Original: U NI F ORMER : U NIFIED T RANSFORMER FOR E FFICIENT S PATIAL -T EMPORAL R EPRESENTATION L EARNING
Revised: U NI F ORMER : U NIFIED T RANSFORMER FOR E FFICIENT S PATIOTEMPORAL R EPRESENTATION L EARNING

Original: Anonymous authors
Revised: Anonymous authors

Original: Paper under double-blind review
Revised: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: It is a challenging task to learn rich and multi-scale spatial-temporal semantics from high-dimensional videos, due to large local redundancy and complex global dependency between video frames.
Revised: It is a challenging task to learn rich and multi-scale spatiotemporal semantics from high-dimensional videos, due to large local redundancy and complex global dependency between video frames.

Original: The recent advances in this research have been mainly driven by 3D convolutional neural networks and vision transformers.
Revised: The recent advances in this research have been mainly driven by 3D convolutional neural networks and vision transformers.

Original: Although 3D convolution can efﬁciently aggregate local context to suppress local redundancy from a small 3D neighborhood, it lacks the capability to capture global dependency because of the limited receptive ﬁeld.
Revised: Although 3D convolution can efficiently aggregate local context to suppress local redundancy from a small 3D neighborhood, it lacks the capability to capture global dependency because of the limited receptive field.

Original: Alternatively, vision transformers can effectively capture long-range dependency by self-attention mechanism, while having limitations on reducing local redundancy with blind similarity comparison among all the tokens in each layer.
Revised: Alternatively, vision transformers can effectively capture long-range dependency by self-attention mechanism, while having the limitation on reducing local redundancy with blind similarity comparison among all the tokens in each layer.

Original: Based on these observations, we propose a novel Uniﬁed transFormer (UniFormer) which seamlessly integrates merits of 3D convolution and spatial-temporal self-attention in a concise transformer format, and achieves a preferable balance between computation and accuracy.
Revised: Based on these observations, we propose a novel Unified transFormer (UniFormer) which seamlessly integrates merits of 3D convolution and spatiotemporal self-attention in a concise transformer format, and achieves a preferable balance between computation and accuracy.

Original: Different from traditional transformers, our relation aggregator can tackle both spatial-temporal redundancy and dependency, by learning local and global token afﬁnity respectively in shallow and deep layers.
Revised: Different from traditional transformers, our relation aggregator can tackle both spatiotemporal redundancy and dependency, by learning local and global token affinity respectively in shallow and deep layers.

Original: We conduct extensive experiments on the popular video benchmarks, e.g., Kinetics-400, Kinetics600, and Something-Something V1&V2.
Revised: We conduct extensive experiments on the popular video benchmarks, e.g., Kinetics-400, Kinetics600, and Something-Something V1&V2.

Original: With only ImageNet-1K pretraining, our UniFormer achieves 82.9%/84.8% top-1 accuracy on Kinetics-400/Kinetics600, while requiring 10 × fewer GFLOPs than other state-of-the-art methods.
Revised: With only ImageNet-1K pretraining, our UniFormer achieves 82.9%/84.8% top-1 accuracy on Kinetics-400/Kinetics600, while requiring 10 × fewer GFLOPs than other state-of-the-art methods.

Original: For
Revised: For

Original: Something-Something V1 and V2, our UniFormer achieves new state-of-the-art performances of 60.8% and 71.4% top-1 accuracy respectively.
Revised: Something-Something V1 and V2, our UniFormer achieves new state-of-the-art performances of 60.8% and 71.4% top-1 accuracy respectively.

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Learning spatial-temporal representations is a fundamental task for video understanding.
Revised: Learning spatiotemporal representations is a fundamental task for video understanding.

Original: Basically, there are two distinct challenges.
Revised: Basically, there are two distinct challenges.

Original: On the one hand, videos contain large spatial-temporal redundancy, where target motions across local neighboring frames are subtle.
Revised: On the one hand, videos contain large spatiotemporal redundancy, where target motions across local neighboring frames are subtle.

Original: On the other hand, videos contain complex spatial-temporal dependency, since target relations across long-range frames are dynamic.
Revised: On the other hand, videos contain complex spatiotemporal dependency, since target relations across long-range frames are dynamic.

Original: The advances in video classiﬁcation have mostly driven by 3D convolutional neural networks (Tran et al., 2015; Carreira & Zisserman, 2017b; Feichtenhofer et al., 2019) and spatial-temporal transformers (Bertasius et al., 2021; Arnab et al., 2021).
Revised: The advances in video classification have mostly driven by 3D convolutional neural networks (Tran et al., 2015; Carreira & Zisserman, 2017b; Feichtenhofer et al., 2019) and spatiotemporal transformers (Bertasius et al., 2021; Arnab et al., 2021).

Original: Unfortunately, each of these two frameworks focuses on one of the aforementioned challenges.
Revised: Unfortunately, each of these two frameworks focuses on one of the aforementioned challenges.

Original: 3D convolution can capture detailed and local spatial-temporal features, by processing each pixel with context from a small 3D neighborhood (e.g., 3 × 3 × 3).
Revised: 3D convolution can capture detailed and local spatiotemporal features, by processing each pixel with context from a small 3D neighborhood (e.g., 3 × 3 × 3).

Original: Hence, it can reduce spatial-temporal redundancy across adjacent frames.
Revised: Hence, it can reduce spatiotemporal redundancy across adjacent frames.

Original: However, due to the limited receptive ﬁeld, 3D convolution suffers from difﬁculties in learning long-range dependency (Wang et al., 2018; Li et al., 2020a).
Revised: However, due to the limited receptive field, 3D convolution suffers from difficulty in learning long-range dependency (Wang et al., 2018; Li et al., 2020a).

Original: Alternatively, vision transformers are good at capturing global dependency, with the help of self-attention among visual tokens (Dosovitskiy et al., 2021).
Revised: Alternatively, vision transformers are good at capturing global dependency, with the help of self-attention among visual tokens (Dosovitskiy et al., 2021).

Original: Recently, this design has been introduced in video classiﬁcation via spatial-temporal attention mechanism (Bertasius et al., 2021).
Revised: Recently, this design has been introduced in video classification via spatiotemporal attention mechanism (Bertasius et al., 2021).

Original: However, we observe that, video transformers are often inefﬁcient to encode local spatial-temporal features in the shallow layers.
Revised: However, we observe that, video transformers are often inefficient to encode local spatiotemporal features in the shallow layers.

Original: We take the well-known and typical TimeSformer (Bertasius et al., 2021) for illustration.
Revised: We take the well-known and typical TimeSformer (Bertasius et al., 2021) for illustration.

Original: As shown in Figure 1, TimeSformer indeed learns detailed video representations in the early layers, but with very redundant spatial and temporal attention.
Revised: As shown in Figure 1, TimeSformer indeed learns detailed video representations in the early layers, but with very redundant spatial and temporal attention.

Original: Speciﬁcally, spatial attention mainly focuses on the neighbor tokens (mostly in 3 × 3 local regions), while learning nothing from the rest tokens in the same frame.
Revised: Specifically, spatial attention mainly focuses on the neighbor tokens (mostly in 3 × 3 local regions), while learning nothing from the rest tokens in the same frame.

Original: Similarly, temporal attention mostly only aggregates tokens in the adjacent frames, while ignoring the rest in the distant frames. 
Revised: Similarly, temporal attention mostly only aggregates tokens in the adjacent frames, while ignoring the rest in the distant frames. More

Original: More importantly, such local representations are learned from global token-to-token similarity comparison in all layers, requiring large computation cost.
Revised: [Figure] importantly, such local representations are learned from global token-to-token similarity comparison in all layers, requiring large computation cost.

Original: This fact clearly deteriorates computation-accuracy balance of such video transformer (Figure 2).
Revised: This fact clearly deteriorates computation-accuracy balance of such video transformer (Figure 2).

Original: To tackle these difﬁculties we introduce a novel Uniﬁed transFormer (UniFormer). It can effectively unify 3D convolution and spatial-temporal self-attention in a concise transformer format, achieving a preferable balance between efﬁciency and effectiveness.
Revised: To tackle these difficulties, we propose to effectively unify 3D convolution and spatiotemporal selfattention in a concise transformer format, thus we name the network Unified transFormer (UniFormer), which can achieve a preferable balance between efficiency and effectiveness.

Original: More speciﬁcally, our UniFormer consists of three core modules, i e.,
Revised: More specifically, our UniFormer consists of three core modules, i.e., Dynamic Position

Original: Dynamical Position Embedding (DPE), Multi-Head Relation Aggregator (MHRA) and Feed-Forward Network (FFN).
Revised: Embedding (DPE), Multi-Head Relation Aggregator (MHRA), and Feed-Forward Network (FFN).

Original: The key difference between our UniFormer and traditional video transformers is the distinct design of our relation aggregator.
Revised: The key difference between our UniFormer and traditional video transformers is the distinct design of our relation aggregator.

Original: First, instead of utilizing a self-attention mechanism in all layers, our proposed relation aggregator tackles video redundancy and dependency respectively.
Revised: First, instead of utilizing a self-attention mechanism in all layers, our proposed relation aggregator tackles video redundancy and dependency respectively.

Original: In the shallow layers, our aggregator learns local relation with a small learnable parameter matrix, which can largely reduce computation burden by aggregating context from adjacent tokens in a small 3D neighborhood.
Revised: In the shallow layers, our aggregator learns local relation with a small learnable parameter matrix, which can largely reduce computation burden by aggregating context from adjacent tokens in a small 3D neighborhood.

Original: In the deep layers, our aggregator learns global relation with similarity comparison, which can ﬂexibly build long-range token dependencies from distant frames in the video.
Revised: In the deep layers, our aggregator learns global relation with similarity comparison, which can flexibly build long-range token dependencies from distant frames in the video.

Original: Second, different from spatial and temporal attention separation in the traditional transformers (Bertasius et al., 2021; Arnab et al., 2021), our relation aggregator jointly encodes spatial-temporal context in all the layers, which can further boost video representations in a joint learning manner.
Revised: Second, different from spatial and temporal attention separation in the traditional transformers (Bertasius et al., 2021; Arnab et al., 2021), our relation aggregator jointly encodes spatiotemporal context in all the layers, which can further boost video representations in a joint learning manner.

Original: Finally, we build up our model by progressively integrating UniFormer blocks in a hierarchical manner.
Revised: Finally, we build up our model by progressively integrating UniFormer blocks in a hierarchical manner.

Original: In this case, we enlarge the cooperative power of local and global UniFormer blocks for efﬁcient spatial-temporal representation learning in videos.
Revised: In this case, we enlarge the cooperative power of local and global UniFormer blocks for efficient spatiotemporal representation learning in videos.

Original: We conduct extensive experiments on the popular video benchmarks, e.g.,Kineticss-400 (Carreira &
Revised: We conduct extensive experiments on the popular video benchmarks, e.g.,

Original:  Zisserman, 2017a), Kinetics-600 (Carreira et al., 2018) and Something-Something V1&V

Revised: Kineticss-400 (Carreira & Zisserman, 2017a), Kinetics-600 (Carreira et al., 2018) and SomethingSomething V1&V

Original: (Goyal et al., 2017b).
Revised: (Goyal et al., 2017b).

Original: With only ImageNet-1K pretraining, our UniFormer achieves 82.9%/84.8% topaccuracy on Kinetics-400/Kinetics-600, while requiring 10 × fewer GFLOPs than other comparable methods (e.g., 16 .
Revised: With only ImageNet-1K pretraining, our UniFormer achieves 82.9%/84.8% top-1 accuracy on Kinetics-400/Kinetics-600, while requiring 10 × fewer GFLOPs than other comparable methods (e.g., 16 .

Original: 7 × fewer GFLOPs than ViViT (Arnab et al., 2021) with JFT-300M pre-training).
Revised: 7 × fewer GFLOPs than ViViT (Arnab et al., 2021) with JFT-300M pre-training).

Original: For Something-Something V1 and V2, our UniFormer achieves 60.8% and 71.4% top-1 accuracy respectively, which are new state-of-the-art performances.
Revised: For Something-Something V1 and V2, our UniFormer achieves 60.8% and 71.4% top-1 accuracy respectively, which are new state-of-the-art performances.

Original:  R ELATED W ORK
Revised:  R ELATED W ORK

Original: Convolution-based Video Networks.
Revised: Convolution-based Video Networks.

Original: 3D Convolution Neural Networks (CNNs) have been dominant in video understanding (Tran et al., 2015; Feichtenhofer et al., 2019).
Revised: 3D Convolution Neural Networks (CNNs) have been dominant in video understanding (Tran et al., 2015; Feichtenhofer et al., 2019).

Original: However, it suffers from difﬁcult optimization problem and large computation cost.
Revised: However, they suffer from the difficult optimization problem and large computation cost.

Original: To resolve this issue, I3D (Carreira & Zisserman, 2017b) inﬂates the pre-trained 2D convolution kernels for better optimization.
Revised: To resolve this issue, I3D (Carreira & Zisserman, 2017b) inflates the pre-trained 2D convolution kernels for better optimization.

Original: To reduce complexity, the prior workstry to factorize 3D convolution kernel in different dimensions (Tran et al., 2018; Qiu et al., 2017; Tran et al., 2019; Feichtenhofer, 2020; Wang et al., 2020a).
Revised: Other prior works (Tran et al., 2018; Qiu et al., 2017; Tran et al., 2019; Feichtenhofer, 2020; Wang et al., 2020a) try to factorize 3D convolution kernel in different dimensions to reduce complexity.

Original: Recent methods propose well-designed modules to enhance the temporal modeling ability for 2D
Revised: Recent methods propose well-designed modules to enhance the temporal modeling ability for 2D

Original: CNNs (Wang et al., 2016; Lin et al., 2019; Luo & Yuille, 2019; Jiang et al., 2019; Liu et al., 2020a;
Revised: CNNs (Wang et al., 2016; Lin et al., 2019; Luo & Yuille, 2019; Jiang et al., 2019; Liu et al., 2020a;

Original: Li et al., 2020b; Kwon et al., 2020; Li et al., 2020a; 2021a; Wang et al., 2020b).
Revised: Li et al., 2020b; Kwon et al., 2020; Li et al., 2020a; 2021a; Wang et al., 2020b).

Original: However, 3D convolution struggles to capture long-range dependency, due to the limited receptive ﬁeld.
Revised: However, 3D convolution struggles to capture long-range dependency, due to the limited receptive field.

Original: Transformer-based Video Networks.
Revised: Transformer-based Video Networks.

Original: Vision Transformers (Dosovitskiy et al., 2021; Touvron et al., 2021a;b; Liu et al., 2021a) have been popular for vision tasks and outperform many CNNs.
Revised: Vision Transformers (Dosovitskiy et al., 2021; Touvron et al., 2021a;b; Liu et al., 2021a) have been popular for vision tasks and outperform many CNNs.

Original: Based on ViT, several prior works (Bertasius et al., 2021; Neimark et al., 2021; Sharir et al., 2021;
Revised: Based on ViT, several prior works (Bertasius et al., 2021; Neimark et al., 2021; Sharir et al., 2021;

Original: Li et al., 2021b; Arnab et al., 2021;
Revised: Li et al., 2021b; Arnab et al., 2021;

Original: Bulat et al., 2021; Patrick et al., 2021; Zha et al., 2021) propose different variants for spatial-temporal learning, verifying the outstanding ability of the transformer to capture long-term dependencies.
Revised: Bulat et al., 2021; Patrick et al., 2021; Zha et al., 2021) propose different variants for spatiotemporal learning, verifying the outstanding ability of the transformer to capture long-term dependencies.

Original: To reduce high dot-product computation, MViT (Fan et al., 2021) introduces the hierarchical structure and pooling self-attention, while Video SwinTransformer (Liu et al., 2021b) advocates an inductive bias of locality for video, achieving state-of-the-art results.
Revised: To reduce high dot-product computation, MViT (Fan et al., 2021) introduces the hierarchical structure and pooling self-attention, while Video Swin (Liu et al., 2021b) advocates an inductive bias of locality for video.

Original: Nevertheless, the transformer is inefﬁcient to encode low-level features, hindering their high potential.
Revised: Nevertheless, the self-attention mechanism is inefficient to encode low-level features, hindering their high potential.

Original: To tackle this challenge,  we propose UniFormer to take advantage of both 3D convolution  and self-attention, achieving a preferable accuracy-computation trade-off for video understanding.
Revised: To tackle this challenge, different from Video Swin that applies self-attention in a local 3D window, we adopt 3D convolution in a concise transformer format to encode local features. Besides, we follow their hierarchical designs and propose our UniFormer, achieving powerful performance for video understanding.

Original:  M ETHOD
Revised:  M ETHOD

Original: In this section, we describe our UniFormer in detail.
Revised: In this section, we describe our UniFormer in detail.

Original: First, we introduce the overall architecture of the UniFormer block.
Revised: First, we introduce the overall architecture of the UniFormer block.

Original: Then, we explain the vital design of our UniFormer for spatial-temporal modeling, i.e., multi-head relation aggregator.
Revised: Then, we explain the vital designs of our UniFormer for spatiotemporal modeling, i.e., multi-head relation aggregator and dynamic position embedding.

Original: Finally, we hierarchically stack UniFormer blocks to build up our video network, achieving state-of-the-art performances with less computation.
Revised: Finally, we hierarchically stack UniFormer blocks to build up our video network.

Original: 3. O VERVIEW OF U NI F ORMER B LOCK
Revised: 3. O VERVIEW OF U NI F ORMER B LOCK

Original: To overcome problems of spatial-temporal redundancy and dependency, we propose a novel and concise Uniﬁed transFormer (UniFormer) shown in Figure 3.
Revised: To overcome problems of spatiotemporal redundancy and dependency, we propose a novel and concise Unified transFormer (UniFormer) shown in Figure 3.

Original: We utilize a basic transformer format (Vaswani et al., 2017) but specially design it for efﬁcient and effective spatial-temporal representation learning.
Revised: We utilize a basic transformer format (Vaswani et al., 2017) but specially design it for efficient and effective spatiotemporal representation learning.

Original: Speciﬁcally, our UniFormer block consists of three key modules: Dynamical Position
Revised: Specifically, our UniFormer block consists of three key modules: Dynamic Position

Original: Embedding (DPE), Multi-Head Relation Aggregator (MHRA), and Feed-Forward Network (FFN):
Revised: Embedding (DPE), Multi-Head Relation Aggregator (MHRA), and Feed-Forward Network (FFN):

Original: [Equation]
Revised: [Equation]

Original: Considering the input token tensor (frame volumes) X in ∈ R C × T × H × W , we ﬁrst introduce DPE to dynamically integrate 3D position information into all the tokens (Eq. 1), which effectively makes use of spatial-temporal order of the tokens for video modeling.
Revised: Considering the input token tensor (frame volumes) X in ∈ R C × T × H × W , we first introduce DPE to dynamically integrate 3D position information into all the tokens (Eq. 1), which effectively makes ×𝐿 # Stage # 3 × 4 × 4 , S t r i d e 2 × 4 × S t a g e

Original: Then, we leverage MHRA to aggregate each token with its contextual tokens (Eq. 2).
Revised: S t a g e S t a g e S t a g e 1 × 2 × 2 , S t r i d e 1 × 2 ×1 × 2 × 2 ,

Revised: S t r i d e 1 × 2 ×1 × 2 × 2 ,

Original: Different from the regular Multi-Head
Revised: S t r i d e 1 × 2 ×3×𝑇×𝐻×𝑊 64×𝑇2×𝐻4×𝑊 128×𝑇2×𝐻8×𝑊 320×𝑇2× 𝐻 16×𝑊 512×𝑇2× 𝐻 32×𝑊 𝐶 A v g P oo l , F C C l a ss i f i c a t i o n

Revised: FFN MHRA

Original:  Self-Attention (MHSA), our MHRA smartly tackles local video redundancy and global video dependency, by ﬂexible designs of token afﬁnity learning in the shallow and deep layers.
Revised: [Figure] use of spatiotemporal order of the tokens for video modeling. Then, we leverage MHRA to aggregate each token with its contextual tokens (Eq. 2). Different from the regular Multi-Head Self-Attention (MHSA), our MHRA smartly tackles local video redundancy and global video dependency, by flexible designs of token affinity learning in the shallow and deep layers.

Original: Finally, we add FFN with two linear layers for pointwise enhancement of each token 
Revised: Finally, we add FFN with two linear layers for pointwise enhancement of each token (Eq. 3).

Original: 3. M ULTI -H EAD R ELATION A GGREGATOR
Revised: 3. M ULTI -H EAD R ELATION A GGREGATOR

Original: As discussed above, we should solve large local redundancy and complex global dependency, for efﬁcient and effective spatial-temporal representation learning.
Revised: As discussed above, we should solve large local redundancy and complex global dependency, for efficient and effective spatiotemporal representation learning.

Original: Unfortunately, the popular 3D CNNs and spatial-temporal transformers only focus one of these two challenges.
Revised: Unfortunately, the popular 3D CNNs and spatiotemporal transformers only focus one of these two challenges.

Original: For this reason, we design an alternative Relation Aggregator (RA), which can ﬂexibly unify 3D convolution and spatialtemporal self-attention in a concise transformer format, solving video redundancy and dependency in  shallow layers and deep layers respectively.
Revised: For this reason, we design an alternative Relation Aggregator (RA), which can flexibly unify 3D convolution and spatiotemporal self-attention in a concise transformer format, solving video redundancy and dependency in the shallow layers and deep layers respectively.

Original: Speciﬁcally, our MHRA conducts token relation learning via multi-head fusion:
Revised: Specifically, our MHRA conducts token relation learning via multi-head fusion:

Original: [Equation]
Revised: [Equation]

Original: [Equation]

Original: Given the input tensor X ∈ R C × T × H × W , we ﬁrst reshape it to a sequence of tokens X ∈ R L × C ,
Revised: Given the input tensor X ∈ R C × T × H × W , we first reshape it to a sequence of tokens X ∈ R L × C ,

Original: L = T × H × W .
Revised: L = T × H × W .

Original: R n ( · ) is the relation aggregator (RA) in the n -th head, and
Revised: R n ( · ) is the relation aggregator (RA) in the n -th head, and

Original: U ∈ R C × C is a learnable parameter matrix to integrate N heads.
Revised: U ∈ R C × C is a learnable parameter matrix to integrate N heads.

Original: Moreover, each RA consists of token context encoding and token afﬁnity learning.
Revised: Moreover, each RA consists of token context encoding and token affinity learning.

Original: Via a linear transformation, one can transform the original token into context
Revised: Via a linear transformation, one can transform the original token into context

Original: V n ( X ) ∈ R L × CN .
Revised: V n ( X ) ∈ R L × CN .

Original: Subsequently, the relation aggregator can summarize context with the guidance of the token afﬁnity A n ∈ R L × L .
Revised: Subsequently, the relation aggregator can summarize context with the guidance of the token affinity A n ∈ R L × L .

Original: The key in our RA is how to learn A n in videos.
Revised: The key in our RA is how to learn A n in videos.

Original:  In the shallow layers, we aim at learning detailed video representation from the local spatialtemporal context in small 3D neighborhoods.
Revised: Local MHRA. In the shallow layers, we aim at learning detailed video representation from the local spatiotemporal context in small 3D neighborhoods.

Original: This coincidentally shares a similar insight with the design of a 3D convolution ﬁlter.
Revised: This coincidentally shares a similar insight with the design of a 3D convolution filter.

Original: As a result, we design the token afﬁnity as a learnable parameter matrix operated in the local 3D neighborhood, i.e., given one anchor token X i , RA learns local spatial-temporal relation (or afﬁnity) between this token and other tokens in the small tube Ω t × h × w i 
Revised: As a result, we design the token affinity as a learnable parameter matrix operated in the local 3D neighborhood, i.e., given one anchor token X i , RA learns local spatiotemporal affinity between this token and other tokens in the small tube Ω t × h × w i : [Equation] i

Original: [Equation]
Revised: [Equation]

Original:  where a n ∈ R t × h × w and X j refers to any neighbor token in Ω t × h × w i .
Revised: n , where j ∈ Ω t [Equation] , (6) where a n ∈ R t × h × w and X j refers to any neighbor token in Ω t × h × w i .

Original: ( i − j ) means the relative token index that determines the aggregating weight (see Appendix A for more details).
Revised: ( i − j ) means the relative token index that determines the aggregating weight (Appendix A shows more details).

Original: In the shallow layers, video contents between adjacent tokens vary subtly, it is signiﬁcant to encode local features  to reduce redundancy.
Revised: In the shallow layers, video contents between adjacent tokens vary subtly, it is significant to encode detailed features with local operator to reduce redundancy.

Original: Hence, the token afﬁnity is designed as a local learnable parameter matrix a n , whose values only depend on the relative 3D position between tokens.
Revised: Hence, the token affinity is designed as a local learnable parameter matrix, whose values only depend on the relative 3D position between tokens.

Original: On the contrary, in the deep
Revised: Comparison to 3D Convolution Block. Interestingly, we found that our local MHRA can be interpreted as a spatiotemporal extension of MobileNet block (Sandler et al., 2018; Tran et al., 2019; Fe-

Original: [Table]
Revised: [Table]

Revised: ichtenhofer, 2020).

Revised: Specifically, the linear transformation V( · ) can be instantiated as pointwise convolution (PWConv).

Revised: Furthermore, the local token affinity A localn is a spatiotemporal matrix that operated on each output channel (or head) V n ( X ) , thus the relation aggregator R n ( X ) =

Revised: A localn V n ( X ) can be explained as a depthwise convolution (DWConv).

Original: layers, we focus on capturing long-term token dependency in the global video clip.
Revised: Finally, all heads are concatenated and fused by a linear matrix U , which can also be instantiated as pointwise convolution (PWConv). As a result, this local MHRA can be reformulated with a manner of PWConv-DWConv-PWConv in the MobileNet block. In our experiments, we flexibly instantiated our local MHRA as such channelseparated spatiotemporal convolution, so that our UniFormer can inherit computation efficiency for light-weight video classification.

Revised: Different from the MobileNet block, our UniFormer block is designed as a generic transformer format, thus an extra FFN is inserted after MHRA, which can further mix token context at each spatiotemporal position to boost classification accuracy.

Revised: Global MHRA.

Revised: In the deep layers, we focus on capturing long-term token dependency in the global video clip.

Original: This naturally shares a similar insight with the design of self-attention.
Revised: This naturally shares a similar insight with the design of self-attention.

Original: Hence, we design the token afﬁnity via comparing content similarity among all the tokens in the global view:
Revised: Hence, we design the token affinity via comparing content similarity among all the tokens in the global view:

Original: [Equation]
Revised: [Equation]

Original: where X j can be any token in the global 3D tube with size of T × H × W , while Q n ( · ) and K n ( · ) are two different linear transformations.
Revised: where X j can be any token in the global 3D tube with size of T × H × W , while Q n ( · ) and K n ( · ) are two different linear transformations.

Original: Most video transformers apply self-attention in all stages, introducing a large amount of calculation.
Revised: Most video transformers apply self-attention in all stages, introducing a large amount of calculation.

Original: To reduce the dot-product computation, the prior works tend to divide spatial and temporal attention (Bertasius et al., 2021; Arnab et al., 2021), but it deteriorates the spatial-temporal relation among tokens.
Revised: To reduce the dot-product computation, the prior works tend to divide spatial and temporal attention (Bertasius et al., 2021; Arnab et al., 2021), but it deteriorates the spatiotemporal relation among tokens.

Original: In contrast, our MHRA performs local relation aggregation in the early layers, which largely saves the computation of token comparison.
Revised: In contrast, our MHRA performs local relation aggregation in the early layers, which largely saves the computation of token comparison.

Revised: Hence, instead of factorizing spatiotemporal attention, we jointly encode spatiotemporal relation in our MHRA for all the stages, in order to achieve a preferable computation-accuracy balance.

Revised: Comparison to Transformer Block .

Original: Hence, instead of factorizing spatial-temporal attention, we jointly encode spatial-temporal relation in our
Revised: In the deep layers, our UniFormer block is equipped with a global MHRA A globaln (Eq. 7). It can be instantiated as a spatiotemporal self attention, where Q n ( · ) , K n ( · ) and V n ( · ) become Query, Key and Value in the transformer (Dosovitskiy et al., 2021).

Original: MHRA for all the stages, in order to achieve a preferable computation-accuracy balance.
Revised: Hence, it can effectively learn long-term dependency. Instead of spatial and temporal factorization in the previous video transformers (Bertasius et al., 2021; Arnab et al., 2021), our global MHRA is based on joint spatiotemporal learning to generate more discriminative video representation. Moreover, we adopt dynamic position embedding (DPE, see Section 3.3) to overcome permutation-invariance, which can maintain translation-invariance and is friendly to different input clip lengths. 3. D YNAMIC P OSITION E MBEDDING

Original: Additionally, since videos are both spatial and temporal variant, it is necessary to encode spatialtemporal position information for token representations.
Revised: Since videos are both spatial and temporal variant, it is necessary to encode spatiotemporal position information for token representations.

Original: The previous methods mainly adapt the absolute or relative position embedding of image tasks to tackle this problem (Bertasius et al., 2021; Arnab et al., 2021).
Revised: The previous methods mainly adapt the absolute or relative position embedding of image tasks to tackle this problem (Bertasius et al., 2021; Arnab et al., 2021).

Original: However, when testing with longer input clips, the absolute one should be interpolated to target input size with ﬁne-tuning.
Revised: However, when testing with longer input clips, the absolute one should be interpolated to target input size with fine-tuning.

Original: Besides, the relative version modiﬁes the self-attention and performs worse due to lack of absolute position information (Islam et al., 2020).
Revised: Besides, the relative version modifies the self-attention and performs worse due to lack of absolute position information (Islam et al., 2020).

Original: To overcome the above problems, we extend the conditional position encoding (CPE)
Revised: To overcome the above problems, we extend the conditional position encoding (CPE)

Original: (Chu et al., 2021), utilizing a simple 3D depthwise convolution with zero paddings as dynamic position embedding (DPE).
Revised: (Chu et al., 2021) to design our DPE: [Equation] where DWConv means simple 3D depthwise convolution with zero paddings.

Original: Thanks to the shared parameters and locality of convolution, DPE can overcome permutation-invariance.
Revised: Thanks to the shared parameters and locality of convolution, DPE can overcome permutation-invariance and is friendly to arbitrary input lengths.

Original: Moreover, it is friendly to arbitrary input lengths and aware of their absolute positions with the help of zero paddings (Chu et al., 2021).
Revised: Moreover, it has been proven in CPE that zero paddings help the tokens on the borders be aware of their absolute positions, thus all tokens can progressively encode their absolute spatiotemporal position information via querying their neighbor. [Table] Comparison with the state-of-the-art on Kinetics-400&600. Our UniFormer outperforms most of the current methods with much fewer computation cost.

Original: 3. M ODEL A RCHITECTURE
Revised: 3. M ODEL A RCHITECTURE

Original: We hierarchically stack UniFormer blocks to build up our network for spatial-temporal learning.
Revised: We hierarchically stack UniFormer blocks to build up our network for spatiotemporal learning.

Original: As shown in Figure 3, our network consists of four stages, the channel numbers of which are 64 , 128 , 256 and 512 respectively.
Revised: As shown in Figure 3, our network consists of four stages, the channel numbers of which are 64 , 128 , 256 and 512 respectively.

Original: We provide two model variants depending on the number of UniFormer blocks in these stages: { 3 , 4 , 8 , 3 } for UniFormer-S and { 5 , 8 , 20 , 7 } for UniFormer-B.
Revised: We provide two model variants depending on the number of UniFormer blocks in these stages: { 3 , 4 , 8 , 3 } for UniFormer-S and { 5 , 8 , 20 , 7 } for UniFormer-B.

Original: In the ﬁrst two stages, we utilize MHRA with local token afﬁnity (Eq. 6) to reduce the short-term spatial-temporal redundancy.
Revised: In the first two stages, we utilize MHRA with local token affinity (Eq. 6) to reduce the short-term spatiotemporal redundancy.

Original: The tube size is set to 5 × 5 × 5 and the head number N is equal to the corresponding channel number.
Revised: The tube size is set to 5 × 5 × 5 and the head number N is equal to the corresponding channel number.

Original: In the last two stages, we apply MHRA with global token afﬁnity (Eq. 7) to capture long-term dependency, the head dimension of which is 64.
Revised: In the last two stages, we apply MHRA with global token affinity (Eq. 7) to capture long-term dependency, the head dimension of which is 64.

Original: We utilize BN (Ioffe & Szegedy, 2015) for local MHRA and LN (Ba et al., 2016) for global MHRA.
Revised: We utilize BN (Ioffe & Szegedy, 2015) for local MHRA and LN (Ba et al., 2016) for global MHRA.

Original: The kernel size of DPE is 3 × 3 × 3 (T × H × W) and the expand ratios of FFN in all layers are 4 .
Revised: The kernel size of DPE is 3 × 3 ×(T × H × W) and the expand ratios of FFN in all layers are 4 .

Original: We adopt a 3 × 4 × 4 convolution with stride 2 × 4 × 4, which means the spatial and temporal dimensions are both downsampled.
Revised: We adopt a 3 × 4 × 4 convolution with stride 2 × 4 × 4 before the first stage, which means the spatial and temporal dimensions are both downsampled.

Original: Before other stages, we apply 1 × 2 × 2 convolutions with stride 1 × 2 × 2.
Revised: Before other stages, we apply 1 × 2 × 2 convolutions with stride 1 × 2 × 2.

Original: Finally, the spatial-temporal average pooling and fully connected layer are utilized to output the ﬁnal predictions.3. D ISCUSSION
Revised: Finally, the spatiotemporal average pooling and fully connected layer are utilized to output the final predictions.

Original: UniFormer Block vs. 3D Convolution Block.

Original: In the shallow layers, our UniFormer block is equipped with a local MHRA (Eq. 6).

Original: Interestingly, we found that, such MHRA can be interpreted as a spatial-temporal extension of MobileNet block (Sandler et al., 2018; Tran et al., 2019; Feichtenhofer, 2020).

Original: Speciﬁcally, the linear transformation V( · ) can be instantiated as pointwise convolution (PWConv).

Original: Furthermore, the local token afﬁnity A localn is a spatial-temporal matrix that operated on each output channel (or head) V n ( X ) , thus the relation aggregator R n ( X ) =

Original: A localn V n ( X )

Original: [Table]

Original: can be explained as a depthwise convolution (DWConv).

Original: Finally, all heads are concatenated and fused by a linear matrix U , which can also be instantiated as pointwise convolution (PWConv).

Original: As a result, this local MHRA can be reformulated with a manner of PWConv-DWConv-PWConv in the

Original: MobileNet block.

Original: In our experiments, we ﬂexibly instantiated our local MHRA as such channelseparated spatial-temporal convolution, so that our UniFormer can inherit computation efﬁciency for light-weight video classiﬁcation.

Original: Different from the MobileNet block, our UniFormer block is designed as a generic transformer format, thus an extra FFN is inserted after MHRA, which can further mix token context at each spatial-temporal position to boost classiﬁcation accuracy.

Original: UniFormer Block vs. Transformer Block .
Revised: Comparison to Convolution+Transformer Network.

Original: In the deep layers, our UniFormer block is equipped with a global MHRA

Original: A globaln (Eq. 7). It can be instantiated as a spatial-temporal self attention, where Q n ( · ) , K n ( · ) and V n ( · ) become Query, Key and Value in the transformer (Dosovitskiy et al., 2021). Hence, our UniFormer can effectively learn long-term dependency. Instead of spatial and temporal factorization in the previous video transformers (Bertasius et al., 2021; Arnab et al., 2021), our global MHRA is based on joint spatial-temporal learning to generate more discriminative video representation.
Revised: The prior works have demonstrate that selfattention can perform convolution (Ramachandran et al., 2019; Cordonnier et al., 2020), but they propose to replace convolution instead of combining them.

Original: Moreover, we adopt DPE to overcome permutation-invariance, which can maintain translation-invariance and is friendly to different input clip lengths.

Original: UniFormer Network vs. Convolution+Transformer Network.

Original: Recent works have attempted to combine convolution with vision transformer (Wu et al., 2021;
Revised: Recent works have attempted to introduce convolution to vision transformers (Wu et al., 2021;

Original: Dai et al., 2021; Gao et al., 2021; Srinivas et al., 2021), but they mainly focus on image recognition, without any spatial-temporal consideration for video understanding.
Revised: Dai et al., 2021; Gao et al., 2021; Srinivas et al., 2021), but they mainly focus on image recognition, without any spatiotemporal consideration for video understanding.

Original: Moreover, the combination is almost straightforward in the prior video transformers, e.g., using transformer as global attention (Wang et al., 2018) or using convolution as patch stem (Liu et al., 2020b).
Revised: Moreover, the combination is almost straightforward in the prior video transformers, e.g., using transformer as global attention (Wang et al., 2018) or using convolution as patch stem (Liu et al., 2020b).

Original: In contrast, our UniFormer tackles both video redundancy and dependency with an insightful uniﬁed framework (Table 1).
Revised: In contrast, our UniFormer tackles both video redundancy and dependency with an insightful unified framework (Table 1).

Original: Via local and global token afﬁnity learning, we can achieve a preferable computation-accuracy balance for video classiﬁcation.
Revised: Via local and global token affinity learning, we can achieve a preferable computation-accuracy balance for video classification.

Original:  E XPERIMENTS 4. D ATASETS AND E XPERIMENTAL S ETUP
Revised:  E XPERIMENTS 4. D ATASETS AND E XPERIMENTAL S ETUP

Original: We conduct experiments on widely-used Kinetics-400 (Carreira & Zisserman, 2017a) and larger benchmark Kinetics-600 (Carreira et al., 2018).
Revised: We conduct experiments on widely-used Kinetics-400 (Carreira & Zisserman, 2017a) and larger benchmark Kinetics-600 (Carreira et al., 2018).

Original: We further verify the transfer learning performance
Revised: We further verify the transfer learning performance

Original: [Table]
Revised: [Table]

Original: on temporal-related datasets Something-Something V1&V2 (Goyal et al., 2017b).
Revised: on temporal-related datasets Something-Something V1&V2 (Goyal et al., 2017b).

Original: For training, we utilize the dense sampling strategy (Wang et al., 2018) for Kinetics and sparse sampling strategy (Wang et al., 2016) for Something-Something.
Revised: For training, we utilize the dense sampling strategy (Wang et al., 2018) for Kinetics and sparse sampling strategy (Wang et al., 2016) for Something-Something.

Original: We adopt the same training recipe as MViT (Fan et al., 2021) by default, but the random horizontal ﬂip is not applied for Something-Something.
Revised: We adopt the same training recipe as MViT (Fan et al., 2021) by default, but the random horizontal flip is not applied for Something-Something.

Original: To reduce the total training cost, we inﬂate the 2D convolution kernels pre-trained on ImageNet for Kinetics (Carreira & Zisserman, 2017b).
Revised: To reduce the total training cost, we inflate the 2D convolution kernels pre-trained on ImageNet for Kinetics (Carreira & Zisserman, 2017b).

Original: More implementation speciﬁcs are shown in Appendix B. For testing, we explore the sampling strategies in our experiments.
Revised: More implementation specifics are shown in Appendix C. For testing, we explore the sampling strategies in our experiments.

Original: To obtain a preferable computationaccuracy balance, we adopt multi-clip testing for Kinetics and multi-crop testing for SomethingSomething.
Revised: To obtain a preferable computationaccuracy balance, we adopt multi-clip testing for Kinetics and multi-crop testing for SomethingSomething.

Original: All scores are averaged for the ﬁnal prediction.
Revised: All scores are averaged for the final prediction.

Original: 4. C OMPARISON TO STATE - OF - THE - ART
Revised: 4. C OMPARISON TO STATE - OF - THE - ART

Original: Kinetics-400&600.
Revised: Kinetics-400&600.

Original: Table 2 presents comparisons to the state-of-the-art methods on Kineticsand Kinetics-600.
Revised: Table 2 presents comparisons to the state-of-the-art methods on Kineticsand Kinetics-600.

Original: The ﬁrst part shows the prior works using CNN.
Revised: The first part shows the prior works using CNN.

Original: Compared with SlowFast (Feichtenhofer et al., 2019), our UniFormer-S 16 f requires 42 × fewer GFLOPs but obtains 1.0% performance gain on both datasets.
Revised: Compared with SlowFast (Feichtenhofer et al., 2019), our UniFormer-S 16 f requires 42 × fewer GFLOPs but obtains 1.0% performance gain on both datasets.

Original: Even compared with MoViNet (Kondratyuk et al., 2021), which is designed through extensive neural architecture search, our model achieves slightly better results with fewer input frames ( 16 f × 4 vs. 120 f ).
Revised: Even compared with MoViNet (Kondratyuk et al., 2021), which is designed through extensive neural architecture search, our model achieves slightly better results with fewer input frames ( 16 f × 4 vs. 120 f ).

Original: The second part lists the recent works based on vision transformers.
Revised: The second part lists the recent works based on vision transformers.

Original: With only ImageNet-1K pre-training, UniFormer-B 16 f surpasses most of the other backbones with large dataset pre-training.
Revised: With only ImageNet-1K pre-training, UniFormer-B 16 f surpasses most of the other backbones with large dataset pre-training.

Original: For example, compared with ViViT-L pre-trained from JFT-300M and Swin-B pre-trained from ImageNet-21K, UniFormer-B 32 f obtains comparable performance with 16 .
Revised: For example, compared with ViViT-L pre-trained from JFT-300M and Swin-B pre-trained from ImageNet-21K, UniFormer-B 32 f obtains comparable performance with 16 .

Original: 7 × and 3 .
Revised: 7 × and 3 .

Original: 3 × fewer computation on both Kinetics-400 and Kinetics-600.
Revised: 3 × fewer computation on both Kinetics-400 and Kinetics-600.

Original: Something-Something V1&V2.
Revised: Something-Something V1&V2.

Original: Results on Something-Something V1&V2 are shown in Table 3.
Revised: Results on Something-Something V1&V2 are shown in Table 3.

Original: Since these datasets depend on temporal relation modeling, it is difﬁcult for the CNN-based methods to capture long-term dependencies, which leads to their worse results.
Revised: Since these datasets depend on temporal relation modeling, it is difficult for the CNN-based methods to capture long-term dependencies, which leads to their worse results.

Original: In contrast, transformerbased backbones are good at processing long sequential data and demonstrate better transfer learning capabilities (Zhou et al., 2021).
Revised: In contrast, transformerbased backbones are good at processing long sequential data and demonstrate better transfer learning capabilities (Zhou et al., 2021).

Original: Our UniFormer pre-trained from Kinetis-600 outperforms all the current methods under the same settings.
Revised: Our UniFormer pre-trained from Kinetis-600 outperforms all the current methods under the same settings.

Original: In fact, our best model achieves the new state-of-theart results: 61.0% top-1 accuracy on Something-Something V1 ( 4.4% higher than CT-Net EN ) (Li et al., 2021a) and 71.2% top-1 accuracy on Something-Something V2 ( 1.6% higher than Swin-B (Liu et al., 2021b)).
Revised: In fact, our best model achieves the new state-of-the-art results: 61.0% top-1 accuracy on Something-Something V1 ( 4.2% higher than TDN EN ) (Wang et al., 2020b) and 71.2% top-1 accuracy on Something-Something V2 ( 1.6% higher than Swin-B (Liu et al., 2021b)).

Original: Such results verify the capability of spatial-temporal learning for UniFormer.
Revised: Such results verify the capability of spatiotemporal learning for UniFormer.

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: 4. A BLATION S TUDIES
Revised: A BLATION S TUDIES

Original: UniFormer vs. Convolution: Does transformer-style FFN help?
Revised: UniFormer vs. Convolution: Does transformer-style FFN help?

Original: As mentioned in Section 3.4, our UniFormer block in the shallow layers can be interpreted as a transformer-style spatial-temporal
Revised: As mentioned in Section 3.2, our UniFormer block in the shallow layers can be interpreted as a transformer-style spatiotemporal

Original: MobileNet block (Tran et al., 2019) with extra FFN.
Revised: MobileNet block (Tran et al., 2019) with extra FFN.

Original: Hence, we ﬁrst investigate its effectiveness by replacing our UniFormer blocks in shallow layers with MobileNet blocks (the expand ratios are set to 3 for similar parameters).
Revised: Hence, we first investigate its effectiveness by replacing our UniFormer blocks in shallow layers with MobileNet blocks (the expand ratios are set to 3 for similar parameters).

Original: As expected, our default UniFormer outperforms such spatial-temporal
Revised: As expected, our default UniFormer outperforms such spatiotemporal

Original: MobileNet block in Table 4a.
Revised: MobileNet block in Table 4a.

Original: It shows that, FFN in our UniFormer can further mix token context at each spatial-temporal position to boost classiﬁcation accuracy.
Revised: It shows that, FFN in our UniFormer can further mix token context at each spatiotemporal position to boost classification accuracy.

Original: UniFormer vs. Transformer: Is joint or divided spatial-temporal attention better?
Revised: UniFormer vs. Transformer: Is joint or divided spatiotemporal attention better?

Original: As discussed in Section 3.4, our UniFormer block in the deep layers can be interpreted as transformer, but our attention is jointly learned in a spatial-temporal manner, instead of dividing spatial and temporal attention (Bertasius et al., 2021; Arnab et al., 2021).
Revised: As discussed in Section 3.2, our UniFormer block in the deep layers can be interpreted as a transformer block, but our attention is jointly learned in a spatiotemporal manner, instead of dividing spatial and temporal attention (Bertasius et al., 2021; Arnab et al., 2021).

Original: As shown in Table 4a, the joint version is more powerful than the separate one, showing that joint spatial-temporal attention can learn more discriminative video representations.
Revised: As shown in Table 4a, the joint version is more powerful than the separate one, showing that joint spatiotemporal attention can learn more discriminative video representations.

Original: What’s more, the joint attention is more friendly to transfer learning with pre-training.
Revised: What’s more, the joint attention is more friendly to transfer learning with pre-training.

Original: As shown in Table 4c, when the model is gradually pre-trained from ImageNet to
Revised: As shown in Table 4c, when the model is gradually pre-trained from ImageNet to

Original: Kinetics-400, the performance of our UniFormer becomes better.
Revised: Kinetics-400, the performance of our UniFormer becomes better.

Original: Such distinct characteristic is not observed in the pure local MHRA structure ( LLLL ) and the splitting version.
Revised: Such distinct characteristic is not observed in the pure local MHRA structure ( LLLL ) and the splitting version.

Original: It demonstrates that the joint learning manner is preferable for video representation learning.
Revised: It demonstrates that the joint learning manner is preferable for video representation learning.

Original: Does dynamic position embedding matter to UniFormer?
Revised: Does dynamic position embedding matter to UniFormer?

Original: With dynamic position embedding, our UniFormer improve the top-1 accuracy by 0.5% and 1.7% on ImageNet and Kinetics-400.
Revised: With dynamic position embedding, our UniFormer improve the top-1 accuracy by 0.5% and 1.7% on ImageNet and Kinetics-400.

Original: It shows that via encoding the position information, our DPE can maintain spatial-temporal order, contributing to better spatial-temporal representation learning.
Revised: It shows that via encoding the position information, our DPE can maintain spatiotemporal order, contributing to better spatiotemporal representation learning.

Original: How much does local MHRA help?
Revised: How much does local MHRA help?

Original: Since our UniFormer is equipped with local and global token afﬁnity respectively in the shallow and deep layers, we investigate the conﬁguration of our network stage by stage.
Revised: Since our UniFormer is equipped with local and global token affinity respectively in the shallow and deep layers, we investigate the configuration of our network stage by stage.

Original: As shown in Table 4a, when we only use local MHRA ( LLLL ), the computation cost will be light.
Revised: As shown in Table 4a, when we only use local MHRA ( LLLL ), the computation cost will be light.

Original: However, the accuracy is largely dropped, since the network lacks the capacity of learning long-term dependency without global MHRA.
Revised: However, the accuracy is largely dropped, since the network lacks the capacity of learning long-term dependency without global MHRA.

Original: When we gradually replace local MHRA with global MHRA, the accuracy becomes better as expected.
Revised: When we gradually replace local MHRA with global MHRA, the accuracy becomes better as expected.

Original: However, the accuracy is dramatically dropped with a heavy computation load when all the layers apply global MHRA ( GGGG ).
Revised: However, the accuracy is dramatically dropped with a heavy computation load when all the layers apply global MHRA ( GGGG ).

Original: It is mainly because that, without local MHRA, the network lacks the capacity of extracting detailed video representations, leading to severe model overﬁtting with redundant spatial-temporal attention.
Revised: It is mainly because that, without local MHRA, the network lacks the capacity of extracting detailed video representations, leading to severe model overfitting with redundant spatiotemporal attention.

Original: In our experiments, we choose local MHRA and global MHRA in the ﬁrst two stages and the last two stages respectively, in order to achieve a preferable computation-accuracy balance.
Revised: In our experiments, we choose local MHRA and global MHRA in the first two stages and the last two stages respectively, in order to achieve a preferable computation-accuracy balance.

Original: Is our UniFormer more transferable?
Revised: Is our UniFormer more transferable?

Original: We further verify the transfer learning ability of our UniFormer in Table 4c.
Revised: We further verify the transfer learning ability of our UniFormer in Table 4c.

Original: All models share the same stage numbers but the stage types are different.
Revised: All models share the same stage numbers but the stage types are different.

Original: Compared with pre-training from ImgeNet, pre-training from Kinetics-400 will further improve the top-1 accuracy by 1.8%.
Revised: Compared with pre-training from ImgeNet, pre-training from Kinetics-400 will further improve the top-1 accuracy by 1.8%.

Original: However, such distinct characteristic is not observed in the pure local
Revised: However, such distinct characteristic is not observed in the pure local

Original: MHRA structure and UniFormer with divided spatial-temporal attention.
Revised: MHRA structure and UniFormer with divided spatiotemporal attention.

Original: It demonstrates that the joint learning manner is preferable for transfer learning.
Revised: It demonstrates that the joint learning manner is preferable for transfer learning.

Original: Empirical investigation on model parameters.
Revised: Empirical investigation on model parameters.

Original: We further evaluate the robustness of our UniFormer network to several important model parameters.
Revised: We further evaluate the robustness of our UniFormer network to several important model parameters.

Original: (1) size of local tube: In our local token afﬁnity (Eq. 6), we aggregate spatial-temporal context from a small local tube.
Revised: (1) size of local tube: In our local token affinity (Eq. 6), we aggregate spatiotemporal context from a small local tube.

Original: Hence, we investigate the inﬂuence of this tube by changing its 3D size (Table 4b).
Revised: Hence, we investigate the influence of this tube by changing its 3D size (Table 4b).

Original: Our network is robust to the tube size.
Revised: Our network is robust to the tube size.

Original: We choose 5 × 5 × 5 for better accuracy.
Revised: We choose 5 × 5 × 5 for better accuracy.

Original: (2) sampling method: We explore the vital sampling method shown in Table 4d.
Revised: (2) sampling method: We explore the vital sampling method shown in Table 4d.

Original: For training, 16 × 4 means that we sample 16 frames with frame stride 4.
Revised: For training, 16 × 4 means that we sample 16 frames with frame stride 4.

Original: For testing, 4 × 1 means four-clip testing.
Revised: For testing, 4 × 1 means four-clip testing.

Original: As expected, sparser sampling method achieves a higher single-clip result.
Revised: As expected, sparser sampling method achieves a higher single-clip result.

Original: For multi-clip testing, dense sampling is slightly better when sampling  few frames.
Revised: For multi-clip testing, dense sampling is slightly better when sampling a few frames.

Original: However, when sampling more frames, sparse sampling is obviously better.
Revised: However, when sampling more frames, sparse sampling is obviously better.

Original: (3) testing strategy: We evaluate our network with different numbers of clips and crops for the validation videos.
Revised: (3) testing strategy: We evaluate our network with different numbers of clips and crops for the validation videos.

Original: As shown in Figure 4, since Kinetics is a scene-related dataset and trained with dense sampling, multi-clip testing is preferable to cover more frames for boosting performance.
Revised: As shown in Figure 4, since Kinetics is a scene-related dataset and trained with dense sampling, multi-clip testing is preferable to cover more frames for boosting performance.

Original: Alternatively,
Revised: Alternatively,

Original: Something-Something is a temporal-related dataset and trained with sparse sampling, so multi-crop testing is better for capturing the discriminative motion for boosting performance.
Revised: Something-Something is a temporal-related dataset and trained with sparse sampling, so multi-crop testing is better for capturing the discriminative motion for boosting performance.

Original: 4. V ISUALIZATION
Revised: 4. V ISUALIZATION

Original: To further verify the effectiveness of UniFormer, we conduct some visualizations of different structures (see Appendix C).
Revised: To further verify the effectiveness of UniFormer, we conduct some visualizations of different structures (see Appendix D).

Original: In Figure 5, We apply Grad-CAM (Selvaraju et al., 2019) to show the areas of the greatest concern in the last layer.
Revised: In Figure 5, We apply Grad-CAM (Selvaraju et al., 2019) to show the areas of the greatest concern in the last layer.

Original: It reveals that GGGG struggles to focus on the key object, i.e., the skateboard and the football, as it blindly compares the similarity of all tokens in all layers.
Revised: It reveals that GGGG struggles to focus on the key object, i.e., the skateboard and the football, as it blindly compares the similarity of all tokens in all layers.

Original: Alternatively, LLLL only performs local aggregation.
Revised: Alternatively, LLLL only performs local aggregation.

Original: Hence, its attention tends to be coarse and inaccurate without a global view.
Revised: Hence, its attention tends to be coarse and inaccurate without a global view.

Original: Different from both cases, our UniFormer with LLGG can cooperatively learn local and global contexts in a joint manner.
Revised: Different from both cases, our UniFormer with LLGG can cooperatively learn local and global contexts in a joint manner.

Original: As a result, it can effectively capture the most discriminative information, by paying precise attention to the skateboard and the football.
Revised: As a result, it can effectively capture the most discriminative information, by paying precise attention to the skateboard and the football.

Original: In
Revised: In

Original: Figure 6, we present the accuracies of different structures on Kinetics-400 (Carreira & Zisserman, 2017a).
Revised: Figure 6, we present the accuracies of different structures on Kinetics-400 (Carreira & Zisserman, 2017a).

Original: It shows that LLGG outperforms other structures in most categories, which demonstrates that our UniFormer takes advantage of both 3D convolution and spatial-temporal self-attention.
Revised: It shows that LLGG outperforms other structures in most categories, which demonstrates that our UniFormer takes advantage of both 3D convolution and spatiotemporal self-attention.

Original:  C ONCLUSION
Revised:  C ONCLUSION

Original: In this paper, we propose a novel UniFormer, which can effectively unify 3D convolution and spatialtemporal self-attention in a concise transformer format to overcome video redundancy and dependency.
Revised: In this paper, we propose a novel UniFormer, which can effectively unify 3D convolution and spatiotemporal self-attention in a concise transformer format to overcome video redundancy and dependency.

Original: We adopt local MHRA in shallow layers to largely reduce computation burden and global
Revised: We adopt local MHRA in shallow layers to largely reduce computation burden and global

Original: MHRA in deep layers to learn global token relation.
Revised: MHRA in deep layers to learn global token relation.

Original: Extensive experiments demonstrate that our
Revised: Extensive experiments demonstrate that our

Original: UniFormer achieves a preferable balance between accuracy and efﬁciency on popular video benchmarks, Kinetics-400/600 and Something-Something V1/V2.
Revised: UniFormer achieves a preferable balance between accuracy and efficiency on popular video benchmarks, Kinetics-400/600 and Something-Something V1/V2.

Original: A M ORE DETAILS ABOUT LOCAL MHRA
Revised: A M ORE DETAILS ABOUT LOCAL MHRA

Original: For local MHRA, it is vital to determine the neighbor tokens.
Revised: For local MHRA, it is vital to determine the neighbor tokens.

Original: Considering any token X k ( k ∈ [0 , L − 1] ), we can calculate its index ( t k , h k , w k ) as follows:
Revised: Considering any token X k ( k ∈ [0 , L − 1] ), we can calculate its index ( t k , h k , w k ) as follows:

Original: [Equation]
Revised: [Equation]

Revised: [Equation]

Original: [Equation]
Revised: [Equation]

Original: Therefore, for an anchor token X i , any of its neighbor tokens X j in Ω t × h × w i should satisfy
Revised: Therefore, for an anchor token X i , any of its neighbor tokens X j in Ω t × h × w i should satisfy

Original: [Equation]
Revised: [Equation]

Revised: [Equation]

Original: [Equation]
Revised: [Equation]

Original: Thus the local spatial-temporal afﬁnity in Eq.
Revised: Thus the local spatiotemporal affinity in Eq.

Original: 6 can be calculated as follows:
Revised: 6 can be calculated as follows:

Revised: [Equation]

Revised: [Equation]

Revised: For other tokens not in Ω t × h × w i , A localn ( X i

Original: [Equation]
Revised: [Equation]

Revised: X

Original: [Equation]
Revised: [Equation]

Revised: = 0 .

Revised: B M ORE DETAILS ABOUT FFN.

Revised: We adopt the standard FFN (Eq. 3) in vision transformers (Dosovitskiy et al., 2021),

Original: [Equation]
Revised: [Equation]

Original: For other tokens not in Ω t × h × w i , A localn ( X i , X j ) = 0 .
Revised: [Equation] where GELU is a non-linear function. The channel number will be first expanded by ratio 4 and then reduced. All token representations will be enhanced after performing FFN .

Original: B A DDITIONAL I MPLEMENTATION D ETAILS
Revised: C A DDITIONAL I MPLEMENTATION D ETAILS

Original: Architecture details.
Revised: Architecture details.

Original: As in ViT (Dosovitskiy et al., 2021), we adopt the pre-normalization conﬁguration (Wang et al., 2019) that applies norm layer at the beginning of the residual function (He et al., 2016).
Revised: As in ViT (Dosovitskiy et al., 2021), we adopt the pre-normalization configuration (Wang et al., 2019) that applies norm layer at the beginning of the residual function (He et al., 2016).

Original: Differently, we utilize BN (Ioffe & Szegedy, 2015) for local MHRA and LN (Ba et al., 2016) for global MHRA.
Revised: Differently, we utilize BN (Ioffe & Szegedy, 2015) for local MHRA and LN (Ba et al., 2016) for global MHRA.

Original: Moreover, we add an extra layer normalization in the downsampling layers.
Revised: Moreover, we add an extra layer normalization in the downsampling layers.

Original: Training details.
Revised: Training details.

Original: We adopt AdamW (Loshchilov & Hutter, 2017a) optimizer with cosine learning rate schedule (Loshchilov & Hutter, 2017b) to train the entire network.
Revised: We adopt AdamW (Loshchilov & Hutter, 2017a) optimizer with cosine learning rate schedule (Loshchilov & Hutter, 2017b) to train the entire network.

Original: The ﬁrst 5 or 10 epochs are used for warm-up (Goyal et al., 2017a) to overcome early optimization difﬁculty.
Revised: The first 5 or 10 epochs are used for warm-up (Goyal et al., 2017a) to overcome early optimization difficulty.

Original: For UniFormerS, the warmup epoch, total epoch, stochastic depth rate, weight decay are set to 10, 110, 0.1 and 0.05 respectively for Kinetics and 5, 50, 0.3 and 0.05 respectively for Something-Something.
Revised: For UniFormerS, the warmup epoch, total epoch, stochastic depth rate, weight decay are set to 10, 110, 0.1 and 0.05 respectively for Kinetics and 5, 50, 0.3 and 0.05 respectively for Something-Something.

Original: For
Revised: For

Original: UniFormer-B, all the hyper-parameters are the same unless the stochastic depth rates are doubled.
Revised: UniFormer-B, all the hyper-parameters are the same unless the stochastic depth rates are doubled.

Original: We linearly scale the base learning rates according to the batch size, which are 1 e − 4 × batchsizeand 2 e − 4 × batchsizefor Kinetics and Something-Something.
Revised: We linearly scale the base learning rates according to the batch size, which are 1 e − 4 × batchsizeand 2 e − 4 × batchsizefor Kinetics and Something-Something.

Original: C V ISUALIZATION
Revised: D V ISUALIZATION

Original: We choose three structures used in our experiments (Table 4a) to make comparisons: LLGG , LLLL and GGGG .
Revised: We choose three structures used in our experiments (Table 4a) to make comparisons: LLGG , LLLL and GGGG .

Original: The stage numbers of them are { 3 , 4 , 8 , 3 } , { 3 , 5 , 10 , 4 } and { 2 , 2 , 7 , 3 } respectively.
Revised: The stage numbers of them are { 3 , 4 , 8 , 3 } , { 3 , 5 , 10 , 4 } and { 2 , 2 , 7 , 3 } respectively.

Original: In Figure 5, we conduct attention visualization of different structures.
Revised: In Figure 5, we conduct attention visualization of different structures.

Original: Part1 shows the input videos selected from Kinetics-400 (Carreira & Zisserman, 2017a).
Revised: Part1 shows the input videos selected from Kinetics-400 (Carreira & Zisserman, 2017a).

Original: In part2, we use Grad-CAM (Selvaraju et al., 2019) to generate the corresponding attention in the last layer.
Revised: In part2, we use Grad-CAM (Selvaraju et al., 2019) to generate the corresponding attention in the last layer.

Original: Since GGGG blindly compares the similarity of all tokens in all, it struggles to focus on the key object, i.e., the skateboard and the football.
Revised: Since GGGG blindly compares the similarity of all tokens in all, it struggles to focus on the key object, i.e., the skateboard and the football.

Original: Alternatively, LLLL only performs local aggregation without a global view, leading to coarse and inaccurate attention.
Revised: Alternatively, LLLL only performs local aggregation without a global view, leading to coarse and inaccurate attention.

Original: Different from both cases, our UniFormer with LLGG can cooperatively learn local and global contexts in a joint manner.
Revised: Different from both cases, our UniFormer with LLGG can cooperatively learn local and global contexts in a joint manner.

Original: As a result, it can effectively capture the most discriminative information, by paying precise attention to the skateboard and the football.
Revised: As a result, it can effectively capture the most discriminative information, by paying precise attention to the skateboard and the football.

Original: Additionally, in Figure 6, we show the top-1 accuracies of different structures on Kinetics-400 (Carreira & Zisserman, 2017a).
Revised: Additionally, in Figure 6, we show the top-1 accuracies of different structures on Kinetics-400 (Carreira & Zisserman, 2017a).

Original: It demonstrates that GGGG surpasses the other two structures in most categories.
Revised: It demonstrates that GGGG surpasses the other two structures in most categories.

Original: Furthermore, we analyze the prediction results of several categories in Figure 7.
Revised: Furthermore, we analyze the prediction results of several categories in Figure 7.

Original: It shows that gargling is often misjudged as brushing teeth , while swing dancing is often misjudged as other types of dancing.
Revised: It shows that gargling is often misjudged as brushing teeth , while swing dancing is often misjudged as other types of dancing.

Original: We argue that these categories are easier to be discriminated against based on the spatial details.
Revised: We argue that these categories are easier to be discriminated against based on the spatial details.

Original: For example, toothbrush often exists in brushing teeth but not in gargling , and the people’s poses are different in different dancing.
Revised: For example, toothbrush often exists in brushing teeth but not in gargling , and the people’s poses are different in different dancing.

Original: Therefore, LLLL performs better than GGGG in these categories thanks to the capacity of encoding detailed spatial-temporal features.
Revised: Therefore, LLLL performs better than GGGG in these categories thanks to the capacity of encoding detailed spatiotemporal features.

Original: What’s more, playing guitar and strumming guitar are difﬁcult to be classiﬁed, since their spatial contents are almost the same.
Revised: What’s more, playing guitar and strumming guitar are difficult to be classified, since their spatial contents are almost the same.

Original: They require the long-range dependency between objects, e.g., the interaction between the people’s hand and the guitar, thus GGGG does better.
Revised: They require the long-range dependency between objects, e.g., the interaction between the people’s hand and the guitar, thus GGGG does better.

Original: More importantly, our UniFormer with LLGG is competitive with the other two methods in these categories, which means it takes advantage of both 3D convolution and spatial-temporal self-attention.
Revised: More importantly, our UniFormer with LLGG is competitive with the other two methods in these categories, which means it takes advantage of both 3D convolution and spatiotemporal self-attention.

Original: D A DDITIONAL R ESULTS D. M ORE RESULTS ON K INETICS
Revised: E A DDITIONAL R ESULTS E. M ORE RESULTS ON K INETICS

Original: Table 5 shows more results on Kinetics-400 (Carreira & Zisserman, 2017a) and Kinetics-600 (Carreira et al., 2018).
Revised: Table 5 shows more results on Kinetics-400 (Carreira & Zisserman, 2017a) and Kinetics-600 (Carreira et al., 2018).

Original: The trends of the results on both datasets are similar.
Revised: The trends of the results on both datasets are similar.

Original: When sampling with a large  frame stride, the corresponding single-clip testing result will be better.
Revised: When sampling with a large [Figure] frame stride, the corresponding single-clip testing result will be better.

Original: It is mainly because sparser sampling covers a larger time range.
Revised: It is mainly because sparser sampling covers a larger time range.

Original: For multi-clip testing, sampling with frame stride 4 always performs better, thus we adopt frame stride 4 by default.
Revised: For multi-clip testing, sampling with frame stride 4 always performs better, thus we adopt frame stride 4 by default.

Original: D. M ORE RESULTS ON S OMETHING -S OMETHING
Revised: E. M ORE RESULTS ON S OMETHING -S OMETHING

Original: Table 6 presents more results on Something-Something V1&V2 (Goyal et al., 2017b).
Revised: Table 6 presents more results on Something-Something V1&V2 (Goyal et al., 2017b).

Original: For
Revised: For

Original: UniFormer-S, pre-training with Kinetics-600 is better than pre-training with Kinetics-400, improving the top-1 accuracy by approximately 1.5%.
Revised: UniFormer-S, pre-training with Kinetics-600 is better than pre-training with Kinetics-400, improving the top-1 accuracy by approximately 1.5%.

Original: However, for UniFormer-B, the improvement is not [Figure] Method
Revised: However, for UniFormer-B, the improvement is not obvious.

Original: Sampling #Frame

Original: GFLOPs #Param

Original: K

Original: K

Original: Method

Original: Top

Original: [Table]

Original: Top

Original: [Table]

Original: Top

Original: [Table]

Original: TopUniFormer-S 16 ×16 × 1 ×41.

Original: 16 × 1 ×125.

Original: 16 ×16 × 1 ×41.

Original: 16 × 1 ×125.

Original: 32 ×32 × 1 ×109.

Original: - - 32 × 1 ×438.

Original: - - 32 ×32 × 1 ×109.

Original: - - 32 × 1 ×438.

Original: UniFormer-B 16 ×16 × 1 ×96.

Original: 16 × 1 ×386.

Original: 16 ×16 × 1 ×96.

Original: 16 × 1 ×386.

Original: 32 ×32 × 1 × 49.

Original: 32 × 1 × 49.

Original: [Table] [Table] obvious. We claim that the small model is difﬁcult to ﬁt, thus larger dataset pre-training can help it ﬁt better.
Revised: We claim that the small model is difficult to fit, thus larger dataset pre-training can help it fit better.

Original: Besides, UniFormer-B with 16 frames performs better than UniFormer-S with 32 frames
Revised: Besides, UniFormer-B with 16 frames performs better than UniFormer-S with 32 frames.

Original: D. C OMPARSION TO STATE - OF - THE - ART ON I MAGE N ET
Revised: E. C OMPARSION TO STATE - OF - THE - ART ON I MAGE N ET

Original: Table 7 compares our method with the state-of-the-art ImageNet (Deng et al., 2009).
Revised: Table 7 compares our method with the state-of-the-art ImageNet (Deng et al., 2009).

Original: We design four model variants as follows:
Revised: We design four model variants as follows:

Original: • UniFormer-S: channel numbers= { 64 , 128 , 256 , 512 } , stage numbers= { 3 , 4 , 8 , 3 } • UniFormer-S † : channel numbers= { 64 , 128 , 256 , 512 } , stage numbers= { 3 , 5 , 9 , 3 } • UniFormer-B: channel numbers= { 64 , 128 , 256 , 512 } , stage numbers= { 5 , 8 , 20 , 7 } • UniFormer-L: channel numbers= { 128 , 192 , 448 , 640 } , stage numbers= { 5 , 10 , 24 , 7 }
Revised: • UniFormer-S: channel numbers= { 64 , 128 , 256 , 512 } , stage numbers= { 3 , 4 , 8 , 3 } • UniFormer-S † : channel numbers= { 64 , 128 , 256 , 512 } , stage numbers= { 3 , 5 , 9 , 3 } • UniFormer-B: channel numbers= { 64 , 128 , 256 , 512 } , stage numbers= { 5 , 8 , 20 , 7 } • UniFormer-L: channel numbers= { 128 , 192 , 448 , 640 } , stage numbers= { 5 , 10 , 24 , 7 }

Original: All the other model parameters are the same as we mention in Section 3.3.
Revised: All the other model parameters are the same as we mention in Section 3.4.

Original: For UniFormer-S † , we adopt overlapped convolutional patch embedding.
Revised: For UniFormer-S † , we adopt overlapped convolutional patch embedding.

Original: All the training hyper-parameters are the same as DeiT (Touvron et al., 2021a) by defaults.
Revised: All the training hyper-parameters are the same as DeiT (Touvron et al., 2021a) by defaults.

Original: When training our models with Token Labeling, we follow the settings used in LV-ViT (Jiang et al., 2021).
Revised: When training our models with Token Labeling, we follow the settings used in LV-ViT (Jiang et al., 2021).

Original: It shows that our models outperform other methods with similar parameters/FLOPs on ImageNet, especially when training with Token
Revised: It shows that our models outperform other methods with similar parameters/FLOPs on ImageNet, especially when training with Token

Original: Labeling.
Revised: Labeling.

Original: Moreover, our model surpasses those models combining CNN with Transformer, e.g.,
Revised: Moreover, our model surpasses those models combining CNN with Transformer, e.g.,

Original: CVT (Wu et al., 2021) and CoAtNet (Dai et al., 2021), which reﬂects our UniFormer can unify convolution and self-attention better for preferable accuracy-computation balance. 
Revised: CVT (Wu et al., 2021) and CoAtNet (Dai et al., 2021), which reflects our UniFormer can unify convolution and self-attention better for preferable accuracy-computation balance. [Table] [Table] Pretrain #Frame

Revised: GFLOPs

Original: [Table]
Revised: [Table]

Original: UniFormer-S
Revised: UniFormer-S

Revised: K

Original: [Table]
Revised: [Table]

Original: Trans
Revised: 1 ×41. 16 × 3 ×125. 16 × 3 ×250. K 16 × 1 ×41.

Original: [Table]
Revised: 16 × 3 ×125. 16 × 3 ×250. K 32 × 1 ×109. 32 × 3 ×328.

Original: [Table]
Revised: 32 × 3 ×657.

Original: 9 UniFormer-S+TL
Revised: K 32 × 1 ×109.

Original: [Table] [Table] [Table]
Revised: 32 × 3 ×328. 32 × 3 ×657.

Original: UniFormer-S †
Revised: UniFormer-B

Original: [Table]
Revised: K 16 × 1 ×96.

Original: +Trans
Revised: 16 × 3 ×290.

Original: [Table] [Table]
Revised: 16 × 3 ×580.

Original: UniFormer-S † +TL
Revised: K 16 × 1 ×96. 16 × 3 ×290.

Original: [Table]
Revised: 16 × 3 ×580.

Original: +Trans
Revised: K 32 × 1 × 49. 32 × 3 × 49.

Original: [Table]
Revised: 32 × 3 × 49. K 32 × 1 × 49. 32 × 3 × 49. 32 × 3 × 49.

Original: [Table]
Revised: [Table]

Original: UniFormer
Revised: UniFormer

Original: [Table]
Revised: [Table]

Original: S † +TL ↑

Original: [Table]
Revised: [Table]

Original: RegNetY-8G (Radosavovic etal., 2020)
Revised: et

Original: [Table]
Revised: [Table]

Original: B7 (

Original: [Table] [Table]
Revised: [Table] [Table]

Original: -M (Tan
Revised: EfficientNetV2-M (

Original: [Table]
Revised: [Table]

Revised: Le

Original: [Table]
Revised: [Table]

Revised: Wang

Original: [Table]
Revised: [Table]

Original: PVT-L (Wang et al., 2021)
Revised: al., 2021)

Original: [Table]
Revised: [Table]

Original: 24 (Yuan et al., 2021)
Revised: Swin

Original: [Table]
Revised: [Table]

Original: Swin-S (Liu et al., 2021a)
Revised: (Liu et al., 2021a)

Original: [Table]
Revised: [Table]

Original: CSwin-S ↑ 384 (Dong et al., 2021)
Revised: CSwin-S ↑ 384 (Dong et al., 2021)

Original: [Table]
Revised: [Table]

Original: [Table] LV-ViT-M (Jiang et al., 2021)
Revised: -ViT-M (

Original: [Table]
Revised: [Table]

Original: LV-ViT-M ↑ 384 (Jiang et al., 2021)
Revised: LV-ViT-M ↑ 384 (Jiang et al., 2021)

Original: Trans

Original: [Table]
Revised: [Table]

Original: [Table]

Original: CVT-21 (Wu et al., 2021)
Revised: CVT-21 (Wu et al., 2021)

Original: [Table]
Revised: [Table]

Original: [Table]

Original: [Table]

Original: CVT-21 ↑ 384 (Wu et al., 2021)
Revised: CVT-21 ↑ 384 (Wu et al., 2021)

Original: [Table]

Original: [Table]

Original: [Table]
Revised: [Table]

Original: CoAtNet-1 (Dai et al., 2021)
Revised: CoAtNet-1 (Dai et al., 2021)

Original: [Table]
Revised: [Table]

Original: [Table] CoAtNet-
Revised: CoAtNet-1 ↑ 384 (Dai et al.

Original: [Table]
Revised: [Table]