# Harmonic Machine Learning Models are Robust

arXiv: https://arxiv.org/abs/2404.18825 · HTML: https://mlsanity.com/paper/2404.18825/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 29 Apr 2024.

## Builds on (most cited first, 11 of 11)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [A Fine-Grained Analysis on Distribution Shift](https://mlsanity.com/paper/2110.11328/) (2021)
- [Measuring Neural Net Robustness with Constraints](https://mlsanity.com/paper/1605.07262/) (2016)
- [Robustness of classifiers: from adversarial to random noise](https://mlsanity.com/paper/1608.08967/) (2016)
- [How Deep Learning Sees the World: A Survey on Adversarial Attacks & Defenses](https://mlsanity.com/paper/2305.10862/) (2023)
- [Mitigating Evasion Attacks to Deep Neural Networks via Region-based Classification](https://mlsanity.com/paper/1709.05583/) (2017)
- [A Comprehensive Evaluation Framework for Deep Model Robustness](https://mlsanity.com/paper/2101.09617/) (2021)
- [Unsupervised anomaly detection algorithms on real-world data: how many do we need?](https://mlsanity.com/paper/2305.00735/) (2023)
- [Adversarial Attacks on Machine Learning Systems for High-Frequency Trading](https://mlsanity.com/paper/2002.09565/) (2020)
- [A Theoretical Framework for Robustness of (Deep) Classifiers against Adversarial Examples](https://mlsanity.com/paper/1612.00334/) (2016)

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

- [Harmonic LLMs are Trustworthy](https://mlsanity.com/paper/2404.19708/) (2024)

## Abstract (arXiv)

We introduce Harmonic Robustness, a powerful and intuitive method to test the robustness of any machine-learning model either during training or in black-box real-time inference monitoring without ground-truth labels. It is based on functional deviation from the harmonic mean value property, indicating instability and lack of explainability. We show implementation examples in low-dimensional trees and feedforward NNs, where the method reliably identifies overfitting, as well as in more complex high-dimensional models such as ResNet-50 and Vision Transformer where it efficiently measures adversarial vulnerability across image classes.