Adaptive Epsilon Adversarial Training for Robust Gravitational Wave Parameter Estimation Using Normalizing Flows

TL;DR

This paper introduces an adaptive epsilon adversarial training method for normalizing flow models in gravitational wave parameter estimation, significantly enhancing robustness against adversarial attacks while preserving accuracy on clean data.

Contribution

It proposes a novel adaptive epsilon approach for FGSM adversarial training combined with a hybrid ResNet and Inverse Autoregressive Flow architecture, improving robustness and reducing overfitting.

Findings

Reduces Negative Log Likelihood by 47% under FGSM attacks.

Maintains low NLL of 4.2 on clean data, only 5% higher than baseline.

Outperforms fixed and progressive epsilon methods in robustness tests.

Abstract

Adversarial training with Normalizing Flow (NF) models is an emerging research area aimed at improving model robustness through adversarial samples. In this study, we focus on applying adversarial training to NF models for gravitational wave parameter estimation. We propose an adaptive epsilon method for Fast Gradient Sign Method (FGSM) adversarial training, which dynamically adjusts perturbation strengths based on gradient magnitudes using logarithmic scaling. Our hybrid architecture, combining ResNet and Inverse Autoregressive Flow, reduces the Negative Log Likelihood (NLL) loss by 47\% under FGSM attacks compared to the baseline model, while maintaining an NLL of 4.2 on clean data (only 5\% higher than the baseline). For perturbation strengths between 0.01 and 0.1, our model achieves an average NLL of 5.8, outperforming both fixed-epsilon (NLL: 6.7) and progressive-epsilon (NLL: 7.2) methods. Under stronger Projected Gradient Descent attacks with perturbation strength of 0.05, our model maintains an NLL of 6.4, demonstrating superior robustness while avoiding catastrophic overfitting.