# Training morphological neural networks with gradient descent: some theoretical insights

arXiv: https://arxiv.org/abs/2403.12975 · HTML: https://mlsanity.com/paper/2403.12975/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 4 of 4)

- [Max-plus Operators Applied to Filter Selection and Model Pruning in Neural Networks](https://mlsanity.com/paper/1903.08072/) (2019)
- [Going beyond p-convolutions to learn grayscale morphological operators](https://mlsanity.com/paper/2102.10038/) (2021)
- [Binary Morphological Neural Network](https://mlsanity.com/paper/2203.12337/) (2022)
- [Morphological adjunctions represented by matrices in max-plus algebra for signal and image processing](https://mlsanity.com/paper/2207.13926/) (2022)

## Abstract (arXiv)

Morphological neural networks, or layers, can be a powerful tool to boost the progress in mathematical morphology, either on theoretical aspects such as the representation of complete lattice operators, or in the development of image processing pipelines. However, these architectures turn out to be difficult to train when they count more than a few morphological layers, at least within popular machine learning frameworks which use gradient descent based optimization algorithms. In this paper we investigate the potential and limitations of differentiation based approaches and back-propagation applied to morphological networks, in light of the non-smooth optimization concept of Bouligand derivative. We provide insights and first theoretical guidelines, in particular regarding initialization and learning rates.