# Shedding More Light on Robust Classifiers under the lens of Energy-based Models

arXiv: https://arxiv.org/abs/2407.06315 · HTML: https://mlsanity.com/paper/2407.06315/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 68 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Builds on (most cited first, 30 of 53)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [Attacks Which Do Not Kill Training Make Adversarial Learning Stronger](https://mlsanity.com/paper/2002.11242/) (2020)
- [Improving Robustness using Generated Data](https://mlsanity.com/paper/2110.09468/) (2021)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Geometry-aware Instance-reweighted Adversarial Training](https://mlsanity.com/paper/2010.01736/) (2020)
- [Disentangling Adversarial Robustness and Generalization](https://mlsanity.com/paper/1812.00740/) (2018)
- [MMA Training: Direct Input Space Margin Maximization through Adversarial Training](https://mlsanity.com/paper/1812.02637/) (2018)

## Built on by (most cited first, 9 of 9)

- [Implicit Inversion turns CLIP into a Decoder](https://mlsanity.com/paper/2505.23161/) (2025)
- [Understanding Adversarial Training with Energy-based Models](https://mlsanity.com/paper/2505.22486/) (2025)
- [Your Classifier Can Do More: Towards Balancing the Gaps in Classification, Robustness, and Generation](https://mlsanity.com/paper/2505.19459/) (2025)
- [Scalable Energy-Based Models via Adversarial Training: Unifying Discrimination and Generation](https://mlsanity.com/paper/2510.13872/) (2025)
- [Spilled Energy in Large Language Models](https://mlsanity.com/paper/2602.18671/) (2026)
- [A Provable Energy-Guided Test-Time Defense Boosting Adversarial Robustness of Large Vision-Language Models](https://mlsanity.com/paper/2603.26984/) (2026)
- [Environment Maps Editing using Inverse Rendering and Adversarial Implicit Functions](https://mlsanity.com/paper/2410.18622/) (2024)
- [What is Adversarial Training for Diffusion Models?](https://mlsanity.com/paper/2505.21742/) (2025)
- [Inverse Language Modeling towards Robust and Grounded LLMs](https://mlsanity.com/paper/2510.01929/) (2025)

## Abstract (arXiv)

By reinterpreting a robust discriminative classifier as Energy-based Model (EBM), we offer a new take on the dynamics of adversarial training (AT). Our analysis of the energy landscape during AT reveals that untargeted attacks generate adversarial images much more in-distribution (lower energy) than the original data from the point of view of the model. Conversely, we observe the opposite for targeted attacks. On the ground of our thorough analysis, we present new theoretical and practical results that show how interpreting AT energy dynamics unlocks a better understanding: (1) AT dynamic is governed by three phases and robust overfitting occurs in the third phase with a drastic divergence between natural and adversarial energies (2) by rewriting the loss of TRadeoff-inspired Adversarial DEfense via Surrogate-loss minimization (TRADES) in terms of energies, we show that TRADES implicitly alleviates overfitting by means of aligning the natural energy with the adversarial one (3) we empirically show that all recent state-of-the-art robust classifiers are smoothing the energy landscape and we reconcile a variety of studies about understanding AT and weighting the loss function under the umbrella of EBMs. Motivated by rigorous evidence, we propose Weighted Energy Adversarial Training (WEAT), a novel sample weighting scheme that yields robust accuracy matching the state-of-the-art on multiple benchmarks such as CIFAR-10 and SVHN and going beyond in CIFAR-100 and Tiny-ImageNet. We further show that robust classifiers vary in the intensity and quality of their generative capabilities, and offer a simple method to push this capability, reaching a remarkable Inception Score (IS) and FID using a robust classifier without training for generative modeling. The code to reproduce our results is available at http://github.com/OmnAI-Lab/Robust-Classifiers-under-the-lens-of-EBM/ .