Fundamental Limits on the Computational Accuracy of Resistive Crossbar-based In-memory Architectures

Saion K. Roy, Ameya Patil, Naresh R. Shanbhag

Abstract: In-memory computing (IMC) architectures exhibit an intrinsic trade-off between computational accuracy and energy efficiency. This paper determines the fundamental limits on the compute SNR of MRAM-, ReRAM-, and FeFET-based crossbars by employing statistical signal and noise models. For a specific dot-product dimension N, the maximum compute SNR (SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</inf> ) is shown to occur at an optimum value of sensing resistance $R_{s}^{*}$ where clipping and quantization noise contributions from the analog-to-digital converter (ADC) are balanced out. SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</inf> can be further improved by choosing devices with higher resistive contrast R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</inf> /R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</inf> , e.g., FeFET, but only until it attains a value in the range 12-15. Beyond this point, mismatch in the input digital-to-analog converters (DACs) and bitcell variations begin to dominate the compute SNR. Finally, by mapping a ResNet20 (CIFAR-10) network onto resistive crossbars, it is shown that the array-level compute SNR maximizing circuit parameters also maximizes the network-level accuracy.