# Higher-Order Function Networks for Learning Composable 3D Object Representations

arXiv: https://arxiv.org/abs/1907.10388 · HTML: https://mlsanity.com/paper/1907.10388/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 6 of 6)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [EvAC3D: From Event-based Apparent Contours to 3D Models via Continuous Visual Hulls](https://mlsanity.com/paper/2304.05296/) (2023)
- [Real-time Simultaneous Multi-Object 3D Shape Reconstruction, 6DoF Pose Estimation and Dense Grasp Prediction](https://mlsanity.com/paper/2305.09510/) (2023)
- [3D Surface Reconstruction in the Wild by Deforming Shape Priors from Synthetic Data](https://mlsanity.com/paper/2302.12883/) (2023)
- [Learning Continuous Cost-to-Go Functions for Non-holonomic Systems](https://mlsanity.com/paper/2103.11168/) (2021)
- [VisDiff: SDF-Guided Polygon Generation for Visibility Reconstruction and Recognition](https://mlsanity.com/paper/2410.05530/) (2024)

## Abstract (arXiv)

We present a new approach to 3D object representation where a neural network encodes the geometry of an object directly into the weights and biases of a second 'mapping' network. This mapping network can be used to reconstruct an object by applying its encoded transformation to points randomly sampled from a simple geometric space, such as the unit sphere. We study the effectiveness of our method through various experiments on subsets of the ShapeNet dataset. We find that the proposed approach can reconstruct encoded objects with accuracy equal to or exceeding state-of-the-art methods with orders of magnitude fewer parameters. Our smallest mapping network has only about 7000 parameters and shows reconstruction quality on par with state-of-the-art object decoder architectures with millions of parameters. Further experiments on feature mixing through the composition of learned functions show that the encoding captures a meaningful subspace of objects.