# On the explainability of max-plus neural networks

arXiv: https://arxiv.org/abs/2605.00889 · HTML: https://mlsanity.com/paper/2605.00889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Grad-CAM: Why did you say that?](https://mlsanity.com/paper/1611.07450/) (2016)
- [Morphological Network: How Far Can We Go with Morphological Neurons?](https://mlsanity.com/paper/1901.00109/) (2019)
- [Min-Max-Plus Neural Networks](https://mlsanity.com/paper/2102.06358/) (2021)
- [Exploiting Subgradient Sparsity in Max-Plus Neural Networks](https://mlsanity.com/paper/2603.04133/) (2026)

## Abstract (arXiv)

We investigate the explanability properties of the recently proposed linear-min-max neural networks. At initialization, they can be interpreted as k-medoids with the infinity norm as a distance. Then, they are trained using subgradient descent to better fit the data. The model has been shown to be a universal approximator. Yet, we can trace the decision process because a single most activated neuron is responsible for the value of the output. Using this property, we designed a pixel fragility measure that determines whether changes to a single pixel may be responsible to a change in the classification output. Experiments on the PneumoniaMnist dataset show that this explanation for the output of the neural network compares favorably to SHAP and Integrated Gradient.