## 3 Results
### Accuracy and Variation Effect  
Figure 7a shows the accuracy according to the simulation time with the different quantization levels transferred by the proposed method. It can be seen that the accuracy of SNNs gradually increased over time. The accuracy loss increased as the quantization level decreased, but the accuracy with 3-level quantization at the steady-state was 97.58%, which was still quite close to that with the full-precision weight. The minimum number of pulse steps (\(N\)) and the accuracy with respect to the quantization level are summarized in Table 1. It indicates that the proposed method can substantially reduce the required pulse steps by more than \(\times 10^{2}\), but there is still a trade-off among the quantization level, the ease of the weight transfer, and the accuracy.  
Figure 5: (**a**) Example of extracting the timing differences from STDP curve with 5-level quantized weights; (**b**) extracted weight map having the value of \(w^{2^{-}},w^{1^{-}},w^{1^{+}},w^{2^{+}}\) connected to the first neuron in the first hidden layer.  
Figure 6: Illustration of the weight mapping process by STDP. The extracted weight map is applied as the voltage inputs. At the same time, a teaching signal with the timing difference obtained from STDP characteristic is applied to the G2 line of the neuron. Then, the weights connected to the neuron are transferred sequentially with the value of \(w^{2^{-}}\), \(w^{1^{-}}\), \(w^{1^{+}}\), \(w^{2^{+}}\).  
Figure 7: (**a**) Classification accuracy according to the simulation time when 3, 7, 5, and 9-level of the quantization weights transferred by the proposed method are used; (**b**) the variation effects on the classification accuracy with 3, 7, 5, and 9-level of the quantization weights.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Weight Level** & **Minimum Steps (N)** & **Accuracy** \\ \hline Full-Precision & 635,200 & 98.23\% \\
3 & 1620 & 97.58\% \\
5 & 3240 & 98.16\% \\
7 & 4860 & 98.22\% \\
9 & 6480 & 98.23\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the \(N\) and the accuracy according to the quantization levels.  
Figure 7b shows the performance by variations of synaptic devices. Since the variation of the initial state of the excitatory and inhibitory synapses as well as the PGM/ERS variation of STDP affects the overall performance, it is necessary to simulate the effect of the variation on the performance of hardware-based SNN. We introduce the variation to the synaptic weights since all the variation sources change the synaptic weights. The variation of the synaptic weights was assumed to show a Gaussian distribution where \(\mu\) and \(\sigma\) were the mean value and the standard deviation, respectively. Here, the mean value was defined as the target weight state, and the variation effect was simulated by varying \(\sigma/\mu\) from 0% to 30% with 5% steps. All the simulation was conducted 10 times for generalization. Overall, as the variation increased, the accuracy decreased more severely. In addition, the accuracy was more vulnerable to the variation as the quantization level increased because the possibility of interfering with the weights of adjacent levels increased. Therefore, as the quantization level increased, the performance can be improved, but more precise variation control is required.