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Invited Paper: Analyzing the Robustness of Neuromorphic Computing in the Presence of Variability in Non-Volatile Memory
Conference proceeding

Invited Paper: Analyzing the Robustness of Neuromorphic Computing in the Presence of Variability in Non-Volatile Memory

Andreia Podasca and Anup Das
Digest of technical papers - IEEE/ACM International Conference on Computer-Aided Design, pp 1-8
26 Oct 2025
DOI: https://doi.org/10.1109/ICCAD66269.2025.11240848

Abstract

Closed-form solutions Computational modeling Convex functions convex optimization cycle-to-cycle variations (CCV) Deep learning device-to-device variability (DDV) KKT minimal perturbation neuromorphic computing Neuromorphic engineering non-volatile memory (NVM) Nonvolatile memory Perturbation methods Quadratic programming Robustness Mathematical Models
Analog neuromorphic architectures using nonvolatile memory (NVM)-based crossbar arrays are a promising approach to accelerate deep learning workloads by efficiently performing the core matrix-vector multiplications (MVMs). A crossbar array leverages the current accumulation property of NVM cells to enable parallel MVM computation naturally through basic circuit laws (Ohm's Law and Kirchhoff's Current Law). Programming a crossbar for MVM involves mapping the synaptic weights of a deep learning model (i.e., the matrix elements) to conductance values of its NVM cells. Unfortunately, NVMs suffer from variability, including stochastic device-to-device (DDV) and cycle-to-cycle (CCV) variations in conductance-versus-pulse characteristics, which lead to imprecise weight mapping and reduced model performance.We present a novel mathematical framework to analyze the robustness of neuromorphic computing in the presence of variability in NVM. Specifically, we formulate this robustness analysis as finding the minimum perturbation in the feature space (hidden layers) that is sufficient to change the estimated output label, thereby resulting in incorrect classification. We model this as a quadratic programming problem with linear constraints, where we minimize the L2 norm squared of the perturbation subject to crossing the decision boundary to the nearest class. This results in a convex optimization problem with a quadratic objective function and linear inequality constraints. We solve the problem using Lagrangian method with Karush-Kuhn-Tucker (KKT) conditions, finding the minimum perturbation as an orthogonal projection onto the closest decision boundary. The closed-form solution provides both the direction (difference of weight vectors) and magnitude (scaled by confidence difference and inverse squared norm of weight difference) of the minimum perturbation. We present an extensive analysis and evaluation of the mathematical framework on a deep neural network trained on MNIST and Fashion-MNIST datasets. We also present an interpretation of the minimum perturbation, outlining the potential for algorithm-hardware co-design.

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