# Volatility in Certainty (VC): A Metric for Detecting Adversarial Perturbations During Inference in Neural Network Classifiers

arXiv: https://arxiv.org/abs/2511.11834 · HTML: https://mlsanity.com/paper/2511.11834/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 14 Nov 2025.

## Builds on (most cited first, 14 of 14)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Beyond I.I.D.: Three Levels of Generalization for Question Answering on Knowledge Bases](https://mlsanity.com/paper/2011.07743/) (2020)
- [Predicting the Generalization Gap in Deep Networks with Margin Distributions](https://mlsanity.com/paper/1810.00113/) (2018)
- [Large Margin Deep Networks for Classification](https://mlsanity.com/paper/1803.05598/) (2018)
- [Are Labels Always Necessary for Classifier Accuracy Evaluation?](https://mlsanity.com/paper/2007.02915/) (2020)
- [Beyond Perturbations: Learning Guarantees with Arbitrary Adversarial Test Examples](https://mlsanity.com/paper/2007.05145/) (2020)
- [Towards Robust Out-of-Distribution Generalization Bounds via Sharpness](https://mlsanity.com/paper/2403.06392/) (2024)
- [An Experimental Study of Trojan Vulnerabilities in UAV Autonomous Landing](https://mlsanity.com/paper/2510.20932/) (2025)
- [Negative Selection Approach to support Formal Verification and Validation of BlackBox Models' Input Constraints](https://mlsanity.com/paper/2209.01411/) (2022)
- [GPS Spoofing Attack Detection in Autonomous Vehicles Using Adaptive DBSCAN](https://mlsanity.com/paper/2510.10766/) (2025)

## Abstract (arXiv)

Adversarial robustness remains a critical challenge in deploying neural network classifiers, particularly in real-time systems where ground-truth labels are unavailable during inference. This paper investigates textitVolatility in Certainty (VC), a recently proposed, label-free metric that quantifies irregularities in model confidence by measuring the dispersion of sorted softmax outputs. Specifically, VC is defined as the average squared log-ratio of adjacent certainty values, capturing local fluctuations in model output smoothness. We evaluate VC as a proxy for classification accuracy and as an indicator of adversarial drift. Experiments are conducted on artificial neural networks (ANNs) and convolutional neural networks (CNNs) trained on MNIST, as well as a regularized VGG-like model trained on CIFAR-10. Adversarial examples are generated using the Fast Gradient Sign Method (FGSM) across varying perturbation magnitudes. In addition, mixed test sets are created by gradually introducing adversarial contamination to assess VC's sensitivity under incremental distribution shifts. Our results reveal a strong negative correlation between classification accuracy and log(VC) (correlation rho < -0.90 in most cases), suggesting that VC effectively reflects performance degradation without requiring labeled data. These findings position VC as a scalable, architecture-agnostic, and real-time performance metric suitable for early-warning systems in safety-critical applications.