Connectionists: three articles on head direction, grid, and place cell learning

[Stephen Grossberg]

The following three articles are now available at http://cns.bu.edu~steve about how head direction, grid, and place cells are learned.

Pilly, P.K. and Grossberg, S. (2012). How do spatial learning and memory occur in the brain? Coordinated learning of entorhinal grid cells and hippocampal place cells. Journal of Cognitive Neuroscience, in press. 

Abstract
Spatial learning and memory are important for navigation and the formation of episodic memories. The hippocampus and medial entorhinal cortex are key brain areas for spatial learning and memory. Place cells in hippocampus fire whenever an animal is located in a specific region in the environment. Grid cells in the superficial layers of medial entorhinal cortex provide inputs to place cells, and exhibit remarkable regular hexagonal spatial firing patterns that tessellate a whole environment during navigation. They also exhibit a gradient of spatial scales along the dorsoventral axis of the medial entorhinal cortex, with neighboring cells at a given dorsoventral location having different spatial phases. A neural model shows how a hierarchy of self- organizing maps, each obeying the same laws, responds to realistic rat trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with unimodal firing fields that fit neurophysiological data about these cells and their development in juvenile rats. The hippocampal place fields represent much larger spaces than the grid cells, indeed spaces large enough to support navigational behaviors. Despite their different appearance, both types of receptive fields are learned because each of the self-organizing maps amplifies and learns to categorize the most energetic and frequent co-occurrences of their inputs. Top-down attentional mechanisms from hippocampus to medial entorhinal cortex help to dynamically stabilize these spatial memories. Neurophysiological data are summarized that support this hypothesis. Spatial learning through medial entorhinal cortex to hippocampus occurs in parallel with temporal learning through lateral entorhinal cortex to hippocampus. Together these homologous spatial and temporal representations illustrate a kind of “neural relativity” that may provide a substrate for episodic learning and memory.
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Grossberg, S., and Pilly, P.K. (2012). How entorhinal grid cells may learn multiple spatial scales from a dorsoventral gradient of cell response rates in a self-organizing map. PLoS Computational Biology, in press.

Abstract
Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.
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Fortenberry, B., Gorchetchnikov, A. and Grossberg, S. (2012). Learned integration of visual, vestibular, and motor cues in multiple brain regions computes head direction during visually-guided navigation. Hippocampus, in press. 

Abstract
Effective navigation depends upon reliable estimates of head direction (HD). Visual, vestibular, and outflow motor signals combine for this purpose in a brain system that includes dorsal tegmental nucleus, lateral mammillary nuclei, anterior dorsal thalamic nucleus, and the postsubiculum. Learning is needed to combine such different cues to provide reliable estimates of HD. A neural model is developed to explain how these three types of signals combine adaptively within the above brain regions to generate a consistent and reliable HD estimate, in both light and darkness, which explains the following experimental facts. Each HD cell is tuned to a preferred head direction. The cell‟s firing rate is maximal at the preferred direction and decreases as the head turns from the preferred direction. The HD estimate is controlled by the vestibular system when visual cues are not available. A well-established visual cue anchors the cell‟s preferred direction when the cue is in the animal‟s field of view. Distal visual cues are more effective than proximal cues for anchoring the preferred direction. The introduction of novel cues in either a novel or familiar environment can gain control over a cell‟s preferred direction within minutes. Turning out the lights or removing all familiar cues does not change the cell‟s firing activity, but it may accumulate a drift in the cell‟s preferred direction. The anticipated time interval (ATI) of the HD estimate is greater in early processing stages of the HD system than at later stages. The model contributes to an emerging unified neural model of how multiple processing stages in spatial navigation, including postsubiculum head direction cells, entorhinal grid cells, and hippocampal place cells, are calibrated through learning in response to multiple types of signals as an animal navigates in the world.

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