# AVT: Unsupervised Learning of Transformation Equivariant Representations by Autoencoding Variational Transformations

arXiv: https://arxiv.org/abs/1903.10863 · HTML: https://mlsanity.com/paper/1903.10863/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2019.

## Built on by (most cited first, 15 of 15)

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- [iDECODe: In-distribution Equivariance for Conformal Out-of-distribution Detection](https://mlsanity.com/paper/2201.02331/) (2022)
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- [Beyond Instance Discrimination: Relation-aware Contrastive Self-supervised Learning](https://mlsanity.com/paper/2211.01796/) (2022)
- [Self-Supervised Multi-View Learning via Auto-Encoding 3D Transformations](https://mlsanity.com/paper/2103.00787/) (2021)
- [Self-Supervised Graph Representation Learning via Topology Transformations](https://mlsanity.com/paper/2105.11689/) (2021)
- [Equivariant Deep Dynamical Model for Motion Prediction](https://mlsanity.com/paper/2111.01892/) (2021)
- [CODiT: Conformal Out-of-Distribution Detection in Time-Series Data](https://mlsanity.com/paper/2207.11769/) (2022)
- [Invariance-based Multi-Clustering of Latent Space Embeddings for Equivariant Learning](https://mlsanity.com/paper/2107.11717/) (2021)
- [Survey on Self-supervised Representation Learning Using Image Transformations](https://mlsanity.com/paper/2202.08514/) (2022)
- [Disentangling Representation using Attributes-based Gaussian Estimation for Medical Sound Diagnosis](https://mlsanity.com/paper/2608.29026/) (2026)
- [Latent evolving World Action Model](https://mlsanity.com/paper/2609.27455/) (2026)

## Abstract (arXiv)

The learning of Transformation-Equivariant Representations (TERs), which is introduced by Hinton et al. citehinton2011transforming, has been considered as a principle to reveal visual structures under various transformations. It contains the celebrated Convolutional Neural Networks (CNNs) as a special case that only equivary to the translations. In contrast, we seek to train TERs for a generic class of transformations and train them in an em unsupervised fashion. To this end, we present a novel principled method by Autoencoding Variational Transformations (AVT), compared with the conventional approach to autoencoding data. Formally, given transformed images, the AVT seeks to train the networks by maximizing the mutual information between the transformations and representations. This ensures the resultant TERs of individual images contain the em intrinsic information about their visual structures that would equivary em extricably under various transformations in a generalized em nonlinear case. Technically, we show that the resultant optimization problem can be efficiently solved by maximizing a variational lower-bound of the mutual information. This variational approach introduces a transformation decoder to approximate the intractable posterior of transformations, resulting in an autoencoding architecture with a pair of the representation encoder and the transformation decoder. Experiments demonstrate the proposed AVT model sets a new record for the performances on unsupervised tasks, greatly closing the performance gap to the supervised models.