# Error-Correcting Output Codes with Ensemble Diversity for Robust Learning in Neural Networks

arXiv: https://arxiv.org/abs/1912.00181 · HTML: https://mlsanity.com/paper/1912.00181/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2019.

## Built on by (most cited first, 11 of 11)

- [Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks](https://mlsanity.com/paper/2110.12976/) (2021)
- [Graph Neural Convection-Diffusion with Heterophily](https://mlsanity.com/paper/2305.16780/) (2023)
- [A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applications](https://mlsanity.com/paper/2111.01968/) (2021)
- [Label Encoding for Regression Networks](https://mlsanity.com/paper/2212.01927/) (2022)
- [The Role of Codeword-to-Class Assignments in Error-Correcting Codes: An Empirical Study](https://mlsanity.com/paper/2302.05334/) (2023)
- [Learning Label Encodings for Deep Regression](https://mlsanity.com/paper/2303.02273/) (2023)
- [Improved Robustness Against Adaptive Attacks With Ensembles and Error-Correcting Output Codes](https://mlsanity.com/paper/2303.02322/) (2023)
- [Contrastive ECOC: Learning Output Codes for Adversarial Defense](https://mlsanity.com/paper/2508.10491/) (2025)
- [Ensemble Learning using Error Correcting Output Codes: New Classification Error Bounds](https://mlsanity.com/paper/2109.08967/) (2021)
- [Constraining Representations Yields Models That Know What They Don't Know](https://mlsanity.com/paper/2208.14488/) (2022)
- [Using Reed-Muller Codes for Classification with Rejection and Recovery](https://mlsanity.com/paper/2309.06359/) (2023)

## Abstract (arXiv)

Though deep learning has been applied successfully in many scenarios, malicious inputs with human-imperceptible perturbations can make it vulnerable in real applications. This paper proposes an error-correcting neural network (ECNN) that combines a set of binary classifiers to combat adversarial examples in the multi-class classification problem. To build an ECNN, we propose to design a code matrix so that the minimum Hamming distance between any two rows (i.e., two codewords) and the minimum shared information distance between any two columns (i.e., two partitions of class labels) are simultaneously maximized. Maximizing row distances can increase the system fault tolerance while maximizing column distances helps increase the diversity between binary classifiers. We propose an end-to-end training method for our ECNN, which allows further improvement of the diversity between binary classifiers. The end-to-end training renders our proposed ECNN different from the traditional error-correcting output code (ECOC) based methods that train binary classifiers independently. ECNN is complementary to other existing defense approaches such as adversarial training and can be applied in conjunction with them. We empirically demonstrate that our proposed ECNN is effective against the state-of-the-art white-box and black-box attacks on several datasets while maintaining good classification accuracy on normal examples.