Topological Schemas of Cognitive Maps and Spatial Learning

Abstract

Spatial navigation in mammals is based on building a mental representation of their environment—a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains vague. A key difficulty is that these maps are collective, emergent phenomena that cannot be reduced to a simple combination of inputs provided by individual neurons. In this paper we suggest computational frameworks for integrating the spiking signals of individual cells into a spatial map, which we call schemas. We provide examples of four schemas defined by different types of topological relations that may be neurophysiologically encoded in the brain and demonstrate that each schema provides its own large-scale characteristics of the environment—the schema integrals. Moreover, we find that, in all cases, these integrals are learned at a rate which is faster than the rate of complete training of neural networks. Thus, the proposed schema framework differentiates between the cognitive aspect of spatial learning and the physiological aspect at the neural network level.

Transient cell assembly networks encode stable spatial memories

“…Physiological vs. schematic learnings. The schematic approach proposed in [23] allows describing the process of spatial learning from two perspectives: as training of the synaptic connections within the cell assembly network-referred to as physiological learning in [23]-or as the process of establishing large-scale topological characteristics of the environment, referred to as "schematic," or "cognitive," learning. The difference between these two concepts is particularly apparent in the case of the rewiring cell assembly network, in which the synaptic configurations may remain unsettled due to the rapid transience of the connections.…”

“…Numerical simulations show that, for a given population of place cells, the clique complex T ς is typically larger and forms faster than the coincidence detector (Čech) complex T ς , and, as a result, T ς reproduces the topological structure of the environment more reliably [23,46]. Moreover, the coincidence detection coactivity complexes can be viewed as a specific case of the input integration coactivity complexes: as the integration period shrinks and approaches the coactivity period → w, the input integration coactivity complex T ς reduces to the coincidence complex T ς .…”

“…In a more detailed approach, the maximal simplexes of the coactivity complex (i.e., the simplexes that are not subsimplexes of any larger simplex) may be selected to represent ignitions of the place cell assemblies, rather than arbitrary place cell combinations. The combinatorial arrangement of the maximal simplexes in the resulting "cell assembly coactivity complex," denoted T CA , schematically represents the network of interconnected cell assemblies [23,46] (Fig. 2A).The specific algorithm of constructing the complex T CA may also reflect how neuronal coactivity is processed by the readout neurons.…”

Through synapses to spatial memory maps via a topological model

“…Studies of place cells' spiking times point out that these neurons tend to fire in "assemblies"-functionally interconnected groups that are believed to synaptically drive a population of "readout" neurons in the downstream networks [25][26][27][28][29]. The latter are wired to integrate spiking inputs from their respective cell assemblies and actualize the connectivity relationships between the regions encoded by the corresponding place cells [29,30].…”

Persistent Memories in Transient Networks

“…On the other hand, the cell assembly complex T CA provides semantics for describing the global spatial memory map in topological terms [24]. For example, a sequence of cell assemblies ignited along a path γ navigated by the rat corresponds to a chain of simplexes Γ ∈ T CA -a "simplicial path" (Fig.…”