Fig. 1. Artificial intelligent computing. (a) Linear and nonlinear computing; (b) deep neural network; (c) reservoir computing

Fig. 2. MRR. (a) All-pass MRR. (b) add-drop MRR

Fig. 3. Schematic of WDM-based MVM system. (a) Basic MVM^[50]; (b) schematic diagram of MRR weight bank^[50]; (c) schematic diagram of single-end detection MRR array^[51]; (d) schematic diagram of crossbar MRR array^[52]; (e) schematic diagram of PCM array^[6]

Fig. 4. MRR MVM weight bank for linear signal processing. (a) Pulse shaping using MRR array^[53]; (b) linear binary MVM using MRR array^[54]; (c) schematic diagram of WDM scalable “broadcast and weight” architecture^[50]; (d) arbitrary continuous positive/negative MVM using MRR weight bank^[55]; (e) optoelectronic recurrent neural network using MRR weight bank^[56]; (f) all optical neuromorphic processing using PCM and MRRs^[57]; (g) ultra-high parallelism MVM using the PCM array^[6]

Fig. 5. Novel optical computing architecture based on the MRRs. (a)(b) Simultaneously achieving neural network forward propagation and back propagation using MRR^[52,58]; (c) high order tensor convolution processing using MRR^[44]; (d) high parallelism convolution using MRR and optical frequency comb^[45]; (e) MRR array based on MDM and WDM^[59]; (f) high-dimensional lightwave and microwave multidomain multiplexing integrated photonic tensor core^[60]; (g) high endurance MRR array based on non-reciprocal magneto-optics with ultra-high endurance^[61]; (h) electrically programmable and non-volatile MRR array based on phase-change materials^[62]

Fig. 6. Microring architecture and its all-optical nonlinear response. (a) Microring architecture and its key parameters; (b) time scale of various nonlinear effects in microrings; (c) resonant response of microrings and the changes in the red and blue shifts of their resonant wavelengths; (d) hysteresis curves of microring output power and input power; (e) temporal variations of output power, intracavity energy, temperature changes, and free carrier concentration in microrings

Fig. 7. All-optical reconfigurable nonlinear activation functions based on MRR. (a)(b) All-optical reconfigurable nonlinear activation functions based on silicon MRR-assisted MZI^[72]; (c)(d) all-optical reconfigurable nonlinear activation functions based on silicon nitride MRR with PCM^[57]; (e)(f) all-optical reconfigurable nonlinear activation functions based on silicon MRR with PCM^[73]; (g)(h) all-optical reconfigurable nonlinear activation functions based on Ge/Si hybrid MRR^[74]

Fig. 8. All-optical MRR spiking neurons. (a) Structure and basic properties of biological spiking neurons; (b1)‒(b4) silicon MRR spiking neuron^[70]; (c1)‒(c3) silicon MRR spiking neuron with suppressed refractory period^[76]; (d1)‒(d4) hybrid graphene-on-silicon MRR spiking neuron^[77]

Fig. 9. Major advances in OEO photonic neurons based on microring resonators. (a) First integrated OEO neuron based on silicon microring modulator^[81]; (b) integrated OEO neuron based on microring modulator and on-chip trans-impedance^[7]; (c) wire-bonded OEO neuron based on microring modulator and off-chip trans-impedance amplifier chip^[9]; (d) integrated OEO neuron based on microring modulator in a programmable configuration^[13]

Fig. 10. Optical computing system based on MRR for AI. (a) DONN based on MRR weight bank and OEO MRR neuron^[7]; (b) DONN based on on-chip optical attenuators and OEO MRR neuron^[9]; (c) DONN based on MZI-mesh and OEO MRR neuron^[13]; (d) space-division-multiplexing optical reservoir computing based on all-optical nonlinearity of MRR^[83]; (e) time-division-multiplexing optical reservoir computing without feedback loop based on all-optical nonlinearity of MRR^[84]; (f) time-division-multiplexing optical reservoir computing with feedback loop based on all-optical nonlinearity of MRR^[85]

Fig. 11. MRR weight control and high-precision computing. (a) Feedback control based on N-doped MRR^[86]; (b) 9 bit weight precision realized by dithering control^[88]; (c) self-calibrating weight with dual-wavelength synchronization^[89]; (d) 11.3 bit weight precision of single MRR based on all-analog circuits^[91]; (e) over 9 bit weight precision realized by calibration-free Chil-in-the-loop optimization^[90]; (f) digital-analog hybrid computing achieves 16 bit computing precision^[92]

Fig. 12. Optical computing system robust optimization. (a) Noise-aware training enables system operates stably with system low precision control^[93]; (b) noise-aware training improves system robustness against high-speed system noise^[94]; (c) noise-aware training improves generative model’s robustness against noise^[95]; (d) hardware-aware training achieves MRR stable operation without TEC by alleviating MRR’s component stability^[96]; (e) hardware-aware training significantly improves model's robustness by simultaneously alleviating component stability and system stability^[97]

Fig. 13. Applications of MRR in photonic computing. (a) MRR array for solving NP-complete problems^[105]; (b) MRR array for solving partial differential equations (PDEs)^[106]; (c) MRR array for compensating nonlinear effects in optical fibers^[7]; (d) MRR array for solving dynamic radio-frequency interference problems^[107]; (e) MRR array for compensating dispersion effects in optical fibers^[108]; (f) MRR array for analog spatiotemporal feature extraction^[109]; (g) MRR array for end-to-end image processing^[110]