Recently, a cross-point synaptic memristor arrays have been employed to implement synaptic cores of various ANNs, i.e., deep neural networks (DNNs), spiking neural networks (SNNs), and convolutional neural networks (CNNs). The most of reported studies conducted training and inference of ANNs using analog synaptic weight modulation of memristors such as resistive random access memory (ReRAM), phase change random access memory (PCRAM), and ferroelectric random access memory (FeRAM). In other words, no case has been reported so far in which a synaptic memristor with quantized multi-bit is utilized onto a synaptic core of a quantized neural network (QNN).In this study, for the first time, we introduced the multi-bit self-rectifying synaptic memristor having tri-layer structure being composed of oxygen-rich AlOx rectifying layer, oxygen-deficient HfOx top switching layer, and oxygen-rich HfOy bottom switching layer for quantization aware training of QNN. The resistive switching and self-rectifying mechanism of the multi-bit self-rectifying synaptic memristor was evidently proven by precisely investigating migration of oxygen ions and vacancies in resistive switching layers via ToF-SIMS and XPS depth profiles depending on the resistance states (i.e., pristine, set, and reset). The designed multi-bit self-rectifying synaptic memristor presented linear, discrete, and quantized 4-bit (i.e., 16-level) conductance level depending on incremental write pulse number, which was 4-bit self-rectifying synaptic memristor for the first time. In addtion, the quantization aware training (QAT) was conducted using 4-bit quantized conductance level of the desgiend multi-bit self-rectifying synaptic memristor via stright through estimator (STE). Finally, three different iris datasets were successfully classified using a quantized neural network designed via SPICE circuit simulation. The conductance mechanism of the self-rectifying synaptic memristor and its application of QNN will be presented in detail. Acknowledgement This research was supported by National R&D Program through the National Research Foundation of Korea(NRF) funded by Ministry of Science and ICT(2021M3F3A2A01037733) Figure 1