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

2025-09-06

AI Summary

Morphological Perceptrons—particularly Morphological Perceptrons with Competitive Layers (MPCLs)—are hindered in multi-class classification due to the non-differentiability of mathematical morphology operators, rendering standard gradient-based optimization inapplicable. To address this, we propose a novel training framework based on the Concave-Convex Procedure (CCP), which reformulates the nonsmooth optimization objective as a difference of convex functions and iteratively solves linear programming subproblems for parameter learning. This marks the first systematic application of CCP to train the competitive layer of MPCLs, circumventing the differentiability requirement inherent in gradient methods. The approach synergistically integrates morphological structural modeling with competitive output mechanisms, ensuring both theoretical interpretability and computational tractability. Extensive experiments demonstrate substantial performance gains for MPCLs on multi-class classification benchmarks, validating the effectiveness and superiority of CCP for training non-gradient-based neural networks.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Non-convex Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• Training morphological perceptrons without gradient-based optimization
• Solving non-differentiable network training using convex-concave procedure
• Addressing multiclass classification with competitive layer networks

Innovation

• Morphological perceptron with competitive layer for classification
• Convex-concave procedure training without gradient optimization
• Solving DC functions via linear programming subproblems