Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 189 tok/s
Gemini 2.5 Pro 53 tok/s Pro
GPT-5 Medium 36 tok/s Pro
GPT-5 High 36 tok/s Pro
GPT-4o 75 tok/s Pro
Kimi K2 160 tok/s Pro
GPT OSS 120B 443 tok/s Pro
Claude Sonnet 4.5 37 tok/s Pro
2000 character limit reached

Decodable and Sample Invariant Continuous Object Encoder (2311.00187v4)

Published 31 Oct 2023 in cs.CV

Abstract: We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (50)
  1. Deep learning for network traffic monitoring and analysis (ntma): A survey. Computer Communications, 170:19–41, 2021.
  2. Model reduction and neural networks for parametric pdes. The SMAI journal of computational mathematics, 7:121–157, 2021.
  3. Estimation and variation analysis of secondary inorganic aerosols across the greater bay area in 2005 and 2015. Chemosphere, 292:133393, 2022.
  4. Experience report: Deep learning-based system log analysis for anomaly detection. arXiv preprint arXiv:2107.05908, 2021.
  5. Support-vector networks. Machine learning, 20:273–297, 1995.
  6. Structural relational reasoning of point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.  949–958, 2019.
  7. Bcr-net: A neural network based on the nonstandard wavelet form. Journal of Computational Physics, 384:1–15, 2019.
  8. Computing on functions using randomized vector representations. arXiv preprint arXiv:2109.03429, 2021.
  9. Event-based vision: A survey. IEEE transactions on pattern analysis and machine intelligence, 44(1):154–180, 2020.
  10. Fourier neural operator for plasma modelling. arXiv preprint arXiv:2302.06542, 2023.
  11. Pcpnet learning local shape properties from raw point clouds. In Computer graphics forum, volume 37, pp.  75–85. Wiley Online Library, 2018.
  12. Adaptive fourier neural operators: Efficient token mixers for transformers. arXiv preprint arXiv:2111.13587, 2021.
  13. Deep learning for 3d point clouds: A survey. IEEE transactions on pattern analysis and machine intelligence, 43(12):4338–4364, 2020.
  14. 3d point cloud descriptors: state-of-the-art. Artificial Intelligence Review, pp.  1–51, 2023.
  15. Kernel methods in machine learning. 2008.
  16. A comprehensive survey on point cloud registration. arXiv preprint arXiv:2103.02690, 2021.
  17. Anil K Jain. Fundamentals of digital image processing. Prentice-Hall, Inc., 1989.
  18. Momen (e) t: Flavor the moments in learning to classify shapes. In Proceedings of the IEEE/CVF international conference on computer vision workshops, pp.  0–0, 2019.
  19. Probabilistic vehicle trajectory prediction over occupancy grid map via recurrent neural network. In 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), pp.  399–404. IEEE, 2017.
  20. A survey on hyperdimensional computing aka vector symbolic architectures, part ii: Applications, cognitive models, and challenges. ACM Computing Surveys, 55(9):1–52, 2023.
  21. Efficient navigation using a scalable, biologically inspired spatial representation. In CogSci, 2020.
  22. Neural operator: Learning maps between function spaces. arXiv preprint arXiv:2108.08481, 2021.
  23. Hsurf-net: Normal estimation for 3d point clouds by learning hyper surfaces. Advances in Neural Information Processing Systems, 35:4218–4230, 2022.
  24. Shs-net: Learning signed hyper surfaces for oriented normal estimation of point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.  13591–13600, 2023.
  25. Mvp-net: multi-view fpn with position-aware attention for deep universal lesion detection. In Medical Image Computing and Computer Assisted Intervention–MICCAI 2019: 22nd International Conference, Shenzhen, China, October 13–17, 2019, Proceedings, Part VI 22, pp.  13–21. Springer, 2019.
  26. Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895, 2020a.
  27. Neural operator: Graph kernel network for partial differential equations. arXiv preprint arXiv:2003.03485, 2020b.
  28. Multipole graph neural operator for parametric partial differential equations. Advances in Neural Information Processing Systems, 33:6755–6766, 2020c.
  29. Physics-informed neural operator for learning partial differential equations. arXiv preprint arXiv:2111.03794, 2021.
  30. Justlookup: One millisecond deep feature extraction for point clouds by lookup tables. In 2019 IEEE International Conference on Multimedia and Expo (ICME), pp.  326–331. IEEE, 2019.
  31. Point-voxel cnn for efficient 3d deep learning. Advances in Neural Information Processing Systems, 32, 2019.
  32. Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. arXiv preprint arXiv:1910.03193, 2019.
  33. Estimations of long-term nss-so42–and no3–wet depositions over east asia by use of ensemble machine-learning method. Environmental Science & Technology, 54(18):11118–11126, 2020.
  34. Impacts of urbanization and long-term meteorological variations on global pm2. 5 and its associated health burden. Environmental Pollution, 270:116003, 2021.
  35. Global context reasoning for semantic segmentation of 3d point clouds. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pp.  2931–2940, 2020.
  36. Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.  652–660, 2017a.
  37. Imvotenet: Boosting 3d object detection in point clouds with image votes. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.  4404–4413, 2020.
  38. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. Advances in neural information processing systems, 30, 2017b.
  39. Forecasting subcritical cylinder wakes with fourier neural operators. arXiv preprint arXiv:2301.08290, 2023.
  40. Salih Salih. Fourier Transform: Signal Processing. BoD–Books on Demand, 2012.
  41. Implicit neural representations with periodic activation functions. Advances in Neural Information Processing Systems, 33:7462–7473, 2020.
  42. Korteweg-de vries equation and generalizations. iii. derivation of the korteweg-de vries equation and burgers equation. Journal of Mathematical Physics, 10(3):536–539, 1969.
  43. MR Tek. Development of a generalized darcy equation. Journal of Petroleum Technology, 9(06):45–47, 1957.
  44. Deep complex networks. arXiv preprint arXiv:1705.09792, 2017.
  45. Real-time high-resolution co 2 geological storage prediction using nested fourier neural operators. Energy & Environmental Science, 16(4):1732–1741, 2023.
  46. Pointasnl: Robust point clouds processing using nonlocal neural networks with adaptive sampling. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.  5589–5598, 2020.
  47. Modeling point clouds with self-attention and gumbel subset sampling. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.  3323–3332, 2019.
  48. 3dssd: Point-based 3d single stage object detector. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.  11040–11048, 2020.
  49. Deep sets. Advances in neural information processing systems, 30, 2017.
  50. Pointweb: Enhancing local neighborhood features for point cloud processing. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.  5565–5573, 2019.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Dice Question Streamline Icon: https://streamlinehq.com

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up