## 4 Result and Discussion  
In this work, we use Neuroptica [33; 34], which is a customized ONN simulator programmed in Python to simulate the PAM4 signal classify by ONN processing. As discussed above, Figure 2 shows the architecture of a Reck-based ONN to classify the experimentally obtained PAM4 signal. We only use two ports for the classification of the distorted PAM4 signal as indicated in Figure 2. The first port is for receiving the PAM4 data, while the second part is for optical pumping. In this work, the optical pumping is needed to increase signal resolvability and provide additional optical power to amplify the PAM4 data. Similar to the case of coherent detection, the pumping light can amplify the optical signal like the local oscillator (LO) light. Here, we did not consider the additional noise of pumping light in our simulation. However, the influence of additional noise from pumping light on the system will be similar to that of a coherent transmission system. To simulate the PD, a square law detection is implemented at the output ports. The classification result depends on the maximum element in the output matrix. Therefore, the target data should be processed by one-hot encode. To update the ONN parameters, cross-entropy loss function is employed, and the optimizer is the Adam. In order to evaluate the performance of proposed ONN, a fully connected ANN using traditional computer simulation is also performed for comparison. This ANN has a four by four fully connected layer with the ReLU activation function. As the ANN is used to compare with the proposed ONN, it has the same number of neurons as the ONN. Hence, it will theoretically have the same performance as the ONN. The dataset used is experimental data obtained from our previous work in [29]. The received waveforms are adjusted by resampling so that there is one sample per symbol. The data length of each transmission data rate experiment is 217 bauds. We use 20% data for training and 80% for testing. In the proof-of-concept demonstration illustrated in Figure 6, the input data are experimentally generated by a bandwidth-limited SiMRM chip. This experimental ISI-distorted optical PAM4 signal will be detected by a separated PD, and a RTO will store the electrical PAM4 signal as shown in Figure 6. Hence, this stored electrical PAM4 signal can be used for the ONN simulation. In the future ONN chip implementation, the ISI distorted optical PAM4 signal can be directly launched into the ONN chip \"RX signal\" port as shown in Figure 2; hence, no additional OE conversion by the PD is needed. In this case, four on-chip PDs on the ONN chip are used as shown in Figure 2. The optical amplification can be realized by the pumping light as discussed before; hence, VOA and EDFA may not be necessary. Figure 7 shows the accuracy and loss curves for the proposed ONN. It is evident from the results that the ONN exhibits convergence at approximately 100 epochs. Figure 8 illustrates the BER performance of PAM4 signals utilizing both the proposed ONN and ANN. The ONN can recover and classify distorted PAM4 signals within the  
Figure 7: The accuracy and loss curves for the proposed ONN. range of 160 Gbit/s to 240 Gbit/s (i.e., 80 Ghaud to 120 Ghaud). The data rate achieving the SD-FEC threshold (i.e., BER = 2.4 \(\times\) 10\({}^{-2}\)) can be up to 200 Gbit/s. It is worth noting that the proposed ONN without an activation function is particularly sensitive to signal power variations. When the signal power is low, the accuracy of the model tends to decrease significantly. Figure 9 illustrates the accuracy and loss performance of different normalized input signal amplitudes. For better understanding, here, the normalized signal amplitude represents the first level of the PAM4 signal, and the four levels in the PAM4 have the same separation. Taking the signal amplitude of 0.8 as an example, the PAM4 values would be 0.8, 1.6, 2.4 and 3.2. We can observe from Figure 9 that the accuracy and loss performance are poor when the normalized input signal amplitude is lower than 0.6.