Lattice theory and algebraic models for deep convolutional learning based on mathematical morphology
A new paper presents an algebraic framework for deep convolutional learning based on lattice theory and mathematical morphology. The research identifies key properties of convolutional neural networks (CNNs) and their components, revealing insights into their representational power. Additionally, the study proposes new layer designs that enhance the understanding of depth in CNN architectures.
- ▪The paper develops a rigorous algebraic framework for deep convolutional architectures, including CNNs and ResNets.
- ▪It identifies that the standard CNN pipeline operates as a cross-lattice operator, providing insights into its representational power.
- ▪Three layer designs that are genuine idempotent openings are fully characterized in the study.
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Computer Science > Artificial Intelligence arXiv:2605.24608 (cs) [Submitted on 23 May 2026] Title:Lattice theory and algebraic models for deep convolutional learning based on mathematical morphology Authors:Gustavo (Jesus)Angulo View a PDF of the paper titled Lattice theory and algebraic models for deep convolutional learning based on mathematical morphology, by Gustavo (Jesus) Angulo View PDF HTML (experimental) Abstract:We develop a rigorous algebraic framework for deep convolutional architectures, CNNs, ResNets, and encoder--decoder networks such as UNet, grounded in lattice theory and mathematical morphology.
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