# Noise Sensitivity and Stability of Deep Neural Networks for Binary Classification

arXiv: https://arxiv.org/abs/2308.09374 · HTML: https://mlsanity.com/paper/2308.09374/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 18 Aug 2023.

## Builds on (most cited first, 3 of 3)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Improving Accuracy of Nonparametric Transfer Learning via Vector Segmentation](https://mlsanity.com/paper/1710.08637/) (2017)

## Built on by (most cited first, 3 of 3)

- [Noise Sensitivity and Learning Lower Bounds for Hierarchical Functions](https://mlsanity.com/paper/2502.05073/) (2025)
- [Random Spiking Neural Networks are Stable and Spectrally Simple](https://mlsanity.com/paper/2511.00904/) (2025)
- [Trapped by simplicity: When Transformers fail to learn from noisy features](https://mlsanity.com/paper/2602.08695/) (2026)

## Abstract (arXiv)

A first step is taken towards understanding often observed non-robustness phenomena of deep neural net (DNN) classifiers. This is done from the perspective of Boolean functions by asking if certain sequences of Boolean functions represented by common DNN models are noise sensitive or noise stable, concepts defined in the Boolean function literature. Due to the natural randomness in DNN models, these concepts are extended to annealed and quenched versions. Here we sort out the relation between these definitions and investigate the properties of two standard DNN architectures, the fully connected and convolutional models, when initiated with Gaussian weights.