Understanding Adversarial Training with Energy-based Models

Abstract

We aim at using Energy-based Model (EBM) framework to better understand adversarial training (AT) in classifiers, and additionally to analyze the intrinsic generative capabilities of robust classifiers. By viewing standard classifiers through an energy lens, we begin by analyzing how the energies of adversarial examples, generated by various attacks, differ from those of the natural samples. The central focus of our work is to understand the critical phenomena of Catastrophic Overfitting (CO) and Robust Overfitting (RO) in AT from an energy perspective. We analyze the impact of existing AT approaches on the energy of samples during training and observe that the behavior of the “delta energy” – change in energy between original sample and its adversarial counterpart – diverges significantly when CO or RO occurs. After a thorough analysis of these energy dynamics and their relationship with overfitting, we propose a novel regularizer, the Delta Energy Regularizer (DER), designed to smoothen the energy landscape during training. We demonstrate that DER is effective in mitigating both CO and RO across multiple benchmarks. We further show that robust classifiers, when being used as generative models, have limits in handling trade-off between image quality and variability. We propose an improved technique based on a local class-wise principal component analysis (PCA) and energy-based guidance for better class-specific initialization and adaptive stopping, enhancing sample diversity and generation quality. Considering that we do not explicitly train for generative modeling, we achieve a competitive Inception Score (IS) and Fréchet inception distance (FID) compared to hybrid discriminative-generative models.

Publication
arXiv preprint (technical report)
Mirza Mujtaba Hussain
Mirza Mujtaba Hussain
PhD Student

Hi there! 👋 I’m Hussain, a Ph.D. student at Sapienza University. Currently I’m diving into Adversarial Machine Learning and Explainable AI to find practical solutions for real-world challenges. My goal is to use AI to make a positive impact on our society.

Maria Rosaria Briglia
Maria Rosaria Briglia
PhD Student

Hello everyone! My name is Maria Rosaria, a Ph.D. student in AI Security, based in Sapienza University. My main research interest is in developing adversarial techniques in the generative AI domain, with a particular focus on Diffusion Model’s technology, and applying them also to the world of Explainable AI. My main research topics are Diffusion Models, Adversarial Machine Learning and Explainble AI by counterfactual examples.

Senad Beadini
Senad Beadini
Machine Learning Engineer and AI Researcher

Research Engineer at Eustema s.p.a.

Iacopo Masi
Iacopo Masi
Associate Professor (PI)

My research interests include computer vision, biometrics, AI.