ArticleNature communications2026
Manifold topological deep learning for biomedical data.
Article in Nature communications, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
5 citing papers in PubMed.
- Graph identification of proteins in tomograms (GRIP-Tomo) 2.0: Topologically aware classification for proteins.Protein science : a publication of the Protein Society · 2026Article
- Article
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data.Advanced intelligent discovery · 2025Article
- A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
Corrections and comments
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Authors and funding
6 authors.
Funding
Abstract
Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved significant success in processing point-cloud data and has emerged as a promising paradigm in data science. However, TDL has not been extended to differentiable-manifold data, including images, due to the challenges introduced by differential topology. We address this challenge by introducing a manifold topological deep learning (MTDL) framework. To apply Hodge theory, we integrate it into a streamlined convolutional neural network within the MTDL framework. In this framework, original images are represented as smooth manifolds with vector fields that are decomposed into three orthogonal components based on Hodge theory. These components are then concatenated to form an input image for the convolutional neural network architecture. The performance of MTDL is evaluated using the MedMNIST v2 benchmark database, which comprises 717,287 biomedical images from eleven 2D and six 3D datasets. MTDL significantly outperforms other competing methods, extending TDL to a wide range of data on smooth manifolds.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the Socratic graph.