# Graph-based Isometry Invariant Representation Learning

arXiv: https://arxiv.org/abs/1703.00356 · HTML: https://mlsanity.com/paper/1703.00356/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2017.

## Built on by (most cited first, 7 of 7)

- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Dynamic Scenario Representation Learning for Motion Forecasting with Heterogeneous Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/2303.04364/) (2023)
- [Message Passing in Graph Convolution Networks via Adaptive Filter Banks](https://mlsanity.com/paper/2106.09910/) (2021)
- [Equivariance-bridged SO(2)-Invariant Representation Learning using Graph Convolutional Network](https://mlsanity.com/paper/2106.09996/) (2021)
- [H-NeXt: The next step towards roto-translation invariant networks](https://mlsanity.com/paper/2311.01111/) (2023)
- [Harmformer: Harmonic Networks Meet Transformers for Continuous Roto-Translation Equivariance](https://mlsanity.com/paper/2411.03794/) (2024)
- [Using Graph Algorithms to Pretrain Graph Completion Transformers](https://mlsanity.com/paper/2210.07453/) (2022)

## Abstract (arXiv)

Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have achieved only limited success in the classification of images that undergo geometric transformations. In this work we present a novel Transformation Invariant Graph-based Network (TIGraNet), which learns graph-based features that are inherently invariant to isometric transformations such as rotation and translation of input images. In particular, images are represented as signals on graphs, which permits to replace classical convolution and pooling layers in deep networks with graph spectral convolution and dynamic graph pooling layers that together contribute to invariance to isometric transformations. Our experiments show high performance on rotated and translated images from the test set compared to classical architectures that are very sensitive to transformations in the data. The inherent invariance properties of our framework provide key advantages, such as increased resiliency to data variability and sustained performance with limited training sets.