MCEL: Margin-Based Cross-Entropy Loss for Error-Tolerant Quantized Neural Networks

TL;DR

This paper introduces MCEL, a novel loss function that enhances neural network robustness to bit errors by promoting output margin separation, reducing the need for error-aware training and enabling efficient deployment on error-prone hardware.

Contribution

The paper proposes MCEL, a new loss function that improves error tolerance in neural networks without training-time bit flip injection, offering a scalable and principled robustness enhancement.

Findings

MCEL improves bit error tolerance by up to 15% accuracy at 1% error rate.

MCEL is simple to implement and can replace standard cross-entropy loss.

Experimental results across multiple datasets and architectures validate MCEL's effectiveness.

Abstract

Robustness to bit errors is a key requirement for the reliable use of neural networks (NNs) on emerging approximate computing platforms and error-prone memory technologies. A common approach to achieve bit error tolerance in NNs is injecting bit flips during training according to a predefined error model. While effective in certain scenarios, training-time bit flip injection introduces substantial computational overhead, often degrades inference accuracy at high error rates, and scales poorly for larger NN architectures. These limitations make error injection an increasingly impractical solution for ensuring robustness on future approximate computing platforms and error-prone memory technologies. In this work, we investigate the mechanisms that enable NNs to tolerate bit errors without relying on error-aware training. We establish a direct connection between bit error tolerance and classification margins at the output layer. Building on this insight, we propose a novel loss function, the Margin Cross-Entropy Loss (MCEL), which explicitly promotes logit-level margin separation while preserving the favorable optimization properties of the standard cross-entropy loss. Furthermore, MCEL introduces an interpretable margin parameter that allows robustness to be tuned in a principled manner. Extensive experimental evaluations across multiple datasets of varying complexity, diverse NN architectures, and a range of quantization schemes demonstrate that MCEL substantially improves bit error tolerance, up to 15 % in accuracy for an error rate of 1 %. Our proposed MCEL method is simple to implement, efficient, and can be integrated as a drop-in replacement for standard CEL. It provides a scalable and principled alternative to training-time bit flip injection, offering new insights into the origins of NN robustness and enabling more efficient deployment on approximate computing and memory systems.