# Orthonormal Convolutions for the Rotation Based Iterative Gaussianization

arXiv: https://arxiv.org/abs/2206.03860 · HTML: https://mlsanity.com/paper/2206.03860/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## Builds on (most cited first, 16 of 16)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [Density Modeling of Images using a Generalized Normalization Transformation](https://mlsanity.com/paper/1511.06281/) (2015)
- [Emerging Convolutions for Generative Normalizing Flows](https://mlsanity.com/paper/1901.11137/) (2019)
- [Iterative Gaussianization: from ICA to Random Rotations](https://mlsanity.com/paper/1602.00229/) (2016)
- [Gaussianization Flows](https://mlsanity.com/paper/2003.01941/) (2020)
- [Contrast Sensitivity Functions in Autoencoders](https://mlsanity.com/paper/2103.00481/) (2021)
- [Self Normalizing Flows](https://mlsanity.com/paper/2011.07248/) (2020)
- [Spatio-Chromatic Information available from different Neural Layers via Gaussianization](https://mlsanity.com/paper/1910.01559/) (2019)
- [Information Theory Measures via Multidimensional Gaussianization](https://mlsanity.com/paper/2010.03807/) (2020)
- [Visual Information flow in Wilson-Cowan networks](https://mlsanity.com/paper/1907.13046/) (2019)
- [Gaussianizing the Earth: Multidimensional Information Measures for Earth Data Analysis](https://mlsanity.com/paper/2010.06476/) (2020)
- [Information Theory in Density Destructors](https://mlsanity.com/paper/2012.01012/) (2020)
- [Unsupervised Anomaly and Change Detection with Multivariate Gaussianization](https://mlsanity.com/paper/2204.05699/) (2022)

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

- [Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flows](https://mlsanity.com/paper/2305.02164/) (2023)
- [Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models](https://mlsanity.com/paper/2405.16475/) (2024)

## Abstract (arXiv)

In this paper we elaborate an extension of rotation-based iterative Gaussianization, RBIG, which makes image Gaussianization possible. Although RBIG has been successfully applied to many tasks, it is limited to medium dimensionality data (on the order of a thousand dimensions). In images its application has been restricted to small image patches or isolated pixels, because rotation in RBIG is based on principal or independent component analysis and these transformations are difficult to learn and scale. Here we present the Convolutional RBIG: an extension that alleviates this issue by imposing that the rotation in RBIG is a convolution. We propose to learn convolutional rotations (i.e. orthonormal convolutions) by optimising for the reconstruction loss between the input and an approximate inverse of the transformation using the transposed convolution operation. Additionally, we suggest different regularizers in learning these orthonormal convolutions. For example, imposing sparsity in the activations leads to a transformation that extends convolutional independent component analysis to multilayer architectures. We also highlight how statistical properties of the data, such as multivariate mutual information, can be obtained from Convolutional RBIG. We illustrate the behavior of the transform with a simple example of texture synthesis, and analyze its properties by visualizing the stimuli that maximize the response in certain feature and layer.