gradient forward-propagation for large-scale temporal video … · 2021. 6. 24. · bp + 3d vgg16...

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Gradient Forward-Propagation for Large-Scale Temporal Video Modelling Supplementary Material Mateusz Malinowski * DeepMind Dimitrios Vytiniotis DeepMind Grzegorz ´ Swirszcz DeepMind Viorica P˘ atr˘ aucean DeepMind João Carreira DeepMind In this supplementary material we provide additional de- tails about the experimental setup used in the main paper, results about the stability of the proposed Skip-Sideways training, and additional qualitative results obtained in the reconstruction task. 1. Notation We denote input temporal sequences by x = (x [t] ) K t=1 , x [t] R d and outputs by y =(y [t] ) K t=1 , y [t] R dy . We mainly focus on video clips, where each frame has dimension d = h × w × 3. In action recognition tasks, we have y [t] = y [1] . We use single-frame 2D CNNs that map inputs to logits M θ : R d R dy . These networks are compositions of layers, written as M θ (x [t] )= H D (·D ) H D-1 (·D-1 ) ... H 1 (x [t] 1 ) where each layer H l (·, ·) is a function H l : R d l-1 × R p l R d l , is a composition, i.e., G F (x [t] )= G(F (x [t] )), and θ =(θ l ) l l R p l are trainable parameters. We also use h [t] l = H l (·l ) ... H 1 (x [t] 1 ) to denote activations at layer l. We use L : R dy × R dy R defined as L(h D , y)= K t=1 l(h [t] D , y [t] ) = t l [t] , where h [t] D are logits, i.e., h [t] D = M θ (x [t] ), and l is a loss at time t, e.g., a cross- entropy loss l(h, y)= - i p(y i ) log q(h i ). We update model parameters with the temporally averaged gradients, i.e., θ := θ - α t θ l [t] , where α is a learning rate. We use the following notation for Jacobian tensors. Let ∂H(h,θ) ∂h (h, θ)= ∂H(h,θ) ∂h h=h be the Jacobian tensor of H(h, θ) with respect to the variable h evaluated at h = h, θ = θ. Note that, we use bold fonts to distinguish between formal and actual values of the variables. We also use a short- hand notation ∂h l ∂h l-1 (h l-1 , θ l )= ∂H l (h l-1 l ) ∂h l-1 (h l-1 , θ l ). * The corresponding author: [email protected] 2. Experimental setup Datasets. We use three datasets: HMDB51 has 6,770 video clips representing 51 ac- tions [7], sampled at 30fps. We use the same train and test splits as [5, 9, 11]. UCF101 [13] has 13,320 videos clips and 101 human actions, sampled at 25fps, with clips having 7.21sec on average. Kinetics600 (K600) is a large-scale dataset for action recognition [2] with around 490,000 videos. It has 600 human actions, and each action has at least 600 video clips per action. The clip duration is 10s, with frame-rate 25fps. Tasks. Here we give additional details for the reconstruction task used in the main paper. At each time-step t, the network predicts the frame at time-step t +8, i.e., we want to learn a mapping M θ (x [t] ; θ) y [t] = x [t+8] for all t. We choose a displacement of 8 frames into the future as this corresponds to the number of Skip-Sideways or Sideways units that we use. That is, the output layer has to make a prediction for the frame that the first layer is about to see. Hence the mod- els have no access to the observation they must predict. To successfully solve this task, it may be helpful for the mod- els to learn to capture the underlying motion in the scene so they can re-distribute pixels accordingly. We minimise the following objective: 1 T T t=1 ||M θ (x [t] ) - x [t+8] || 2 l2 . We compare Skip-Sideways against Sideways. The results of Skip-Sideways are significantly better than the equiva- lent model trained with Sideways (see additional qualitative results included in Figure 6) and it shows the benefit of in- tegrating temporal information through direct and shortcut connections. Distributed setting. We experiment on K600 using two multi-host setups, where we use either 8 or 16 hosts. Each host has 8 TPUs (Tensor Processing Units) amounting to 64

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Page 1: Gradient Forward-Propagation for Large-Scale Temporal Video … · 2021. 6. 24. · BP + 3D VGG16 1:9 1 BP + 3D VGG16 (Remat) 1:5 1 BP + Causal 3D VGG16 2:4 1 BP + I3D [2] 2:9 1 BP

Gradient Forward-Propagation for Large-Scale Temporal Video ModellingSupplementary Material

Mateusz Malinowski∗

DeepMindDimitrios Vytiniotis

DeepMindGrzegorz Swirszcz

DeepMindViorica Patraucean

DeepMind

João CarreiraDeepMind

In this supplementary material we provide additional de-tails about the experimental setup used in the main paper,results about the stability of the proposed Skip-Sidewaystraining, and additional qualitative results obtained in thereconstruction task.

1. Notation

We denote input temporal sequences by x =(x[t])Kt=1,x

[t] ∈ Rd and outputs by y = (y[t])Kt=1,y[t] ∈

Rdy . We mainly focus on video clips, where each framehas dimension d = h× w × 3. In action recognition tasks,we have y[t] = y[1]. We use single-frame 2D CNNs thatmap inputs to logitsMθ : Rd → Rdy . These networks arecompositions of layers, written as

Mθ(x[t]) = HD(·, θD)◦HD−1(·, θD−1)◦. . .◦H1(x

[t], θ1)

where each layer Hl(·, ·) is a function Hl : Rdl−1 × Rpl →Rdl , ◦ is a composition, i.e., G ◦F (x[t]) = G(F (x[t])), andθ = (θl)l , θl ∈ Rpl are trainable parameters. We also useh[t]l = Hl(·, θl) ◦ . . . ◦H1(x

[t], θ1) to denote activations atlayer l.

We use L : Rdy × Rdy → R defined as L(hD,y) =∑Kt=1 l(h

[t]D ,y

[t]) =∑t l

[t], where h[t]D are logits, i.e.,

h[t]D = Mθ(x

[t]), and l is a loss at time t, e.g., a cross-entropy loss l(h,y) = −

∑i p(yi) log q(hi). We update

model parameters with the temporally averaged gradients,i.e., θ := θ − α

∑t∇θl[t], where α is a learning rate.

We use the following notation for Jacobian tensors. Let∂H(h,θ)∂h (h,θ) = ∂H(h,θ)

∂h

∣∣∣h=h

be the Jacobian tensor of

H(h, θ) with respect to the variable h evaluated at h = h,θ = θ. Note that, we use bold fonts to distinguish betweenformal and actual values of the variables. We also use a short-hand notation ∂hl

∂hl−1(hl−1,θl) =

∂Hl(hl−1,θl)∂hl−1

(hl−1,θl).

∗The corresponding author: [email protected]

2. Experimental setupDatasets. We use three datasets:

• HMDB51 has 6,770 video clips representing 51 ac-tions [7], sampled at 30fps. We use the same train andtest splits as [5, 9, 11].

• UCF101 [13] has 13,320 videos clips and 101 humanactions, sampled at 25fps, with clips having 7.21sec onaverage.

• Kinetics600 (K600) is a large-scale dataset for actionrecognition [2] with around 490,000 videos. It has600 human actions, and each action has at least 600video clips per action. The clip duration is 10s, withframe-rate 25fps.

Tasks. Here we give additional details for the reconstructiontask used in the main paper. At each time-step t, the networkpredicts the frame at time-step t+ 8, i.e., we want to learn amappingMθ(x

[t]; θ)→ y[t] = x[t+8] for all t. We choosea displacement of 8 frames into the future as this correspondsto the number of Skip-Sideways or Sideways units that weuse. That is, the output layer has to make a prediction forthe frame that the first layer is about to see. Hence the mod-els have no access to the observation they must predict. Tosuccessfully solve this task, it may be helpful for the mod-els to learn to capture the underlying motion in the sceneso they can re-distribute pixels accordingly. We minimisethe following objective: 1

T

∑Tt=1 ||Mθ(x

[t]) − x[t+8]||2l2 .We compare Skip-Sideways against Sideways. The resultsof Skip-Sideways are significantly better than the equiva-lent model trained with Sideways (see additional qualitativeresults included in Figure 6) and it shows the benefit of in-tegrating temporal information through direct and shortcutconnections.Distributed setting. We experiment on K600 using twomulti-host setups, where we use either 8 or 16 hosts. Eachhost has 8 TPUs (Tensor Processing Units) amounting to 64

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TPUs in the first setup, and 128 in the second setup. We usethe second setup only for large batch-size experiments shownin Table 6, in the main paper. Unless we write otherwise, weuse batch-size 16 per host. Hence, the total batch-size is 128in the first setup and 256 in the second setup.

For VGG8, we put each layer of the network into a singleSkip-Sideways unit and stick all units to different devices.For VGG16, we group two consecutive layers into a singleSkip-Sideways unit and also stick all units to different devices.Note that VGG’s design is convenient for the experimentsas it has no shortcut connections and has roughly the samenumber of layers as the maximal number of devices (oneper device for VGG8 and two for VGG16) that we use todistribute Skip-Sideways units. In the distributed setup, weuse JAX [1] and Haiku [3].GPipe. We have adapted GPipe [4], another realisationof a distributed training by pipelining. Here, we use thesame breakdown of our models to different pipeline stages,e.g., two consecutive VGG16 layers are allocated to a singlepipeline stage and hence to a single device. Since the originalGPipe has been designed to work with non-temporal data,we have extended it to work with videos by creating batchesof frames as micro-batches, using the GPipe terminology. AsGPipe implements correct BP, it also has two phases, forwardand backward, with a parameters update that follows thaton each device separately. Figure 1 illustrates comparisonbetween GPipe and Skip-Sideways training in terms of deviceallocation.

In summary, in GPipe, (i) every micro-batch induces aforward and a backward computation on every device, (ii)activations on every device have to be kept alive until thebackwards pass, hence increasing memory pressure, (iii) un-less the number of micro-batches is sufficiently large thereexists a non-negligible pipeline ‘bubble’ effect, and (iv) la-tency, and hence the overall performance, varies as the resultof the moving ‘bubble’. By contrast, (i) we only pay the costof the backward computation (to simultaneously computeactivations and gradients), (ii) each device does not have tohold previous activations as we exploit temporal correlation,(iii) we induce no bubble, (iv) latency is the same for eachframe.

3. Models3D VGG and Causal 3D VGG. We ‘inflate’ [2] 2D VGGto 3D VGG and train it from scratch, following the I3Dmodel. That is, we extend spatial VGG16 [12] kernels toinclude temporal direction. We use 3×3×3 kernel shapes forconvolutions and max-pooling. Since Skip-Sideways trainingis real-time and hence causal, for a fair comparison, we havealso implemented Causal 3D VGG. We have observed aslightly better performance with kernels 3 × 3 × 3 over2× 3× 3 (from 63.7 to 64.2). For simiplicity, we illustratethe later variant in Figure 2a). We train all the models with

ADAM [6] and a cosine learning rate schedule.Full-Res network. As a proof-of-concept, we have imple-mented a network that maintains the input resolution throughall the layers. We have designed the architecture to be (i) con-ceptually simple, (ii) not reduce spatial dimensions, and (iii)be better at utilising hardware resources in a distributed set-ting. Even though it better utilises the distributed hardwareresources, its training is expensive with BP and using a sin-gle device. The network consists of a stack of convolutionalkernels with 3× 3 filters, and pooling layers with the samekernel shape (3×3). In all cases, we use striding one, so thatthere is no reduction in spatial dimensions. We use 64 chan-nels in the first two consecutive blocks, and next 32 channelsfor rest of the network except from the last layer that mapsback the latent space into 3 channels, which we interpretas RGB channels. We use Rectified Linear Units (ReLU)after each convolution, and hard hyperbolic tangent [10] inthe last layer. Each two consecutive convolutional layersare followed by a single pooling layer. We use eight suchblocks that we assign to different distributed devices withinthe Skip-Sideways units. We do not use a pooling layer afterthe last convolutional layer. We use batch-normalization justbefore ReLU. Figure 2b) illustrates the architecture showingall the blocks.

4. Speed and Memory

We show results on speed improvements and memorysavings.Space-to-depth. In all our experiments, we use space-to-depth transformation, which makes computations more TPU-friendly. More precisely, we first divide each frame into2-by-2 non-overlapping patches and then we align themalong the channel dimension. This transformation decreaseseach spatial dimension by two, and increases the channeldimension by four. Equivalently, it also increases the spatialreceptive field of convolutional neural networks two timesper spatial dimension and results in fewer but more costlyconvolutions (see Figure 4 in [14])1. Overall, however, space-to-depth transformation often speeds up training withoutaffecting the accuracy of the model, but this is hardwareand model specific. We also experiment with spacetime-to-depth transformation where we repeat the same procedurealso along the time dimension. It further speeds up thecomputations as shown in Table 1. For our experiments withSideways and Skip-Sideways, we keep a more pure setupwith only space-to-depth transformation. This is because wewant to explicitly model the temporal transitions through theSideways or Skip-Sideways temporal connections.Rematerialization. Rematerialization [8] is a method thatsaves memory at the cost of extra computation. That is,

1https://www.tensorflow.org/api_docs/python/tf/nn/space_to_depth

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stepssec Devices

Skip-Sideways + VGG16 2.3 1Skip-Sideways + VGG16 3.6 2Skip-Sideways + VGG16 7.2 8GPipe [4] + VGG16 4.2 8BP + 3D VGG16 1.9 1BP + 3D VGG16 (Remat) 1.5 1BP + Causal 3D VGG16 2.4 1BP + I3D [2] 2.9 1

BP + 3D VGG16 (Batch) 5.5 8BP + I3D (Batch) 6.5 8BP + I3D (Batch)∗ 7.9 8

Table 1: Speed comparisons of various training strategies andarchitectures in number of steps per second. Column devicesindicates the number of parallel devices used for distributedtraining. All models use K600, 32 frames, resolution 224×224, and batch-size 8. (Remat) denotes rematerialization [8].The last two rows are the exceptions and use batch-size 1per device. We use space-to-depth transformation. ∗ denotesspace-time-to-depth transformation.

the technique recomputes some intermediate activationsinstead of storing them in memory. Specifically, we use‘haiku.remat’ where we rematerialize each vgg-block con-sisting of two or three 3D CNNs.

5. Theoretical savings

Sideways and Skip-Sideways do not propagate gradientsback in time, only forward in time. This means that, incontrast to the traditional backpropagation, both mecha-nisms do not need to store activations over a long sequence.Therefore the memory cost is the same as the cost of do-ing backpropagation of per-frame models and is indepen-dent of the number of frames. Hence, as long as thememory savings are concerned, both mechanisms shouldscale up indefinitely with respect to the duration of thevideo. Moreover, in a distributed setting, if we do not countthe costs of inter-device communication, the overall speedshould be bounded only by the speed of the slowest de-vice. That is, if the network is a composition of D modulesMθ(x

[t]) = HD(·, θD)◦HD−1(·, θD−1)◦ . . .◦H1(x[t], θ1)

and each module Hj sits on the j-th device, the run-timeT ofMθ is T (Mθ) = maxj T (Hj). Notice that with reg-ular backprop the same runtime is the sum of runtimes ofindividual modules.

6. Stability

Our method assumes smoothness of the input signal. Inthis section, we investigate two settings that break that as-

sumption and see how those impact our training.Frame-rate. We run experiments on HMDB51 to inves-tigate the effect of hyperparameters (learning rate and in-put frame rate) on training stability for the proposed Skip-Sideways compared to the original Sideways [9]. Intuitively,the higher the learning rate or the lower the frame-rate,the more we depart from our initial assumptions about thesmoothness of the input or intermediate activations acrosstime steps, hence the less stable the training should be. Forframe-rate, we consider the values 30fps, 15fps, 7fps, 4fps.For learning rates, we use the values 1.0, 0.1, 0.01.

Figure 3 shows the behaviour when using different ini-tial learning rates and Figure 4 shows the behaviour whenvarying the input frame-rate.

In both figures, it can be observed that the proposed Skip-Sideways (on the right) has a more stable training comparedto Sideways. In particular, our Skip-Sideways is much morerobust w.r.t. frame-rate. We hypothesise that through short-cut and direct connections, the network can build smootherrepresentation, for instance, by interpolating between framesin the hidden space.Montage shots. We run experiments on HMDB51, wherewe create training sequences by assembling a new video fromtwo or more different clips, which we call montage shots.Here, we investigate two scenarios. In the first scenario, weassemble 32 frames videos by concatenating 16 frames fromone video and 16 frames from another video sampled fromthe same batch. Labels follow the same procedure. That is,the first 16 labels come from the first video, and the next16 labels come from the second video. We also experimentwith the concatenation of 3 video clips, each with 16 frames.Figure 5 shows the results. We can see a certain degree ofrobustness to cuts in a video clip. The more cuts, the worsethe performance of the method.

In the second scenario, we interleave frames from allvideos. That is, we use the 1st frame from the video 1, thenthe 1st frame from the video 2, then the 1st frame from thevideo 3, then the 2nd frame from the video 1, then the 2ndframe from the video 2, then the 2nd frame from the video3, and repeat that for a total of 48 frames, with 16 framesper clip. Note that the method, by design, is robust forinterleaving 2 video clips as there is no interference betweenneurons operating on consecutive frames (e.g., x[1] and x[2]

in Figure 1, in the main paper). We did not manage to trainthe network with Skip-Sideways in that setting.

In both experiments, we use per-frame losses with per-frame labels. All the results above indicate that our Skip-Sideways training is robust if the input is reasonably smooth.

7. Qualitative resultsWe provide further qualitative results for the future frame

prediction task. Here, we use higher frame resolution 224×224. Note that the same resolution is maintained over all the

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layers of our neural networks, from the input input towardsthe output. We compare Sideways with Skip-Sideways toshow the difference between both when the information isaggregated temporally. As noted in the main paper, usingFull-Res models is expensive for BP. This shows that wecan possibly use computationally or memory-wise moreexpensive models in video modelling. We show the resultsin Figure 6.

References[1] James Bradbury, Roy Frostig, Peter Hawkins, Matthew James

Johnson, Chris Leary, Dougal Maclaurin, George Necula,Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne,and Qiao Zhang. JAX: composable transformations ofPython+NumPy programs, 2018.

[2] João Carreira and Andrew Zisserman. Quo vadis, actionrecognition? a new model and the kinetics dataset. In Confer-ence on Computer Vision and Pattern Recognition (CVPR),2017.

[3] Tom Hennigan, Trevor Cai, Tamara Norman, and IgorBabuschkin. Haiku: Sonnet for JAX, 2020.

[4] Yanping Huang, Yonglong Cheng, Dehao Chen, HyoukJoongLee, Jiquan Ngiam, Quoc V. Le, and Zhifeng Chen. Gpipe:Efficient training of giant neural networks using pipelineparallelism. In Advances in Neural Information ProcessingSystems (NeurIPS), 2018.

[5] Longlong Jing and Yingli Tian. Self-supervised spatiotem-poral feature learning by video geometric transformations.arXiv preprint arXiv:1811.11387, 2018.

[6] Diederik Kingma and Jimmy Ba. Adam: A method forstochastic optimization. International Conference on Learn-ing Representations (ICLR), 12 2014.

[7] Hildegard Kuehne, Hueihan Jhuang, Estíbaliz Garrote,Tomaso Poggio, and Thomas Serre. Hmdb: a large videodatabase for human motion recognition. In Proceedings of theIEEE International Conference on Computer Vision (ICCV),2011.

[8] Ravi Kumar, Manish Purohit, Zoya Svitkina, Erik Vee,and Joshua Wang. Efficient rematerialization for deep net-works. Advances in Neural Information Processing Systems(NeurIPS), 2019.

[9] Mateusz Malinowski, Grzegorz Swirszcz, Joao Carreira, andViorica Patraucean. Sideways: Depth-parallel training ofvideo models. In Computer Vision and Pattern Recognition(CVPR), 2020.

[10] Chigozie Nwankpa, Winifred Ijomah, Anthony Gachagan,and Stephen Marshall. Activation functions: Comparisonof trends in practice and research for deep learning. arXivpreprint arXiv:1811.03378, 2018.

[11] Karen Simonyan and Andrew Zisserman. Two-stream con-volutional networks for action recognition in videos. In Ad-vances in Neural Information Processing Systems (NeurIPS),2014.

[12] Karen Simonyan and Andrew Zisserman. Very deep convo-lutional networks for large-scale image recognition. Inter-national Conference on Learning Representations (ICLR),2015.

[13] Khurram Soomro, Amir Roshan Zamir, and Mubarak Shah.Ucf101: A dataset of 101 human actions classes from videosin the wild. arXiv preprint arXiv:1212.0402, 2012.

[14] Longguang Wang, Yulan Guo, Zaiping Lin, Xinpu Deng,and Wei An. Learning for video super-resolution through hroptical flow estimation. In Asian Conference on ComputerVision (ACCV), 2018.

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BubbleDevice 0

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F 00

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F 01<latexit sha1_base64="C+79Spa5lrIWrDy1Uogh+ugj+Yo=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeiwK4rGCaQttLJvtpF262YTdjVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXpoJr47rfzsrq2vrGZmmrvL2zu7dfOThs6iRTDH2WiES1Q6pRcIm+4UZgO1VI41BgKxzdTP3WEyrNE/lgxikGMR1IHnFGjZX825736PYqVbfmzkCWiVeQKhRo9Cpf3X7CshilYYJq3fHc1AQ5VYYzgZNyN9OYUjaiA+xYKmmMOshnx07IqVX6JEqULWnITP09kdNY63Ec2s6YmqFe9Kbif14nM9FVkHOZZgYlmy+KMkFMQqafkz5XyIwYW0KZ4vZWwoZUUWZsPmUbgrf48jJpntc8t+bdX1Tr10UcJTiGEzgDDy6hDnfQAB8YcHiGV3hzpPPivDsf89YVp5g5gj9wPn8A4piOEA==</latexit><latexit sha1_base64="C+79Spa5lrIWrDy1Uogh+ugj+Yo=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeiwK4rGCaQttLJvtpF262YTdjVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXpoJr47rfzsrq2vrGZmmrvL2zu7dfOThs6iRTDH2WiES1Q6pRcIm+4UZgO1VI41BgKxzdTP3WEyrNE/lgxikGMR1IHnFGjZX825736PYqVbfmzkCWiVeQKhRo9Cpf3X7CshilYYJq3fHc1AQ5VYYzgZNyN9OYUjaiA+xYKmmMOshnx07IqVX6JEqULWnITP09kdNY63Ec2s6YmqFe9Kbif14nM9FVkHOZZgYlmy+KMkFMQqafkz5XyIwYW0KZ4vZWwoZUUWZsPmUbgrf48jJpntc8t+bdX1Tr10UcJTiGEzgDDy6hDnfQAB8YcHiGV3hzpPPivDsf89YVp5g5gj9wPn8A4piOEA==</latexit><latexit sha1_base64="C+79Spa5lrIWrDy1Uogh+ugj+Yo=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeiwK4rGCaQttLJvtpF262YTdjVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXpoJr47rfzsrq2vrGZmmrvL2zu7dfOThs6iRTDH2WiES1Q6pRcIm+4UZgO1VI41BgKxzdTP3WEyrNE/lgxikGMR1IHnFGjZX825736PYqVbfmzkCWiVeQKhRo9Cpf3X7CshilYYJq3fHc1AQ5VYYzgZNyN9OYUjaiA+xYKmmMOshnx07IqVX6JEqULWnITP09kdNY63Ec2s6YmqFe9Kbif14nM9FVkHOZZgYlmy+KMkFMQqafkz5XyIwYW0KZ4vZWwoZUUWZsPmUbgrf48jJpntc8t+bdX1Tr10UcJTiGEzgDDy6hDnfQAB8YcHiGV3hzpPPivDsf89YVp5g5gj9wPn8A4piOEA==</latexit><latexit sha1_base64="C+79Spa5lrIWrDy1Uogh+ugj+Yo=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeiwK4rGCaQttLJvtpF262YTdjVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXpoJr47rfzsrq2vrGZmmrvL2zu7dfOThs6iRTDH2WiES1Q6pRcIm+4UZgO1VI41BgKxzdTP3WEyrNE/lgxikGMR1IHnFGjZX825736PYqVbfmzkCWiVeQKhRo9Cpf3X7CshilYYJq3fHc1AQ5VYYzgZNyN9OYUjaiA+xYKmmMOshnx07IqVX6JEqULWnITP09kdNY63Ec2s6YmqFe9Kbif14nM9FVkHOZZgYlmy+KMkFMQqafkz5XyIwYW0KZ4vZWwoZUUWZsPmUbgrf48jJpntc8t+bdX1Tr10UcJTiGEzgDDy6hDnfQAB8YcHiGV3hzpPPivDsf89YVp5g5gj9wPn8A4piOEA==</latexit>

F 02<latexit sha1_base64="oFImhRYIktmK9V1BwhlcfDEwmhs=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7ZXe3R75Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqadaqnlv17i8q9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f5B6OEQ==</latexit><latexit sha1_base64="oFImhRYIktmK9V1BwhlcfDEwmhs=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7ZXe3R75Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqadaqnlv17i8q9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f5B6OEQ==</latexit><latexit sha1_base64="oFImhRYIktmK9V1BwhlcfDEwmhs=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7ZXe3R75Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqadaqnlv17i8q9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f5B6OEQ==</latexit><latexit sha1_base64="oFImhRYIktmK9V1BwhlcfDEwmhs=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7ZXe3R75Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqadaqnlv17i8q9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f5B6OEQ==</latexit>

F 10

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F 20

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B00

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B11<latexit sha1_base64="yqoyVoXvFrQuarDIoHRDBm4u78U=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMdSLx4r2A9o15JNs21sNlmSrFCW/gcvHhTx6v/x5r8x2/agrQ8GHu/NMDMvTAQ31ve/vcLa+sbmVnG7tLO7t39QPjxqGZVqyppUCaU7ITFMcMmallvBOolmJA4Fa4fjm9xvPzFtuJL3dpKwICZDySNOiXVSq97HD7jUL1f8qj8DWiV4QSqwQKNf/uoNFE1jJi0VxJgu9hMbZERbTgWblnqpYQmhYzJkXUcliZkJstm1U3TmlAGKlHYlLZqpvycyEhsziUPXGRM7MsteLv7ndVMbXQcZl0lqmaTzRVEqkFUofx0NuGbUiokjhGrubkV0RDSh1gWUh4CXX14lrYsq9qv47rJSqy/iKMIJnMI5YLiCGtxCA5pA4RGe4RXePOW9eO/ex7y14C1mjuEPvM8fE4COIQ==</latexit><latexit sha1_base64="yqoyVoXvFrQuarDIoHRDBm4u78U=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMdSLx4r2A9o15JNs21sNlmSrFCW/gcvHhTx6v/x5r8x2/agrQ8GHu/NMDMvTAQ31ve/vcLa+sbmVnG7tLO7t39QPjxqGZVqyppUCaU7ITFMcMmallvBOolmJA4Fa4fjm9xvPzFtuJL3dpKwICZDySNOiXVSq97HD7jUL1f8qj8DWiV4QSqwQKNf/uoNFE1jJi0VxJgu9hMbZERbTgWblnqpYQmhYzJkXUcliZkJstm1U3TmlAGKlHYlLZqpvycyEhsziUPXGRM7MsteLv7ndVMbXQcZl0lqmaTzRVEqkFUofx0NuGbUiokjhGrubkV0RDSh1gWUh4CXX14lrYsq9qv47rJSqy/iKMIJnMI5YLiCGtxCA5pA4RGe4RXePOW9eO/ex7y14C1mjuEPvM8fE4COIQ==</latexit><latexit sha1_base64="yqoyVoXvFrQuarDIoHRDBm4u78U=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMdSLx4r2A9o15JNs21sNlmSrFCW/gcvHhTx6v/x5r8x2/agrQ8GHu/NMDMvTAQ31ve/vcLa+sbmVnG7tLO7t39QPjxqGZVqyppUCaU7ITFMcMmallvBOolmJA4Fa4fjm9xvPzFtuJL3dpKwICZDySNOiXVSq97HD7jUL1f8qj8DWiV4QSqwQKNf/uoNFE1jJi0VxJgu9hMbZERbTgWblnqpYQmhYzJkXUcliZkJstm1U3TmlAGKlHYlLZqpvycyEhsziUPXGRM7MsteLv7ndVMbXQcZl0lqmaTzRVEqkFUofx0NuGbUiokjhGrubkV0RDSh1gWUh4CXX14lrYsq9qv47rJSqy/iKMIJnMI5YLiCGtxCA5pA4RGe4RXePOW9eO/ex7y14C1mjuEPvM8fE4COIQ==</latexit><latexit sha1_base64="yqoyVoXvFrQuarDIoHRDBm4u78U=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMdSLx4r2A9o15JNs21sNlmSrFCW/gcvHhTx6v/x5r8x2/agrQ8GHu/NMDMvTAQ31ve/vcLa+sbmVnG7tLO7t39QPjxqGZVqyppUCaU7ITFMcMmallvBOolmJA4Fa4fjm9xvPzFtuJL3dpKwICZDySNOiXVSq97HD7jUL1f8qj8DWiV4QSqwQKNf/uoNFE1jJi0VxJgu9hMbZERbTgWblnqpYQmhYzJkXUcliZkJstm1U3TmlAGKlHYlLZqpvycyEhsziUPXGRM7MsteLv7ndVMbXQcZl0lqmaTzRVEqkFUofx0NuGbUiokjhGrubkV0RDSh1gWUh4CXX14lrYsq9qv47rJSqy/iKMIJnMI5YLiCGtxCA5pA4RGe4RXePOW9eO/ex7y14C1mjuEPvM8fE4COIQ==</latexit>

B10

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B21<latexit sha1_base64="qWCHYYL1VljZax5St+FsGgAZMWI=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9ktQj2WevFYwX5Au5Zsmm1js8mSZIWy9D948aCIV/+PN/+N2XYP2vpg4PHeDDPzgpgzbVz32ylsbG5t7xR3S3v7B4dH5eOTjpaJIrRNJJeqF2BNORO0bZjhtBcriqOA024wvcn87hNVmklxb2Yx9SM8FixkBBsrdZpD76FWGpYrbtVdAK0TLycVyNEalr8GI0mSiApDONa677mx8VOsDCOczkuDRNMYkyke076lAkdU++ni2jm6sMoIhVLZEgYt1N8TKY60nkWB7YywmehVLxP/8/qJCa/9lIk4MVSQ5aIw4chIlL2ORkxRYvjMEkwUs7ciMsEKE2MDykLwVl9eJ51a1XOr3t1VpdHM4yjCGZzDJXhQhwbcQgvaQOARnuEV3hzpvDjvzseyteDkM6fwB87nDxUFjiI=</latexit><latexit sha1_base64="qWCHYYL1VljZax5St+FsGgAZMWI=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9ktQj2WevFYwX5Au5Zsmm1js8mSZIWy9D948aCIV/+PN/+N2XYP2vpg4PHeDDPzgpgzbVz32ylsbG5t7xR3S3v7B4dH5eOTjpaJIrRNJJeqF2BNORO0bZjhtBcriqOA024wvcn87hNVmklxb2Yx9SM8FixkBBsrdZpD76FWGpYrbtVdAK0TLycVyNEalr8GI0mSiApDONa677mx8VOsDCOczkuDRNMYkyke076lAkdU++ni2jm6sMoIhVLZEgYt1N8TKY60nkWB7YywmehVLxP/8/qJCa/9lIk4MVSQ5aIw4chIlL2ORkxRYvjMEkwUs7ciMsEKE2MDykLwVl9eJ51a1XOr3t1VpdHM4yjCGZzDJXhQhwbcQgvaQOARnuEV3hzpvDjvzseyteDkM6fwB87nDxUFjiI=</latexit><latexit sha1_base64="qWCHYYL1VljZax5St+FsGgAZMWI=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9ktQj2WevFYwX5Au5Zsmm1js8mSZIWy9D948aCIV/+PN/+N2XYP2vpg4PHeDDPzgpgzbVz32ylsbG5t7xR3S3v7B4dH5eOTjpaJIrRNJJeqF2BNORO0bZjhtBcriqOA024wvcn87hNVmklxb2Yx9SM8FixkBBsrdZpD76FWGpYrbtVdAK0TLycVyNEalr8GI0mSiApDONa677mx8VOsDCOczkuDRNMYkyke076lAkdU++ni2jm6sMoIhVLZEgYt1N8TKY60nkWB7YywmehVLxP/8/qJCa/9lIk4MVSQ5aIw4chIlL2ORkxRYvjMEkwUs7ciMsEKE2MDykLwVl9eJ51a1XOr3t1VpdHM4yjCGZzDJXhQhwbcQgvaQOARnuEV3hzpvDjvzseyteDkM6fwB87nDxUFjiI=</latexit><latexit sha1_base64="qWCHYYL1VljZax5St+FsGgAZMWI=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9ktQj2WevFYwX5Au5Zsmm1js8mSZIWy9D948aCIV/+PN/+N2XYP2vpg4PHeDDPzgpgzbVz32ylsbG5t7xR3S3v7B4dH5eOTjpaJIrRNJJeqF2BNORO0bZjhtBcriqOA024wvcn87hNVmklxb2Yx9SM8FixkBBsrdZpD76FWGpYrbtVdAK0TLycVyNEalr8GI0mSiApDONa677mx8VOsDCOczkuDRNMYkyke076lAkdU++ni2jm6sMoIhVLZEgYt1N8TKY60nkWB7YywmehVLxP/8/qJCa/9lIk4MVSQ5aIw4chIlL2ORkxRYvjMEkwUs7ciMsEKE2MDykLwVl9eJ51a1XOr3t1VpdHM4yjCGZzDJXhQhwbcQgvaQOARnuEV3hzpvDjvzseyteDkM6fwB87nDxUFjiI=</latexit>

B20

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F 30

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B30

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Device 0

Device 1

Device 2

F 00

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F 01<latexit sha1_base64="C+79Spa5lrIWrDy1Uogh+ugj+Yo=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeiwK4rGCaQttLJvtpF262YTdjVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXpoJr47rfzsrq2vrGZmmrvL2zu7dfOThs6iRTDH2WiES1Q6pRcIm+4UZgO1VI41BgKxzdTP3WEyrNE/lgxikGMR1IHnFGjZX825736PYqVbfmzkCWiVeQKhRo9Cpf3X7CshilYYJq3fHc1AQ5VYYzgZNyN9OYUjaiA+xYKmmMOshnx07IqVX6JEqULWnITP09kdNY63Ec2s6YmqFe9Kbif14nM9FVkHOZZgYlmy+KMkFMQqafkz5XyIwYW0KZ4vZWwoZUUWZsPmUbgrf48jJpntc8t+bdX1Tr10UcJTiGEzgDDy6hDnfQAB8YcHiGV3hzpPPivDsf89YVp5g5gj9wPn8A4piOEA==</latexit><latexit sha1_base64="C+79Spa5lrIWrDy1Uogh+ugj+Yo=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeiwK4rGCaQttLJvtpF262YTdjVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXpoJr47rfzsrq2vrGZmmrvL2zu7dfOThs6iRTDH2WiES1Q6pRcIm+4UZgO1VI41BgKxzdTP3WEyrNE/lgxikGMR1IHnFGjZX825736PYqVbfmzkCWiVeQKhRo9Cpf3X7CshilYYJq3fHc1AQ5VYYzgZNyN9OYUjaiA+xYKmmMOshnx07IqVX6JEqULWnITP09kdNY63Ec2s6YmqFe9Kbif14nM9FVkHOZZgYlmy+KMkFMQqafkz5XyIwYW0KZ4vZWwoZUUWZsPmUbgrf48jJpntc8t+bdX1Tr10UcJTiGEzgDDy6hDnfQAB8YcHiGV3hzpPPivDsf89YVp5g5gj9wPn8A4piOEA==</latexit><latexit sha1_base64="C+79Spa5lrIWrDy1Uogh+ugj+Yo=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeiwK4rGCaQttLJvtpF262YTdjVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXpoJr47rfzsrq2vrGZmmrvL2zu7dfOThs6iRTDH2WiES1Q6pRcIm+4UZgO1VI41BgKxzdTP3WEyrNE/lgxikGMR1IHnFGjZX825736PYqVbfmzkCWiVeQKhRo9Cpf3X7CshilYYJq3fHc1AQ5VYYzgZNyN9OYUjaiA+xYKmmMOshnx07IqVX6JEqULWnITP09kdNY63Ec2s6YmqFe9Kbif14nM9FVkHOZZgYlmy+KMkFMQqafkz5XyIwYW0KZ4vZWwoZUUWZsPmUbgrf48jJpntc8t+bdX1Tr10UcJTiGEzgDDy6hDnfQAB8YcHiGV3hzpPPivDsf89YVp5g5gj9wPn8A4piOEA==</latexit><latexit sha1_base64="C+79Spa5lrIWrDy1Uogh+ugj+Yo=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeiwK4rGCaQttLJvtpF262YTdjVBCf4MXD4p49Qd589+4bXPQ1gcDj/dmmJkXpoJr47rfzsrq2vrGZmmrvL2zu7dfOThs6iRTDH2WiES1Q6pRcIm+4UZgO1VI41BgKxzdTP3WEyrNE/lgxikGMR1IHnFGjZX825736PYqVbfmzkCWiVeQKhRo9Cpf3X7CshilYYJq3fHc1AQ5VYYzgZNyN9OYUjaiA+xYKmmMOshnx07IqVX6JEqULWnITP09kdNY63Ec2s6YmqFe9Kbif14nM9FVkHOZZgYlmy+KMkFMQqafkz5XyIwYW0KZ4vZWwoZUUWZsPmUbgrf48jJpntc8t+bdX1Tr10UcJTiGEzgDDy6hDnfQAB8YcHiGV3hzpPPivDsf89YVp5g5gj9wPn8A4piOEA==</latexit>

F 02<latexit sha1_base64="oFImhRYIktmK9V1BwhlcfDEwmhs=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7ZXe3R75Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqadaqnlv17i8q9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f5B6OEQ==</latexit><latexit sha1_base64="oFImhRYIktmK9V1BwhlcfDEwmhs=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7ZXe3R75Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqadaqnlv17i8q9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f5B6OEQ==</latexit><latexit sha1_base64="oFImhRYIktmK9V1BwhlcfDEwmhs=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7ZXe3R75Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqadaqnlv17i8q9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f5B6OEQ==</latexit><latexit sha1_base64="oFImhRYIktmK9V1BwhlcfDEwmhs=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7ZXe3R75Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqadaqnlv17i8q9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f5B6OEQ==</latexit>

F 10

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F 20

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F 30

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B0,21

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F 31<latexit sha1_base64="7JRZnXNRIV4BnujvgEfNaBx2Dao=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GNREI8VTFtoY9lsp+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dgorq2vrG8XN0tb2zu5eef+goeNUMfRZLGLVCqlGwSX6hhuBrUQhjUKBzXB0M/WbT6g0j+WDGScYRHQgeZ8zaqzk33a9x/NuueJW3RnIMvFyUoEc9W75q9OLWRqhNExQrduem5ggo8pwJnBS6qQaE8pGdIBtSyWNUAfZ7NgJObFKj/RjZUsaMlN/T2Q00nochbYzomaoF72p+J/XTk3/Ksi4TFKDks0X9VNBTEymn5MeV8iMGFtCmeL2VsKGVFFmbD4lG4K3+PIyaZxVPbfq3V9Uatd5HEU4gmM4BQ8uoQZ3UAcfGHB4hld4c6Tz4rw7H/PWgpPPHMIfOJ8/5ySOEw==</latexit><latexit sha1_base64="7JRZnXNRIV4BnujvgEfNaBx2Dao=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GNREI8VTFtoY9lsp+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dgorq2vrG8XN0tb2zu5eef+goeNUMfRZLGLVCqlGwSX6hhuBrUQhjUKBzXB0M/WbT6g0j+WDGScYRHQgeZ8zaqzk33a9x/NuueJW3RnIMvFyUoEc9W75q9OLWRqhNExQrduem5ggo8pwJnBS6qQaE8pGdIBtSyWNUAfZ7NgJObFKj/RjZUsaMlN/T2Q00nochbYzomaoF72p+J/XTk3/Ksi4TFKDks0X9VNBTEymn5MeV8iMGFtCmeL2VsKGVFFmbD4lG4K3+PIyaZxVPbfq3V9Uatd5HEU4gmM4BQ8uoQZ3UAcfGHB4hld4c6Tz4rw7H/PWgpPPHMIfOJ8/5ySOEw==</latexit><latexit sha1_base64="7JRZnXNRIV4BnujvgEfNaBx2Dao=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GNREI8VTFtoY9lsp+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dgorq2vrG8XN0tb2zu5eef+goeNUMfRZLGLVCqlGwSX6hhuBrUQhjUKBzXB0M/WbT6g0j+WDGScYRHQgeZ8zaqzk33a9x/NuueJW3RnIMvFyUoEc9W75q9OLWRqhNExQrduem5ggo8pwJnBS6qQaE8pGdIBtSyWNUAfZ7NgJObFKj/RjZUsaMlN/T2Q00nochbYzomaoF72p+J/XTk3/Ksi4TFKDks0X9VNBTEymn5MeV8iMGFtCmeL2VsKGVFFmbD4lG4K3+PIyaZxVPbfq3V9Uatd5HEU4gmM4BQ8uoQZ3UAcfGHB4hld4c6Tz4rw7H/PWgpPPHMIfOJ8/5ySOEw==</latexit><latexit sha1_base64="7JRZnXNRIV4BnujvgEfNaBx2Dao=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GNREI8VTFtoY9lsp+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dgorq2vrG8XN0tb2zu5eef+goeNUMfRZLGLVCqlGwSX6hhuBrUQhjUKBzXB0M/WbT6g0j+WDGScYRHQgeZ8zaqzk33a9x/NuueJW3RnIMvFyUoEc9W75q9OLWRqhNExQrduem5ggo8pwJnBS6qQaE8pGdIBtSyWNUAfZ7NgJObFKj/RjZUsaMlN/T2Q00nochbYzomaoF72p+J/XTk3/Ksi4TFKDks0X9VNBTEymn5MeV8iMGFtCmeL2VsKGVFFmbD4lG4K3+PIyaZxVPbfq3V9Uatd5HEU4gmM4BQ8uoQZ3UAcfGHB4hld4c6Tz4rw7H/PWgpPPHMIfOJ8/5ySOEw==</latexit>

F 40

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B0,2,40

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F 22<latexit sha1_base64="S6kDq/Xo3U34a1mH3Tkm/yMW2z0=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZTtqlm03Y3Qil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSq4Nq777RTW1jc2t4rbpZ3dvf2D8uFRUyeZYuizRCSqHVKNgkv0DTcC26lCGocCW+HoZua3nlBpnsgHM04xiOlA8ogzaqzk3/Zqj7VeueJW3TnIKvFyUoEcjV75q9tPWBajNExQrTuem5pgQpXhTOC01M00ppSN6AA7lkoaow4m82On5MwqfRIlypY0ZK7+npjQWOtxHNrOmJqhXvZm4n9eJzPRVTDhMs0MSrZYFGWCmITMPid9rpAZMbaEMsXtrYQNqaLM2HxKNgRv+eVV0qxVPbfq3V9U6td5HEU4gVM4Bw8uoQ530AAfGHB4hld4c6Tz4rw7H4vWgpPPHMMfOJ8/5yaOEw==</latexit><latexit sha1_base64="S6kDq/Xo3U34a1mH3Tkm/yMW2z0=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZTtqlm03Y3Qil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSq4Nq777RTW1jc2t4rbpZ3dvf2D8uFRUyeZYuizRCSqHVKNgkv0DTcC26lCGocCW+HoZua3nlBpnsgHM04xiOlA8ogzaqzk3/Zqj7VeueJW3TnIKvFyUoEcjV75q9tPWBajNExQrTuem5pgQpXhTOC01M00ppSN6AA7lkoaow4m82On5MwqfRIlypY0ZK7+npjQWOtxHNrOmJqhXvZm4n9eJzPRVTDhMs0MSrZYFGWCmITMPid9rpAZMbaEMsXtrYQNqaLM2HxKNgRv+eVV0qxVPbfq3V9U6td5HEU4gVM4Bw8uoQ530AAfGHB4hld4c6Tz4rw7H4vWgpPPHMMfOJ8/5yaOEw==</latexit><latexit sha1_base64="S6kDq/Xo3U34a1mH3Tkm/yMW2z0=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZTtqlm03Y3Qil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSq4Nq777RTW1jc2t4rbpZ3dvf2D8uFRUyeZYuizRCSqHVKNgkv0DTcC26lCGocCW+HoZua3nlBpnsgHM04xiOlA8ogzaqzk3/Zqj7VeueJW3TnIKvFyUoEcjV75q9tPWBajNExQrTuem5pgQpXhTOC01M00ppSN6AA7lkoaow4m82On5MwqfRIlypY0ZK7+npjQWOtxHNrOmJqhXvZm4n9eJzPRVTDhMs0MSrZYFGWCmITMPid9rpAZMbaEMsXtrYQNqaLM2HxKNgRv+eVV0qxVPbfq3V9U6td5HEU4gVM4Bw8uoQ530AAfGHB4hld4c6Tz4rw7H4vWgpPPHMMfOJ8/5yaOEw==</latexit><latexit sha1_base64="S6kDq/Xo3U34a1mH3Tkm/yMW2z0=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoMeiIB4rmLbQxrLZTtqlm03Y3Qil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSq4Nq777RTW1jc2t4rbpZ3dvf2D8uFRUyeZYuizRCSqHVKNgkv0DTcC26lCGocCW+HoZua3nlBpnsgHM04xiOlA8ogzaqzk3/Zqj7VeueJW3TnIKvFyUoEcjV75q9tPWBajNExQrTuem5pgQpXhTOC01M00ppSN6AA7lkoaow4m82On5MwqfRIlypY0ZK7+npjQWOtxHNrOmJqhXvZm4n9eJzPRVTDhMs0MSrZYFGWCmITMPid9rpAZMbaEMsXtrYQNqaLM2HxKNgRv+eVV0qxVPbfq3V9U6td5HEU4gVM4Bw8uoQ530AAfGHB4hld4c6Tz4rw7H4vWgpPPHMMfOJ8/5yaOEw==</latexit>

B1,31

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F 41<latexit sha1_base64="aGtd5lCi23BO91AmL8wIQReazHk=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7bnPdZ65Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqaV5UPbfq3dcq9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f6KiOFA==</latexit><latexit sha1_base64="aGtd5lCi23BO91AmL8wIQReazHk=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7bnPdZ65Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqaV5UPbfq3dcq9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f6KiOFA==</latexit><latexit sha1_base64="aGtd5lCi23BO91AmL8wIQReazHk=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7bnPdZ65Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqaV5UPbfq3dcq9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f6KiOFA==</latexit><latexit sha1_base64="aGtd5lCi23BO91AmL8wIQReazHk=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoMeiIB4rmLbQxrLZbtqlm03YnQil9Dd48aCIV3+QN/+N2zYHbX0w8Hhvhpl5YSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoaZJMM+6zRCa6HVLDpVDcR4GSt1PNaRxK3gpHNzO/9cS1EYl6wHHKg5gOlIgEo2gl/7bnPdZ65Ypbdecgq8TLSQVyNHrlr24/YVnMFTJJjel4borBhGoUTPJpqZsZnlI2ogPesVTRmJtgMj92Ss6s0idRom0pJHP198SExsaM49B2xhSHZtmbif95nQyjq2AiVJohV2yxKMokwYTMPid9oTlDObaEMi3srYQNqaYMbT4lG4K3/PIqaV5UPbfq3dcq9es8jiKcwCmcgweXUIc7aIAPDAQ8wyu8Ocp5cd6dj0VrwclnjuEPnM8f6KiOFA==</latexit>

B1,3,50

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F 50

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F 42<latexit sha1_base64="ktgEaDnVB/aTABOcc7llHBypm44=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4Kkkp6LEoiMcKpi20sWy2k3bpZhN2N0Ip/Q1ePCji1R/kzX/jts1BWx8MPN6bYWZemAqujet+O2vrG5tb24Wd4u7e/sFh6ei4qZNMMfRZIhLVDqlGwSX6hhuB7VQhjUOBrXB0M/NbT6g0T+SDGacYxHQgecQZNVbyb3vVx1qvVHYr7hxklXg5KUOORq/01e0nLItRGiao1h3PTU0wocpwJnBa7GYaU8pGdIAdSyWNUQeT+bFTcm6VPokSZUsaMld/T0xorPU4Dm1nTM1QL3sz8T+vk5noKphwmWYGJVssijJBTEJmn5M+V8iMGFtCmeL2VsKGVFFmbD5FG4K3/PIqaVYrnlvx7mvl+nUeRwFO4QwuwINLqMMdNMAHBhye4RXeHOm8OO/Ox6J1zclnTuAPnM8f6i6OFQ==</latexit><latexit sha1_base64="ktgEaDnVB/aTABOcc7llHBypm44=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4Kkkp6LEoiMcKpi20sWy2k3bpZhN2N0Ip/Q1ePCji1R/kzX/jts1BWx8MPN6bYWZemAqujet+O2vrG5tb24Wd4u7e/sFh6ei4qZNMMfRZIhLVDqlGwSX6hhuB7VQhjUOBrXB0M/NbT6g0T+SDGacYxHQgecQZNVbyb3vVx1qvVHYr7hxklXg5KUOORq/01e0nLItRGiao1h3PTU0wocpwJnBa7GYaU8pGdIAdSyWNUQeT+bFTcm6VPokSZUsaMld/T0xorPU4Dm1nTM1QL3sz8T+vk5noKphwmWYGJVssijJBTEJmn5M+V8iMGFtCmeL2VsKGVFFmbD5FG4K3/PIqaVYrnlvx7mvl+nUeRwFO4QwuwINLqMMdNMAHBhye4RXeHOm8OO/Ox6J1zclnTuAPnM8f6i6OFQ==</latexit><latexit sha1_base64="ktgEaDnVB/aTABOcc7llHBypm44=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4Kkkp6LEoiMcKpi20sWy2k3bpZhN2N0Ip/Q1ePCji1R/kzX/jts1BWx8MPN6bYWZemAqujet+O2vrG5tb24Wd4u7e/sFh6ei4qZNMMfRZIhLVDqlGwSX6hhuB7VQhjUOBrXB0M/NbT6g0T+SDGacYxHQgecQZNVbyb3vVx1qvVHYr7hxklXg5KUOORq/01e0nLItRGiao1h3PTU0wocpwJnBa7GYaU8pGdIAdSyWNUQeT+bFTcm6VPokSZUsaMld/T0xorPU4Dm1nTM1QL3sz8T+vk5noKphwmWYGJVssijJBTEJmn5M+V8iMGFtCmeL2VsKGVFFmbD5FG4K3/PIqaVYrnlvx7mvl+nUeRwFO4QwuwINLqMMdNMAHBhye4RXeHOm8OO/Ox6J1zclnTuAPnM8f6i6OFQ==</latexit><latexit sha1_base64="ktgEaDnVB/aTABOcc7llHBypm44=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4Kkkp6LEoiMcKpi20sWy2k3bpZhN2N0Ip/Q1ePCji1R/kzX/jts1BWx8MPN6bYWZemAqujet+O2vrG5tb24Wd4u7e/sFh6ei4qZNMMfRZIhLVDqlGwSX6hhuB7VQhjUOBrXB0M/NbT6g0T+SDGacYxHQgecQZNVbyb3vVx1qvVHYr7hxklXg5KUOORq/01e0nLItRGiao1h3PTU0wocpwJnBa7GYaU8pGdIAdSyWNUQeT+bFTcm6VPokSZUsaMld/T0xorPU4Dm1nTM1QL3sz8T+vk5noKphwmWYGJVssijJBTEJmn5M+V8iMGFtCmeL2VsKGVFFmbD5FG4K3/PIqaVYrnlvx7mvl+nUeRwFO4QwuwINLqMMdNMAHBhye4RXeHOm8OO/Ox6J1zclnTuAPnM8f6i6OFQ==</latexit>

F 60

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F 70

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F 61<latexit sha1_base64="/Sdo7QJ9FdDytPPynyy11GLUSkY=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE1GNREI8VTFtoY9lsp+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dgorq2vrG8XN0tb2zu5eef+goeNUMfRZLGLVCqlGwSX6hhuBrUQhjUKBzXB0M/WbT6g0j+WDGScYRHQgeZ8zaqzk3z5edL1uueJW3RnIMvFyUoEc9W75q9OLWRqhNExQrduem5ggo8pwJnBS6qQaE8pGdIBtSyWNUAfZ7NgJObFKj/RjZUsaMlN/T2Q00nochbYzomaoF72p+J/XTk3/Ksi4TFKDks0X9VNBTEymn5MeV8iMGFtCmeL2VsKGVFFmbD4lG4K3+PIyaZxVPbfq3Z9Xatd5HEU4gmM4BQ8uoQZ3UAcfGHB4hld4c6Tz4rw7H/PWgpPPHMIfOJ8/67iOFg==</latexit><latexit sha1_base64="/Sdo7QJ9FdDytPPynyy11GLUSkY=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE1GNREI8VTFtoY9lsp+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dgorq2vrG8XN0tb2zu5eef+goeNUMfRZLGLVCqlGwSX6hhuBrUQhjUKBzXB0M/WbT6g0j+WDGScYRHQgeZ8zaqzk3z5edL1uueJW3RnIMvFyUoEc9W75q9OLWRqhNExQrduem5ggo8pwJnBS6qQaE8pGdIBtSyWNUAfZ7NgJObFKj/RjZUsaMlN/T2Q00nochbYzomaoF72p+J/XTk3/Ksi4TFKDks0X9VNBTEymn5MeV8iMGFtCmeL2VsKGVFFmbD4lG4K3+PIyaZxVPbfq3Z9Xatd5HEU4gmM4BQ8uoQZ3UAcfGHB4hld4c6Tz4rw7H/PWgpPPHMIfOJ8/67iOFg==</latexit><latexit sha1_base64="/Sdo7QJ9FdDytPPynyy11GLUSkY=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE1GNREI8VTFtoY9lsp+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dgorq2vrG8XN0tb2zu5eef+goeNUMfRZLGLVCqlGwSX6hhuBrUQhjUKBzXB0M/WbT6g0j+WDGScYRHQgeZ8zaqzk3z5edL1uueJW3RnIMvFyUoEc9W75q9OLWRqhNExQrduem5ggo8pwJnBS6qQaE8pGdIBtSyWNUAfZ7NgJObFKj/RjZUsaMlN/T2Q00nochbYzomaoF72p+J/XTk3/Ksi4TFKDks0X9VNBTEymn5MeV8iMGFtCmeL2VsKGVFFmbD4lG4K3+PIyaZxVPbfq3Z9Xatd5HEU4gmM4BQ8uoQZ3UAcfGHB4hld4c6Tz4rw7H/PWgpPPHMIfOJ8/67iOFg==</latexit><latexit sha1_base64="/Sdo7QJ9FdDytPPynyy11GLUSkY=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE1GNREI8VTFtoY9lsp+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dgorq2vrG8XN0tb2zu5eef+goeNUMfRZLGLVCqlGwSX6hhuBrUQhjUKBzXB0M/WbT6g0j+WDGScYRHQgeZ8zaqzk3z5edL1uueJW3RnIMvFyUoEc9W75q9OLWRqhNExQrduem5ggo8pwJnBS6qQaE8pGdIBtSyWNUAfZ7NgJObFKj/RjZUsaMlN/T2Q00nochbYzomaoF72p+J/XTk3/Ksi4TFKDks0X9VNBTEymn5MeV8iMGFtCmeL2VsKGVFFmbD4lG4K3+PIyaZxVPbfq3Z9Xatd5HEU4gmM4BQ8uoQZ3UAcfGHB4hld4c6Tz4rw7H/PWgpPPHMIfOJ8/67iOFg==</latexit>

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B2,41

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B3,51

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B2,4,60

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B3,5,70

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Figure 1: We show our adaptation of GPipe [4] to video modelling (left) and compare it with Sideways [9] and our Skip-Sideways (right). We only show the device placement during the forward pass (F ) and backward pass (B). Because of that, weignore shortcut connections in Skip-Sideways in this illustration. Here, we consider three distributed devices. F tk denotes thatactivations computed in the forward pass from the t-th input frame are placed on the k-th device. We use similar notation forgradients during the backward pass, i.e., Blk. For Sideways and Skip-Sideways, we use Bl1,l2k to denote that the gradient wasobtained from the incoming gradient computed based on the l1-th input frame and Jacobian based on the l2-th input frame. Weextend this notation to Bl1,l2,l3k that denotes the gradient Bl1,l2k+1 is combined with Jacobian computed based on the l3-th inputframe on the k-th device. For the sake of clarity, we only show four input frames for GPipe. However, we can see that in thesame number of twelve computation steps, Skip-Sideways can process more input frames and does not induce the ‘bubble’.The vertical axis denote different devices and horizontal axis computation time.

Input Time

Dep

th

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a) Causal 3D VGG. b) Full-Res.

Figure 2: Our two baseline architectures. Causal 3D VGG and Full-Res. Note that, contrary to the Figure 1 in the main paper,here we only show the connectivity of the architecture, and not the flow of pseudo-gradients nor activations. Moreover, thetime in the figure refers to input data frames – not the computation time.

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Figure 3: Robustness on the training fold with respect to the choice of the initial learning rate for Sideways (left) and ourSkip-Sideways (right). Red, green and blue denote the initial learning rate as 0.01, 0.1, 1.0. Solid curves depict the mean andshaded areas show variance across various input frame-rates.

Figure 4: Robustness on the training fold with respect to the choice of the input frame-rate for Sideways (left) and ourSkip-Sideways (right). Red, olive, green and violet denote the input frame-rate as 30, 15, 7, 4 respectively. Solid curves depictthe mean and shaded areas show variance across various input initial learning rates.

Figure 5: Robustness of Skip-Sideways on the montage experiments where we concatenate two (left) or three (right) videoclips into a larger video. Red, green and blue denote the initial learning rate as 0.0001, 0.001, 0.01. We can see that in generalmore video cuts hurt the performance. Sometimes the learning collapses for larger learning rates.

Page 7: Gradient Forward-Propagation for Large-Scale Temporal Video … · 2021. 6. 24. · BP + 3D VGG16 1:9 1 BP + 3D VGG16 (Remat) 1:5 1 BP + Causal 3D VGG16 2:4 1 BP + I3D [2] 2:9 1 BP

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Figure 6: Qualitative results for two video sequences from the validation fold of Kinetics600, where the models need togenerate the frame at step t+ 8 into the future given frames up to t. From top to bottom: input frames, ground-truth outputframes, predictions of Full-Res trained with Sideways, predictions of Full-Res trained with Skip-Sideways. We can observethat the predictions of the model trained with Sideways are blurry and semantically similar to inputs, indicating that the modellags behind. On the contrary, the predictions of the model trained with Skip-Sideways are sharper and semantically closer tothe ground-truth output frames. We use resolution 224× 224.