# Max-Mahalanobis Linear Discriminant Analysis Networks

arXiv: https://arxiv.org/abs/1802.09308 · HTML: https://mlsanity.com/paper/1802.09308/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2018.

## Built on by (most cited first, 18 of 18)

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- [Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safety](https://mlsanity.com/paper/2104.14235/) (2021)
- [Recognizing Object by Components with Human Prior Knowledge Enhances Adversarial Robustness of Deep Neural Networks](https://mlsanity.com/paper/2212.01806/) (2022)
- [It Is All About Data: A Survey on the Effects of Data on Adversarial Robustness](https://mlsanity.com/paper/2303.09767/) (2023)
- [Unified Classification and Rejection: A One-versus-All Framework](https://mlsanity.com/paper/2311.13355/) (2023)
- [An Orthogonal Classifier for Improving the Adversarial Robustness of Neural Networks](https://mlsanity.com/paper/2105.09109/) (2021)
- [Generative Max-Mahalanobis Classifiers for Image Classification, Generation and More](https://mlsanity.com/paper/2101.00122/) (2021)
- [Tracklet-Switch Adversarial Attack against Pedestrian Multi-Object Tracking Trackers](https://mlsanity.com/paper/2111.08954/) (2021)
- [Enhancing Classifier Conservativeness and Robustness by Polynomiality](https://mlsanity.com/paper/2203.12693/) (2022)
- [Adaptive Random Feature Regularization on Fine-tuning Deep Neural Networks](https://mlsanity.com/paper/2403.10097/) (2024)
- [Improving Transformation-based Defenses against Adversarial Examples with First-order Perturbations](https://mlsanity.com/paper/2103.04565/) (2021)
- [Introducing the DOME Activation Functions](https://mlsanity.com/paper/2109.14798/) (2021)
- [Stationary Point Losses for Robust Model](https://mlsanity.com/paper/2302.09575/) (2023)
- [Unitary Multi-Margin BERT for Robust Natural Language Processing](https://mlsanity.com/paper/2410.12759/) (2024)
- [Simplex Deep Linear Discriminant Analysis](https://mlsanity.com/paper/2601.01679/) (2026)
- [Rethinking the Harmonic Loss via Non-Euclidean Distance Layers](https://mlsanity.com/paper/2603.10225/) (2026)

## Abstract (arXiv)

A deep neural network (DNN) consists of a nonlinear transformation from an input to a feature representation, followed by a common softmax linear classifier. Though many efforts have been devoted to designing a proper architecture for nonlinear transformation, little investigation has been done on the classifier part. In this paper, we show that a properly designed classifier can improve robustness to adversarial attacks and lead to better prediction results. Specifically, we define a Max-Mahalanobis distribution (MMD) and theoretically show that if the input distributes as a MMD, the linear discriminant analysis (LDA) classifier will have the best robustness to adversarial examples. We further propose a novel Max-Mahalanobis linear discriminant analysis (MM-LDA) network, which explicitly maps a complicated data distribution in the input space to a MMD in the latent feature space and then applies LDA to make predictions. Our results demonstrate that the MM-LDA networks are significantly more robust to adversarial attacks, and have better performance in class-biased classification.