Ternary locality sensitive hashing

Ternary locality-sensitive hashing introduces a wildcard “X” to the hashing vector to alleviate the analog computing error from nonideal factors. We have demonstrated that this modified hashing scheme can achieve software-equivalent performance (LSH with the same hashing bits) on our crossbar arrays. The threshold current I_th applied in the experiment should be carefully chosen according to the typical value of the computing error caused by device fluctuation. The value we chose throughout the experiment is 4 μA. We also show the dependence of classification accuracy on different threshold currents in Supplementary Fig. ⁸.

For the simulation results in Fig. 4d and e, where the device fluctuation varies, we chose different threshold currents I_th according to the fluctuation levels. Specifically, for our memristor model which can be described by Eq. (⁴), we empirically set the threshold current to be 5σ ⋅ V_in where V_in is the maximum input voltage to the row line when performing VMM. The V_in is chosen to be 0.2V in our experiments.

To generate random hashing planes in crossbar arrays (Fig. 2c), we RESET the devices from an arbitrary high conductance state to near 0 μS, where the conductance is ultimately decided by the intrinsic stochastic switching process. Regardless of the initial states, we use 5 RESET pulses with an amplitude of 1.5V and a width of 20 ns. The RESET voltage is carefully controlled to protect memristor devices because larger voltages may cause devices to be stuck at low conductance states.