7.2.4 Forward model: Multi-layer perceptron

All tasks in this chapter depend on a forward model. It gets as input the sensory information (figure 7.4) of one time step and the motor command consisting of the velocities v_L and v_R, and it predicts the sensory information of the next time step. Training data were collected as described in section 7.2.2.

To anticipate future sensory information beyond the 2 sec prediction horizon of a single forward model, we feed the sensory output back into the sensory input (figure 7.5). This feedback completely overwrites the previous input. At each time step t, the corresponding motor command M_t (here, velocity combinations) of the sequence is fed into the network. Thus, for illustration it seems more intuitive to replace the feedback by a chain of identical forward models (figure 7.6).

Figure 7.5: Forward model with feedback loop. The model maps the sensory information S_t onto S_t+1 in the context of the motor command M_t. The boxes labeled D delay the feedback by one time step.

Figure 7.6: Concatenated chain of forward models. The sensory output of link t is the sensory input of link t + 1.

First, as a forward model, an MLP with one hidden layer was used. The network's activation functions were the identity on input and output layer, and the sigmoidal function in the hidden layer. The MLP had 12 input neurons (two velocity values and the ten sector values) and ten output neurons (ten sector values). The hidden layer comprises 15 hidden units. This number seemed to be a good compromise between recall speed and accuracy. Higher numbers did not improve the performance noticeably. The weights were initialized with random values drawn uniformly from the interval [- 0.5;0.5]. The network was trained on 5466 patterns with 3000 epochs of resilient propagation (RPROP) (Riedmiller and Braun, 1993). The performance of the MLP is shown in section 7.3.1.