mlsanityData to 7 Oct 2026

Point Cloud Synthesis Using Inner Product Transforms

arXiv 2410.18987 ↗First posted 9 Oct 2024cs.CV cs.LGcited by 2

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Abstract (arXiv)

Point cloud synthesis, i.e. the generation of novel point clouds from an input distribution, remains a challenging task, for which numerous complex machine learning models have been devised. We develop a novel method that encodes geometrical-topological characteristics of point clouds using inner products, leading to a highly-efficient point cloud representation with provable expressivity properties. Integrated into deep learning models, our encoding exhibits high quality in typical tasks like reconstruction, generation, and interpolation, with inference times orders of magnitude faster than existing methods.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 24 of its 48 references that are in the map. First posted on arXiv 9 Oct 2024.

Builds on

24 of 48 references.

References · 24

  1. 2017Attention Is All You Needcited by 59,932
  2. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  3. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  4. 2017Deep Setscited by 1,394
  5. 2022LION: Latent Point Diffusion Models for 3D Shape Generationcited by 552
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  12. 2020SoftFlow: Probabilistic Framework for Normalizing Flow on Manifoldscited by 97
12 more
  1. 2021SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Datacited by 78
  2. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  3. 2018Learning to Reconstruct Shapes from Unseen Classescited by 60
  4. 2022Fast Point Cloud Generation with Straight Flowscited by 56
  5. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 38
  6. 2022Autoregressive 3D Shape Generation via Canonical Mappingcited by 37
  7. 2023Differentiable Euler Characteristic Transforms for Shape Classificationcited by 18
  8. 2024MANTRA: The Manifold Triangulations Assemblagecited by 12
  9. 2023An Invitation to the Euler Characteristic Transformcited by 9
  10. 2023Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slicescited by 6
  11. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  12. 2018Challenges in Reconstructing Shapes from Euler Characteristic Curvescited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025LEAP: Local ECT-Based Learnable Positional Encodings for Graphscited by 2
  2. 2026Encoding the Euler Characteristic Transformcited by 0