# Staying in Shape: Learning Invariant Shape Representations using Contrastive Learning

arXiv: https://arxiv.org/abs/2107.03552 · HTML: https://mlsanity.com/paper/2107.03552/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 50 references that are in the map.
- First posted on arXiv 8 Jul 2021.

## Builds on (most cited first, 27 of 27)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [PointContrast: Unsupervised Pre-training for 3D Point Cloud Understanding](https://mlsanity.com/paper/2007.10985/) (2020)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [What Should Not Be Contrastive in Contrastive Learning](https://mlsanity.com/paper/2008.05659/) (2020)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [Learning Features by Watching Objects Move](https://mlsanity.com/paper/1612.06370/) (2016)
- [PointMixup: Augmentation for Point Clouds](https://mlsanity.com/paper/2008.06374/) (2020)
- [PointAugment: an Auto-Augmentation Framework for Point Cloud Classification](https://mlsanity.com/paper/2002.10876/) (2020)
- [Learning Descriptor Networks for 3D Shape Synthesis and Analysis](https://mlsanity.com/paper/1804.00586/) (2018)
- [On Isometry Robustness of Deep 3D Point Cloud Models under Adversarial Attacks](https://mlsanity.com/paper/2002.12222/) (2020)
- [View Inter-Prediction GAN: Unsupervised Representation Learning for 3D Shapes by Learning Global Shape Memories to Support Local View Predictions](https://mlsanity.com/paper/1811.02744/) (2018)

## Built on by (most cited first, 4 of 4)

- [Addressing Token Uniformity in Transformers via Singular Value Transformation](https://mlsanity.com/paper/2208.11790/) (2022)
- [Upsampling Autoencoder for Self-Supervised Point Cloud Learning](https://mlsanity.com/paper/2203.10768/) (2022)
- [A Simple Strategy to Provable Invariance via Orbit Mapping](https://mlsanity.com/paper/2209.11916/) (2022)
- [Advancing Perception in Artificial Intelligence through Principles of Cognitive Science](https://mlsanity.com/paper/2310.08803/) (2023)

## Abstract (arXiv)

Creating representations of shapes that are invari-ant to isometric or almost-isometric transforma-tions has long been an area of interest in shape anal-ysis, since enforcing invariance allows the learningof more effective and robust shape representations.Most existing invariant shape representations arehandcrafted, and previous work on learning shaperepresentations do not focus on producing invariantrepresentations. To solve the problem of learningunsupervised invariant shape representations, weuse contrastive learning, which produces discrimi-native representations through learning invarianceto user-specified data augmentations. To producerepresentations that are specifically isometry andalmost-isometry invariant, we propose new dataaugmentations that randomly sample these transfor-mations. We show experimentally that our methodoutperforms previous unsupervised learning ap-proaches in both effectiveness and robustness.