Self-organizing path integration using a linked continuous attractor and competitive network: Path integration of head direction

Abstract

A key issue is how networks in the brain learn to perform path integration, that is update a represented position using a velocity signal. Using head direction cells as an example, we show that a competitive network could self-organize to learn to respond to combinations of head direction and angular head rotation velocity. These combination cells can then be used to drive a continuous attractor network to the next head direction based on the incoming rotation signal. An associative synaptic modification rule with a short term memory trace enables preceding combination cell activity during training to be associated with the next position in the continuous attractor network. The network accounts for the presence of neurons found in the brain that respond to combinations of head direction and angular head rotation velocity. Analogous networks in the hippocampal system could self-organize to perform path integration of place and spatial view representations.

Keywords:

• Continuous attractor networks
• self-organization
• trace learning
• competitive learning
• head direction cells
• path integration

Notes

¹The scaling factor (ϕ₁/C^{HD → HD}) controls the overall strength of the recurrent inputs to the layer of head direction cells, where ϕ₁ is a constant and C^{HD → HD} is the number of presynaptic connections received by each head direction cell from other head direction cells.

²The scaling factor controls the overall strength of the combination cell inputs, where ϕ₂ is a constant, and C^{COMB → HD} is the number of connections received by each head direction cell.

³The scaling factor controls the overall strength of the inputs from the head direction cells, where ϕ₃ is a constant, and C^{HD → COMB} is the number of connections received by each combination cell from head direction cells. The scaling factor for the rotation inputs is defined equivalently.