Topological Schemas of Memory Spaces

Abstract

Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.

Through synapses to spatial memory maps via a topological model

“…However, the combinations of the coactive place cells, modeled as simplexes of T eff , may represent generic memory elements [84,85]. In other words, it can be argued that the net structure of T eff represents not only spatial, but also nonspatial memories-a larger memory framework that can be viewed as a "memory space" [86,87]. Thus, a disintegration of the cell assembly complex caused by deteriorating synapses discussed above may also be viewed as a model of the full memory space decay.…”

From Topological Analyses to Functional Modeling: The Case of Hippocampus

“…Both complexes and provide a contextual framework for representing spatial information encoded by the place cells (Babichev et al, 2016b ). For example, a sequence of place fields traversed during the rat's moves over a particular trajectory γ and the place cell combinations ignited along this trajectory can be represented, respectively, by a “nerve path” —a chain of nerve-simplexes in , or by a “coactivity path” —a chain of the coactivity-simplexes in (see also Babichev and Dabaghian, 2018 ). These simplicial paths qualitatively represent the shape of the physical trajectories: a closed simplicial path represents a closed physical route; a non-contractible simplicial path corresponds to a class of the physical paths that enclose unreachable or yet unexplored parts of the environment; two topologically equivalent simplicial paths Γ 1 ~ Γ 2 represent physical paths γ 1 and γ 2 that can be deformed into one another and so forth (Brown et al, 1998 ; Jensen and Lisman, 2000 ; Guger et al, 2011 ; Dabaghian, 2016 ).…”

“…A computational framework developed in Dabaghian et al ( 2012 ), Arai et al ( 2014 ), Hoffman et al ( 2016 ), Basso et al ( 2016 ), Babichev et al ( 2016a , b ), Babichev and Dabaghian ( 2018 ), Dabaghian ( 2019 ), and Dabaghian ( 2016 ) helps to understand these phenomena by integrating the activity of the individual neurons into a large-scale map of the environment and to study the dynamics of its appearance, using algebraic topology techniques. Below we review some basic ideas and key concepts used in this framework, and discuss how they may apply to hippocampal physiology and cognitive realm.…”

Replays of spatial memories suppress topological fluctuations in cognitive map

“…Neurophysiologically, place cell replays are viewed as manifestations of the animal’s “mental explorations” (Babichev & Dabaghian, 2018; Dabaghian, 2016; Hopfield, 2010; Zeithamova, Schlichting, & Preston, 2012), which help constructing the cognitive maps and consolidating memories (Ego-Stengel & Wilson, 2010; Gerrard, Kudrimoti, McNaughton, & Barnes, 2001; Girardeau, Benchenane, Wiener, Buzsáki, & Zugaro, 2009; Girardeau & Zugaro, 2011; Roux, Hu, Eichler, Stark, & Buzsáki, 2017). Although the detailed mechanisms of these phenomena remain unknown, it is believed that replays may reinforce synaptic connections that deteriorate over extended periods of inactivity (Sadowski, Jones, & Mellor, 2011, 2016; Singer, Carr, Karlsson, & Frank, 2013).…”