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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 ($\textit{g}^\textit{n}$Conv) 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. $\textit{g}^\textit{n}$Conv 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 $\textit{g}^\textit{n}$Conv can be applied to task-specific decoders and consistently improve dense prediction performance with less computation. Our results demonstrate that $\textit{g}^\textit{n}$Conv 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