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

Matheus Farias, Wanghley Martins, H. T. Kung

TL;DR

The paper tackles parasitic-resistance nonidealities in memristive CIM DNN accelerators by introducing Manhattan Distance Mapping (MDM), a post-training weight remapping that reverses dataflow and reorders rows to place dense, low-order-bit activity near the I/O rails, reducing the nonideality factor $NF$ without retraining. It grounds the approach in the Manhattan Hypothesis and bit-level structured sparsity, and models PR as spatially dependent noise to assess distortion in PyTorch. The authors validate their method with circuit-level SPICE simulations and ImageNet-1K benchmarks, reporting NF reductions up to $46\%$ and average ResNet accuracy gains of $3.6\%$, demonstrating how MDM enables larger crossbars with manageable distortion. By bridging device-level nonidealities and algorithmic remapping, MDM offers a lightweight, scalable path to more efficient CIM-based DNN accelerators.

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.

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

TL;DR

The paper tackles parasitic-resistance nonidealities in memristive CIM DNN accelerators by introducing Manhattan Distance Mapping (MDM), a post-training weight remapping that reverses dataflow and reorders rows to place dense, low-order-bit activity near the I/O rails, reducing the nonideality factor without retraining. It grounds the approach in the Manhattan Hypothesis and bit-level structured sparsity, and models PR as spatially dependent noise to assess distortion in PyTorch. The authors validate their method with circuit-level SPICE simulations and ImageNet-1K benchmarks, reporting NF reductions up to and average ResNet accuracy gains of , demonstrating how MDM enables larger crossbars with manageable distortion. By bridging device-level nonidealities and algorithmic remapping, MDM offers a lightweight, scalable path to more efficient CIM-based DNN accelerators.

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.

Paper Structure

This paper contains 13 sections, 1 theorem, 20 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Memristive Crossbar Assumptions
  4. Nonideality Measurement
  5. Theoretical Framework
  6. Bit-level Structured Sparsity
  7. The Manhattan Hypothesis
  8. Manhattan Distance Weight Mapping
  9. Experiments
  10. The Manhattan Hypothesis Accuracy
  11. Nonideality Factor Reduction
  12. Model Accuracy Evaluation
  13. Conclusion

Key Result

Theorem 1

Let $W$ be a nonnegative random variable with probability density function $f : [0, \infty[ \to [0, \infty[$ such that: Let where $\mathbb{P}(b_k = 1)$ is the probability of $b_k = 1$. Then In particular, $p_k < 1/2$ for every $k$ and $p_k \to 1/2$ as $k \to \infty$.

Figures (6)

  • Figure 1: Summary of the Manhattan Distance Mapping (MDM).
  • Figure 2: Circuit-level simulations in SPICE shows anti-diagonal symmetry for $r = 2.5$$\Omega$, $R_{\text{on}} = 300$ k$\Omega$, and $R_{\text{off}} = 3$ M$\Omega$ (values within range suggested in the literature chakraborty2020cao2025cao2021.)
  • Figure 3: MDM example. Arrows on the left/right indicate dataflow and numbers on top of each arrow indicate row score.
  • Figure 4: Error distribution of the Manhattan Hypothesis linear fit has mean $\mu = -0.126\%$ and standard deviation $\sigma = 11.2\%$.
  • Figure 5: NF reduction with MDM for different dataflows.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof