# OneDConv: Generalized Convolution For Transform-Invariant Representation

arXiv: https://arxiv.org/abs/2201.05781 · HTML: https://mlsanity.com/paper/2201.05781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 15 Jan 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Deep Pyramidal Residual Networks](https://mlsanity.com/paper/1610.02915/) (2016)
- [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)
- [Gabor Convolutional Networks](https://mlsanity.com/paper/1705.01450/) (2017)
- [Towards Learning Affine-Invariant Representations via Data-Efficient CNNs](https://mlsanity.com/paper/1909.00114/) (2019)
- [Transform-Invariant Convolutional Neural Networks for Image Classification and Search](https://mlsanity.com/paper/1912.01447/) (2019)
- [Feature Lenses: Plug-and-play Neural Modules for Transformation-Invariant Visual Representations](https://mlsanity.com/paper/2004.05554/) (2020)

## Abstract (arXiv)

Convolutional Neural Networks (CNNs) have exhibited their great power in a variety of vision tasks. However, the lack of transform-invariant property limits their further applications in complicated real-world scenarios. In this work, we proposed a novel generalized one dimension convolutional operator (OneDConv), which dynamically transforms the convolution kernels based on the input features in a computationally and parametrically efficient manner. The proposed operator can extract the transform-invariant features naturally. It improves the robustness and generalization of convolution without sacrificing the performance on common images. The proposed OneDConv operator can substitute the vanilla convolution, thus it can be incorporated into current popular convolutional architectures and trained end-to-end readily. On several popular benchmarks, OneDConv outperforms the original convolution operation and other proposed models both in canonical and distorted images.