Device-aware quantization in resistive random access memory-based crossbar arrays to account for device non-idealities

Abstract

Vector-Matrix-Multiplication (VMM) via multiply and accumulate operation (MAC) is essential in computations encompassing neuromorphic and deep learning applications ( Fig. 1a ) [1] . The research has been focused on emerging non-volatile memories (NVMs) with resistive random-access memories (RRAM) as a leading candidate for a viable alternate technology [2] . In crossbar arrays, the currents through the columns/bit lines follow KCL and Ohm’s law, resulting in MAC, thereby reducing computational complexity ( Fig. 1b ) [3] . However, given the device’s non-idealities, it poses challenges in achieving accuracy levels. The accumulated current collected at the bit line is susceptible to bit-cell variability (I var ), a finite current ratio (k) , and the current contribution from the “off” state (high resistance state- I HRS ) ( Fig. 1c ) [4] . This work emphasizes the importance of a device-aware quantization scheme, i.e., considering device non-idealities at MAC outputs. We analyze the contribution of different non-idealities in defining the quantization scheme using Pr 1-x Ca x MnO 3 (PCMO) based RRAM arrays. Using non-uniform quantization, we show a successful VMM via MAC operation in PCMO-RRAM arrays. Further, we show how non-uniform quantization for non-ideal current can facilitate (2x) the size of the array compared to uniform quantization. While non-uniform quantization allows for a larger array, the constraints by tolerable device variability can be stringent and limit the array size. For an array size (n) of 4 and a current ratio (k) of 5, the estimated tolerable I var is less than 0.2I HRS .