# Evolution: A Unified Formula for Feature Operators from a High-level Perspective

arXiv: https://arxiv.org/abs/2305.14409 · HTML: https://mlsanity.com/paper/2305.14409/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 29 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [Stand-Alone Self-Attention in Vision Models](https://mlsanity.com/paper/1906.05909/) (2019)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [Dynamic Convolution: Attention over Convolution Kernels](https://mlsanity.com/paper/1912.03458/) (2019)
- [ResMLP: Feedforward networks for image classification with data-efficient training](https://mlsanity.com/paper/2105.03404/) (2021)
- [On the Relationship between Self-Attention and Convolutional Layers](https://mlsanity.com/paper/1911.03584/) (2019)
- [CondConv: Conditionally Parameterized Convolutions for Efficient Inference](https://mlsanity.com/paper/1904.04971/) (2019)
- [Local Relation Networks for Image Recognition](https://mlsanity.com/paper/1904.11491/) (2019)
- [Involution: Inverting the Inherence of Convolution for Visual Recognition](https://mlsanity.com/paper/2103.06255/) (2021)
- [Do You Even Need Attention? A Stack of Feed-Forward Layers Does Surprisingly Well on ImageNet](https://mlsanity.com/paper/2105.02723/) (2021)
- [Omni-Dimensional Dynamic Convolution](https://mlsanity.com/paper/2209.07947/) (2022)
- [WeightNet: Revisiting the Design Space of Weight Networks](https://mlsanity.com/paper/2007.11823/) (2020)
- [DyNet: Dynamic Convolution for Accelerating Convolutional Neural Networks](https://mlsanity.com/paper/2004.10694/) (2020)
- [X-volution: On the unification of convolution and self-attention](https://mlsanity.com/paper/2106.02253/) (2021)

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

- [NSTR: Neural Spectral Transport Representation for Space-Varying Frequency Fields](https://mlsanity.com/paper/2511.18384/) (2025)
- [Scaling Implicit Fields via Hypernetwork-Driven Multiscale Coordinate Transformations](https://mlsanity.com/paper/2511.18387/) (2025)

## Abstract (arXiv)

Traditionally, different types of feature operators (e.g., convolution, self-attention and involution) utilize different approaches to extract and aggregate the features. Resemblance can be hardly discovered from their mathematical formulas. However, these three operators all serve the same paramount purpose and bear no difference in essence. Hence we probe into the essence of various feature operators from a high-level perspective, transformed their components equivalently, and explored their mathematical expressions within higher dimensions. We raise one clear and concrete unified formula for different feature operators termed as Evolution. Evolution utilizes the Evolution Function to generate the Evolution Kernel, which extracts and aggregates the features in certain positions of the input feature map. We mathematically deduce the equivalent transformation from the traditional formulas of these feature operators to Evolution and prove the unification. In addition, we discuss the forms of Evolution Functions and the properties of generated Evolution Kernels, intending to give inspirations to the further research and innovations of powerful feature operators.