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

arXiv: https://arxiv.org/abs/2309.15386 · HTML: https://mlsanity.com/paper/2309.15386/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 27 Sep 2023.

## Builds on (most cited first, 13 of 13)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Multi-level Residual Networks from Dynamical Systems View](https://mlsanity.com/paper/1710.10348/) (2017)
- [iDECODe: In-distribution Equivariance for Conformal Out-of-distribution Detection](https://mlsanity.com/paper/2201.02331/) (2022)
- [On learning optimized reaction diffusion processes for effective image restoration](https://mlsanity.com/paper/1503.05768/) (2015)
- [Attribution-driven Causal Analysis for Detection of Adversarial Examples](https://mlsanity.com/paper/1903.05821/) (2019)
- [Protein Folding Neural Networks Are Not Robust](https://mlsanity.com/paper/2109.04460/) (2021)
- [Explanation of Unintended Radiated Emission Classification via LIME](https://mlsanity.com/paper/2009.02418/) (2020)

## Built on by (most cited first, 1 of 1)

- [Data Augmentation for Image Classification using Generative AI](https://mlsanity.com/paper/2409.00547/) (2024)

## Abstract (arXiv)

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.