Are Grid-Like Representations a Component of All Perception and Cognition?

Abstract

Grid cells or grid-like responses have been reported in the rodent, bat and human brains during various spatial and non-spatial tasks. However, the functions of grid-like representations beyond the classical hippocampal formation remain elusive. Based on accumulating evidence from recent rodent recordings and human fMRI data, we make speculative accounts regarding the mechanisms and functional significance of the sensory cortical grid cells and further make theory-driven predictions. We argue and reason the rationale why grid responses may be universal in the brain for a wide range of perceptual and cognitive tasks that involve locomotion and mental navigation. Computational modeling may provide an alternative and complementary means to investigate the grid code or grid-like map. We hope that the new discussion will lead to experimentally testable hypotheses and drive future experimental data collection.

Keywords: attractor; cognition; grid cell; perception; recurrent neural network.

Figure 1

Grid-like responses across rodent and human brains. (A) Electrophysiological data show grid-like firing patterns from the rat primary somatosensory cortex (S1) (images are modified from Long and Zhang, , Cell Research; reprinted with permission, Creative Commons CC BY license) and the secondary visual cortex (V2) while animals navigated in an open field arena. Color bar shows the firing rate in spikes/s (figure is modified from Long et al., , bioRxiv). (B) Human invasive electrophysiological data show grid-like representations in the anterior cingulate cortex during a virtual navigation task. Color bar shows the firing rate (Hz) (figures are modified from Jacobs et al., , Nature Neuroscience; reprinted with permission, from the authors and Springer Nature). (C) Human fMRI data show grid-like representations in the ventromedial prefrontal cortex (vmPFC) during a two-dimensional olfactory navigation task (figures are modified from Bao et al., , Neuron; reprinted with permission, from the authors and Elsevier). (D) Left panel: example of audiovisual object—Nine audiovisual objects were created by manipulating the size of a shape and the pitch of an associated sound, produced during a short squeezing animation. Middle panel: Each audiovisual object was given an abstract name, that could be conceived as a location in a 2D word space. Right panel: Illustration of detection of grid code (figures are modified from Vigano et al., , Neuroimage; reprinted with permission, from the authors and Elsevier).

Figure 2

Computational models that explain grid-like computation in spatial and conceptual domains. (A) To model the grid cells in the rat V2 visual cortex, we trained an excitatory-inhibitory (E/I) recurrent neural network (RNN) using both velocity input (V_x, V_y) and visual input of varying dimension (based on dimensionality reduction from PCA) to decode a simulated agent's trajectory (x,y) in an open field environment. Emergent grid-like responses were found in the RNN's hidden units (Z.S. Chen, Data unpublished). (B) A schematic of continuous attractor model for V2 grid cells based on excitatory-inhibitory neuron population interaction. (C) Schematic of clustering in spatial and conceptual domains based on the cluster-monitoring/error-monitoring mechanism (figures are modified from Mok and Love, , Nature Communications; reprinted with permission, from the authors and Springer Nature). (D) E/I feedforward neural network for clustering or learning similarity-preserving map based on local Hebbian rules (Sengupta et al., 2018). (E) Illustration of grid cells in cognitive space. Left: 3D feature space that defines independent dimensions satisfying geometric constraints for vehicle. Middle left: 2D space spanned by the dimensions of engine power and car weight. Middle center: Multiple place cells with different firing fields. Middle right: single grid cell with regular periodic firing field. Right: Navigation in a continuous cognitive “car” space (figures are modified from Bellmund et al., , Science; reprinted with permission, from AAAS).

Figure 3

Schematic of identified brain structures with four major types of spatial tunings. ATN, anterior thalamic nuclei; S1, primary somatosensory cortex; PPC, posterior parietal cortex; V1, primary visual cortex; V2, secondary visual cortex; A1, primary auditory cortex; PC, piriform cortex; RSC, retrosplenial cortex; HPC, hippocampus; mEC, medial entorhinal cortex; POR, postrhinal cortex; PER, perirhinal cortex; preSub, presubciculum), paraSub (parasubiculum); postSub, postsubiculum; OFC, orbitofrontal cortex; mPFC, medial prefrontal cortex; ACC, anterior cingulate cortex. Arrow indicates the connectivity.