\begin{table*}[t]\small
	\centering
	\renewcommand{\arraystretch}{0.93}
	\footnotesize
    \setlength\tabcolsep{1.65mm}{
    \begin{tabular}{l|cc|cccccc|cccccc}
        \multirow{2}{*}{Method} & \multirow{2}{*}{\#Params} & \multirow{2}{*}{\#FLOPs} &
        \multicolumn{6}{c|}{Mask R-CNN 1$\times$ schedule} & \multicolumn{6}{c}{Mask R-CNN 3$\times$+MS schedule}\\
        ~ &  &
        & $\rm AP^b$ & $\rm AP^b_{50}$ & $\rm AP^b_{75}$ & $\rm AP^m$ & $\rm AP^m_{50}$ & $\rm AP^m_{75}$ 
        & $\rm AP^b$ & $\rm AP^b_{50}$ & $\rm AP^b_{75}$ & $\rm AP^m$ & $\rm AP^m_{50}$ & $\rm AP^m_{75}$   \\
	    \hline
        Swin-T~\cite{liu2021swin} & 48M & 267G
        & 42.7 & 65.2 & 46.8 & 39.3 & 62.2 & 42.2 & 46.0 & 68.1 & 50.3 & 41.6 & 65.1 & 44.9  \\
        ConvNeXt-T~\cite{liu2022convnet} & 48M & 262G
        & 44.2 & 66.6 & 48.3 & 40.1 & 63.3 & 42.8 & 46.2 & 67.9 & 50.8 & 41.7 & 65.0 & 44.9  \\
        PVTv2-B2~\cite{wang2021pvtv2} & 45M & 309G
        & 45.3 & 67.1 & 49.6 & 41.2 & 64.2 & 44.4 & 47.8 & 69.7 & 52.6 & 43.1 & 66.8 & 46.7  \\
        ViT-S~\cite{chen2022vitadapter} & 48M & 353G & 44.7 & 65.8 & 48.3 & 39.9 & 62.5 & 42.8 & 48.2 & 69.7 & 52.5 & 42.8 & 66.4 & 45.9   \\
        \rowcolor{gray!20}
        InternImage-T (ours)  & 49M & 270G
        & 47.2 & 69.0 & 52.1 & 42.5 & 66.1 & 45.8 & 49.1 & 70.3 & 54.0 & 43.7 & 67.3 & 47.1  \\
        \hline
        Swin-S~\cite{liu2021swin} & 69M & 354G
        & 44.8 & 66.6 & 48.9 & 40.9 & 63.4 & 44.2 & 48.2 & 69.8 & 52.8 & 43.2 & 67.0 & 46.1 \\
        ConvNeXt-S~\cite{liu2022convnet} & 70M & 348G
        & 45.4 & 67.9 & 50.0 & 41.8 & 65.2 & 45.1 & 47.9 & 70.0 & 52.7 & 42.9 & 66.9 & 46.2 \\
        PVTv2-B3~\cite{wang2021pvtv2} & 65M & 397G
        & 47.0 & 68.1 & 51.7 & 42.5 & 65.7 & 45.7 & 48.4 & 69.8 & 53.3 & 43.2 & 66.9 & 46.7 \\
        \rowcolor{gray!20}
        InternImage-S (ours)  & 69M & 340G
        & 47.8 & 69.9 & 52.8 & 43.3 & 67.1 & 46.7 & 49.7 & 71.1 & 54.5 & 44.4 & 68.5 & 47.8 \\
        \hline
        Swin-B~\cite{liu2021swin} & 107M & 496G
        & 46.9 & $-$ & $-$ & 42.3 & $-$ & $-$ & 48.6 & 70.0 & 53.4 & 43.3 & 67.1 & 46.7  \\
        ConvNeXt-B~\cite{liu2022convnet} & 108M & 486G & 47.0 & 69.4 & 51.7 & 42.7 & 66.3 & 46.0 & 48.5 & 70.1 & 53.3 & 43.5 & 67.1 & 46.7 \\
        PVTv2-B5~\cite{wang2021pvtv2} & 102M & 557G
        & 47.4 & 68.6 & 51.9 & 42.5 & 65.7 & 46.0 & 48.4 & 69.2 & 52.9 & 42.9 & 66.6 & 46.2  \\
        ViT-B~\cite{chen2022vitadapter}  & 120M & 781G
        & 47.0 & 68.2 & 51.4 & 41.8 & 65.1 & 44.9 & 49.6 & 70.6 & 54.0 & 43.6 & 67.7 & 46.9  \\
        \rowcolor{gray!20}
        InternImage-B (ours) & 115M & 501G
        & 48.8 & 71.0 & 53.9 & 44.0 & 67.8 & 47.5 & 50.3 & 71.4 & 55.3 & 44.8 & 68.7 & 48.0 \\
    \end{tabular}}
    
    \caption{
    \textbf{Object detection and instance segmentation with Mask R-CNN on COCO \texttt{val2017}.}
    The FLOPs are measured with 1280$\times$800 inputs.
    AP$^\text{b}$ and AP$^\text{m}$ represent box AP and mask AP, respectively.
    ``MS" means multi-scale training. 
	}
    \label{tab:results_detection_mask}
    \label{tab:mask}
\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.

where $G$ denotes the total number of aggregation groups.
For the $g$-th group,
$\mathbf{w}_g\!\in\!\mathbb{R}^{C\times C'}$, $\mathbf{m}_{gk}\!\in\!\mathbb{R}$ denote the location-irrelevant projection weights of the group, where $C'\!=\!C/G$ represents the group dimension.
$\mathbf{m}_{gk}\!\in\!\mathbb{R}$ denotes the modulation scalar of the $k$-th sampling point in the $g$-th group, normalized by the softmax function along the dimension $K$.
$\mathbf{x}_g\!\in\!\mathbb{R}^{C'\times H \times W}$ represents the sliced input feature map.
$\Delta p_{gk}$ is the offset corresponding to the grid sampling location $p_k$ in the $g$-th group.

\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{Settings.}
We verify the effectiveness of our InternImage\ on the COCO benchmark~\cite{lin2014microsoft}, on top of two representative object detection frameworks: Mask R-CNN~\cite{he2017mask}, and Cascade Mask R-CNN~\cite{cai2018cascade}.
We follow common practices~\cite{liu2021swin,wang2021pvtv2} to initialize the backbone with pre-trained classification weights, and by default use a 1$\times$ (12 epochs) or 3$\times$ (36 epochs) training schedule to train detection models.

\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).
{"value": "48M", "type": "Hyper-parameter/Architecture", "model": "Swin-T", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "COCO"} {"value": "267G", "type": "Hyper-parameter/Architecture", "model": "Swin-T", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "COCO"} {"value": "42.7", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b", "AP"], "experimental settings": {"schedule": "1$\\times$"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "65.2", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{50}", "AP_{50}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "46.8", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{75}", "AP_{75}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "39.3", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m", "AP"], "experimental settings": {"schedule": "1$\\times$"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "62.2", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{50}", "AP_{50}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "42.2", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{75}", "AP_{75}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "46.0", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b", "AP"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "68.1", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{50}", "AP_{50}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "50.3", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{75}", "AP_{75}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "41.6", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m", "AP"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "65.1", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{50}", "AP_{50}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "44.9", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{75}", "AP_{75}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "Swin-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "48M", "type": "Hyper-parameter/Architecture", "model": "ConvNeXt-T", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "COCO"} {"value": "262G", "type": "Hyper-parameter/Architecture", "model": "ConvNeXt-T", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "COCO"} {"value": "44.2", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b", "AP"], "experimental settings": {"schedule": "1$\\times$"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "66.6", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{50}", "AP_{50}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "48.3", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{75}", "AP_{75}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "40.1", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m", "AP"], "experimental settings": {"schedule": "1$\\times$"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "63.3", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{50}", "AP_{50}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "42.8", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{75}", "AP_{75}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "46.2", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b", "AP"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "67.9", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{50}", "AP_{50}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "50.8", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{75}", "AP_{75}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "41.7", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m", "AP"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "65.0", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{50}", "AP_{50}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "44.9", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{75}", "AP_{75}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "ConvNeXt-T", "model settings": {"backbone": "Mask R-CNN"}} {"value": "45M", "type": "Hyper-parameter/Architecture", "model": "PVTv2-B2", "parameter/architecture name": ["# Params", "number of parameters"], "dataset": "COCO"} {"value": "309G", "type": "Hyper-parameter/Architecture", "model": "PVTv2-B2", "parameter/architecture name": ["# FLOPs", "number of FLOPs"], "dataset": "COCO"} {"value": "45.3", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b", "AP"], "experimental settings": {"schedule": "1$\\times$"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "67.1", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{50}", "AP_{50}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "49.6", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{75}", "AP_{75}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "41.2", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m", "AP"], "experimental settings": {"schedule": "1$\\times$"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "64.2", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{50}", "AP_{50}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "44.4", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{75}", "AP_{75}"], "experimental settings": {"schedule": "1$\\times$"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "47.8", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b", "AP"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "69.7", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{50}", "AP_{50}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "52.6", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "object detection", "metric": ["AP^b_{75}", "AP_{75}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "43.1", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m", "AP"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "66.8", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": "instance segmentation", "metric": ["AP^m_{50}", "AP_{50}"], "experimental settings": {"schedule": "3$\\times$+MS"}, "model": "PVTv2-B2", "model settings": {"backbone": "Mask R-CNN"}} {"value": "46.7", "type": "Result", "training data/set": "COCO", "test data/set": "COCO val2017", "task": 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