mlsanityData to 7 Oct 2026

Topological Deep Learning

arXiv 2101.05778 ↗First posted 14 Jan 2021cs.LG cs.CVcited by 6

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Abstract (arXiv)

This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used as convolutional weights in a TCNN. These manifolds also parameterize slices in layers of a TCNN across which the weights are localized. We show evidence that TCNNs learn faster, on less data, with fewer learned parameters, and with greater generalizability and interpretability than conventional CNNs. We introduce and explore TCNN layers for both image and video data. We propose extensions to 3D images and 3D video.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 5 of its 30 references that are in the map. First posted on arXiv 14 Jan 2021.

Builds on

5 of 30 references.

References · 5

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2017Quo Vadis, Action Recognition? A New Model and the Kinetics Datasetcited by 3,259
  3. 2019Learning Spatio-Temporal Representation with Local and Global Diffusioncited by 61
  4. 2018Topological Approaches to Deep Learningcited by 29
  5. 2014Robust Topological Inference: Distance To a Measure and Kernel Distancecited by 25

Built on by

Cited by year

Citing papers per year: 2021: 2; 2022: 2; 2023: 1; 2024: 1.

6 papers.

  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  2. 2021Dist2Cycle: A Simplicial Neural Network for Homology Localizationcited by 16
  3. 2023Topology-Aware Focal Loss for 3D Image Segmentationcited by 12
  4. 2021A Random Persistence Diagram Generatorcited by 6
  5. 2022A Topological Deep Learning Framework for Neural Spike Decodingcited by 6
  6. 2022Topological structure of complex predictionscited by 1