Emergence of Functional Hierarchy in a Multiple Timescale Neural Network Model: A Humanoid Robot Experiment
Figure 10
The main part of the system is the CTRNN. The total number of CTRNN units was 180. The first 100 units (indices i = 1‥100) correspond to input-output units (O). Among input units, the first 64 units (indices i = 1‥64) correspond to proprioceptive inputs (M), whereas the last 36 units (indices i = 65‥100) correspond to vision inputs (S). The remaining 80 units (indices i = 101‥180) correspond to the context units. Among the context units, the first 60 units (indices i = 101‥160) correspond to the fast context units (Cf), and the last 20 units (indices i = 161‥180) correspond to the slow context units (Cs). Inputs to the system were the proprioception mˆ t and the vision sense ŝ t , which were transformed into sparsely encoded vectors using topology preserving maps (TPM, Equation 3), one map corresponding to proprioception (TPMm) and one map corresponding to vision (TPMs). A 100-dimensional vector, transformed by the TPM (pi,t) and previous activation levels of the context units yi,t−1, is set to the neural states xi,t (Equation 7). Membrane potential (ui,t) and activation (yi,t) of each unit are calculated using Equation 5 and Equation 6, respectively. Outputs of the CTRNN (yi,t, i∈O) are transformed into 10 dimensional vectors (mt+1 and st+1) using inverse computation of the TPM (iTPM, Equation 4). These 10 dimensional vectors correspond to predictions of the proprioception mt+1 and the vision sense st+1 for the next time step. This prediction of the proprioception mt+1 was sent to the robot in the form of target joint angles, which acted as motor commands for the robot in generating movements and interacting with the physical environment. Changes in the environment resulting from this interaction were sent back to the system in the form of sensory feedback. In training, output of the CTRNN (yi,t, i∈O) is compared with the desired output y* i,t calculated from target sensori-motor states m*t+1 and s*t+1, using the same TPMs.