Neurons in the medial entorhinal cortex exhibit multiple, periodically organized, firing fields which collectively appear to form an internal representation of space. Neuroimaging data suggest that this grid coding is also present in other cortical areas such as the prefrontal cortex, indicating that it may be a general principle of neural functionality in the brain. In a recent analysis through the lens of dynamical systems theory, we showed how grid coding can lead to the generation of a diversity of empirically observed sequential reactivations of hippocampal place cells corresponding to traversals of cognitive maps. Here, we extend this sequence generation model by describing how the synthesis of multiple dynamical systems can support compositional cognitive computations. To empirically validate the model, we simulate two experiments demonstrating compositionality in space or in time during sequence generation. Finally, we describe several neural network architectures supporting various types of compositionality based on grid coding and highlight connections to recent work in machine learning leveraging analogous techniques.
Keywords: compositionality; entorhinal cortex; generative models; hippocampus.