The synaptic weights from the Combination (COMB) cell network to the Head Direction (HD) cell network after learning with the time-delayed Hebbian associative learning rule (10) and weight normalization (13).

<p>These results are from a simulation with an axonal conduction delay of 100 ms, and a rotational velocity during training of (all other parameters are as given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058330#pone-0058330-t001" target="_blank">Table 1</a>). Each of the four plots shows the learned synaptic weights from a different presynaptic COMB cell to the 500 postsynaptic HD cells. The postsynaptic HD cells are arranged in the plots according to where they fire maximally in the head-direction space of the agent when visual input is available. For each plot, a dashed vertical line indicates the postsynaptic HD cell with which the presynaptic COMB cell has maximal synaptic weight as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058330#pone-0058330-g004" target="_blank">Figure 4</a>. In each plot, the synaptic weight profile is asymmetric about the postsynaptic HD cell with maximal synaptic weight, indicating that the presynaptic COMB cell preferentially stimulates an HD cell representing a different head direction to the HD cell from which the COMB cell receives maximal synaptic weight. This reflects the fact that the packet of HD cell activity will have moved through the head-direction space of the agent in the time it takes for a signal to travel from the HD cells through the synapses to the COMB cells, and back again to the HD cells through the synapses. Thus, the axonal conduction delays in the and synapses act, through learning, as a timing mechanism that enables the update of the packet of head-direction cell activity at the same speed as the agent is rotating.