# Learning Generalized Transformation Equivariant Representations via Autoencoding Transformations

arXiv: https://arxiv.org/abs/1906.08628 · HTML: https://mlsanity.com/paper/1906.08628/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2019.

## Built on by (most cited first, 22 of 22)

- [Contrastive Learning with Stronger Augmentations](https://mlsanity.com/paper/2104.07713/) (2021)
- [Preservational Learning Improves Self-supervised Medical Image Models by Reconstructing Diverse Contexts](https://mlsanity.com/paper/2109.04379/) (2021)
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- [Exploring Complementary Strengths of Invariant and Equivariant Representations for Few-Shot Learning](https://mlsanity.com/paper/2103.01315/) (2021)
- [Equivariant Similarity for Vision-Language Foundation Models](https://mlsanity.com/paper/2303.14465/) (2023)
- [Self-Interpretable Model with TransformationEquivariant Interpretation](https://mlsanity.com/paper/2111.04927/) (2021)
- [Learning Equivariant Segmentation with Instance-Unique Querying](https://mlsanity.com/paper/2210.00911/) (2022)
- [GenView: Enhancing View Quality with Pretrained Generative Model for Self-Supervised Learning](https://mlsanity.com/paper/2403.12003/) (2024)
- [Sampling Equivariant Self-attention Networks for Object Detection in Aerial Images](https://mlsanity.com/paper/2111.03420/) (2021)
- [Beyond Instance Discrimination: Relation-aware Contrastive Self-supervised Learning](https://mlsanity.com/paper/2211.01796/) (2022)
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- [Self-Supervised Graph Representation Learning via Topology Transformations](https://mlsanity.com/paper/2105.11689/) (2021)
- [Adversarial Pretraining of Self-Supervised Deep Networks: Past, Present and Future](https://mlsanity.com/paper/2210.13463/) (2022)
- [Scale-Rotation-Equivariant Lie Group Convolution Neural Networks (Lie Group-CNNs)](https://mlsanity.com/paper/2306.06934/) (2023)
- [Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions](https://mlsanity.com/paper/2510.21706/) (2025)
- [Quantised Transforming Auto-Encoders: Achieving Equivariance to Arbitrary Transformations in Deep Networks](https://mlsanity.com/paper/2111.12873/) (2021)
- [Sample Efficient Dynamics Learning for Symmetrical Legged Robots:Leveraging Physics Invariance and Geometric Symmetries](https://mlsanity.com/paper/2210.07329/) (2022)
- [Bayesian Unsupervised Disentanglement of Anatomy and Geometry for Deep Groupwise Image Registration](https://mlsanity.com/paper/2401.02141/) (2024)
- [Neural TMDlayer: Modeling Instantaneous flow of features via SDE Generators](https://mlsanity.com/paper/2108.08891/) (2021)
- [GenView++: Unifying Adaptive Generative Augmentation and Quality-Driven Supervision for Contrastive Representation Learning](https://mlsanity.com/paper/2509.23770/) (2025)
- [Disentanglement-Based Equivariant Learning for Compositional VQA](https://mlsanity.com/paper/2606.02168/) (2026)
- [Disentangling Representation using Attributes-based Gaussian Estimation for Medical Sound Diagnosis](https://mlsanity.com/paper/2608.29026/) (2026)

## Abstract (arXiv)

Transformation Equivariant Representations (TERs) aim to capture the intrinsic visual structures that equivary to various transformations by expanding the notion of em translation equivariance underlying the success of Convolutional Neural Networks (CNNs). For this purpose, we present both deterministic AutoEncoding Transformations (AET) and probabilistic AutoEncoding Variational Transformations (AVT) models to learn visual representations from generic groups of transformations. While the AET is trained by directly decoding the transformations from the learned representations, the AVT is trained by maximizing the joint mutual information between the learned representation and transformations. This results in Generalized TERs (GTERs) equivariant against transformations in a more general fashion by capturing complex patterns of visual structures beyond the conventional linear equivariance under a transformation group. The presented approach can be extended to (semi-)supervised models by jointly maximizing the mutual information of the learned representation with both labels and transformations. Experiments demonstrate the proposed models outperform the state-of-the-art models in both unsupervised and (semi-)supervised tasks.