MDM: Manhattan Distance Mapping of DNN Weights for Parasitic-Resistance-Resilient Memristive Crossbars

TL;DR

This paper introduces MDM, a novel weight mapping technique for memristive crossbars that reduces parasitic resistance effects, improves accuracy, and enhances the efficiency of CIM-based DNN accelerators.

Contribution

MDM optimizes active-memristor placement using Manhattan distance and bit-level sparsity, reducing nonideality and improving DNN performance on memristive crossbars.

Findings

Reduces nonideality factor by up to 46%

Improves accuracy under analog distortion by 3.6% on average

Enhances CIM crossbar efficiency and scalability

Abstract

Manhattan Distance Mapping (MDM) is a post-training deep neural network (DNN) weight mapping technique for memristive bit-sliced compute-in-memory (CIM) crossbars that reduces parasitic resistance (PR) nonidealities. PR limits crossbar efficiency by mapping DNN matrices into small crossbar tiles, reducing CIM-based speedup. Each crossbar executes one tile, requiring digital synchronization before the next layer. At this granularity, designers either deploy many small crossbars in parallel or reuse a few sequentially-both increasing analog-to-digital conversions, latency, I/O pressure, and chip area. MDM alleviates PR effects by optimizing active-memristor placement. Exploiting bit-level structured sparsity, it feeds activations from the denser low-order side and reorders rows according to the Manhattan distance, relocating active cells toward regions less affected by PR and thus lowering the nonideality factor (NF). Applied to DNN models on ImageNet-1k, MDM reduces NF by up to 46% and improves accuracy under analog distortion by an average of 3.6% in ResNets. Overall, it provides a lightweight, spatially informed method for scaling CIM DNN accelerators.