mlsanityData to 14 Oct 2026

Differentiable Euler Characteristic Transforms for Shape Classification

arXiv 2310.07630 ↗First posted 11 Oct 2023cs.LGcited by 18

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Abstract (arXiv)

The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We overcome this issue and develop a novel computational layer that enables learning the ECT in an end-to-end fashion. Our method, the Differentiable Euler Characteristic Transform (DECT), is fast and computationally efficient, while exhibiting performance on a par with more complex models in both graph and point cloud classification tasks. Moreover, we show that this seemingly simple statistic provides the same topological expressivity as more complex topological deep learning layers.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 30 of its 45 references that are in the map. First posted on arXiv 11 Oct 2023.

Builds on

30 of 45 references.

References · 30

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Inductive Representation Learning on Large Graphscited by 6,320
  4. 2018How Powerful are Graph Neural Networks?cited by 4,393
  5. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,576
  6. 2017Deep Setscited by 1,421
  7. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 728
  8. 2020Benchmarking Graph Neural Networkscited by 680
  9. 2019Deep Learning for 3D Point Clouds: A Surveycited by 558
  10. 2018Spherical CNNscited by 456
  11. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  12. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
18 more
  1. 2019Topological Autoencoderscited by 127
  2. 2017Deep Learning with Topological Signaturescited by 114
  3. 2020Simplicial Neural Networkscited by 110
  4. 2022Topological Deep Learning: Going Beyond Graph Datacited by 97
  5. 2021Topological Graph Neural Networkscited by 87
  6. 2019A Topology Layer for Machine Learningcited by 80
  7. 2014A Stable Multi-Scale Kernel for Topological Machine Learningcited by 75
  8. 2019Graph Filtration Learningcited by 69
  9. 2020Cell Complex Neural Networkscited by 67
  10. 2019Connectivity-Optimized Representation Learning via Persistent Homologycited by 44
  11. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  12. 2023Learning Topology-Preserving Data Representationscited by 31
  13. 2020k-simplex2vec: a simplicial extension of node2veccited by 13
  14. 2020The Weighted Euler Curve Transform for Shape and Image Analysiscited by 10
  15. 2023Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slicescited by 6
  16. 2018Inverse Problems in Topological Persistencecited by 5
  17. 2021Topologically Regularized Data Embeddingscited by 5
  18. 2022GPU Computation of the Euler Characteristic Curve for Imaging Datacited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 5; 2025: 7; 2026: 6.

18 papers.

Sort:

  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  2. 2024MANTRA: The Manifold Triangulations Assemblagecited by 12
  3. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  4. 2024Topology meets Machine Learning: An Introduction using the Euler Characteristic Transformcited by 4
  5. 2026A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classificationcited by 4
  6. 2025On topological descriptors for graph productscited by 3
  7. 2024Point Cloud Synthesis Using Inner Product Transformscited by 2
  8. 2025LEAP: Local ECT-Based Learnable Positional Encodings for Graphscited by 2
  9. 2025Latent Manifold Reconstruction and Representation with Topological and Geometrical Regularizationcited by 1
  10. 2025Molecular Machine Learning Using Euler Characteristic Transformscited by 1
  11. 2025Scalable GPU-Accelerated Euler Characteristic Curves: Optimization and Differentiable Learning for PyTorchcited by 1
  12. 2026Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Requirecited by 1
6 more
  1. 2025Barycentric Neural Networks and Length-Weighted Persistent Entropy Loss: A Green Geometric and Topological Framework for Function Approximationcited by 0
  2. 2025Tensor Computation of Euler Characteristic Functions and Transformscited by 0
  3. 2026Global and Local Topology-Aware Attention with Persistent Homology and Euler Biases for Time-Series Forecastingcited by 0
  4. 2026Geometry-Aware Simplicial Message Passingcited by 0
  5. 2026Encoding the Euler Characteristic Transformcited by 0
  6. 2026Collapsed Effective Operators for Higher-order Structurescited by 0