Neural Stochastic Differential Equations for Robust and Explainable Analysis of Electromagnetic Unintended Radiated Emissions

TL;DR

This paper introduces Neural Stochastic Differential Equations (SDEs) for classifying electromagnetic emissions, demonstrating improved robustness to noise and more meaningful explanations compared to traditional ResNet models.

Contribution

The paper proposes a novel Neural SDE approach for URE classification, enhancing robustness to noise and interpretability over ResNet-like models.

Findings

Neural SDEs maintain high accuracy under noise perturbations.

ResNet models' explanations do not reflect data periodicity.

Neural SDEs recover inherent periodic features in data.

Abstract

We present a comprehensive evaluation of the robustness and explainability of ResNet-like models in the context of Unintended Radiated Emission (URE) classification and suggest a new approach leveraging Neural Stochastic Differential Equations (SDEs) to address identified limitations. We provide an empirical demonstration of the fragility of ResNet-like models to Gaussian noise perturbations, where the model performance deteriorates sharply and its F1-score drops to near insignificance at 0.008 with a Gaussian noise of only 0.5 standard deviation. We also highlight a concerning discrepancy where the explanations provided by ResNet-like models do not reflect the inherent periodicity in the input data, a crucial attribute in URE detection from stable devices. In response to these findings, we propose a novel application of Neural SDEs to build models for URE classification that are not only robust to noise but also provide more meaningful and intuitive explanations. Neural SDE models maintain a high F1-score of 0.93 even when exposed to Gaussian noise with a standard deviation of 0.5, demonstrating superior resilience to ResNet models. Neural SDE models successfully recover the time-invariant or periodic horizontal bands from the input data, a feature that was conspicuously missing in the explanations generated by ResNet-like models. This advancement presents a small but significant step in the development of robust and interpretable models for real-world URE applications where data is inherently noisy and assurance arguments demand interpretable machine learning predictions.