# Adversarial Examples from Dimensional Invariance

arXiv: https://arxiv.org/abs/2304.06575 · HTML: https://mlsanity.com/paper/2304.06575/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 15 references that are in the map.
- First posted on arXiv 13 Apr 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Generating Adversarial Examples with Adversarial Networks](https://mlsanity.com/paper/1801.02610/) (2018)
- [Are adversarial examples inevitable?](https://mlsanity.com/paper/1809.02104/) (2018)
- [Most ReLU Networks Suffer from ℓ2 Adversarial Perturbations](https://mlsanity.com/paper/2010.14927/) (2020)
- [Why Deep Learning Generalizes](https://mlsanity.com/paper/2211.09639/) (2022)

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

- [Language Model Memory and Memory Models for Language](https://mlsanity.com/paper/2602.13466/) (2026)

## Abstract (arXiv)

Adversarial examples have been found for various deep as well as shallow learning models, and have at various times been suggested to be either fixable model-specific bugs, or else inherent dataset feature, or both. We present theoretical and empirical results to show that adversarial examples are approximate discontinuities resulting from models that specify approximately bijective maps f: Bbb Rn → Bbb Rm; n neq m over their inputs, and this discontinuity follows from the topological invariance of dimension.