Human action recognition is a fundamental and well studied problem in computer vision. Traditional approaches to action recognition relied on object detectiondesai10action ; gupta09pami ; yao10actions2 , articulated pose maji2011action ; pishchulin14gcpr ; ramanan2003automatic ; yang10poseaction ; yao10actions2 , dense trajectories WangCVPR11 ; IDT_Wang_13 and part-based/structured models Delaitre10 ; yao10actions ; yao11actions . However, more recently these methods have been surpassed by deep CNN-based representations gkioxari15rstar ; mallya16actions ; Simonyan_14b ; Tran_15 . Interestingly, even video based action recognition has benefited greatly from advancements in image-based CNN models He_16 ; Ioffe_15 ; Simonyan_14a ; Szegedy_16 . With the exception of a few 3D-conv-based methods Tran_15 ; Varol_16 ; piergiovanni2017learning , most approaches LRCN ; Feichtenhofer_16b ; Feichtenhofer_16 ; Girdhar_17a_ActionVLAD ; WangL_16a , including the current state of the art WangL_16a , use a variant of discriminatively trained 2D-CNN Ioffe_15 over the appearance (frames) and in some cases motion (optical flow) modalities of the input video.
Attention: While using standard deep networks over the full image have shown great promise for the task WangL_16a , it raises the question of whether action recognition can be considered as a general classification problem. Some recent works have tried to generate more fine-grained representations by extracting features around human pose keypoints cheronICCV15 or on object/person bounding boxes gkioxari15rstar ; mallya16actions . This form of ‘hard-coded attention’ helps improve performance, but requires labeling (or detecting) objects or human pose. Moreover, these methods assume that focusing on the human or its parts is always useful for discriminating actions. This might not necessarily be true for all actions; some actions might be easier to distinguish using the background and context, like a ‘basketball shoot’ vs a ‘throw’; while others might require paying close attention to objects being interacted by the human, like in case of ‘drinking from mug’ vs ‘drinking from water bottle’.
Our work: In this work, we propose a simple yet surprisingly powerful network modification that learns attention maps which focus computation on specific parts of the input relevant to the task at hand. Our attention maps can be learned without any additional supervision and automatically lead to significant improvements over the baseline architecture. Our formulation is simple-to-implement, and can be seen as a natural extension of average pooling into a “weighted” average pooling with image-specific weights. Our formulation also provides a novel factorization of attentional processing into bottom-up saliency combined with top-down attention. We further experiment with adding human pose as an intermediate supervision to train our attention module, which encourages the network to look for human object interactions. While this makes little difference to the performance of image-based recognition models, it leads to a larger improvement on video datasets as videos consist of large number of ‘non-iconic’ frames where the subject of object of actions may not be at the center of focus.
Our contributions: (1) An easy-to-use extension of state-of-the-art base architectures that incorporates attention to give significant improvement in action recognition performance at virtually negligible increase in computation cost; (2) Extensive analysis of its performance on three action recognition datasets across still images and videos, obtaining state of the art on MPII and HMDB-51 (RGB, single-frame models) and competitive on HICO; (3) Analysis of different base architectures for applicability of our attention module; and (4) Mathematical analysis of our proposed attention module and showing its equivalence to a rank-1 approximation of second order or bilinear pooling (typically used in fine grained recognition methods gao16cbp ; kong2016low ; lin2015bilinear ) suggesting a novel characterization of action recognition as a fine grained recognition problem.
2 Related Work
Human action recognition is a well studied problem with various standard benchmarks spanning across still images chao15hico ; Everingham2010 ; pishchulin14gcpr ; ronchi15cocoa ; yao11actions and videos kay2017kinetics ; hmdb51 ; charades ; ucf101 . The newer image based datasets such as HICO chao15hico and MPII pishchulin14gcpr are large and highly diverse, containing 600 and 393 classes respectively. In contrast, collecting such diverse video based action datasets is hard, and hence existing popular benchmarks like UCF101 ucf101 or HMDB51 hmdb51 contain only 101 and 51 categories each. This in turn has lead to much higher baseline performance on videos, eg. WangL_16a classification accuracy on UCF101, compared to images, eg. mallya16actions mean average precision (mAP) on MPII.
Video based action recognition methods focus on two main problems: action classification and (spatio-)temporal detection. While image based recognition problems, including action recognition, have seen a large boost with the recent advancements in deep learning (e.g., MPII performance went up from 5% mAPpishchulin14gcpr to 27% mAP gkioxari15rstar ), video based recognition still relies on hand crafted features such as iDT IDT_Wang_13
to obtain competitive performance. These features are computed by extracting appearance and motion features along densely sampled point trajectories in the video, aggregated into a fixed length representation by using fisher vectorsPerronnin_07
. Convolutional neural network (CNN) based approaches to video action recognition have broadly followed two main paradigms: (1) Multi-stream networksSimonyan_14b ; WangL_16a which split the input video into multiple modalities such as RGB, optical flow, warped flow etc, train standard image based CNNs on top of those, and late-fuse the predictions from each of the CNNs; and (2) 3D Conv Networks Tran_15 ; Varol_16 which represent the video as a spatio-temporal blob and train a 3D convolutional model for action prediction. In terms of performance, 3D conv based methods have been harder to scale and multi-stream methods WangL_16a currently hold state of the art performance on standard benchmarks. Our approach is complementary to these paradigms and the attention module can be applied on top of either. We show results on improving action classification over state of the art multi-stream model WangL_16a in experiments. Pose: There have also been previous works in incorporating human pose into action recognition cheronICCV15 ; delaitre11hoi ; zolf17chained . In particular, P-CNN cheronICCV15 computes local appearance and motion features along the pose keypoints and aggregates those over the video for action prediction, but is not end-to-end trainable. More recent work zolf17chained adds pose as an additional stream in chained multi-stream fashion and shows significant improvements. Our approach is complementary to these approaches as we use pose as a regularizer in learning spatial attention maps to weight regions of the RGB frame. Moreover, our method is not constrained by pose labels, and as we show in experiments, can show effective performance with pose predicted by existing methods cao2017realtime or even without using pose.
Hard attention: Previous works in image based action recognition have shown impressive performance by incorporating evidence from the human, context and pose keypoint bounding boxes cheronICCV15 ; gkioxari15rstar ; mallya16actions . Gkioxari el al. gkioxari15rstar modified R-CNN pipeline to propose R*CNN, where they choose an auxiliary box to encode context apart from the human bounding box. Mallya and Lazebnik mallya16actions improve upon it by using the full image as the context and using multiple instance learning (MIL) to reason over all humans present in the image to predict an action label for the image. Our approach gets rid of the bounding box detection step and improves over both these methods by automatically learning to attend to the most informative parts of the image for the task.
Soft attention: There has been relatively little work that explores unconstrained ‘soft’ attention for action recognition, with the exception of sharma2015attention ; song2016end for spatio-temporal and shi2016joint for temporal attention. Importantly, all these consider a video setting, where a LSTM network predicts a spatial attention map for the current frame. Our method, however, uses a single frame to both predict and apply spatial attention, making it amenable to both single image and video based use cases. song2016end
also uses pose keypoints labeled in 3D videos to drive attention to parts of the body. In contrast, we learn an unconstrained attention model that frequently learns to look around the human body for objects that make it easier to classify the action.
Second-order pooling: Because our model uses a single set of appearance features to both predict and apply an attention map, this makes the output quadratic in the features (Sec. 3.1). This observation allows us to implement attention through second-order or bilinear pooling operations lin2015bilinear , made efficient through low-rank approximations gao16cbp ; kim2016hadamard ; kong2016low . Our work is most related to kong2016low , who point out when efficiently implemented, low-rank approximations avoid explicitly computing second-order features. We point out that a rank-1 approximation of second-order features is equivalent to an attentional model sometimes denoted as “self attention” vaswani2017attention . Exposing this connection allows us to explore several extensions, including variations of bottom-up and top-down attention, as well as regularized attention maps that make use of additional supervised pose labels.
Our attentional pooling module is a trainable layer that plugs in as a replacement for a pooling operation in any standard CNN. As most contemporary architectures He_16 ; Ioffe_15 ; Szegedy_16 are fully convolutional with an average pooling operation at the end, our module can be used to replace that operation with an attention-weighted pooling. We now derive the pooling layer as an efficient low-rank approximation to second order pooling (Sec. 3.1). Then, we describe our network architecture that incorporates this attention module and explore a pose-regularized variant of the same (Sec. 3.2).
3.1 Attentional pooling as low-rank approximation of second-order pooling
Let us write the layer to be pooled as , where is the number of spatial locations (e.g., ) and is the number of channels (e.g.,
). Standard sum (or max) pooling would reduce this to vector in, which could then be processed by a “fully-connected” weight vector
to generate a classification score. We will denote matrices with upper case letters, and vectors with lower-case bold letters. For the moment, assume we are training a binary classifier (we generalize to more classes later in the derivation). We can formalize this pipeline with the following notation:
where is a vector of all ones and is the (transposed) sum-pooled feature.
Second-order pooling: Following past work on second-order pooling carreira2012semantic , let us construct the feature . Prior work has demonstrated that such second-order statistics can be useful for fine-grained classification lin2015bilinear . Typically, one then “vectorizes” this feature, and learns a vector of weights to generate a score. If we write the vector of weights as a matrix, the inner product between the two vectorized quantities can be succinctly written using the trace operator111https://en.wikipedia.org/wiki/Trace_(linear_algebra). The key identity, (using matlab notation), can easily be verified by plugging in the definition of a trace operator. This allows us to write the classification score as follows:
Low-rank second-order pooling: Let us approximate matrix with a rank-1 approximation, where . Plugging this into the above yields a novel formulation of attentional pooling:
where (4) makes use of the trace identity that and (5) uses the fact that the trace of a scalar is simply the scalar. The last line (6) gives efficient implementation of attentional pooling: given a feature map , compute an attention map over all spatial locations with , that is then used to compute a weighted average of features . This weighted-average feature is then pushed through a linear model to produce the final score.
Interestingly, (6) can also be written as the following:
The first line illustrates that the attentional heatmap can also be seen as , with being the classifier of the attentionally-pooled feature. The second line illustrates that our formulation is in fact symmetric, where the final score can be seen as the inner product between two attentional heatmaps defined over all spatial locations. Fig. 0(a) illustrates our approach.
Top-down attention: To generate prediction for multiple classes, we replace the weight matrix from (2) with class-specific weights:
One could apply a similar derivation to produce class-specific vectors and , each of them generating a class-specific attention map. Instead, we choose to distinctly model class-specific “top-down” attention baluch2011mechanisms ; zhou2016learning ; ullman1984visual from bottom-up visual saliency that is class-agnostic rutishauser2004bottom . We do so by forcing one of the attention parameter vectors to be class-agnostic - e.g., . This makes our final low-rank attentional model
equivalent to an inner product between top-down (class-specific) and bottom-up (saliency-based) attention maps. Our approach of combining top-down and botom-up attentional maps is reminiscent of biologically-motivated schemes that modulate saliency maps with top-down cues navalpakkam2006integrated . This suggests that our attentional model can also be implemented using a single, combined attention map defined over all spatial locations:
where denotes element-wise multiplication and is defined as before. We visualize the combined, top-down, and bottom-up attention maps in our experimental results.
Average pooling (revisited): The above derivation allows us to revisit our average pooling formulation from (1), replacing weights with class-specific weights as follows:
From this perspective, the above derivation gives the ability to generate top-down attentional maps from existing average-pooling networks. While similar observations have been pointed out before zhou2016learning , it naturally emerges as a special case of our bottom-up and top-down formulation of attention.
3.2 Network Architecture
We now describe our network architecture to implement the attentional pooling described above. We start from a state of the art base architecture, ResNet-101 He_16 . It consists of a stack of ‘modules’, each of which contains multiple convolutional, pooling or identity mapping streams. It finally generates a spatial feature map, which is average pooled to get a -dimensional vector and is then classified using a linear classifier.
Our attention module plugs in at the last layer, after the spatial feature map. As shown in Fig. 0(b) (Method 1), we predict a single channel bottom-up saliency map of same spatial resolution as the last feature map, using a linear classifier on top of it (). Similarly, we also generate the dimensional top-down attention map , where is number of classes. The two attention maps are multiplied and spatially averaged to generate the -dimensional output predictions (). These operations are equivalent to first multiplying the features with saliency () and then passing through a classifier ().
Pose: While this unconstrained attention module automatically learns to focus on relevant parts and gives a sizable boost in accuracy, we take inspiration from previous work cheronICCV15 and use human pose keypoints to guide the attention. As shown in Fig. 0(b) (Method 2), we use a two-layer MLP on top of the last layer to predict a 17 channel heatmap. The first 16 channels correspond to human pose keypoints and incur a loss against labeled (or detected, using cao2017realtime ) pose) The final channel is used as an unconstrained bottom-up attention map, as before. We refer to this method as pose-regularized attention, and it can be thought of as a non-linear extension of previous attention map.
We experiment with three recent, large scale action recognition
datasets, across still images and videos, namely
MPII, HICO and HMDB51. MPII Human Pose Dataset pishchulin14gcpr contains
labeled with up to 16 human body keypoints, and classified into one of
393 action classes.
It is split into train, val (from authors of gkioxari15rstar )
and test sets, with 8218, 6987 and 5708 images each.
We use the val set to compare with gkioxari15rstar and for ablative
analysis while the
final test results are obtained by
emailing our results to authors of pishchulin14gcpr .
The dataset is highly
and the evaluation is performed using mean average
precision (mAP) to equally weight all classes.
HICO chao15hico is
a recently introduced dataset with labels
for 600 human object interactions (HOI) combining 117 actions
with 80 objects.
It contains 38116 training and 9658 test images, with
each image labeled with all the HOIs active
for that image (multi-label setting).
Like MPII, this dataset is also highly unbalanced and
evaluation is performed using mAP over classes.
Finally, to verify our method’s applicability to video based action recognition,
we experiment with
a challenging trimmed action classification dataset,
HMDB51 hmdb51 . It contains 6766 realistic and varied
video clips from 51 action classes.
Evaluation is performed using average classification accuracy
over three train/test splits from THUMOS13 , each with 3570 train
and 1530 test videos.
Baselines: Throughout the following sections, we compare our approach first to the standard base architecture, mostly ResNet-101 He_16 , without the attention-weighted pooling. Then we compare to other reported methods and previous state of the art on the respective datasets.
MPII: We train our models for 393-way action classification on MPII with softmax cross-entropy loss for both the baseline ResNet and our attentional model. We compare our performance in Tab. 1. Our unconstrained attention model clearly out-performs the base ResNet model, as well as previous state of the art methods involving detection of multiple contextual bounding boxes gkioxari15rstar and fusion of full image with human bounding box features mallya16actions . Our pose-regularized model performs best, though the improvement is small. We visualize the attention maps learned in Fig. 2.
|Method||Full Img||Bbox||Pose||MIL||Val (mAP)||Test (mAP)|
|Attn. Pool. (I-V2) (ours)||✓||24.3||-|
|Attn. Pool. (R-101) (ours)||✓||30.3||36.0|
|Dense Trajectory + Pose pishchulin14gcpr||✓||✓||-||5.5|
|VGG16, RCNN gkioxari15rstar||✓||16.5||-|
|VGG16, R*CNN gkioxari15rstar||✓||21.7||26.7|
|VGG16, Fusion (best) mallya16actions||✓||✓||-||32.2|
|VGG16, Fusion+MIL (best) mallya16actions||✓||✓||✓||-||31.9|
|Pose Reg. Attn. Pooling (R-101) (ours)||✓||✓||30.6||36.1|
HICO: We train our model on HICO similar to MPII, and compare our performance in Tab. 2. Again, we see a significant 5% boost over our base ResNet model. Moreover, we out-perform all previous methods, including ones that use detection bounding boxes at test time except one mallya16actions , when that is trained with a specialized weighted loss for this dataset. It is also worth noting that the full image-only performance of VGG and ResNet were comparable in our experiments (29.4% and 30.2%), suggesting that our approach shows larger relative improvement over a similar starting baseline. Though we did not experiment with the same optimization setting as mallya16actions , we believe it will give similar improvements there as well. Since this dataset also comes with labels decomposed into actions and objects, we visualize what our attention model looks for, given images containing interactions with a specific object. As Fig. 3 shows, the attention peak is typically close to the object of interest, showing the importance of detecting objects in HOI detection tasks. Moreover, this suggests that our attention maps can also function as weak-supervision for object detection.
|Method||Full Im.||Bbox/Pose||MIL||Wtd Loss||mAP|
|VGG16, full image mallya16actions||✓||29.4|
|ResNet101, full image (ours)||✓||30.2|
|ResNet101 with CBP gao16cbp (impl. from cbp_tf )||✓||26.8|
|Attentional Pooling (R-101) (ours)||✓||35.0|
|R*CNN gkioxari15rstar (reported in mallya16actions )||✓||✓||28.5|
|Scene-RCNN gkioxari15rstar (reported in mallya16actions )||✓||✓||✓||29.0|
|Fusion (best reported) mallya16actions||✓||✓||✓||33.8|
|Pose Regularized Attentional Pooling (R101) (ours)||✓||✓||34.6|
|Fusion, weighted loss (best reported) mallya16actions||✓||✓||✓||✓||36.1|
HMDB51: Next, we apply our attentional method to the RGB stream of the current state of the art single-frame deep model on this dataset, TSN WangL_16a . TSN extends the standard two-stream Simonyan_14b architecture by using a much deeper base architecture Ioffe_15 along with enforcing consensus over multiple frames from the video at training time. For the purpose of this work, we focus on the RGB stream only but our method is applicable to flow/warped-flow streams as well. We first train a TSN model using ResNet-101 as base architecture after re-sizing input frames to 450px. This ensures larger spatial dimensions of the output (), hence ensuring the last-layer features are amenable to attention. Though our base ResNet model does worse than BN-inception TSN model, as Tab. 3 shows, using our attention module improves the base model to do comparably well. Interestingly, on this dataset regularizing the attention through pose gives a significant boost in performance, out-performing TSN and establishing new state of the art on the RGB-only single-frame model for HMDB. We visualize the attention maps with normal and pose-regularized attention in Fig. 4. The pose regularized attention are more peaky near the human than their linear counterparts. This potentially explains the improvement using pose on HMDB while it does not help as much on HICO or MPII; HICO and MPII, being image based datasets typically have ‘iconic’ images, with the subjects and objects of action typically in the center and focus of the image. Video frames in HMDB, on the other hand, may have the subject move all across the frame throughout the video, and hence additional supervision through pose at training time helps focus the attention at the right spot.
|Method||Split 1||Split 2||Split 3||Avg|
|TSN, BN-inception (RGB) WangL_16a (Via email with authors)||54.4||49.5||49.2||51.0|
|RGB Stream, ResNet50 (RGB) Feichtenhofer_16b (reported at twofusion_web )||-||-||-||48.9|
|RGB Stream, ResNet152 (RGB) Feichtenhofer_16b (reported at twofusion_web )||-||-||-||46.7|
|TSN, ResNet101 (RGB) (ours)||48.2||46.5||46.7||47.1|
|Linear Attentional Pooling (ours)||51.1||51.6||49.7||50.8|
|Pose regularized Attentional Pooling (ours)||54.4||51.1||50.9||52.2|
Full-rank pooling: Given our formulation of attention as low-rank second-order pooling, a natural question is what would be the performance of a full-rank model? Explicitly computing the second-order features of size for (and learning the associated classifier) is cumbersome. Instead, we make use of the compact bilinear approach (CBP) of gao16cbp , which generates a low-dimensional
approximation of full bilinear pooling lin2015bilinear
using the TensorSketch algorithm. To keep the final output comparable to our attentional-pooled model, we project to dimensions. We find it performs slightly worse than simple average pooling in Table 2.
Note that we use an existing implementation cbp_tf with minimal hyper-parameter optimization, and leave a more rigorous comparison to future work.
Rank- approximation: While a full-rank model is cumbersome, we can still explore the effect of using a higher, -rank approximation. Essentially, a rank- approximation generates (1-channel) bottom-up and ( channel) top-down attention maps, and the final prediction is the product of corresponding heatmaps, summed over . On MPII, we obtain mAP of 30.3, 29.9, 30.0 for =1, 2 and 5 respectively, showing that the validation performance is relatively stable with . We do observe a drop in training loss with a higher , indicating that a higher-rank approximation could be useful for harder datasets and tasks. Per-class attention maps: As we described in Sec. 3.1, our inspiration for combining class-specific and class-agnostic classifiers (i.e. top-down and bottom-up attention respectively), came from the Neuroscience literature on integrating top-down and bottom-up attention navalpakkam2006integrated . However, our model can also be extended to learn completely class-specific attention maps, by predicting bottom-up attention maps, and combining each map with the corresponding softmax classifier for that class. We experiment with this idea on MPII and obtain a mAP of 27.9 with 393 (=num-classes) attention maps, compared to 30.3% with 1 map, and 26.2% without attention. On further analysis we observe that both models achieve near perfect mAP on training data, implying that adding more parameters with multiple attention maps leads to over-fitting on the relatively small MPII trainset. However, this may be a viable approach for larger datasets.
Diagnostics: It is natural to consider variants of our model that only consider the bottom-up or top-down attentional map. As derived in (12), baseline models with average pooling are equivalent to “top-down-only” attention models, which are resoundingly outperformed by our joint bottom-up and top-down model. It is not clear how to construct a bottom-up only model, since it is class-agnostic, making it difficult to produce class-specific scores. Rather, a reasonable approximation might be applying an off-the-shelf (bottom-up) saliency method used to limit the spatial region that features are averaged over. Our initial experiments with existing saliency-based methods huang2015salicon were not promising.
Base Network: Finally, we analyze the choice of base architecture for the effectiveness of our proposed attentional pooling module. In Tab. 1, we compare the improvement using attention over ResNet-101 (R-101) He_16 and an BN-Inception (I-V2) Ioffe_15
. Both models perform comparably when trained for full image, however, while we see a 4% improvement on R-101 on using attention, we do not see similar improvements for I-V2. This points to an important distinction in the two architectures, i.e., Inception-style models are designed to be faster in inference and training by rapidly down sampling input images in initial layers through max-pooling. While this reduces the computational cost for later layers, it leads to most layers having very large receptive fields, and hence later neurons have effective access to all of the image pixels. This suggests that all the spatial features at the last layer could be highly similar. In contrast, R-101 downscales the spatial resolution gradually, allowing the last layer features to specialize to different parts of the image, hence benefiting more from attentional pooling. This effect was further corroborated by our experiments on HMDB, where using the standard 224px input resolution showed no improvement with attention, while the same image resized to 450px at input time did. This initial resize ensures the last-layer features are sufficiently distinct to benefit from attentional pooling.
5 Discussion and Conclusion
An important distinction of our model from some previous works gkioxari15rstar ; mallya16actions is that it does not explicitly model action at an instance or bounding-box level. This, in fact, is a strength of our model; making it capable of attending to objects outside of any person-instance bounding box (such as bags of garbage for “garbage collecting”, in Fig 2). In theory, our model can also be applied to instance-level action recognition by applying attentional pooling over an instance’s RoI features. Such a model would learn to look at different parts of human body and its interactions with nearby objects. However, it’s notable that most existing action datasets, including carreira2017quo ; chao15hico ; hmdb51 ; pishchulin14gcpr ; charades ; ucf101 , come with only frame or video level labels; and though gkioxari15rstar ; mallya16actions are designed for instance-level recognition, they are not applied as such. They either copy image level labels to instances or use multiple-instance learning, either of which can be used in conjunction with our model. Another interesting connection that emerges from our work is the relation between second-order pooling and attention. The two communities are traditionally seen as distinct, and our work strongly suggests that they should mix: as newer action datasets become more fine-grained, we should explore second-order pooling techniques for action recognition. Similarly, second-order pooling can serve as a simple but strong baseline for the attention community, which tends to focus on more complex sequential attention networks (based on RNNs or LSTMs). It is also worth noting that similar ideas involving self attention and bilinear models have recently also shown significant improvements in other tasks like image classification wang2017residual , language translation vaswani2017attention and visual question answering santoro2017simple .
We have introduced a simple formulation of attention as low-rank second-order pooling, and illustrate it on the task of action classification from single (RGB) images. Our formulation allows for explicit integration of bottom-up saliency and top-down attention, and can take advantage of additional supervision when needed (through pose labels). Our model produces competitive or state-of-the-art results on widely benchmarked datasets, by learning where to look when pooling features across an image. Finally, it is easy to implement and requires few additional parameters, making it an attractive alternative to standard pooling, which is a ubiquitous operation in nearly all contemporary deep networks.
Authors would like to thank Olga Russakovsky for initial review. This research was supported in part by the National Science Foundation (NSF) under grant numbers CNS-1518865 and IIS-1618903, and the Defense Advanced Research Projects Agency (DARPA) under Contract No. HR001117C0051. Additional support was provided by the Intel Science and Technology Center for Visual Cloud Systems (ISTC-VCS). Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the view(s) of their employers or the above-mentioned funding sources.
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