# FILTRA: Rethinking Steerable CNN by Filter Transform

arXiv: https://arxiv.org/abs/2105.11636 · HTML: https://mlsanity.com/paper/2105.11636/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 19 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 17 of 17)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Oriented Response Networks](https://mlsanity.com/paper/1701.01833/) (2017)
- [TI-POOLING: transformation-invariant pooling for feature learning in Convolutional Neural Networks](https://mlsanity.com/paper/1604.06318/) (2016)
- [Deep Roto-Translation Scattering for Object Classification](https://mlsanity.com/paper/1412.8659/) (2014)
- [Learning the Irreducible Representations of Commutative Lie Groups](https://mlsanity.com/paper/1402.4437/) (2014)
- [Equivariant Transformer Networks](https://mlsanity.com/paper/1901.11399/) (2019)
- [PDO-eConvs: Partial Differential Operator Based Equivariant Convolutions](https://mlsanity.com/paper/2007.10408/) (2020)
- [Warped Convolutions: Efficient Invariance to Spatial Transformations](https://mlsanity.com/paper/1609.04382/) (2016)
- [RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks](https://mlsanity.com/paper/1805.06846/) (2018)

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

- [Homomorphic Self-Supervised Learning](https://mlsanity.com/paper/2211.08282/) (2022)

## Abstract (arXiv)

Steerable CNN imposes the prior knowledge of transformation invariance or equivariance in the network architecture to enhance the the network robustness on geometry transformation of data and reduce overfitting. It has been an intuitive and widely used technique to construct a steerable filter by augmenting a filter with its transformed copies in the past decades, which is named as filter transform in this paper. Recently, the problem of steerable CNN has been studied from aspect of group representation theory, which reveals the function space structure of a steerable kernel function. However, it is not yet clear on how this theory is related to the filter transform technique. In this paper, we show that kernel constructed by filter transform can also be interpreted in the group representation theory. This interpretation help complete the puzzle of steerable CNN theory and provides a novel and simple approach to implement steerable convolution operators. Experiments are executed on multiple datasets to verify the feasibility of the proposed approach.