Parasitic-Aware Modeling and Neural Network Training Scheme for Energy-Efficient Processing-in-Memory With Resistive Crossbar Array

Abstract

This paper presents a parasitic-aware modeling method for fast and accurate simulation of Processing-in-Memory (PIM) neural network (NN) implemented in resistive memristor crossbar array. This work proposed an efficient and accurate crossbar line resistance estimation model named <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> -compact model, and the associated NN training scheme that takes the impact of line resistance into consideration with time complexity of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(mn)</i> for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}\times \text{n}$ </tex-math></inline-formula> resistive crossbar. The impact of the crossbar array parasitics to the vector-matrix multiplication (VMM) computation accuracy and multi-layer PIM NN inference accuracy are analyzed in detail. The advantage of the proposed model is demonstrated by a multilayer perceptron (MLP) of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$784\times 128\times 10$ </tex-math></inline-formula> implemented with resistive random access memory (RRAM) crossbar arrays for MNIST hand-written digits classification. The proposed method reduced the VMM computation error by 186 and 17 times compared to uncompensated method and the state-of-art compensation method, respectively. Maximum 98.1% inference accuracy is achieved with only 0.17% degradation compared to the ideal model.