# Training Image Derivatives: Increased Accuracy and Universal Robustness

arXiv: https://arxiv.org/abs/2310.14045 · HTML: https://mlsanity.com/paper/2310.14045/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 48 of its 99 references that are in the map.
- First posted on arXiv 21 Oct 2023.

## Builds on (most cited first, 30 of 48)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Recent Advances in Adversarial Training for Adversarial Robustness](https://mlsanity.com/paper/2102.01356/) (2021)
- [Improving the Adversarial Robustness and Interpretability of Deep Neural Networks by Regularizing their Input Gradients](https://mlsanity.com/paper/1711.09404/) (2017)
- [Disentangling Adversarial Robustness and Generalization](https://mlsanity.com/paper/1812.00740/) (2018)
- [Is Robustness the Cost of Accuracy? -- A Comprehensive Study on the Robustness of 18 Deep Image Classification Models](https://mlsanity.com/paper/1808.01688/) (2018)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Stabilizing Training of Generative Adversarial Networks through Regularization](https://mlsanity.com/paper/1705.09367/) (2017)
- [Adversarial Examples Are a Natural Consequence of Test Error in Noise](https://mlsanity.com/paper/1901.10513/) (2019)
- [Improving Robustness Without Sacrificing Accuracy with Patch Gaussian Augmentation](https://mlsanity.com/paper/1906.02611/) (2019)
- [Towards the first adversarially robust neural network model on MNIST](https://mlsanity.com/paper/1805.09190/) (2018)
- [Improving DNN Robustness to Adversarial Attacks using Jacobian Regularization](https://mlsanity.com/paper/1803.08680/) (2018)
- [On the effectiveness of adversarial training against common corruptions](https://mlsanity.com/paper/2103.02325/) (2021)
- [A Boundary Tilting Persepective on the Phenomenon of Adversarial Examples](https://mlsanity.com/paper/1608.07690/) (2016)
- [Excessive Invariance Causes Adversarial Vulnerability](https://mlsanity.com/paper/1811.00401/) (2018)
- [Fundamental Tradeoffs between Invariance and Sensitivity to Adversarial Perturbations](https://mlsanity.com/paper/2002.04599/) (2020)
- [Efficient Defenses Against Adversarial Attacks](https://mlsanity.com/paper/1707.06728/) (2017)
- [Score-Based Generative Classifiers](https://mlsanity.com/paper/2110.00473/) (2021)
- [Triple Wins: Boosting Accuracy, Robustness and Efficiency Together by Enabling Input-Adaptive Inference](https://mlsanity.com/paper/2002.10025/) (2020)
- [A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologies](https://mlsanity.com/paper/2203.14046/) (2022)
- [A Unified Gradient Regularization Family for Adversarial Examples](https://mlsanity.com/paper/1511.06385/) (2015)
- [Are Perceptually-Aligned Gradients a General Property of Robust Classifiers?](https://mlsanity.com/paper/1910.08640/) (2019)
- [Jacobian Adversarially Regularized Networks for Robustness](https://mlsanity.com/paper/1912.10185/) (2019)

## Abstract (arXiv)

Derivative training is an established method that can significantly increase the accuracy of neural networks in certain low-dimensional tasks. In this paper, we extend this improvement to an illustrative image analysis problem: reconstructing the vertices of a cube from its image. By training the derivatives with respect to the cube's six degrees of freedom, we achieve a 25-fold increase in accuracy for noiseless inputs. Additionally, derivative knowledge offers a novel approach to enhancing network robustness, which has traditionally been understood in terms of two types of vulnerabilities: excessive sensitivity to minor perturbations and failure to detect significant image changes. Conventional robust training relies on output invariance, which inherently creates a trade-off between these two vulnerabilities. By leveraging derivative information we compute non-trivial output changes in response to arbitrary input perturbations. This resolves the trade-off, yielding a network that is twice as robust and five times more accurate than the best case under the invariance assumption. Unlike conventional robust training, this outcome can be further improved by simply increasing the network capacity. This approach is applicable to phase retrieval problems and other scenarios where a sufficiently smooth manifold parametrization can be obtained.