present. M is a transform function that maps this grid activity to behavior and M-1 is the inverse transform function. To navigate to the student union, this grid code could serve as the basis for navigating from one location (Psychology Building) to the next (Student Union) based on aligning the grid to a landmark and calculating the vector addition of linear paths (b) Dynamical systems perspective: Here, r(t+1) is the cortical activity at time t+1, which is modulated from neuronal inputs {h_n(t+1)… h_n+N(t+1)}, which themselves are modulated by behavior b(t). G is a non-invertible transform function that maps neuronal activity to behavior. The gray box signifies the internal representation of the environment and whether it is Euclidean or not depends on task demands T(). T(), in turn, a function of environmental complexity c(), prior experience e() and other latent factors. Navigating, in this scenario will involve a dynamic interaction between neural activity from multiple senses (visual, vestibular, somatosensory, and auditory), memory systems, and other knowledge (west is to my left) to optimize the strategy employed. For example, when navigating from the Psychology Building, one may initially take a sub-optimal path around a building, but then seeing another building reminds one that they are close to the Student Union and need only head north-west to get there. Once the Student Union is in sight, a beaconing strategy is sufficient to arrive there.