# Beyond Convolution: A Taxonomy of Structured Operators for Learning-Based Image Processing

arXiv: https://arxiv.org/abs/2603.12067 · HTML: https://mlsanity.com/paper/2603.12067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 44 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [ECA-Net: Efficient Channel Attention for Deep Convolutional Neural Networks](https://mlsanity.com/paper/1910.03151/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Dynamic Convolution: Attention over Convolution Kernels](https://mlsanity.com/paper/1912.03458/) (2019)
- [An Intriguing Failing of Convolutional Neural Networks and the CoordConv Solution](https://mlsanity.com/paper/1807.03247/) (2018)
- [cuDNN: Efficient Primitives for Deep Learning](https://mlsanity.com/paper/1410.0759/) (2014)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Fast Algorithms for Convolutional Neural Networks](https://mlsanity.com/paper/1509.09308/) (2015)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [Multi-level Wavelet Convolutional Neural Networks](https://mlsanity.com/paper/1907.03128/) (2019)
- [Omni-Dimensional Dynamic Convolution](https://mlsanity.com/paper/2209.07947/) (2022)
- [Convolutional Kernel Networks](https://mlsanity.com/paper/1406.3332/) (2014)
- [Optimal Density Functions for Weighted Convolution in Learning Models](https://mlsanity.com/paper/2505.24527/) (2025)
- [Optimal Weighted Convolution for Classification and Denosing](https://mlsanity.com/paper/2505.24558/) (2025)

## Abstract (arXiv)

The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear, locally-averaging operator limits its ability to capture structured signal properties such as low-rank decompositions, adaptive basis representations, and non-uniform spatial dependencies. This paper presents a systematic taxonomy of operators that extend or replace the standard convolution in learning-based image processing pipelines. We organise the landscape of alternative operators into five families: (i) decomposition-based operators, which separate structural and noise components through singular value or tensor decompositions; (ii) adaptive weighted operators, which modulate kernel contributions as a function of spatial position or signal content; (iii) basis-adaptive operators, which optimise the analysis bases together with the network weights; (iv) integral and kernel operators, which generalise the convolution to position-dependent and non-linear kernels; and (v) attention-based operators, which relax the locality assumption entirely. For each family, we provide a formal definition, a discussion of its structural properties with respect to the convolution, and a critical analysis of the tasks for which the operator is most appropriate. We further provide a comparative analysis of all families across relevant dimensions -- linearity, locality, equivariance, computational cost, and suitability for image-to-image and image-to-label tasks -- and outline the open challenges and future directions of this research area.