\begin{table}[t]
    \centering
    \renewcommand{\arraystretch}{1.0}
    \setlength{\tabcolsep}{1.3mm}
    \footnotesize
    \begin{tabular}{l|c|c|c|cc}
    	\multirow{2}{*}{Method} & Crop & \multirow{2}{*}{\#Params} & \multirow{2}{*}{\#FLOPs} & mIoU & mIoU\\
    	& Size & & & (ss) & (ms)   \\
    	\whline
    	Swin-T~\cite{liu2021swin} & 512$^2$ & 60M  & 945G & 44.5 & 45.8 \\
    	ConvNeXt-T~\cite{liu2022convnet} & 512$^2$ & 60M & 939G & 46.0 & 46.7 \\
    	SLaK-T~\cite{liu2022slak} & 512$^2$ & 65M & 936G & 47.6 & $-$ \\
    	\rowcolor{gray!20}
    	InternImage-T (ours) & 512$^2$ & 59M & 944G & 47.9 & 48.1  \\
    	\hline
        Swin-S~\cite{liu2021swin} & 512$^2$ & 81M &  1038G &  47.6 &  49.5 \\
        ConvNeXt-S~\cite{liu2022convnet}  & 512$^2$ &82M & 1027G  & 48.7 & 49.6  \\
        SLaK-S~\cite{liu2022slak} & 512$^2$ &91M & 1028G & 49.4 & $-$ \\
        \rowcolor{gray!20}
        InternImage-S (ours) & 512$^2$ & 80M & 1017G & 50.1 & 50.9 \\
        \hline
        Swin-B~\cite{liu2021swin} 
        & 512$^2$ & 121M & 1188G & 48.1 & 49.7  \\
        ConvNeXt-B~\cite{liu2022convnet}  
        & 512$^2$ & 122M & 1170G & 49.1 & 49.9  \\
        RepLKNet-31B~\cite{ding2022replknet} 
        & 512$^2$ & 112M & 1170G & 49.9 & 50.6  \\
        SLaK-B~\cite{liu2022slak} & 512$^2$ & 135M & 1172G & 50.2 & $-$    \\
        \rowcolor{gray!20}
        InternImage-B (ours) 
        & 512$^2$ & 128M & 1185G & 50.8 & 51.3 \\
        \hline
        Swin-L$^\ddagger$~\cite{liu2021swin} 
        & 640$^2$ & 234M & 2468G & 52.1 & 53.5 \\
        RepLKNet-31L$^\ddagger$~\cite{ding2022replknet} 
        & 640$^2$ & 207M & 2404G & 52.4 & 52.7 \\
        ConvNeXt-L$^\ddagger$~\cite{liu2022convnet} 
        & 640$^2$ & 235M & 2458G & 53.2 & 53.7 \\
        ConvNeXt-XL$^\ddagger$~\cite{liu2022convnet} 
        & 640$^2$ & 391M & 3335G & 53.6 & 54.0 \\
        \rowcolor{gray!10}
        InternImage-L$^\ddagger$ (ours) 
        & 640$^2$ & 256M  & 2526G  & 53.9 & 54.1 \\
        \rowcolor{gray!20}
        InternImage-XL$^\ddagger$ (ours)
        & 640$^2$ & 368M & 3142G & 55.0 & 55.3 \\
        \hline
        SwinV2-G$^\#$~\cite{liu2021swinv2}
        & 896$^2$ & 3.00B & $-$ & $-$ & 59.9 \\
        \rowcolor{gray!10}
        InternImage-H$^\#$ (ours)
        & 896$^2$ & 1.12B & 3566G & 59.9 & 60.3 \\
        \hline
        BEiT-3$^\#$~\cite{wang2022beit3} & 896$^2$ & 1.90B & $-$ & $-$ & 62.8 \\ 
        \rowcolor{gray!20}
        InternImage-H$^\#$ (ours) + &  &  &  &  &  \\
        \rowcolor{gray!20}
        Mask2Former~\cite{cheng2021masked}
        & \multirow{-2}{*}{896$^2$}& \multirow{-2}{*}{1.31B}& \multirow{-2}{*}{4635G}& \multirow{-2}{*}{62.5}& \multirow{-2}{*}{62.9}\\
    \end{tabular}
    \caption{\textbf{Semantic segmentation performance on the ADE20K validation set.}
    	``SS'' and ``MS" means single-scale and multi-scale testing, respectively. 
    }
    \label{tab:seg}
\end{table}
\author{
    Wenhai Wang$^{1*}$, 
    Jifeng Dai$^{2,1*}$,
    Zhe Chen$^{3,1*}$,
    Zhenhang Huang$^{1*}$,
    Zhiqi Li$^{3,1*}$,
    Xizhou Zhu$^{4*}$,\\
    Xiaowei Hu$^{1}$,
    Tong Lu$^{3}$,
    Lewei Lu$^{4}$,
    Hongsheng Li$^{5}$,
    Xiaogang Wang$^{3,5}$,
    Yu Qiao$^{1}$\textsuperscript{\Letter}\\
    $^1$ Shanghai AI Laboratory~~~
    $^2$Tsinghua University~~~\\
    $^3$Nanjing University~~~
    $^4$SenseTime Research~~~
    $^5$The Chinese University of Hong Kong\\
    {\small \url{https://github.com/OpenGVLab/InternImage}}
}

where $K$ represents the total number of sampling points, and $k$ enumerates the sampling point. 
$\mathbf{w}_k\!\in\!\mathbb{R}^{C\times C}$ denotes the projection weights of the $k$-th sampling point,
and $\mathbf{m}_k\!\in\!\mathbb{R}$ represents the modulation scalar of the $k$-th sampling point, which is normalized by sigmoid function.
$p_k$ denotes the $k$-th location of the pre-defined grid sampling $\{(-1, -1), (-1, 0), ..., (0, +1), ..., (+1, +1)\}$ as in regular convolutions,
and $\Delta p_k$ is the offset corresponding to the $k$-th grid sampling location.
We see from the equation that (1) for long-range dependencies, the sampling offset $\Delta p_k$ is flexible and able to interact with short- or long-range features; and (2) for adaptive spatial aggregation, both the sampling offset $\Delta p_k$ and modulation scalar $\mathbf{m}_k$ are learnable and conditioned by input $\mathbf{x}$. 
So it can be found that \emph{DCNv2 shares similar favorable properties with MHSA}, which motivated us to develop large-scale CNN-based foundation models on the basis of this operator.

\textbf{Stem \& downsampling layers.}
To obtain hierarchical feature maps, we use 
convolutional stem and downsampling layers to resize the feature maps to different scales.
As shown in Fig. \ref{fig:arch}, the stem layer is placed before the first stage to reduce the input resolution by 4 times.
It consists of two convolutions, two LN layers, and one GELU layer,
where the kernel size of the two convolutions is 3, the stride is 2, the padding is 1,
and the output channel of the first convolution is half of the second one.
Similarly, the downsampling layer is made up of a 3$\times$3 convolution with a stride of 2 and a padding of 1, followed by one LN layer.
It sits between the two stages and is used to downsample the input feature map by 2 times.

where $\alpha\!\geq\!1$, $\beta\!\geq\!1$, and $\alpha\beta^{1.99}\!\approx\!2$. Here, 1.99 is specific for InternImage and calculated by doubling the model width and keeping the depth constant.
We experimentally find out that the best scaling setting is $\alpha\!=\!1.09$ and $\beta\!=\!1.36$, and then we base on it to construct InternImage\ variants with different parameter scales, namely InternImage-T/S/B/L/XL, whose complexity is similar to those of ConvNeXt~\cite{liu2022convnet}. 
To further test the capability, we built a larger InternImage-H with 1 billion parameters.
The detailed configurations are summarized in Table~\ref{tab:model_size}.

\subsection{Image Classification}
\textbf{Settings.}
We evaluate the classification performance of InternImage\ on ImageNet~\cite{deng2009imagenet}. 
For fair comparisons, following common practices~\cite{touvron2021training,wang2021pyramid,liu2021swin,liu2022convnet}, InternImage-T/S/B are trained on ImageNet-1K ($\sim$1.3 million) for 300 epochs, 
and InternImage-L/XL are first trained on ImageNet-22K ($\sim$14.2 million) for 90 epochs and then fine-tuned on ImageNet-1K for 30 epochs.
To further explore the capability of our model and match the large-scale private data used in previous methods~\cite{dai2021coatnet,liu2021swinv2,yuan2021florence}, we adopt M3I Pre-training~\cite{anonymous2022m2i}, an effective pre-training approach, to pre-train InternImage-H on a 427 million joint dataset of public Laion-400M~\cite{schuhmann2021laion}, YFCC-15M~\cite{thomee2016yfcc100m}, and CC12M~\cite{changpinyo2021conceptual} for 30 epochs,
and then we fine-tune the model on ImageNet-22K and -1K for 30 epochs, respectively.

\textbf{Results.}
As shown in Table~\ref{tab:results_detection_mask}, when using Mask R-CNN for object detection, 
we find that under a comparable number of parameters, our models significantly surpass their counterparts. 
For example, with the $1\times$ training schedule, the box AP (AP$^{\rm b}$) of InternImage-T is 4.5 points better than Swin-T~\cite{liu2021swin} (47.2 \vs 42.7),
and 3.0 points higher than ConvNeXt-T~\cite{liu2022convnet} (47.2 \vs 44.2).
As reported in Table~\ref{tab:results_detection_cascade}, with more parameters and more advanced Cascade Mask R-CNN, InternImage-XL achieves AP$^{\rm b}$ of 55.3, surpassing ConvNeXt-XL by 2.7 points (55.3 \vs 53.6).

To further push the performance bound of object detection, we follow the advanced setting used in leading methods~\cite{wang2022beit3, liu2021swinv2, zhang2022dino} to initialize the model with the weights pre-trained on ImageNet-22K or the large-scale joint dataset,
and fine-tune it along with the DINO~\cite{zhang2022dino} detector on the Objects365~\cite{shao2019objects365} and COCO datasets one after another for 26 epochs and 12 epochs, respectively.
As shown in Table~\ref{tab:sota}, our method establishes a new record of 65.0 AP$^\text{b}$ and 65.4 AP$^\text{b}$ on COCO val2017 and test-dev.
Compared to previous state-of-the-art models, we surpass FD-SwinV2-G~\cite{wei2022fdswin} by 1.2 points (65.4 \vs 64.2), using 27\% fewer parameters, 
which shows the effectiveness of our models on the object detection task.

\textbf{Results.}
As shown in Table~\ref{tab:seg}, when using UperNet~\cite{xiao2018unified} for semantic segmentation, our InternImage~consistently outperforms prior arts~\cite{liu2021swin, liu2022convnet, liu2022slak, ding2022replknet}.
For example, with almost the same parameter numbers and FLOPs, our InternImage-B reports 50.8 mIoU on the ADE20K val, which is outstanding from the strong counterparts such as ConvNeXt-B (50.8 \emph{vs.}~49.1) and RepLKNet-31B (50.8 \emph{vs.}~49.9).
Furthermore, our InternImage-H yields 60.3 MS mIoU, which is slightly better than SwinV2-G~\cite{liu2021swinv2}, while the parameter number is much smaller (1.12B \emph{vs.}~3.00B). 
{"value": "60M", "type": "Hyper-parameter/Architecture", "model": "Swin-T", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "945G", "type": "Hyper-parameter/Architecture", "model": "Swin-T", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "44.5", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "Swin-T", "model settings": {"number of parameters": "60M", "number of FLOPs": "945G"}} {"value": "45.8", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "multi-scale testing": "true", "ms": "true"}, "model": "Swin-T", "model settings": {"number of parameters": "60M", "number of FLOPs": "945G"}} {"value": "60M", "type": "Hyper-parameter/Architecture", "model": "ConvNeXt-T", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "939G", "type": "Hyper-parameter/Architecture", "model": "ConvNeXt-T", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "46.0", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "ConvNeXt-T", "model settings": {"number of parameters": "60M", "number of FLOPs": "939G"}} {"value": "46.7", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "multi-scale testing": "true", "ms": "true"}, "model": "ConvNeXt-T", "model settings": {"number of parameters": "60M", "number of FLOPs": "939G"}} {"value": "65M", "type": "Hyper-parameter/Architecture", "model": "SLaK-T", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "936G", "type": "Hyper-parameter/Architecture", "model": "SLaK-T", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "47.6", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "SLaK-T", "model settings": {"number of parameters": "65M", "number of FLOPs": "936G"}} {"value": "59M", "type": "Hyper-parameter/Architecture", "model": "InternImage-T", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "944G", "type": "Hyper-parameter/Architecture", "model": "InternImage-T", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "47.9", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "InternImage-T", "model settings": {"number of parameters": "59M", "number of FLOPs": "944G"}} {"value": "48.1", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "multi-scale testing": "true", "ms": "true"}, "model": "InternImage-T", "model settings": {"number of parameters": "59M", "number of FLOPs": "944G"}} {"value": "81M", "type": "Hyper-parameter/Architecture", "model": "Swin-S", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "1038G", "type": "Hyper-parameter/Architecture", "model": "Swin-S", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "47.6", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "Swin-S", "model settings": {"number of parameters": "81M", "number of FLOPs": "1038G"}} {"value": "49.5", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "multi-scale testing": "true", "ms": "true"}, "model": "Swin-S", "model settings": {"number of parameters": "81M", "number of FLOPs": "1038G"}} {"value": "82M", "type": "Hyper-parameter/Architecture", "model": "ConvNeXt-S", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "1027G", "type": "Hyper-parameter/Architecture", "model": "ConvNeXt-S", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "48.7", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "ConvNeXt-S", "model settings": {"number of parameters": "82M", "number of FLOPs": "1027G"}} {"value": "49.6", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "multi-scale testing": "true", "ms": "true"}, "model": "ConvNeXt-S", "model settings": {"number of parameters": "82M", "number of FLOPs": "1027G"}} {"value": "91M", "type": "Hyper-parameter/Architecture", "model": "SLaK-S", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "1028G", "type": "Hyper-parameter/Architecture", "model": "SLaK-S", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "49.4", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "SLaK-S", "model settings": {"number of parameters": "91M", "number of FLOPs": "1028G"}} {"value": "80M", "type": "Hyper-parameter/Architecture", "model": "InternImage-S", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "1017G", "type": "Hyper-parameter/Architecture", "model": "InternImage-S", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "50.1", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale 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"512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "Swin-B", "model settings": {"number of parameters": "121M", "number of FLOPs": "1188G"}} {"value": "49.7", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "multi-scale testing": "true", "ms": "true"}, "model": "Swin-B", "model settings": {"number of parameters": "121M", "number of FLOPs": "1188G"}} {"value": "122M", "type": "Hyper-parameter/Architecture", "model": "ConvNeXt-B", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "1170G", "type": "Hyper-parameter/Architecture", "model": "ConvNeXt-B", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "49.1", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental 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"metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "RepLKNet-31B", "model settings": {"number of parameters": "112M", "number of FLOPs": "1170G"}} {"value": "50.6", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "multi-scale testing": "true", "ms": "true"}, "model": "RepLKNet-31B", "model settings": {"number of parameters": "112M", "number of FLOPs": "1170G"}} {"value": "135M", "type": "Hyper-parameter/Architecture", "model": "SLaK-B", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "1172G", "type": "Hyper-parameter/Architecture", "model": "SLaK-B", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "50.2", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "SLaK-B", "model settings": {"number of parameters": "135M", "number of FLOPs": "1172G"}} {"value": "128M", "type": "Hyper-parameter/Architecture", "model": "InternImage-B", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "ADE20K"} {"value": "1185G", "type": "Hyper-parameter/Architecture", "model": "InternImage-B", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "ADE20K"} {"value": "50.8", "type": "Result", "training data/set": "ADE20K", "test data/set": "ADE20K", "task": "Semantic Segmentation", "metric": "mIoU", "experimental settings": {"crop size": "512$^2$", "single-scale testing": "true", "ss": "true"}, "model": "InternImage-B", "model settings": {"number of parameters": "128M", "number of FLOPs": "1185G"}} {"value": "51.3", "type": "Result", "training data/set": "ADE20K", 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