# Compositionally Equivariant Representation Learning

arXiv: https://arxiv.org/abs/2306.07783 · HTML: https://mlsanity.com/paper/2306.07783/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 58 references that are in the map.
- First posted on arXiv 13 Jun 2023.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Semi-Supervised Semantic Segmentation with Cross Pseudo Supervision](https://mlsanity.com/paper/2106.01226/) (2021)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [FedDG: Federated Domain Generalization on Medical Image Segmentation via Episodic Learning in Continuous Frequency Space](https://mlsanity.com/paper/2103.06030/) (2021)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Emergence of Invariance and Disentanglement in Deep Representations](https://mlsanity.com/paper/1706.01350/) (2017)
- [FSDR: Frequency Space Domain Randomization for Domain Generalization](https://mlsanity.com/paper/2103.02370/) (2021)
- [Shape-aware Meta-learning for Generalizing Prostate MRI Segmentation to Unseen Domains](https://mlsanity.com/paper/2007.02035/) (2020)
- [Domain Generalization for Medical Imaging Classification with Linear-Dependency Regularization](https://mlsanity.com/paper/2009.12829/) (2020)
- [Uncertainty-aware multi-view co-training for semi-supervised medical image segmentation and domain adaptation](https://mlsanity.com/paper/2006.16806/) (2020)
- [Learning to Compose Visual Relations](https://mlsanity.com/paper/2111.09297/) (2021)
- [Disentangled Representation Learning in Cardiac Image Analysis](https://mlsanity.com/paper/1903.09467/) (2019)
- [Enhancing Pseudo Label Quality for Semi-Supervised Domain-Generalized Medical Image Segmentation](https://mlsanity.com/paper/2201.08657/) (2022)
- [Learning Compositional Representations for Few-Shot Recognition](https://mlsanity.com/paper/1812.09213/) (2018)
- [Compositional Convolutional Neural Networks: A Deep Architecture with Innate Robustness to Partial Occlusion](https://mlsanity.com/paper/2003.04490/) (2020)
- [Self-Supervised Learning Disentangled Group Representation as Feature](https://mlsanity.com/paper/2110.15255/) (2021)
- [Learning Disentangled Representations in the Imaging Domain](https://mlsanity.com/paper/2108.12043/) (2021)
- [Semi-supervised Meta-learning with Disentanglement for Domain-generalised Medical Image Segmentation](https://mlsanity.com/paper/2106.13292/) (2021)
- [Learning Visual Representations via Language-Guided Sampling](https://mlsanity.com/paper/2302.12248/) (2023)

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

- [Contrastive representations of high-dimensional, structured treatments](https://mlsanity.com/paper/2411.19245/) (2024)
- [Compositional Representation Learning for Brain Tumour Segmentation](https://mlsanity.com/paper/2310.06562/) (2023)

## Abstract (arXiv)

Deep learning models often need sufficient supervision (i.e. labelled data) in order to be trained effectively. By contrast, humans can swiftly learn to identify important anatomy in medical images like MRI and CT scans, with minimal guidance. This recognition capability easily generalises to new images from different medical facilities and to new tasks in different settings. This rapid and generalisable learning ability is largely due to the compositional structure of image patterns in the human brain, which are not well represented in current medical models. In this paper, we study the utilisation of compositionality in learning more interpretable and generalisable representations for medical image segmentation. Overall, we propose that the underlying generative factors that are used to generate the medical images satisfy compositional equivariance property, where each factor is compositional (e.g. corresponds to the structures in human anatomy) and also equivariant to the task. Hence, a good representation that approximates well the ground truth factor has to be compositionally equivariant. By modelling the compositional representations with learnable von-Mises-Fisher (vMF) kernels, we explore how different design and learning biases can be used to enforce the representations to be more compositionally equivariant under un-, weakly-, and semi-supervised settings. Extensive results show that our methods achieve the best performance over several strong baselines on the task of semi-supervised domain-generalised medical image segmentation. Code will be made publicly available upon acceptance at https://github.com/vios-s.