## 3 Results
### Bandwidth Limitations  
To evaluate bandwidth's impact on the proposed PSCNN, an analysis of the two modes of operation, training and inference, is presented. When the network operates in inference or training mode then there are bandwidth limitations related to the electro-optic synapses; meaning that optical spikes generated by the neurons are detected by analog PDs (with appropriate bandwidth). The electrical spikes generated are processed also in the analog domain and are used to modulate (excite) subsequent neurons; meaning that the spiking nature of the pulses can be reproduced with reliability by PDs and electronics of 20 GHz that can drive state of the art VCSELs of similar modulation bandwidth. Furthermore, aiming to render our scheme hardware-friendly and avoid high performance PDs, we can use photodiodes with lower bandwidth at the cost of lower spike amplitude. This drawback can be amended by scaling the synaptic weights, which will be realized using RF electronics [9]. More importantly, real-life VCSELs generate neural spikes with significantly broader temporal width (>200 ps) [43], compared to the VCSEL assumed in this work. In this case, the minimum bandwidth requirements drop significantly (1-5 GHz) and can be realized with low-cost PDs. This spike duration increase could also affect the refractory period of the VCSELs; thus, it could potentially affect time-multiplexing capabilities but not accuracy. Taking into consideration that nanosecond refractory period is extreme for realistic image processing, but the basic concept of this work remains valid even with such a modification. In terms of training, bandwidth demands are anticipated to be enhanced, mainly due to the STDP technique. In particular, hardware realizations of STDP dictate the precise knowledge of the time of arrival of each spike at each synapse, so as to preserve accuracy [38; 41]. Taking into consideration that potentiation/depression window in our case is \(\approx\)1 ns and the refractory period is 5 ns, then a 20 GHz bandwidth can guarantee temporal accuracy. An alternative approach could include offline training through a physically accurate model and limiting the hardware module in an inference  
Figure 9: PSCNN classification error for different values of the intensity noise. The intensity noise is drawn from a normal distribution whose standard deviation is expressed as a percentage of the nominal input power \(P_{IN}~{}=~{}0.2\) mW (\(x\)-axis). For intensity noise values up to 6% (12 \(\upmu\)W) no classification error is monitored. However, for higher values of intensity noise there is a sharp increase in network’s classification error and for a standard deviation of 11% (22 \(\upmu\)W) the system collapses since it cannot classify the input images. In this figure, digit ‘6’ is presented as an indicative example of the intensity noise’s impact. The left image of digit ‘6’ represents the case of no intensity noise while the right one corresponds to an intensity noise of 16%.  
mode. In this case, structural deviations could be fine-tuned through optimization of spike delays at the synchronization layer and by adjusting the synaptic weights.