Training and testing: in the model, and in a cortical implementation.

<p>(A) The training and testing procedure in the model. Three discrete times steps are arrayed vertically. At each one, the current arm position (<b>θ</b>_<i>t</i>) is reported by the proprioceptive population (orange) with Poisson-distributed spike counts, as shown in the first column. The current motor command is likewise reported by an “efference-copy” population (purple). Second column: this spiking, along with recurrent activities (dark turqoise), stochastically drives single spikes in the hidden layer (turquoise). Third column: these spikes in turn drive the three “input” populations (this is not required during testing); a “copy” of the hidden vector is also saved to serve as recurrent activity at the next time step (curved black arrow). Fourth column: finally, the input populations drive the hidden layer once more, after which the weights are changed according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004554#pcbi.1004554.e040" target="_blank">Eq. 9</a> (also not required during testing). At every time step, the current joint angle and current control are decoded naïvely from the current activities of their respective input populations; with Kalman filters that are recursively updated based on these activities (not depicted in this figure); and from the hidden units of the rEFH. (B) A possible cortical implementation of the rEFH. The cortical layers of Brodmann Area 5 and its inputs are identified with elements of the rEFH by color. The synaptic connections are denoted by the arrows and their corresponding weight matrices. Primary somatosensory cortex (S1) provides feedforward proprioceptive input to layer IV, while primary motor cortex (M1) provides feedback input—a copy of the efferent command—to layer II/III. The recurrent signal of the rEFH (heavy curved arrow in (A)) is identified with a reverberatory loop from II/III to VI, to V, and back to II/III.