Fig. 1 shows typical bipolar resistive switching characteristics of the Pt/HfOx/TiN device with 10 voltage sweeps from 0 to 2V for set and 0 to -2.5V for reset, respectively. A 100 μA current compliance was applied to protect the device during the set process. We will utilize the gradual reset process for analog weight tuning. Fig. 2 shows our optimization flow of the programing protocol. It is expected that larger amplitude pulses may reach a target state faster but with less precision, while smaller amplitude pulses will approach the state more precisely but require an exponentially longer time . Therefore, our tuning process is based on a sequence of pulses with increasing amplitude steps (Vstep) ramps, and the voltage polarity depends on the relative difference between the current conductance state and the target conductance state (Gtarg). The device conductance state (G) is checked with a read pulse (0.1 V) after each programming pulse. If the conductance reaches the target, the program stops. If the conductance overshoots the tolerance of Gtarg. Then, a new voltage ramp of opposite polarity starts. Fig. 3 shows that the tuning process with fixed 100 μs pulse width but different Vstep (10mV, 20mV, 40mV, 60mV, and 80mV) starting from 0.6V and -0.6V for set and reset sequences, respectively. For each Vstep, the experiments were repeated 5 times. Fig. 4 shows the representative tuning process to illustrate the overshoot problem. Using pulses with larger Vstep (e.g., 80mV) takes shorter time to reach Gtarg, but it runs a risk of overshoot due to the stochastic nature of the atomic oxygen ions and vacancies migration . Once overshoot occurs, then we need to set the device and restart the reset process. Table 1 counts the number of overshoot for different Vstep and the average pulses needed to reach Gtarg. Vstep=40mV gives a balance in between. Fig. 5 shows the tuning process with fixed pulse amplitude (1.2V) but different pulse widths (Tstep=500ns, 10μs, and 100μs), the tuning time is much longer than that of increasing pulse amplitude, which indicates that tuning Vstep is more effective. Therefore, using optimized tuning parameters (Vstep=40mV, Tstep=0), we were able to tune the device with 5% tolerance with respect to the target conductance state (i.e. 50μS, 10μS, 5μS, 1μS) within the dynamic range (Fig. 6), and all these intermediate states can maintain the conductance over time (Fig. 7).