**6.1 Chaotic time series prediction**

To evaluate the precision of our analog DFR system, a chaotic time series prediction benchmark, the tenth-order nonlinear autoregressive moving average system (NARMA10), is carried out, which can be governed by the following equation

$$\begin{array}{c} \mathcal{O}(t) = \mathcal{O} . \mathcal{I} \cdot \mathcal{O}(t) \text{ + } \mathcal{O} . \mathcal{O} . \mathcal{O}(t) \cdot \sum\_{i=0}^{9} \mathcal{O}(t - i) \text{ + } \mathbf{1.5} \cdot \mathcal{D}(t - 9) \text{ & } \mathcal{O} \end{array} \tag{14}$$

**23**

**Figure 16.**

*Target signals versus predicted signals for NARMA10 benchmark.*

*Opening the "Black Box" of Silicon Chip Design in Neuromorphic Computing*

In the training phase, output weights were trained by minimizing the deviation between target and predicted outputs. Both training and testing errors were

√

output signals against target outputs with our analog DFR computing system is plotted in **Figure 16**. From experimental results, the training and testing errors are

where *yi* defines the predicted output, *y*̂*i* is the target output, *N* is the number of

In this task, the application of video frame recognition is chosen to examine the performance of our analog DFR system. In this experiment, 48 images, which comprise three different persons with various face angles, were drawn from the Head Pose Image dataset [58], as demonstrated in **Figure 17a**. Twenty images were used for the training, while another 24 images were used for the testing. In the training phase, the face angle changes from 0 to 75° horizontally. In the testing phase, the rotational angle of face follows the training phase but with additional 15° applied

As illustrated in Section 4.3, our fabricated analog DFR chip is capable to operate at the edge-of-chaos region as the delay changes. To demonstrate the importance of delay, our model was evaluated through several delayed time constants. As depicted in **Figure 18**, it can be observed that the recognition rate changes with regard to the delay time. For instance, the recognition rate maintains above 98% when the system operates at the edge-of-chaos regime (*T* = 20 ms) with 10% or less salt-and-pepper noise. As the noise level approaches to 50%, the recognition rate still maintains above 93%. However, if the dynamic behavior of the system deviates from the edgeof-chaos regime, the recognition rate significantly reduces due to the change in the

∑ *i*=1 *N* (*yi* − *y*̂*i*) 2

\_\_\_\_\_\_\_\_\_\_\_

\_\_\_\_\_\_\_\_\_\_ *N*σ*<sup>y</sup>*̂

determines the output variance. Experimental results of predicted

<sup>2</sup> , (15)

*DOI: http://dx.doi.org/10.5772/intechopen.83832*

achieved by the NRMSE, which can be defined as

*NRMSE* =

found to be 8.49 and 6.83%, respectively.

samples, and σ*<sup>y</sup>*̂

vertically.

dynamic behavior.

2

**6.2 Video frame recognition**

where *D*(*t*) is the random input signal at time *t*, and *O*(*t*) is the output signal. In this experiment, 10,000 sampling points were generated through Eq. (14) for training and testing phases. 6000 samples were used for the training while rest samples were used for the testing. The prediction error was then examined through the normalized root mean square error (NRMSE).

*Opening the "Black Box" of Silicon Chip Design in Neuromorphic Computing DOI: http://dx.doi.org/10.5772/intechopen.83832*

In the training phase, output weights were trained by minimizing the deviation between target and predicted outputs. Both training and testing errors were achieved by the NRMSE, which can be defined as

$$\text{NRMSE} = \sqrt{\frac{\sum\_{i=1}^{N} (y\_i - \hat{y}\_i)^2}{N\sigma\_\beta^2}},\tag{15}$$

where *yi* defines the predicted output, *y*̂*i* is the target output, *N* is the number of samples, and σ*<sup>y</sup>*̂ 2 determines the output variance. Experimental results of predicted output signals against target outputs with our analog DFR computing system is plotted in **Figure 16**. From experimental results, the training and testing errors are found to be 8.49 and 6.83%, respectively.
