# HorNet: Efficient High-Order Spatial Interactions with Recursive Gated Convolutions

arXiv: https://arxiv.org/abs/2207.14284 · HTML: https://mlsanity.com/paper/2207.14284/

## Key facts

- Cited by 103 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 82 references that are in the map.
- First posted on arXiv 28 Jul 2022.

## Builds on (most cited first, 30 of 59)

- [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)
- [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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [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)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [DINO: DETR with Improved DeNoising Anchor Boxes for End-to-End Object Detection](https://mlsanity.com/paper/2203.03605/) (2022)
- [Cascade R-CNN: Delving into High Quality Object Detection](https://mlsanity.com/paper/1712.00726/) (2017)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Per-Pixel Classification is Not All You Need for Semantic Segmentation](https://mlsanity.com/paper/2107.06278/) (2021)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [CvT: Introducing Convolutions to Vision Transformers](https://mlsanity.com/paper/2103.15808/) (2021)
- [Multiscale Vision Transformers](https://mlsanity.com/paper/2104.11227/) (2021)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)

## Built on by (most cited first, 30 of 103)

- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [EVA: Exploring the Limits of Masked Visual Representation Learning at Scale](https://mlsanity.com/paper/2211.07636/) (2022)
- [Image as a Foreign Language: BEiT Pretraining for All Vision and Vision-Language Tasks](https://mlsanity.com/paper/2208.10442/) (2022)
- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
- [MambaOut: Do We Really Need Mamba for Vision?](https://mlsanity.com/paper/2405.07992/) (2024)
- [Meta-Transformer: A Unified Framework for Multimodal Learning](https://mlsanity.com/paper/2307.10802/) (2023)
- [MetaFormer Baselines for Vision](https://mlsanity.com/paper/2210.13452/) (2022)
- [Autoencoders as Cross-Modal Teachers: Can Pretrained 2D Image Transformers Help 3D Representation Learning?](https://mlsanity.com/paper/2212.08320/) (2022)
- [Delivering Arbitrary-Modal Semantic Segmentation](https://mlsanity.com/paper/2303.01480/) (2023)
- [InceptionNeXt: When Inception Meets ConvNeXt](https://mlsanity.com/paper/2303.16900/) (2023)
- [Conv2Former: A Simple Transformer-Style ConvNet for Visual Recognition](https://mlsanity.com/paper/2211.11943/) (2022)
- [P2P: Tuning Pre-trained Image Models for Point Cloud Analysis with Point-to-Pixel Prompting](https://mlsanity.com/paper/2208.02812/) (2022)
- [RMT: Retentive Networks Meet Vision Transformers](https://mlsanity.com/paper/2309.11523/) (2023)
- [UniRepLKNet: A Universal Perception Large-Kernel ConvNet for Audio, Video, Point Cloud, Time-Series and Image Recognition](https://mlsanity.com/paper/2311.15599/) (2023)
- [MogaNet: Multi-order Gated Aggregation Network](https://mlsanity.com/paper/2211.03295/) (2022)
- [Rewrite the Stars](https://mlsanity.com/paper/2403.19967/) (2024)
- [OpenSTL: A Comprehensive Benchmark of Spatio-Temporal Predictive Learning](https://mlsanity.com/paper/2306.11249/) (2023)
- [Scale-Aware Modulation Meet Transformer](https://mlsanity.com/paper/2307.08579/) (2023)
- [SpectFormer: Frequency and Attention is what you need in a Vision Transformer](https://mlsanity.com/paper/2304.06446/) (2023)
- [UltraLight VM-UNet: Parallel Vision Mamba Significantly Reduces Parameters for Skin Lesion Segmentation](https://mlsanity.com/paper/2403.20035/) (2024)
- [MambaMixer: Efficient Selective State Space Models with Dual Token and Channel Selection](https://mlsanity.com/paper/2403.19888/) (2024)
- [H-vmunet: High-order Vision Mamba UNet for Medical Image Segmentation](https://mlsanity.com/paper/2403.13642/) (2024)
- [Frequency-Adaptive Dilated Convolution for Semantic Segmentation](https://mlsanity.com/paper/2403.05369/) (2024)
- [Breaking the Low-Rank Dilemma of Linear Attention](https://mlsanity.com/paper/2411.07635/) (2024)
- [Lightweight Vision Transformer with Bidirectional Interaction](https://mlsanity.com/paper/2306.00396/) (2023)
- [OverLoCK: An Overview-first-Look-Closely-next ConvNet with Context-Mixing Dynamic Kernels](https://mlsanity.com/paper/2502.20087/) (2025)
- [DAT++: Spatially Dynamic Vision Transformer with Deformable Attention](https://mlsanity.com/paper/2309.01430/) (2023)
- [TransXNet: Learning Both Global and Local Dynamics with a Dual Dynamic Token Mixer for Visual Recognition](https://mlsanity.com/paper/2310.19380/) (2023)
- [Frequency Dynamic Convolution for Dense Image Prediction](https://mlsanity.com/paper/2503.18783/) (2025)
- [Scattering Vision Transformer: Spectral Mixing Matters](https://mlsanity.com/paper/2311.01310/) (2023)

## Abstract (arXiv)

Recent progress in vision Transformers exhibits great success in various tasks driven by the new spatial modeling mechanism based on dot-product self-attention. In this paper, we show that the key ingredients behind the vision Transformers, namely input-adaptive, long-range and high-order spatial interactions, can also be efficiently implemented with a convolution-based framework. We present the Recursive Gated Convolution (textitg^textitnConv) that performs high-order spatial interactions with gated convolutions and recursive designs. The new operation is highly flexible and customizable, which is compatible with various variants of convolution and extends the two-order interactions in self-attention to arbitrary orders without introducing significant extra computation. textitg^textitnConv can serve as a plug-and-play module to improve various vision Transformers and convolution-based models. Based on the operation, we construct a new family of generic vision backbones named HorNet. Extensive experiments on ImageNet classification, COCO object detection and ADE20K semantic segmentation show HorNet outperform Swin Transformers and ConvNeXt by a significant margin with similar overall architecture and training configurations. HorNet also shows favorable scalability to more training data and larger model sizes. Apart from the effectiveness in visual encoders, we also show textitg^textitnConv can be applied to task-specific decoders and consistently improve dense prediction performance with less computation. Our results demonstrate that textitg^textitnConv can be a new basic module for visual modeling that effectively combines the merits of both vision Transformers and CNNs. Code is available at https://github.com/raoyongming/HorNet