Fig. 1. Schematic diagram of DW-based learning in a single-layer photonic SNN.

Fig. 2. Schematic illustration of the ReSuMe incorporated with optical STDP rule. i, d, and o denote the input, the target, and the output, respectively.

Fig. 3. (a1) and (b1) Input pattern and output pattern before delay adjustment. (a2) and (b2) After 7 training epochs.

Fig. 4. Comparison of the learning capability of a single neuron based on (a) weight-based ReSuMe and (b) DW-ReSuMe. The value of SSD after the 50th, 100th, and 300th training epoch is presented for different ti. (c) The valid input window as a function of ηω for different ω0 based on DW-ReSuMe. (d) The valid input window as a function of ω0 for different ηω based on DW-ReSuMe. n=1, td=8  ns.

Fig. 5. (a1) Carrier density of the POST after training and (b1) the evolution of output spikes based on the DW-ReSuMe; (a2) and (b2) those based on ReSuMe. The black solid line is na and the red solid line represents P.

Fig. 6. Evolution of (a1) synaptic weights ωi and (a2) delays di during the first 20 training epochs.

Fig. 7. Learning spike sequences with ununiformed ISI. (a1) and (b1) The evolution of output spikes for spike sequence [10 ns, 12 ns, 14 ns, 18 ns, 20 ns, 22 ns, 24 ns, 26 ns, 29 ns] and [10 ns, 11 ns, 13 ns, 14.5 ns, 17 ns, 21 ns, 23 ns, 25.5 ns, 27 ns], respectively. (a2) and (b2) The evolution for the corresponding distance.

Fig. 8. (a) Training accuracy and (b) testing accuracy varying with training epochs for weight-based ReSuMe (blue solid line) and DW-ReSuMe (red solid line). Td=1  ns, Tω=4  ns. The blue dotted line indicates an accuracy of 90%.

Fig. 9. Illustration of classification results for (a) training data set and (b) testing data set. The orange cycles denote target spiking time, the blue squares represent the actual spiking time, and misclassified samples are highlighted in bright blue.

Fig. 10. Testing accuracy as a function of (a) weight learning window Tω and (b) delay learning window Td.

Fig. 11. (a) Training accuracy and (b) testing accuracy varying with training epochs based on DW-ReSuMe (red solid line) and ReSuMe (blue solid line), respectively. Td=4  ns, Tω=5  ns.

Fig. 12. (a1) Training accuracy and (a2) testing accuracy for the Iris data set after 60 training epochs with different initial delay d0. (b1) and (b2) The results for the breast cancer data set.

Fig. 13. Learning accuracy of the breast cancer data set based on DW-ReSuMe with different cases of ηd. The left column corresponds to the training accuracy with (a1) constant ηd and with (b1) decaying ηd. (a2) and (b2) The right column shows the corresponding results of testing accuracy. Td=4  ns, Tω=5  ns.