# Involution: Inverting the Inherence of Convolution for Visual Recognition

arXiv: https://arxiv.org/abs/2103.06255 · HTML: https://mlsanity.com/paper/2103.06255/

## Key facts

- Cited by 99 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 70 references that are in the map.
- First posted on arXiv 10 Mar 2021.

## Builds on (most cited first, 30 of 62)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Dual Attention Network for Scene Segmentation](https://mlsanity.com/paper/1809.02983/) (2018)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)

## Built on by (most cited first, 30 of 99)

- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Co-Scale Conv-Attentional Image Transformers](https://mlsanity.com/paper/2104.06399/) (2021)
- [Focal Modulation Networks](https://mlsanity.com/paper/2203.11926/) (2022)
- [VOLO: Vision Outlooker for Visual Recognition](https://mlsanity.com/paper/2106.13112/) (2021)
- [More ConvNets in the 2020s: Scaling up Kernels Beyond 51x51 using Sparsity](https://mlsanity.com/paper/2207.03620/) (2022)
- [KVT: k-NN Attention for Boosting Vision Transformers](https://mlsanity.com/paper/2106.00515/) (2021)
- [ACTION-Net: Multipath Excitation for Action Recognition](https://mlsanity.com/paper/2103.07372/) (2021)
- [On the Connection between Local Attention and Dynamic Depth-wise Convolution](https://mlsanity.com/paper/2106.04263/) (2021)
- [TransNeXt: Robust Foveal Visual Perception for Vision Transformers](https://mlsanity.com/paper/2311.17132/) (2023)
- [The Ninth NTIRE 2024 Efficient Super-Resolution Challenge Report](https://mlsanity.com/paper/2404.10343/) (2024)
- [Contextformer: A Transformer with Spatio-Channel Attention for Context Modeling in Learned Image Compression](https://mlsanity.com/paper/2203.02452/) (2022)
- [MixFormer: Mixing Features across Windows and Dimensions](https://mlsanity.com/paper/2204.02557/) (2022)
- [Change Detection Methods for Remote Sensing in the Last Decade: A Comprehensive Review](https://mlsanity.com/paper/2305.05813/) (2023)
- [A survey on efficient vision transformers: algorithms, techniques, and performance benchmarking](https://mlsanity.com/paper/2309.02031/) (2023)
- [Co-advise: Cross Inductive Bias Distillation](https://mlsanity.com/paper/2106.12378/) (2021)
- [Container: Context Aggregation Network](https://mlsanity.com/paper/2106.01401/) (2021)
- [PointFlow: Flowing Semantics Through Points for Aerial Image Segmentation](https://mlsanity.com/paper/2103.06564/) (2021)
- [Scaled ReLU Matters for Training Vision Transformers](https://mlsanity.com/paper/2109.03810/) (2021)
- [Adaptive Dynamic Filtering Network for Image Denoising](https://mlsanity.com/paper/2211.12051/) (2022)
- [Learned Queries for Efficient Local Attention](https://mlsanity.com/paper/2112.11435/) (2021)
- [The Tenth NTIRE 2025 Efficient Super-Resolution Challenge Report](https://mlsanity.com/paper/2504.10686/) (2025)
- [OverLoCK: An Overview-first-Look-Closely-next ConvNet with Context-Mixing Dynamic Kernels](https://mlsanity.com/paper/2502.20087/) (2025)
- [Content-Adaptive Non-Local Convolution for Remote Sensing Pansharpening](https://mlsanity.com/paper/2404.07543/) (2024)
- [Frequency Dynamic Convolution for Dense Image Prediction](https://mlsanity.com/paper/2503.18783/) (2025)
- [ELSA: Enhanced Local Self-Attention for Vision Transformer](https://mlsanity.com/paper/2112.12786/) (2021)
- [Cumulative Spatial Knowledge Distillation for Vision Transformers](https://mlsanity.com/paper/2307.08500/) (2023)
- [KPConvX: Modernizing Kernel Point Convolution with Kernel Attention](https://mlsanity.com/paper/2405.13194/) (2024)
- [Relational Self-Attention: What's Missing in Attention for Video Understanding](https://mlsanity.com/paper/2111.01673/) (2021)
- [HazyDet: Open-Source Benchmark for Drone-View Object Detection with Depth-Cues in Hazy Scenes](https://mlsanity.com/paper/2409.19833/) (2024)
- [LSNet: See Large, Focus Small](https://mlsanity.com/paper/2503.23135/) (2025)

## Abstract (arXiv)

Convolution has been the core ingredient of modern neural networks, triggering the surge of deep learning in vision. In this work, we rethink the inherent principles of standard convolution for vision tasks, specifically spatial-agnostic and channel-specific. Instead, we present a novel atomic operation for deep neural networks by inverting the aforementioned design principles of convolution, coined as involution. We additionally demystify the recent popular self-attention operator and subsume it into our involution family as an over-complicated instantiation. The proposed involution operator could be leveraged as fundamental bricks to build the new generation of neural networks for visual recognition, powering different deep learning models on several prevalent benchmarks, including ImageNet classification, COCO detection and segmentation, together with Cityscapes segmentation. Our involution-based models improve the performance of convolutional baselines using ResNet-50 by up to 1.6% top-1 accuracy, 2.5% and 2.4% bounding box AP, and 4.7% mean IoU absolutely while compressing the computational cost to 66%, 65%, 72%, and 57% on the above benchmarks, respectively. Code and pre-trained models for all the tasks are available at https://github.com/d-li14/involution.