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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| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.24608 |
| Publication time | Tue, 26 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-26T04:07:43.013Z |
| Last seen | 2026-05-26T04:07:43.013Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | D2hDM8xcTI9u |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
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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Excerpt limited to ~120 words for fair-use compliance. The full article is at arXiv cs.AI.
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