Topological Schemas of Memory Spaces

TL;DR

This paper introduces a topological model of hippocampal memory spaces, integrating spatial and nonspatial memories, and links it to cognitive maps and Morris' schemas, offering a new theoretical framework for understanding memory representation.

Contribution

It proposes modeling hippocampal memory spaces as finite topological spaces, providing a unified theoretical approach for spatial and nonspatial memories.

Findings

Memory spaces can be modeled as finite topological spaces.

The model naturally incorporates cognitive maps.

Connection established between memory spaces and Morris' schemas.

Abstract

Hippocampal cognitive map---a neuronal representation of the spatial environment---is broadly discussed in the computational neuroscience literature for decades. More recent studies point out that hippocampus plays a major role in producing yet another cognitive framework that incorporates not only spatial, but also nonspatial memories---the memory space. However, unlike cognitive maps, memory spaces have been barely studied from a theoretical perspective. Here we propose an approach for modeling hippocampal memory spaces as an epiphenomenon of neuronal spiking activity. First, we suggest that the memory space may be viewed as a finite topological space---a hypothesis that allows treating both spatial and nonspatial aspects of hippocampal function on equal footing. We then model the topological properties of the memory space to demonstrate that this concept naturally incorporates the notion of a cognitive map. Lastly, we suggest a formal description of the memory consolidation process and point out a connection between the proposed model of the memory spaces to the so-called Morris' schemas, which emerge as the most compact representation of the memory structure.