On the explainability of max-plus neural networks

arXiv cs.CV / 5/5/2026

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Key Points

The paper analyzes explainability characteristics of recently proposed linear–min–max neural networks, showing how they can be interpreted at initialization as k-medoids using the infinity norm as a distance metric.
Training is performed with subgradient descent to improve data fit, while the authors emphasize that the model’s decision process remains traceable via the single most activated neuron driving the output.
They introduce a “pixel fragility” measure to assess whether a classification change can be caused by alterations to a single input pixel.
Experiments on the PneumoniaMNIST dataset indicate that the proposed explanation method performs favorably compared with SHAP and Integrated Gradients.
Overall, the work connects a specific network structure to practical, pixel-level interpretability and compares it against established attribution techniques.

Abstract

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.