Compositional Sequence Generation in the Entorhinal–Hippocampal System

Abstract

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.

Constructing Condensed Memories in Functorial Time

“…Recent experimental work indicates that space and time representations are dissociable at the functional-network level in humans for short-duration event sequences (Schonhaut, Aghajan, Kahana & Fried, 2022), suggesting at least that the same is true for the long-time representations of interest here. Such dissociability is assumed by all models that treat spatial representations as "maps" that are invariant across time, as they must be to support flexible composition of sequences of actions either in memories or in plans (McNamee et al, 2022).…”

Determinantal point process attention over grid cell code supports out of distribution generalization

“…Although grid cells were discovered for representations of space ( Hafting et al, 2005 ; Sreenivasan and Fiete, 2011 ; Mathis et al, 2012 ) and used for guiding spatial behavior ( Erdem and Hasselmo, 2014 ; Bush et al, 2015 ), they have since been identified in non-spatial domains, such as auditory tones ( Aronov et al, 2017 ), odor ( Bao et al, 2019 ), episodic memory ( Chandra et al, 2023 ), and conceptual dimensions ( Constantinescu et al, 2016 ). These findings suggest that the coding scheme used by grid cells may serve as a general representation of metric structure that may be exploited for reasoning about the abstract conceptual dimensions required for higher-level reasoning tasks, such as analogy and mathematics ( McNamee et al, 2022 ). Of interest here, the periodic response function displayed by grid cells belonging to a particular frequency is invariant to translation by its period, and increasing the scale of a higher-frequency response gives a lower-frequency response and vice versa, making it invariant to scale across frequencies.…”