We utilized our proposed learning block (Figure 2, B-C ) to realize neuromorphic representation with PES learning, using the input signal itself as a reference signal (Figure 3, A ). We used the system to encode and decode exponential and sinusoidal signals with two, four, and eight OZ neurons (Figure 3, B-D ). As expected, followingEquation 4 , as the number of neurons increases, the learning system’s performance improves. Our hardware simulation-derived results (Figure 3, D, red traces ) closely follow Nengo’s NEF-based software simulation (Figure 3, D, purple traces ), with a cross-correlation similarity (sliding dot product) of 0.872±0.032. We show that an analog learning system comprising only 8 OZ neurons can accurately represent the input with a swift convergence toward the represented value.
As described above, representation is highly dependent on neuron tuning. The results shown in Figure 3, B-D were derived using neurons with a bounded activation distribution. We further represented the sinusoidal input with neurons characterized by uniform and pure activations, following Figure 1, C. The results are shown inFigure 3, E. We evaluated this representation using the three activation schemes with one to eight neurons by calculating the error’s root mean square (RMS). Our results demonstrate the superior performance for a bounded distribution of neuron tuning (Figure 3, F ). The continually changing weights of each neuron are shown in Figure 3, G , demonstrating continual online learning.