# Morphological Perceptron with Competitive Layer: Training Using Convex-Concave Procedure

arXiv: https://arxiv.org/abs/2509.05697 · HTML: https://mlsanity.com/paper/2509.05697/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 6 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Disciplined Convex-Concave Programming](https://mlsanity.com/paper/1604.02639/) (2016)
- [Reduced Dilation-Erosion Perceptron for Binary Classification](https://mlsanity.com/paper/2003.02306/) (2020)
- [Learning Deep Morphological Networks with Neural Architecture Search](https://mlsanity.com/paper/2106.07714/) (2021)
- [Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure](https://mlsanity.com/paper/2011.06512/) (2020)
- [Training Single-Layer Morphological Perceptron Using Convex-Concave Programming](https://mlsanity.com/paper/2401.02296/) (2024)

## Abstract (arXiv)

A morphological perceptron is a multilayer feedforward neural network in which neurons perform elementary operations from mathematical morphology. For multiclass classification tasks, a morphological perceptron with a competitive layer (MPCL) is obtained by integrating a winner-take-all output layer into the standard morphological architecture. The non-differentiability of morphological operators renders gradient-based optimization methods unsuitable for training such networks. Consequently, alternative strategies that do not depend on gradient information are commonly adopted. This paper proposes the use of the convex-concave procedure (CCP) for training MPCL networks. The training problem is formulated as a difference of convex (DC) functions and solved iteratively using CCP, resulting in a sequence of linear programming subproblems. Computational experiments demonstrate the effectiveness of the proposed training method in addressing classification tasks with MPCL networks.