# Rotated Digit Recognition by Variational Autoencoders with Fixed Output Distributions

arXiv: https://arxiv.org/abs/2206.13388 · HTML: https://mlsanity.com/paper/2206.13388/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 18 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [Variational Autoencoders Pursue PCA Directions (by Accident)](https://mlsanity.com/paper/1812.06775/) (2018)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Unsupervised deep learning identifies semantic disentanglement in single inferotemporal neurons](https://mlsanity.com/paper/2006.14304/) (2020)
- [Reconstruction-Based Disentanglement for Pose-invariant Face Recognition](https://mlsanity.com/paper/1702.03041/) (2017)
- [Scale-, shift- and rotation-invariant diffractive optical networks](https://mlsanity.com/paper/2010.12747/) (2020)
- [Transform-Invariant Convolutional Neural Networks for Image Classification and Search](https://mlsanity.com/paper/1912.01447/) (2019)
- [The Accuracy of Restricted Boltzmann Machine Models of Ising Systems](https://mlsanity.com/paper/2004.12867/) (2020)
- [Variational Autoencoder Analysis of Ising Model Statistical Distributions and Phase Transitions](https://mlsanity.com/paper/2104.06368/) (2021)
- [Patch Reordering: a Novel Way to Achieve Rotation and Translation Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/1911.12682/) (2019)

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

- [Neural Network Characterization and Entropy Regulated Data Balancing through Principal Component Analysis](https://mlsanity.com/paper/2312.01392/) (2023)
- [Branched Variational Autoencoder Classifiers](https://mlsanity.com/paper/2401.02526/) (2024)

## Abstract (arXiv)

This paper demonstrates that a simple modification of the variational autoencoder (VAE) formalism enables the method to identify and classify rotated and distorted digits. In particular, the conventional objective (cost) function employed during the training process of a VAE both quantifies the agreement between the input and output data records and ensures that the latent space representation of the input data record is statistically generated with an appropriate mean and standard deviation. After training, simulated data realizations are generated by decoding appropriate latent space points. Since, however, standard VAE:s trained on randomly rotated MNIST digits cannot reliably distinguish between different digit classes since the rotated input data is effectively compared to a similarly rotated output data record. In contrast, an alternative implementation in which the objective function compares the output associated with each rotated digit to a corresponding fixed unreferenced reference digit is shown here to discriminate accurately among the rotated digits in latent space even when the dimension of the latent space is 2 or 3.