# Improved Representation Learning Through Tensorized Autoencoders

arXiv: https://arxiv.org/abs/2212.01046 · HTML: https://mlsanity.com/paper/2212.01046/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 2 Dec 2022.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization](https://mlsanity.com/paper/1704.06327/) (2017)
- [A Survey on Masked Autoencoder for Self-supervised Learning in Vision and Beyond](https://mlsanity.com/paper/2208.00173/) (2022)
- [Loss Landscapes of Regularized Linear Autoencoders](https://mlsanity.com/paper/1901.08168/) (2019)
- [Regularized linear autoencoders recover the principal components, eventually](https://mlsanity.com/paper/2007.06731/) (2020)
- [Learning Dynamics of Linear Denoising Autoencoders](https://mlsanity.com/paper/1806.05413/) (2018)
- [Learning A Task-Specific Deep Architecture For Clustering](https://mlsanity.com/paper/1509.00151/) (2015)
- [Provable Estimation of the Number of Blocks in Block Models](https://mlsanity.com/paper/1705.08580/) (2017)

## Built on by (most cited first, 1 of 1)

- [Theoretical Foundations of Representation Learning using Unlabeled Data: Statistics and Optimization](https://mlsanity.com/paper/2509.18997/) (2025)

## Abstract (arXiv)

The central question in representation learning is what constitutes a good or meaningful representation. In this work we argue that if we consider data with inherent cluster structures, where clusters can be characterized through different means and covariances, those data structures should be represented in the embedding as well. While Autoencoders (AE) are widely used in practice for unsupervised representation learning, they do not fulfil the above condition on the embedding as they obtain a single representation of the data. To overcome this we propose a meta-algorithm that can be used to extend an arbitrary AE architecture to a tensorized version (TAE) that allows for learning cluster-specific embeddings while simultaneously learning the cluster assignment. For the linear setting we prove that TAE can recover the principle components of the different clusters in contrast to principle component of the entire data recovered by a standard AE. We validated this on planted models and for general, non-linear and convolutional AEs we empirically illustrate that tensorizing the AE is beneficial in clustering and de-noising tasks.