Semi-Supervised Learning of Cartesian Factors: A Top-Down Model of the Entorhinal Hippocampal Complex

Abstract

The existence of place cells (PCs), grid cells (GCs), border cells (BCs), and head direction cells (HCs) as well as the dependencies between them have been enigmatic. We make an effort to explain their nature by introducing the concept of Cartesian Factors. These factors have specific properties: (i) they assume and complement each other, like direction and position and (ii) they have localized discrete representations with predictive attractors enabling implicit metric-like computations. In our model, HCs make the distributed and local representation of direction. Predictive attractor dynamics on that network forms the Cartesian Factor “direction.” We embed these HCs and idiothetic visual information into a semi-supervised sparse autoencoding comparator structure that compresses its inputs and learns PCs, the distributed local and direction independent (allothetic) representation of the Cartesian Factor of global space. We use a supervised, information compressing predictive algorithm and form direction sensitive (oriented) GCs from the learned PCs by means of an attractor-like algorithm. Since the algorithm can continue the grid structure beyond the region of the PCs, i.e., beyond its learning domain, thus the GCs and the PCs together form our metric-like Cartesian Factors of space. We also stipulate that the same algorithm can produce BCs. Our algorithm applies (a) a bag representation that models the “what system” and (b) magnitude ordered place cell activities that model either the integrate-and-fire mechanism, or theta phase precession, or both. We relate the components of the algorithm to the entorhinal-hippocampal complex and to its working. The algorithm requires both spatial and lifetime sparsification that may gain support from the two-stage memory formation of this complex.

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“…Semantic memory forms an associative structure that is robust against timing requirements. We reinforce the view that time compression is a key to understanding the time-independent nature of semantic memory that leads to efficient bag-like rep-resentations (Lőrincz and Sárkány, 2017). We quickly review why we adopt this view.…”

“…They are necessary for the formation of both place cells and grid cells (Taube, 2007). This specific feature was exploited as a semi-supervisory signal in the deep learning model that developed both place cells and grid cells from visual and head direction information (Lőrincz and Sárkány, 2017).…”

“…However, Boyce et al (2016) showed causal evidence that contextual memory consolidation depends on theta rhythms during REM sleep: they developed a REM sleep-specific optogenetic silencing method for medium septal GABAergic neurons and showed that silencing during REM sleep impairs the formation of fear-conditioned contextual memory. In this regard it may be worth mentioning that according to simulations (Lőrincz and Sárkány, 2017) both temporal and semantic memories can be important for component formation accompanied by the development of the related metric, important elements of cognition.…”

“…We have collected some factors that may influence component learning and manipulation, but the list is not exhaustive. The starting point is the autoencoder model Lőrincz and Sárkány, 2017). The autoencoder is a comparator that computes the difference between input and the estimated input, the latter of which is derived from the representation.…”

“…To control the components -e.g., to navigate in allothetic coordinates -a representation of the metric is necessary to estimate the magnitude and the direction of control outputs. Particular forms of metric learning exploit the interplay between semantic and episodic memories; see, e.g., (Dragoi and Buzsáki, 2006;Buzsáki and Moser, 2013;Lőrincz and Sárkány, 2017) and the references cited therein. Imprecise interplay including imprecise timing can corrupt component formation and the learning of precise models.…”