# Decodable and Sample Invariant Continuous Object Encoder

arXiv: https://arxiv.org/abs/2311.00187 · HTML: https://mlsanity.com/paper/2311.00187/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 51 references that are in the map.
- First posted on arXiv 31 Oct 2023.

## Builds on (most cited first, 30 of 32)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Event-based Vision: A Survey](https://mlsanity.com/paper/1904.08405/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [3DSSD: Point-based 3D Single Stage Object Detector](https://mlsanity.com/paper/2002.10187/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [PointASNL: Robust Point Clouds Processing using Nonlocal Neural Networks with Adaptive Sampling](https://mlsanity.com/paper/2003.00492/) (2020)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Modeling Point Clouds with Self-Attention and Gumbel Subset Sampling](https://mlsanity.com/paper/1904.03375/) (2019)
- [ImVoteNet: Boosting 3D Object Detection in Point Clouds with Image Votes](https://mlsanity.com/paper/2001.10692/) (2020)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [Probabilistic Vehicle Trajectory Prediction over Occupancy Grid Map via Recurrent Neural Network](https://mlsanity.com/paper/1704.07049/) (2017)
- [Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operators](https://mlsanity.com/paper/2210.17051/) (2022)
- [Computing on Functions Using Randomized Vector Representations](https://mlsanity.com/paper/2109.03429/) (2021)
- [Experience Report: Deep Learning-based System Log Analysis for Anomaly Detection](https://mlsanity.com/paper/2107.05908/) (2021)
- [HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces](https://mlsanity.com/paper/2210.07158/) (2022)
- [MVP-Net: Multi-view FPN with Position-aware Attention for Deep Universal Lesion Detection](https://mlsanity.com/paper/1909.04247/) (2019)
- [BCR-Net: a neural network based on the nonstandard wavelet form](https://mlsanity.com/paper/1810.08754/) (2018)
- [Momen(e)t: Flavor the Moments in Learning to Classify Shapes](https://mlsanity.com/paper/1812.07431/) (2018)

## Built on by (most cited first, 2 of 2)

- [A Linear Time and Space Local Point Cloud Geometry Encoder via Vectorized Kernel Mixture (VecKM)](https://mlsanity.com/paper/2404.01568/) (2024)
- [Learning Normal Flow Directly From Event Neighborhoods](https://mlsanity.com/paper/2412.11284/) (2024)

## Abstract (arXiv)

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.