Datasets:

zai-org
/

RPC-Bench

+# EFFICIENT CONVOLUTIONAL NEURAL NETWORKTRAINING WITH DIRECT FEEDBACK ALIGNMENT
+Anonymous authors Paper under double-blind review
+# ABSTRACT
+There were many algorithms to substitute the back-propagation (BP) in the deep neural network (DNN) training. However, they could not become popular because their training accuracy and the computational efficiency were worse than BP. One of them was direct feedback alignment (DFA), but it showed low training performance especially for the convolutional neural network (CNN). In this paper, we overcome the limitation of the DFA algorithm by combining with the conventional BP during the CNN training. To improve the training stability, we also suggest the feedback weight initialization method by analyzing the patterns of the fixed random matrices in the DFA. Finally, we propose the new training algorithm, binary direct feedback alignment (BDFA) to minimize the computational cost while maintaining the training accuracy compared with the DFA. In our experiments, we use the CIFAR-10 and CIFAR-100 dataset to simulate the CNN learning from the scratch and apply the BDFA to the online learning based object tracking application to examine the training in the small dataset environment. Our proposed algorithms show better performance than conventional BP in both two different training tasks especially when the dataset is small.
+# 1 INTRODUCTION
+Deep learning becomes the core of the machine learning and it has been utilized for many applications such as machine translation (Singh et al. (2017)), speech recognition (Wang et al. (2017)), and object classification (Rawat & Wang (2017)). Training the deep neural network (DNN) is an important portion of the deep learning because we need different pre-trained models to cover the various deep learning tasks. One well-known method of DNN training is the algorithm called backpropagation (BP) (Rumelhart et al. (1986)). The BP is the gradient descent based training method which follows the steepest gradient to find the optimum weights. Therefore, BP based training can be applied to any DNN configurations if the network consists of any differentiable operations. For instance, not only multi-layer perceptron (MLP) but also both convolutional neural network (CNN, LeCun et al. (1998)) and recurrent neural network (RNN, Hopfield (1982)) can be trained by using the BP.
+Even though the BP shows the outstanding performance in DNN training, BP based training suffers from the overfitting problem. Since the BP easily sinks into a local minimum, we need a large scale of the dataset to avoid the overfitting. In addition, we use various data augmentation techniques such as flipping and cropping. If the DNN training is done in the limited resources and dataset, BP based DNN training is too slow to be converged and shows low accuracy. One example is MDNet (Nam & Han (2016)) which introduces an object tracking algorithm with the online learning concept. Realtime implementation is an important issue in object tracking, so it has the limitation to utilize various data augmentation and large dataset for online learning.
+To break the BP based DNN training paradigm, a lot of new training methods have been developed. Salimans et al. (2017) proposed the evolution strategy which searches various weight without the gradient descent. It has a chance to be computed in parallel, but it needs a lot of seeds to find the global optimal solution. Moreover, evolution strategy has a slow convergence problem which can be an obstacle for fast online learning application. Another algorithm, feedback alignment (FA, Lillicrap et al. (2014)), was proposed based on the gradient descent methodology, but without following the steepest gradient. The FA pre-defines a feedback weight before starting the training, and the weight is determined by the random values.1 It is also known to converge slowly, and shows worse performance compared with the previous BP.
+Direct feedback alignment (DFA, Nokland (2016)) was developed by getting the idea from the FA. Although the FA propagates errors from the last layer back to the first layer step-by-step, the DFA propagates errors from the last layer directly to each layer. This approach gives the opportunity of the parallel processing. Since the errors of every layer are generated independently in DFA, we can immediately calculate each layer’s gradient if the DNN inference is finished. Moreover, the number of required computation is reduced in the DFA. This is because the number of neurons in the last layer is usually fewer than the prior layer, so the size of the feedback weight becomes smaller than the BP. In spite of these advantages, the DFA suffers from accuracy degradation problem. The accuracy degradation problem becomes more serious when the DFA is applied to the CNN case. It is known that the DNN is not learnable with the DFA if the DNN becomes much deeper than AlexNet (Krizhevsky et al. (2012)).
+In this paper, we explain the new DFA algorithm to improve the training accuracy in CNN, and suggest a feedback weight initialization method for the fast convergence. Moreover, we propose the binary direct feedback alignment (BDFA) to maximize the computational efficiency. We verified the training performance in the VGG-16 (Simonyan & Zisserman (2015)) without any data augmentation, and DFA shows higher accuracy compared with the BP. And then, the training with small dataset was proved through the online learning based object tracking application. Our proposed algorithm shows better performance than the conventional BP approach in both the learning from the scratch and the object tracking tasks.
+The remaining part of the paper is organized as follows. The mathematical notation of the BP, FA, and DFA will be introduced in Section 2. Then, the details of the proposed algorithms will be explained in Section 3. The experiment will be followed in Section 4 and the paper will be concluded in Section 5.
+# 2 PRELIMINARIES
+# 2.1 BACK-PROPAGATION
+Back-propagation is a general algorithm for the DNN training, suggested by Rumelhart et al. (1986). Let $\mathbf { o } _ { i }$ be the $i ^ { t h }$ layer’s feature map, when $W _ { i + 1 , i }$ be the weight and bias between the $i ^ { t h }$ layer and the $i + 1 ^ { t h }$ layer. If the activation function is represented as $f ( \cdot )$ , and $L$ is the total number of layers, the feature map of the $i + 1 ^ { t h }$ layer can be calculated as
+$$
+i _ { i + 1 } = W _ { i + 1 , i } \ o _ { i } , \quad o _ { i + 1 } = f ( i _ { i + 1 } ) , \quad i \in \{ 0 , 1 , \ldots , L - 1 \}
+$$
+Various activation functions such as sigmoid, tanh, and ReLU (Nair & Hinton (2010)) can be one of candidates of the $f ( \cdot )$ . Some DNNs such as generative adversarial networks (Goodfellow et al. (2014)) use more advanced activation functions like Leaky ReLU and PReLU $\mathrm { \Delta X u }$ et al. (2015)). Once the inference is over, the inference result is compared with the pre-defined labels, and the error map $e _ { L }$ is calculated by a loss function such as cross-entropy. The error is propagated gradually from the last layer to the first layer, and the $i ^ { t h }$ layer’s error map can be calculated as
+$$
+\pmb { e } _ { i } = ( W _ { i + 1 , i } ^ { T } \pmb { e } _ { i + 1 } ) \odot f ^ { \prime } ( i _ { i + 1 } ) , \quad i \in \{ 1 , 2 , . . . , L - 1 \}
+$$
+where $\odot$ is an element-wise multiplication operator and $f ^ { \prime } ( )$ is the derivative of the non-linear function. We need the transposed weight matrix, $W _ { i + 1 , i } ^ { T }$ , to propagate the errors in MLP case. After the BP, the gradient of each layer is computed by using both the $i ^ { t h }$ layer’s feature map and $i + 1 ^ { t h }$ layer’s error map. The $i ^ { t h }$ layer’s gradient, $G _ { i }$ is calculated as following.
+$$
+G _ { i , b } = e _ { i + 1 } \ o _ { i } ^ { T } , \quad i \in \{ 0 , 1 , \ldots , L - 1 \} , \quad b \in \{ 0 , 1 , \ldots , B \}
+$$
+$$
+\pmb { G } _ { i } = \frac { 1 } { B } \sum _ { b } \pmb { G } _ { i , b } , \quad \pmb { W } _ { i + 1 , i } ^ { \prime } = \pmb { W } _ { i + 1 , i } - \eta \ \pmb { G } _ { i }
+$$
+If we use the mini-batch gradient descent with the batch size $B$ , total $B$ gradients, $G _ { i , b }$ are averaged and get the $G _ { i }$ . $G _ { i }$ is used to update the $W _ { i + 1 , i }$ by multiplying learning rate, $\eta$ . In the CNN case, the matrix multiplication operations in every step described in MLP is substituted with the convolution operations. One more different thing is that it uses $1 8 0 ^ { \circ }$ flipped kernel instead of the transposed weight used in the BP. Other operations are as same as in the MLP case.
+# 2.2 FEEDBACK ALIGNMENT
+Feedback alignment (FA) which was introduced by Lillicrap et al. (2016) substituted the transposed weight with the fixed random matrix in error propagation operation. In other words, they pre-defined the feedback weight which has the same size as the transposed weight, but the values of the feedback weight are determined randomly. Although the weights used in the training are updated for every iteration, the pre-defined random matrix is maintained until the training is finished. Let $R _ { i + 1 , i }$ be the feedback weight of the $i ^ { t h }$ layer, the propagated error in the FA is calculated as
+$$
+e _ { i } = ( R _ { i + 1 , i } ^ { T } ~ e _ { i + 1 } ) \odot f ^ { \prime } ( i _ { i + 1 } )
+$$
+, and the other procedures such as gradient generation and weight updating are same as BP does.
+# 2.3 DIRECT FEEDBACK ALIGNMENT
+Even though, both the BP and the FA propagate errors from the last layer to the first layer in order, the DFA (Nokland (2016)) directly propagates errors from the last layer to other layers. If the number of neurons in the last layer and the $\bar { i } ^ { t h }$ layer, are represented by $N _ { L }$ and $N _ { i }$ respectively, the size of the feedback weight is determined as $N _ { i } \times N _ { L }$ . Let, $i ^ { t h }$ layer’s feedback weight in the DFA be $D _ { i } ^ { T }$ , then the error is calculated as
+$$
+\pmb { e } _ { i } = ( D _ { i } ^ { T } \pmb { e } _ { L } ) \odot f ^ { \prime } ( \pmb { i } _ { i + 1 } )
+$$
+One of the interesting characteristics is that there is no data dependency between different errors because the DFA propagates the errors directly from the last layer. This characteristic gives the opportunity of parallel processing in the DFA based error propagation operation.
+Compared with the BP, DFA showed similar training performance for the multi-layer perceptron (MLP) structure. Moreover, DFA requires fewer computations because $N _ { L }$ is generally smaller than the number of neurons in the intermediate layers. However, the DFA dramatically degrades the accuracy when it applied in the CNN training as shown in Figure 1. Furthermore, the elements of the intermediate feature map are all connected with the last layer neurons, so it requires much more computations compared with BP based CNN training. In summary, the DFA’s computational efficiency can be induced in the MLP training, but not in the CNN.
+# 3 OUR APPROACH
+As mentioned in Section 2, the DFA is efficient for MLP training, because it can be computed in parallel without accuracy degradation. However, this advantage is diminished when the DFA is applied in the CNN. To solve this problem, we propose the new training method to make the DFA applied to the CNN. In addition, the initialization method of the feedback weight is suggested for the fast and stable learning curve. At last, we propose the advanced training algorithm, binary direct feedback alignment (BDFA), which shows high computing efficiency and robust training performance in various conditions.
+![](images/a5ad26d059c99378a4fd14d3a6c18d5419391e11c682cdad631dba4f46028885.jpg)
+Figure 1: BP (Black) vs Conventional DFA (Read) for CNN Training (Tested in CIFAR-10)
+# 3.1 CDFA: CNN TRAINING BY COMBINING BOTH BP AND DFA
+Generally, CNN consists of the convolutional layers and fully-connected (FC) layers. The two different kinds of layers have different roles. For example in object classification, convolutional layers are considered as the feature extractor by using the characteristics of the convolution computation. In contrast, FC layers receive the result of the feature extractor and judge what the object is. However, in the initial iterations of the BP based CNN training, training the convolutional layers can be ambiguous because the FC layers cannot be considered as a good object classifier. During some iterations of BP, the weight of the FC layers will be changed and the convolutional layers should be adaptive to the changed FC layers. In other words, convolutional layers can be confused if the propagated error’s domain is changed for every iteration.
+If the error is propagated from the last FC layer to convolutional layer through the constant domain shifting, the training of the convolutional layer can be more stable than conventional BP. From this motivation, we use DFA instead of BP in the FC layers. As shown in Figure 2, the network maintains the BP in the convolutional layers but adopts the DFA for the FC layers. Since there is no data dependency among the FC layers, the DFA can directly propagate the error to the FC1. Since the DFA uses fixed feedback weight for error propagation, convolutional layers do not have to be adaptive to various errors which are derived from the different domain. In this method, the error propagation in the convolutional layers can be started even though the errors are not propagated for the remained FC layers. Therefore, the error propagation of both the convolutional layers and the FC layers can be computed in parallel right after DFA is done for the first FC layer.
+Nokland (2016) shows that the randomly initialized feedback weight can be used for DFA based DNN training. However, both the FA and the DFA are sensitive to the initialization method of the feedback weight because it affects the training accuracy and the convergence speed significantly. As shown in Liao et al. (2015), it is observed that the batch-normalization (BN) seems to make the FA become not sensitive to the initialization method, but it is still a problem because of the slow convergence. To make the DFA robust to the initialization method, we fixed the feedback weight as the multiplication of the transposed weights in multiple layers. To sum up, the feedback weight of the $i ^ { t h }$ layer, $\mathbf { \nabla } D _ { i }$ , can be calculated as
+$$
+D _ { i } = W _ { L , L - 1 } \dots W _ { i + 2 , i + 1 } W _ { i + 1 , i }
+$$
+, and finally, the error propagation operation can be summarized as follow.
+$$
+e _ { i } = ( D _ { i } ^ { T } e _ { L } ) \odot f ^ { \prime } ( i _ { i + 1 } ) = ( W _ { i + 1 , i } ^ { T } \dots W _ { L - 1 , L - 2 } ^ { T } W _ { L , L - 1 } ^ { T } e _ { L } ) \odot f ^ { \prime } ( i _ { i + 1 } )
+$$
+The suggested initialization method is suitable for other various functions such as sigmoid, tanh and ReLU. Moreover, other normalization or optimization methods such as BN and dropout (Srivastava et al. (2014)) are also applicable with the proposed initialization with the equation (7).
+![](images/d430f8e3754a9d7423daa939460b1f81bc5c5213c3f8e48e4ca82be448b8cf7a.jpg)
+Figure 2: Conventional DFA in CNN and Proposed DFA based Error Propagation
+# 3.2 BINARY DIRECT FEEDBACK ALIGNMENT (BDFA)
+The DFA needs the feedback weight addition to the forward weight matrix, and it occupies a larger memory to store both two matrices. Moreover, the DFA has the chance to be computed in parallel, but it requires much larger memory bandwidth. Since the throughput in the FC computing is vulnerable to the memory bandwidth, loading the additional feedback weight degrades the throughput compared with the unlimited bandwidth case.
+To solve the throughput bottleneck problem caused limited bandwidth, we propose the binary direct feedback alignment (BDFA) algorithm. BDFA uses the binarized feedback weight, $B _ { i }$ , whose values are determined as either $+ 1$ or $^ { - 1 }$ . In other words, the $B _ { i }$ can be stored as a single bit to represent only the sign value of the feedback weight’s element. As a result, required memory to store the $\mathbf { \delta } _ { B _ { i } }$ is reduced by $9 6 . 9 \%$ compared with the 32-bit floating point representation which now becomes the general numeric representation in CPU or GPU. As we determined in the DFA, BDFA’s feedback weight, $\mathbf { \delta } _ { B _ { i } }$ can be similarly defined by a modification of the equation (7). $\mathbf { \delta } _ { B _ { i } }$ is determined as
+$$
+B _ { i } = s i g n ( W _ { L , L - 1 } \ldots W _ { i + 2 , i + 1 } W _ { i + 1 , i } ) , \quad e _ { i } = ( B _ { i } ^ { T } e _ { L } ) \odot f ^ { \prime } ( i _ { i + 1 } )
+$$
+, when the $s i g n ( \cdot )$ is the function which indicates the sign value of each element. The difference between equation (7) and (9) is only whether the $s i g n ( \cdot )$ is applied or not. By applying equation (9), BDFA shows faster and stable training convergence compared with the random initialization case. The effect of the binarization and initialization will be discussed in section 4.
+# 4 EXPERIMENTS
+In this section, we compared the training accuracy of the conventional BP and suggested training algorithm. We measured the relative accuracy by training CNN from the scratch in CIFAR-10 and CIFAR-100 dataset (Krizhevsky (2009)). We used the network configuration as described in Figure 3. The base network follows the VGG-16 (Simonyan & Zisserman (2015)) configuration, but has one additional FC layer. To sum up, it consists of 13 convolutional layers with BN and ReLU activation functions, followed by three FC layers without BN. The number of neurons in the last FC layer is determined by the number of classification categories in each different dataset. In the BP based approach, both the convolutional layers and the FC layers are trained by using BP. In contrast, the training method of the last three FC layers is substituted with the DFA or the BDFA to measure the performance of the proposed training algorithm. The simulation was based on minibatch gradient descent with the batch size 100 and uses momentum(Sutskever et al. (2013)) for the optimization method. The parameters of the network are initialized as introduced by He et al. (2015), and the learning rate decay and the weight decay method is adopted. Other hyper parameters are not changed for fair comparison.
+# 4.1 CNN TRAINING FROM THE SCRATCH
+The CNN training with the DFA and BDFA, are renamed as CDFA and CBDFA respectively for the simple explanation. Table 1 shows Top5 and Top1 test accuracy after the CNN training is done in the two different CIFAR datasets. In this simulation, there is no data augmentation to make an environment which has a limited dataset. This condition can examine whether the algorithm is robust to the training in the small dataset. To sum up, only 50,000 images in the CIFAR-10 and CIFAR-100 is only used for DNN training and the other 10,000 images are tested to evaluate the test accuracy. As a result, both the CDFA and the CBDFA show higher test accuracy compared with the conventional BP even though the feedback weight is randomly initialized. In CIFAR-10, the CDFA and CBDFA are $7 . 5 \%$ and $8 . 3 \%$ higher in Top1 test accuracy than the BP respectively. The accuracy improvement by the CDFA and the CBDFA seems much more remarkable in CIFAR-100. As shown in Figure 4, the training curve of the CDFA and CBDFA is much slower, but they achieve $2 1 . 3 \%$ and $1 9 . 6 \%$ better performance respectively compared with the BP. However, the feedback weight with the random initialization has critical problems for training. One of the problems is the slow training curve described in Figure 4. DFA requires time to be adaptive to the randomly initialized feedback weights, so it takes a long latency to be converged. In the BP approach, we generally take the larger learning rate to make the training faster. However, the test accuracy of the DFA and BDFA is swung up and down dramatically when the large learning rate is applied. Moreover, it still spends a long time to converge. In this problem, the initialization with the equation (7) and (9) can be useful to solve the learning speed and stability problem. After the feedback weight is initialized by the proposed equations, it shows faster and more stable convergence characteristic as shown in Figure 5. When the proposed initialization method is combined with the large learning rate, it shows the best training performance compared with the other results.
+![](images/1397f2721dd69bba7e3df64bc1b13e90c10aa7b1eefebb6638658f05997ff0ad.jpg)
+Figure 3: Overall network configuration for training
+Table 1: CNN Training Result in CIFAR-10 & CIFAR-100 (Small Learning Rate)
+<table><tr><td>CIFAR 10</td><td>BP</td><td>BP w/ BN</td><td>CDFA Random</td><td>CDFA Eq (7)</td><td>CDFA w/ BN</td><td>CBDFA Random</td><td>CBDFA Eq(9)</td><td>CBDFA w/BN</td></tr><tr><td>Top5 Top1</td><td>98.63 81.11</td><td>98.24 76.91</td><td>98.42 88.68</td><td>98.55 86.36</td><td>98.56 87.41</td><td>98.63 89.39</td><td>98.88 87.65</td><td>98.83 86.46</td></tr></table>
+<table><tr><td>CIFAR 100</td><td>BP</td><td>BP w/ BN</td><td>CDFA Random</td><td>CDFA Eq (7)</td><td>CDFA w/BN</td><td>CBDFA Random</td><td>CBDFA Eq (9)</td><td>CBDFA w/BN</td></tr><tr><td>Top5 Top1</td><td>67.80 40.29</td><td>63.91 37.80</td><td>77.05 61.42</td><td>72.82 48.24</td><td>77.55 55.11</td><td>75.07 59.92</td><td>71.92 47.48</td><td>76.85 54.47</td></tr></table>
+![](images/ff81cfbe9a2121a1d175c4379344f62f86043acaf726cb260f77964bb1a815ca.jpg)
+< CIFAR-10o Training Result - Random Initialization & Small LR>
+Figure 4: Training and Test Accuracy with Proposed Training Algorithm
+When the dataset is augmented with the flipping and cropping, the training performance of the BP and CBDFA becomes higher than before. The simulation uses the large learning rate, and CBDFA takes the initialization with equation (9). In table 2, the performance of the CBDFA shows the highest accuracy compared with not only BP but also the training suggested by Hoffer et al. (2018). It trains only the convolutional layers, and the parameters of the FC layers are fixed. Even considering the data augmentation, CBDFA still shows higher training accuracy compared with the other two methods. As a result, CBDFA seems robust to the size of the dataset.
+![](images/f8e7c9fe9df953778ecd2a9e6583228191fe9924653b17621ccbad33f295fb77.jpg)
+Figure 5: Training and Test Accuracy with Proposed Training Algorithm
+Table 2: CNN Training Result with Data Augmentation (CIFAR-10)
+<table><tr><td></td><td colspan="3">w/o Data Augmentation</td><td colspan="3">w/ Data Augmentation</td></tr><tr><td></td><td>BP</td><td>CBDFA</td><td>Conv. only Training</td><td>BP</td><td>CBDFA</td><td>Conv. only Training</td></tr><tr><td>Top5</td><td>99.15</td><td>99.07</td><td>98.84</td><td>99.33</td><td>99.49</td><td>99.46</td></tr><tr><td>Top1</td><td>82.33</td><td>87.35</td><td>82.06</td><td>87.97</td><td>90.13</td><td>88.48</td></tr></table>
+There are some interesting observations in our simulation. First of all, the CBDFA shows negligible accuracy degradation compared with the CDFA based training. Sometimes, the CBDFA has a rather better performance than the CDFA case. Refer to the learning curve described in both Figure 4 and Figure 5, the CBDFA’s learning speed is slightly degraded, but the final training results are approximately the same. Therefore, CBDFA can improve the training performance and take the hardware benefits such as smaller memory bandwidth by adopting binarized feedback weights. The second one is the effect of the BN. Even though the suggested initialization method achieves the fast and stable training, it has a little accuracy degradation compared with the random initialization method. This accuracy degradation can be reduced when the BN layer is added after the FC layer. This result is counter characteristic compared with the BP case because the BP shows the worse training result when the BN layer is followed right after the FC layer. To sum up, the equation (7) and (9) are much more powerful when the BN is followed after the convolutional layer.
+# 4.2 EXAMPLE OF ONLINE LEARNING WITH SMALL DATASET: OBJECT TRACKING
+Nam & Han (2016) suggested online FC learning based object tracking algorithm, MDNet. The online learning concept in MDNet has derived many other algorithms such as BranchOut (Han et al. (2017)) and ADNet (Yun et al. (2017)). In the MDNet, both the convolutional layers and FC layers are pre-trained with the VOT (Kristan et al. (2013), Kristan et al. (2016)) and OTB (Wu et al. (2015)) object tracking dataset. However, the last layer of the FC layers is randomly initialized for the new tracking task. The convolutional layers do not need to be trained during the tracking but the FC layers are fine-tuned by using the BP. To apply BDFA to FC online learning with the small dataset, we replace the BP by the BDFA for FC layers in the MDNet.
+![](images/31487bb566301a24c7d55fac0d6937165872564cc84240dfc82c95ee1bac0db2.jpg)
+Figure 6: Object Tracking Result with the Proposed Training Algorithm, CBDFA
+We compared the object tracking performance by drawing the precision and the success plots of the one-pass evaluation (OPE) in the OTB dataset. As shown in Figure 6, the object tracking with the BDFA based online learning shows similar performance compared with the BP case. However, the BDFA shows better performance than BP when the batch size becomes smaller. Since the object tracking application is very sensitive to the online learning speed and the BDFA has a chance to be computed in parallel, BDFA based online learning becomes much more beneficial than conventional BP. Moreover, the BDFA can dramatically reduce the required data transaction in error propagation because of the fewer neuron interconnections and the binarization. As pointed out in the paper, Han et al. (2018), BP based online learning is inefficient for online learning in the devices which have limited memory bandwidth, computing resources, and small dataset. In this case, the effect of the BDFA can be maximized because of its profits.
+# 5 CONCLUSION
+In this work, we propose the new DNN learning algorithms to maximize the computation efficiency without accuracy degradation. We adopt one of the training method, DFA and combine it with the conventional BP. The combination of the DFA and the BP shows much better test accuracy in CNN training through the simulation in the CIFAFR-10 and CIFAR-100 dataset. BDFA takes one step further, binarizing the feedback weight while maintaining a similar performance compared with the full-precision DFA. The stability problem induced in the DFA and BDFA simulation (Figure 5) can be solved by the new feedback weight initialization method, equation (7) and (9). The BDFA is also simulated in the object tracking application, and it shows better tracking results compared with the conventional BP based online FC tuning.
+In this research, we can see that the DFA can reduce the computational complexity and achieve better training performance than conventional training method. However, the feedback path of the DFA cannot still be applied directly into convolutional layer because of the significant accuracy degradation. To break the limitation of the current research, We will continue the research about expanding the usage of the DFA to not only convolutional layers but also other RNN networks such as LSTM (Hochreiter & Schmidhubers (1997)) and GRU (Chung et al. (2014)).
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+T. Salimans, J. Ho, X. Chen, S. Sidor, and I. Sutskever. Evolution strategies as a scalable alternative to reinforcement learning. ArXiv, 2017.
+K. Simonyan and A. Zisserman. Very deep convolutional networks for large-scale image recognition. In Proceedings of Computer Vision and Pattern Recognition (CVPR), 2015.
+S. P. Singh, A. Kumar, H. Darbari, L. Singh, A. Rastogi, and S. Jain. Machine translation using deep learning: An overview. International Conference on Computer, Communications and Electronics (Comptelix), pp. 162–167, 2017.
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+I. Sutskever, J. Martens, G. Dahl, and G. E. Hinton. On the importance of initialization and momentum in deep learning. In Proceedings of International Conference on Machine Learning (ICML), pp. 1139–1147, 2013.
+Y. Wang, R. Skerry-Ryan, D. Stanton, Y. Wu, R. J. Weiss, N. Jaitly, Z. Yang, Y. Xiao, Z. Chen, and S. Bengio. Tacotron: Towards end-to-end speech synthesis. Interspeech, 2017.
+Y. Wu, J. Lim, and M. Yang. Object tracking benchmark. Transactions on Pattern Analysis and Machine Intelligence, 37:1834–1848, 2015.
+B. Xu, N. Wang, T. Chen, and M. Li. Empirical evaluation of rectified activations in convolutional network. arXiv:1505.00853, 2015.
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parse/train/BkGiPoC5FX/BkGiPoC5FX_content_list.json ADDED Viewed

	@@ -0,0 +1,1085 @@

+[
+    {
+        "type": "text",
+        "text": "EFFICIENT CONVOLUTIONAL NEURAL NETWORKTRAINING WITH DIRECT FEEDBACK ALIGNMENT",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            171,
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+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There were many algorithms to substitute the back-propagation (BP) in the deep neural network (DNN) training. However, they could not become popular because their training accuracy and the computational efficiency were worse than BP. One of them was direct feedback alignment (DFA), but it showed low training performance especially for the convolutional neural network (CNN). In this paper, we overcome the limitation of the DFA algorithm by combining with the conventional BP during the CNN training. To improve the training stability, we also suggest the feedback weight initialization method by analyzing the patterns of the fixed random matrices in the DFA. Finally, we propose the new training algorithm, binary direct feedback alignment (BDFA) to minimize the computational cost while maintaining the training accuracy compared with the DFA. In our experiments, we use the CIFAR-10 and CIFAR-100 dataset to simulate the CNN learning from the scratch and apply the BDFA to the online learning based object tracking application to examine the training in the small dataset environment. Our proposed algorithms show better performance than conventional BP in both two different training tasks especially when the dataset is small. ",
+        "bbox": [
+            233,
+            267,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            516,
+            334,
+            532
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep learning becomes the core of the machine learning and it has been utilized for many applications such as machine translation (Singh et al. (2017)), speech recognition (Wang et al. (2017)), and object classification (Rawat & Wang (2017)). Training the deep neural network (DNN) is an important portion of the deep learning because we need different pre-trained models to cover the various deep learning tasks. One well-known method of DNN training is the algorithm called backpropagation (BP) (Rumelhart et al. (1986)). The BP is the gradient descent based training method which follows the steepest gradient to find the optimum weights. Therefore, BP based training can be applied to any DNN configurations if the network consists of any differentiable operations. For instance, not only multi-layer perceptron (MLP) but also both convolutional neural network (CNN, LeCun et al. (1998)) and recurrent neural network (RNN, Hopfield (1982)) can be trained by using the BP. ",
+        "bbox": [
+            174,
+            547,
+            825,
+            700
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Even though the BP shows the outstanding performance in DNN training, BP based training suffers from the overfitting problem. Since the BP easily sinks into a local minimum, we need a large scale of the dataset to avoid the overfitting. In addition, we use various data augmentation techniques such as flipping and cropping. If the DNN training is done in the limited resources and dataset, BP based DNN training is too slow to be converged and shows low accuracy. One example is MDNet (Nam & Han (2016)) which introduces an object tracking algorithm with the online learning concept. Realtime implementation is an important issue in object tracking, so it has the limitation to utilize various data augmentation and large dataset for online learning. ",
+        "bbox": [
+            174,
+            708,
+            823,
+            819
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To break the BP based DNN training paradigm, a lot of new training methods have been developed. Salimans et al. (2017) proposed the evolution strategy which searches various weight without the gradient descent. It has a chance to be computed in parallel, but it needs a lot of seeds to find the global optimal solution. Moreover, evolution strategy has a slow convergence problem which can be an obstacle for fast online learning application. Another algorithm, feedback alignment (FA, Lillicrap et al. (2014)), was proposed based on the gradient descent methodology, but without following the steepest gradient. The FA pre-defines a feedback weight before starting the training, and the weight is determined by the random values.1 It is also known to converge slowly, and shows worse performance compared with the previous BP. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Direct feedback alignment (DFA, Nokland (2016)) was developed by getting the idea from the FA. Although the FA propagates errors from the last layer back to the first layer step-by-step, the DFA propagates errors from the last layer directly to each layer. This approach gives the opportunity of the parallel processing. Since the errors of every layer are generated independently in DFA, we can immediately calculate each layer’s gradient if the DNN inference is finished. Moreover, the number of required computation is reduced in the DFA. This is because the number of neurons in the last layer is usually fewer than the prior layer, so the size of the feedback weight becomes smaller than the BP. In spite of these advantages, the DFA suffers from accuracy degradation problem. The accuracy degradation problem becomes more serious when the DFA is applied to the CNN case. It is known that the DNN is not learnable with the DFA if the DNN becomes much deeper than AlexNet (Krizhevsky et al. (2012)). ",
+        "bbox": [
+            174,
+            138,
+            825,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we explain the new DFA algorithm to improve the training accuracy in CNN, and suggest a feedback weight initialization method for the fast convergence. Moreover, we propose the binary direct feedback alignment (BDFA) to maximize the computational efficiency. We verified the training performance in the VGG-16 (Simonyan & Zisserman (2015)) without any data augmentation, and DFA shows higher accuracy compared with the BP. And then, the training with small dataset was proved through the online learning based object tracking application. Our proposed algorithm shows better performance than the conventional BP approach in both the learning from the scratch and the object tracking tasks. ",
+        "bbox": [
+            174,
+            297,
+            825,
+            410
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The remaining part of the paper is organized as follows. The mathematical notation of the BP, FA, and DFA will be introduced in Section 2. Then, the details of the proposed algorithms will be explained in Section 3. The experiment will be followed in Section 4 and the paper will be concluded in Section 5. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 PRELIMINARIES ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 BACK-PROPAGATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Back-propagation is a general algorithm for the DNN training, suggested by Rumelhart et al. (1986). Let $\\mathbf { o } _ { i }$ be the $i ^ { t h }$ layer’s feature map, when $W _ { i + 1 , i }$ be the weight and bias between the $i ^ { t h }$ layer and the $i + 1 ^ { t h }$ layer. If the activation function is represented as $f ( \\cdot )$ , and $L$ is the total number of layers, the feature map of the $i + 1 ^ { t h }$ layer can be calculated as ",
+        "bbox": [
+            173,
+            551,
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+            609
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/defeca7f209b619d627257b9841de5320b173857fea8de1eaedda6a2f7bb6467.jpg",
+        "text": "$$\ni _ { i + 1 } = W _ { i + 1 , i } \\ o _ { i } , \\quad o _ { i + 1 } = f ( i _ { i + 1 } ) , \\quad i \\in \\{ 0 , 1 , \\ldots , L - 1 \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            276,
+            617,
+            691,
+            635
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Various activation functions such as sigmoid, tanh, and ReLU (Nair & Hinton (2010)) can be one of candidates of the $f ( \\cdot )$ . Some DNNs such as generative adversarial networks (Goodfellow et al. (2014)) use more advanced activation functions like Leaky ReLU and PReLU $\\mathrm { \\Delta X u }$ et al. (2015)). Once the inference is over, the inference result is compared with the pre-defined labels, and the error map $e _ { L }$ is calculated by a loss function such as cross-entropy. The error is propagated gradually from the last layer to the first layer, and the $i ^ { t h }$ layer’s error map can be calculated as ",
+        "bbox": [
+            173,
+            641,
+            825,
+            726
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e5481ace97d8d537c37f5a636584c438013f385cae398f661585cf5e87171def.jpg",
+        "text": "$$\n\\pmb { e } _ { i } = ( W _ { i + 1 , i } ^ { T } \\pmb { e } _ { i + 1 } ) \\odot f ^ { \\prime } ( i _ { i + 1 } ) , \\quad i \\in \\{ 1 , 2 , . . . , L - 1 \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            294,
+            733,
+            671,
+            752
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where $\\odot$ is an element-wise multiplication operator and $f ^ { \\prime } ( )$ is the derivative of the non-linear function. We need the transposed weight matrix, $W _ { i + 1 , i } ^ { T }$ , to propagate the errors in MLP case. After the BP, the gradient of each layer is computed by using both the $i ^ { t h }$ layer’s feature map and $i + 1 ^ { t h }$ layer’s error map. The $i ^ { t h }$ layer’s gradient, $G _ { i }$ is calculated as following. ",
+        "bbox": [
+            174,
+            761,
+            825,
+            820
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6cd20ca589b2ced3c54106429994e29677ebff486d9b79bf9516e24d27e1a82a.jpg",
+        "text": "$$\nG _ { i , b } = e _ { i + 1 } \\ o _ { i } ^ { T } , \\quad i \\in \\{ 0 , 1 , \\ldots , L - 1 \\} , \\quad b \\in \\{ 0 , 1 , \\ldots , B \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            276,
+            828,
+            691,
+            845
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fddd701ea201c0626806a0c7bcaee484bc50546dacc1cce03b3a02054516cad4.jpg",
+        "text": "$$\n\\pmb { G } _ { i } = \\frac { 1 } { B } \\sum _ { b } \\pmb { G } _ { i , b } , \\quad \\pmb { W } _ { i + 1 , i } ^ { \\prime } = \\pmb { W } _ { i + 1 , i } - \\eta \\ \\pmb { G } _ { i }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            325,
+            862,
+            642,
+            898
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "If we use the mini-batch gradient descent with the batch size $B$ , total $B$ gradients, $G _ { i , b }$ are averaged and get the $G _ { i }$ . $G _ { i }$ is used to update the $W _ { i + 1 , i }$ by multiplying learning rate, $\\eta$ . In the CNN case, the matrix multiplication operations in every step described in MLP is substituted with the convolution operations. One more different thing is that it uses $1 8 0 ^ { \\circ }$ flipped kernel instead of the transposed weight used in the BP. Other operations are as same as in the MLP case. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            174
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 FEEDBACK ALIGNMENT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            190,
+            382,
+            204
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Feedback alignment (FA) which was introduced by Lillicrap et al. (2016) substituted the transposed weight with the fixed random matrix in error propagation operation. In other words, they pre-defined the feedback weight which has the same size as the transposed weight, but the values of the feedback weight are determined randomly. Although the weights used in the training are updated for every iteration, the pre-defined random matrix is maintained until the training is finished. Let $R _ { i + 1 , i }$ be the feedback weight of the $i ^ { t h }$ layer, the propagated error in the FA is calculated as ",
+        "bbox": [
+            173,
+            215,
+            825,
+            301
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d82cc9316d471b62c7b6d026efce2a2d385c8ac0eb85d283a0494bf6464c4eb6.jpg",
+        "text": "$$\ne _ { i } = ( R _ { i + 1 , i } ^ { T } ~ e _ { i + 1 } ) \\odot f ^ { \\prime } ( i _ { i + 1 } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            379,
+            308,
+            588,
+            328
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": ", and the other procedures such as gradient generation and weight updating are same as BP does. ",
+        "bbox": [
+            173,
+            332,
+            805,
+            347
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3 DIRECT FEEDBACK ALIGNMENT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            363,
+            439,
+            377
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Even though, both the BP and the FA propagate errors from the last layer to the first layer in order, the DFA (Nokland (2016)) directly propagates errors from the last layer to other layers. If the number of neurons in the last layer and the $\\bar { i } ^ { t h }$ layer, are represented by $N _ { L }$ and $N _ { i }$ respectively, the size of the feedback weight is determined as $N _ { i } \\times N _ { L }$ . Let, $i ^ { t h }$ layer’s feedback weight in the DFA be $D _ { i } ^ { T }$ , then the error is calculated as ",
+        "bbox": [
+            173,
+            388,
+            825,
+            459
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f5d6cd73815be90a4e255ec88cf4b0c160bce4bd68829142b91229d98055e0dc.jpg",
+        "text": "$$\n\\pmb { e } _ { i } = ( D _ { i } ^ { T } \\pmb { e } _ { L } ) \\odot f ^ { \\prime } ( \\pmb { i } _ { i + 1 } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            393,
+            465,
+            573,
+            484
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "One of the interesting characteristics is that there is no data dependency between different errors because the DFA propagates the errors directly from the last layer. This characteristic gives the opportunity of parallel processing in the DFA based error propagation operation. ",
+        "bbox": [
+            174,
+            489,
+            825,
+            532
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Compared with the BP, DFA showed similar training performance for the multi-layer perceptron (MLP) structure. Moreover, DFA requires fewer computations because $N _ { L }$ is generally smaller than the number of neurons in the intermediate layers. However, the DFA dramatically degrades the accuracy when it applied in the CNN training as shown in Figure 1. Furthermore, the elements of the intermediate feature map are all connected with the last layer neurons, so it requires much more computations compared with BP based CNN training. In summary, the DFA’s computational efficiency can be induced in the MLP training, but not in the CNN. ",
+        "bbox": [
+            173,
+            537,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 OUR APPROACH",
+        "text_level": 1,
+        "bbox": [
+            176,
+            656,
+            341,
+            672
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As mentioned in Section 2, the DFA is efficient for MLP training, because it can be computed in parallel without accuracy degradation. However, this advantage is diminished when the DFA is applied in the CNN. To solve this problem, we propose the new training method to make the DFA applied to the CNN. In addition, the initialization method of the feedback weight is suggested for the fast and stable learning curve. At last, we propose the advanced training algorithm, binary direct feedback alignment (BDFA), which shows high computing efficiency and robust training performance in various conditions. ",
+        "bbox": [
+            174,
+            688,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a5ad26d059c99378a4fd14d3a6c18d5419391e11c682cdad631dba4f46028885.jpg",
+        "image_caption": [
+            "Figure 1: BP (Black) vs Conventional DFA (Read) for CNN Training (Tested in CIFAR-10) "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            753,
+            820,
+            890
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 CDFA: CNN TRAINING BY COMBINING BOTH BP AND DFA ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            183,
+            635,
+            198
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Generally, CNN consists of the convolutional layers and fully-connected (FC) layers. The two different kinds of layers have different roles. For example in object classification, convolutional layers are considered as the feature extractor by using the characteristics of the convolution computation. In contrast, FC layers receive the result of the feature extractor and judge what the object is. However, in the initial iterations of the BP based CNN training, training the convolutional layers can be ambiguous because the FC layers cannot be considered as a good object classifier. During some iterations of BP, the weight of the FC layers will be changed and the convolutional layers should be adaptive to the changed FC layers. In other words, convolutional layers can be confused if the propagated error’s domain is changed for every iteration. ",
+        "bbox": [
+            174,
+            212,
+            825,
+            337
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "If the error is propagated from the last FC layer to convolutional layer through the constant domain shifting, the training of the convolutional layer can be more stable than conventional BP. From this motivation, we use DFA instead of BP in the FC layers. As shown in Figure 2, the network maintains the BP in the convolutional layers but adopts the DFA for the FC layers. Since there is no data dependency among the FC layers, the DFA can directly propagate the error to the FC1. Since the DFA uses fixed feedback weight for error propagation, convolutional layers do not have to be adaptive to various errors which are derived from the different domain. In this method, the error propagation in the convolutional layers can be started even though the errors are not propagated for the remained FC layers. Therefore, the error propagation of both the convolutional layers and the FC layers can be computed in parallel right after DFA is done for the first FC layer. ",
+        "bbox": [
+            174,
+            344,
+            825,
+            483
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Nokland (2016) shows that the randomly initialized feedback weight can be used for DFA based DNN training. However, both the FA and the DFA are sensitive to the initialization method of the feedback weight because it affects the training accuracy and the convergence speed significantly. As shown in Liao et al. (2015), it is observed that the batch-normalization (BN) seems to make the FA become not sensitive to the initialization method, but it is still a problem because of the slow convergence. To make the DFA robust to the initialization method, we fixed the feedback weight as the multiplication of the transposed weights in multiple layers. To sum up, the feedback weight of the $i ^ { t h }$ layer, $\\mathbf { \\nabla } D _ { i }$ , can be calculated as ",
+        "bbox": [
+            173,
+            489,
+            825,
+            602
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d32f3835e4d67407edb974311cab7e88873dee42568b21ae2eaad595459393d8.jpg",
+        "text": "$$\nD _ { i } = W _ { L , L - 1 } \\dots W _ { i + 2 , i + 1 } W _ { i + 1 , i }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            361,
+            614,
+            602,
+            632
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": ", and finally, the error propagation operation can be summarized as follow. ",
+        "bbox": [
+            176,
+            645,
+            660,
+            660
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8fba10e2275d4ef12e20a4912bd796d94d86a59ce0f0ec7fe9d1d2ab2799beed.jpg",
+        "text": "$$\ne _ { i } = ( D _ { i } ^ { T } e _ { L } ) \\odot f ^ { \\prime } ( i _ { i + 1 } ) = ( W _ { i + 1 , i } ^ { T } \\dots W _ { L - 1 , L - 2 } ^ { T } W _ { L , L - 1 } ^ { T } e _ { L } ) \\odot f ^ { \\prime } ( i _ { i + 1 } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            230,
+            671,
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+            693
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The suggested initialization method is suitable for other various functions such as sigmoid, tanh and ReLU. Moreover, other normalization or optimization methods such as BN and dropout (Srivastava et al. (2014)) are also applicable with the proposed initialization with the equation (7). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/d430f8e3754a9d7423daa939460b1f81bc5c5213c3f8e48e4ca82be448b8cf7a.jpg",
+        "image_caption": [
+            "Figure 2: Conventional DFA in CNN and Proposed DFA based Error Propagation "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.2 BINARY DIRECT FEEDBACK ALIGNMENT (BDFA) ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The DFA needs the feedback weight addition to the forward weight matrix, and it occupies a larger memory to store both two matrices. Moreover, the DFA has the chance to be computed in parallel, but it requires much larger memory bandwidth. Since the throughput in the FC computing is vulnerable to the memory bandwidth, loading the additional feedback weight degrades the throughput compared with the unlimited bandwidth case. ",
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+        "type": "text",
+        "text": "To solve the throughput bottleneck problem caused limited bandwidth, we propose the binary direct feedback alignment (BDFA) algorithm. BDFA uses the binarized feedback weight, $B _ { i }$ , whose values are determined as either $+ 1$ or $^ { - 1 }$ . In other words, the $B _ { i }$ can be stored as a single bit to represent only the sign value of the feedback weight’s element. As a result, required memory to store the $\\mathbf { \\delta } _ { B _ { i } }$ is reduced by $9 6 . 9 \\%$ compared with the 32-bit floating point representation which now becomes the general numeric representation in CPU or GPU. As we determined in the DFA, BDFA’s feedback weight, $\\mathbf { \\delta } _ { B _ { i } }$ can be similarly defined by a modification of the equation (7). $\\mathbf { \\delta } _ { B _ { i } }$ is determined as ",
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+    {
+        "type": "equation",
+        "img_path": "images/66e8cc37832129a282846fe23533353df7d146a96d4194a4f4958fc9608d8e02.jpg",
+        "text": "$$\nB _ { i } = s i g n ( W _ { L , L - 1 } \\ldots W _ { i + 2 , i + 1 } W _ { i + 1 , i } ) , \\quad e _ { i } = ( B _ { i } ^ { T } e _ { L } ) \\odot f ^ { \\prime } ( i _ { i + 1 } )\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": ", when the $s i g n ( \\cdot )$ is the function which indicates the sign value of each element. The difference between equation (7) and (9) is only whether the $s i g n ( \\cdot )$ is applied or not. By applying equation (9), BDFA shows faster and stable training convergence compared with the random initialization case. The effect of the binarization and initialization will be discussed in section 4. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+        "text": "In this section, we compared the training accuracy of the conventional BP and suggested training algorithm. We measured the relative accuracy by training CNN from the scratch in CIFAR-10 and CIFAR-100 dataset (Krizhevsky (2009)). We used the network configuration as described in Figure 3. The base network follows the VGG-16 (Simonyan & Zisserman (2015)) configuration, but has one additional FC layer. To sum up, it consists of 13 convolutional layers with BN and ReLU activation functions, followed by three FC layers without BN. The number of neurons in the last FC layer is determined by the number of classification categories in each different dataset. In the BP based approach, both the convolutional layers and the FC layers are trained by using BP. In contrast, the training method of the last three FC layers is substituted with the DFA or the BDFA to measure the performance of the proposed training algorithm. The simulation was based on minibatch gradient descent with the batch size 100 and uses momentum(Sutskever et al. (2013)) for the optimization method. The parameters of the network are initialized as introduced by He et al. (2015), and the learning rate decay and the weight decay method is adopted. Other hyper parameters are not changed for fair comparison. ",
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+    {
+        "type": "text",
+        "text": "4.1 CNN TRAINING FROM THE SCRATCH ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "The CNN training with the DFA and BDFA, are renamed as CDFA and CBDFA respectively for the simple explanation. Table 1 shows Top5 and Top1 test accuracy after the CNN training is done in the two different CIFAR datasets. In this simulation, there is no data augmentation to make an environment which has a limited dataset. This condition can examine whether the algorithm is robust to the training in the small dataset. To sum up, only 50,000 images in the CIFAR-10 and CIFAR-100 is only used for DNN training and the other 10,000 images are tested to evaluate the test accuracy. As a result, both the CDFA and the CBDFA show higher test accuracy compared with the conventional BP even though the feedback weight is randomly initialized. In CIFAR-10, the CDFA and CBDFA are $7 . 5 \\%$ and $8 . 3 \\%$ higher in Top1 test accuracy than the BP respectively. The accuracy improvement by the CDFA and the CBDFA seems much more remarkable in CIFAR-100. As shown in Figure 4, the training curve of the CDFA and CBDFA is much slower, but they achieve $2 1 . 3 \\%$ and $1 9 . 6 \\%$ better performance respectively compared with the BP. However, the feedback weight with the random initialization has critical problems for training. One of the problems is the slow training curve described in Figure 4. DFA requires time to be adaptive to the randomly initialized feedback weights, so it takes a long latency to be converged. In the BP approach, we generally take the larger learning rate to make the training faster. However, the test accuracy of the DFA and BDFA is swung up and down dramatically when the large learning rate is applied. Moreover, it still spends a long time to converge. In this problem, the initialization with the equation (7) and (9) can be useful to solve the learning speed and stability problem. After the feedback weight is initialized by the proposed equations, it shows faster and more stable convergence characteristic as shown in Figure 5. When the proposed initialization method is combined with the large learning rate, it shows the best training performance compared with the other results. ",
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+        "type": "image",
+        "img_path": "images/1397f2721dd69bba7e3df64bc1b13e90c10aa7b1eefebb6638658f05997ff0ad.jpg",
+        "image_caption": [
+            "Figure 3: Overall network configuration for training "
+        ],
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+    {
+        "type": "table",
+        "img_path": "images/f557de91a8a87ec4315b7801c333cd27ab959bd121ee1c1a3a46d8d0d010ab49.jpg",
+        "table_caption": [
+            "Table 1: CNN Training Result in CIFAR-10 & CIFAR-100 (Small Learning Rate) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>CIFAR 10</td><td>BP</td><td>BP w/ BN</td><td>CDFA Random</td><td>CDFA Eq (7)</td><td>CDFA w/ BN</td><td>CBDFA Random</td><td>CBDFA Eq(9)</td><td>CBDFA w/BN</td></tr><tr><td>Top5 Top1</td><td>98.63 81.11</td><td>98.24 76.91</td><td>98.42 88.68</td><td>98.55 86.36</td><td>98.56 87.41</td><td>98.63 89.39</td><td>98.88 87.65</td><td>98.83 86.46</td></tr></table>",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>CIFAR 100</td><td>BP</td><td>BP w/ BN</td><td>CDFA Random</td><td>CDFA Eq (7)</td><td>CDFA w/BN</td><td>CBDFA Random</td><td>CBDFA Eq (9)</td><td>CBDFA w/BN</td></tr><tr><td>Top5 Top1</td><td>67.80 40.29</td><td>63.91 37.80</td><td>77.05 61.42</td><td>72.82 48.24</td><td>77.55 55.11</td><td>75.07 59.92</td><td>71.92 47.48</td><td>76.85 54.47</td></tr></table>",
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+        "img_path": "images/ff81cfbe9a2121a1d175c4379344f62f86043acaf726cb260f77964bb1a815ca.jpg",
+        "image_caption": [
+            "< CIFAR-10o Training Result - Random Initialization & Small LR> ",
+            "Figure 4: Training and Test Accuracy with Proposed Training Algorithm "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "When the dataset is augmented with the flipping and cropping, the training performance of the BP and CBDFA becomes higher than before. The simulation uses the large learning rate, and CBDFA takes the initialization with equation (9). In table 2, the performance of the CBDFA shows the highest accuracy compared with not only BP but also the training suggested by Hoffer et al. (2018). It trains only the convolutional layers, and the parameters of the FC layers are fixed. Even considering the data augmentation, CBDFA still shows higher training accuracy compared with the other two methods. As a result, CBDFA seems robust to the size of the dataset. ",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f8e7c9fe9df953778ecd2a9e6583228191fe9924653b17621ccbad33f295fb77.jpg",
+        "image_caption": [
+            "Figure 5: Training and Test Accuracy with Proposed Training Algorithm "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/66388988a280bfd4312e3a89f91039f0ae39d5c2386c99f17f8e7c812ea20295.jpg",
+        "table_caption": [
+            "Table 2: CNN Training Result with Data Augmentation (CIFAR-10) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">w/o Data Augmentation</td><td colspan=\"3\">w/ Data Augmentation</td></tr><tr><td></td><td>BP</td><td>CBDFA</td><td>Conv. only Training</td><td>BP</td><td>CBDFA</td><td>Conv. only Training</td></tr><tr><td>Top5</td><td>99.15</td><td>99.07</td><td>98.84</td><td>99.33</td><td>99.49</td><td>99.46</td></tr><tr><td>Top1</td><td>82.33</td><td>87.35</td><td>82.06</td><td>87.97</td><td>90.13</td><td>88.48</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "There are some interesting observations in our simulation. First of all, the CBDFA shows negligible accuracy degradation compared with the CDFA based training. Sometimes, the CBDFA has a rather better performance than the CDFA case. Refer to the learning curve described in both Figure 4 and Figure 5, the CBDFA’s learning speed is slightly degraded, but the final training results are approximately the same. Therefore, CBDFA can improve the training performance and take the hardware benefits such as smaller memory bandwidth by adopting binarized feedback weights. The second one is the effect of the BN. Even though the suggested initialization method achieves the fast and stable training, it has a little accuracy degradation compared with the random initialization method. This accuracy degradation can be reduced when the BN layer is added after the FC layer. This result is counter characteristic compared with the BP case because the BP shows the worse training result when the BN layer is followed right after the FC layer. To sum up, the equation (7) and (9) are much more powerful when the BN is followed after the convolutional layer. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 EXAMPLE OF ONLINE LEARNING WITH SMALL DATASET: OBJECT TRACKING",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Nam & Han (2016) suggested online FC learning based object tracking algorithm, MDNet. The online learning concept in MDNet has derived many other algorithms such as BranchOut (Han et al. (2017)) and ADNet (Yun et al. (2017)). In the MDNet, both the convolutional layers and FC layers are pre-trained with the VOT (Kristan et al. (2013), Kristan et al. (2016)) and OTB (Wu et al. (2015)) object tracking dataset. However, the last layer of the FC layers is randomly initialized for the new tracking task. The convolutional layers do not need to be trained during the tracking but the FC layers are fine-tuned by using the BP. To apply BDFA to FC online learning with the small dataset, we replace the BP by the BDFA for FC layers in the MDNet. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/31487bb566301a24c7d55fac0d6937165872564cc84240dfc82c95ee1bac0db2.jpg",
+        "image_caption": [
+            "Figure 6: Object Tracking Result with the Proposed Training Algorithm, CBDFA "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We compared the object tracking performance by drawing the precision and the success plots of the one-pass evaluation (OPE) in the OTB dataset. As shown in Figure 6, the object tracking with the BDFA based online learning shows similar performance compared with the BP case. However, the BDFA shows better performance than BP when the batch size becomes smaller. Since the object tracking application is very sensitive to the online learning speed and the BDFA has a chance to be computed in parallel, BDFA based online learning becomes much more beneficial than conventional BP. Moreover, the BDFA can dramatically reduce the required data transaction in error propagation because of the fewer neuron interconnections and the binarization. As pointed out in the paper, Han et al. (2018), BP based online learning is inefficient for online learning in the devices which have limited memory bandwidth, computing resources, and small dataset. In this case, the effect of the BDFA can be maximized because of its profits. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose the new DNN learning algorithms to maximize the computation efficiency without accuracy degradation. We adopt one of the training method, DFA and combine it with the conventional BP. The combination of the DFA and the BP shows much better test accuracy in CNN training through the simulation in the CIFAFR-10 and CIFAR-100 dataset. BDFA takes one step further, binarizing the feedback weight while maintaining a similar performance compared with the full-precision DFA. The stability problem induced in the DFA and BDFA simulation (Figure 5) can be solved by the new feedback weight initialization method, equation (7) and (9). The BDFA is also simulated in the object tracking application, and it shows better tracking results compared with the conventional BP based online FC tuning. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this research, we can see that the DFA can reduce the computational complexity and achieve better training performance than conventional training method. However, the feedback path of the DFA cannot still be applied directly into convolutional layer because of the significant accuracy degradation. To break the limitation of the current research, We will continue the research about expanding the usage of the DFA to not only convolutional layers but also other RNN networks such as LSTM (Hochreiter & Schmidhubers (1997)) and GRU (Chung et al. (2014)). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
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+# CONDITIONAL FLOW VARIATIONAL AUTOENCODERS FOR STRUCTURED SEQUENCE PREDICTION
+Anonymous authors Paper under double-blind review
+# ABSTRACT
+Prediction of future states of the environment and interacting agents is a key competence required for autonomous agents to operate successfully in the real world. Prior work for structured sequence prediction based on latent variable models imposes priors with limited expressiveness or are difficult to optimize e.g. determining the number of Gaussian mixture components which makes it challenging to fully capture the multi-modality of the distribution of the future states. In this work, we introduce Conditional Flow Variational Autoencoders $C F .$ VAE) using our novel conditional normalizing flow based prior to capture complex multi-modal conditional distributions for effective structured sequence prediction. Moreover, we propose two novel regularization schemes which stabilizes training and deals with posterior collapse for stable training and better fit to the target data distribution. Our experiments on three multi-modal structured sequence prediction datasets – MNIST Sequences, Stanford Drone and HighD – show that the proposed method obtains state of art results across different evaluation metrics.
+# 1 INTRODUCTION
+Anticipating future states of the environment is a key competence necessary for the success of autonomous agents. In complex real world environments, the future is highly uncertain. Therefore, structured predictions, one to many mappings of the likely future states of the world, are important. In many scenarios, these tasks can be cast as sequence prediction problems. Particularly, Conditional Variational Autoencoders (CVAE) (Sohn et al., 2015; Bayer & Osendorfer, 2014; Chung et al., 2015) have been very successful – from prediction of pedestrians trajectories (Lee et al., 2017; Bhattacharyya et al., 2018; Pajouheshgar & Lampert, 2018) to outcomes of robotic actions (Babaeizadeh et al., 2018). The distribution of future sequences is diverse and highly multi-modal. CVAEs model diverse futures by factorizing the distribution of future states using a set of latent variables which are mapped to likely future states. However, CVAEs assume a standard Gaussian prior on the latent variables which induces a strong model bias (Hoffman & Johnson, 2016; Tomczak & Welling, 2018) which makes it challenging to capture multi-modal distributions. This also leads to missing modes due to posterior collapse (Bowman et al., 2016; Razavi et al., 2019).
+Recent work (Tomczak & Welling, 2018; Wang et al., 2017; Gu et al., 2018) has therefore focused on more complex Gaussian mixture based priors. Gaussian mixtures still have limited expressiveness and optimization suffers from complications e.g. determining the number of mixture components. Normalizing flows are more expressive and enable the modelling of complex multi-modal priors. Recent work on flow based priors (Chen et al., 2017; Ziegler & Rush, 2019), have focused only on the unconditional (plain VAE) case. However, this not sufficient for CVAEs because in the conditional case the complexity of the distributions are highly dependent on the condition.
+In this work, 1. We propose Conditional Flow Variational Autoencoders (CF-VAE) based on novel conditional normalizing flow based priors In order to model complex multi-modal conditional distributions over sequences. In Figure 1, we show example predictions of MNIST handwriting stroke of our CF-VAE. We observe that, given a starting stroke, our CF-VAE model with data dependent normalizing flow based latent prior captures the two main modes of the conditional distribution – i.e. 1 and 8 – while CVAEs with fixed uni-modal Gaussian prior predictions have limited diversity. 2. We propose a regularization scheme that stabilizes the optimization of the evidence lower bound and leads to better fit to the target data distribution. 3. We leverage our conditional flow prior to deal with posterior collapse which causes standard CVAEs to ignore modes in sequence prediction tasks. 4. Finally, our method outperforms the state of the art on three structured sequence prediction tasks – handwriting stroke prediction on MNIST, trajectory prediction on Stanford Drone and HighD.
+![](images/2dd848aa9b523138419d8ded367d1d10054388c6945d9c0432ce1d1d2c0baa35.jpg)
+Figure 1: Clustered stroke predictions on MNIST sequences. Our multi-modal Conditional Normalizing Flow based prior (right) enables our regularized CF-VAE to capture the two modes of the conditional distribution, while predictions with uni-modal Gaussian prior (left) have limited diversity. Note, our 64D CF-VAE latent distribution is (approximately) projected to 2D using tSNE and KDE.
+# 2 RELATED WORK
+Normalizing Flows. Normalizing flows are a powerful class of density estimation methods with exact inference. (Dinh et al., 2015) introduced affine normalizing flows with triangular Jacobians. (Dinh et al., 2017) extend flows with masked convolutions which allow for complex (non-autoregessive) dependence between the dimensions. In (Kingma & Dhariwal, 2018), $1 \times 1$ convolutions were proposed for improved image generation compared to (Dinh et al., 2017). In (Huang et al., 2018) normalizing flows are auto-regressive and (Behrmann et al., 2019) extend it to ResNet. (Lu & Huang, 2019) extended normalizing flows to model conditional distributions. Here, we propose conditional normalizing flows to learn conditional priors for variational latent models.
+Variational Autoencoders. The original variational autoencoder (Kingma & Welling, 2014) used uni-modal Gaussian prior and posterior distributions. Thereafter, two lines of work have focused on developing either more expressive prior or posterior distributions. Rezende & Mohamed (2015) propose normalizing flows to model complex posterior distributions. Kingma et al. (2016); Tomczak & Welling (2016); Berg et al. (2018) present more complex inverse autoregessive flows, householder and Sylvester normalizing flow based posteriors. Here, we focus on the orthogonal direction of more expressive priors and the above approaches are compatible with our approach.
+Recent work which focus more expressive priors include (Nalisnick & Smyth, 2017) which proposes a Dirichlet process prior and (Goyal et al., 2017) which proposes a nested Chinese restaurant process prior. However, these methods require sophisticated learning methods. In contrast, (Tomczak & Welling, 2018) proposes a mixture of Gaussians based prior (with fixed number of components) which is easier to train and shows promising results on some image generation tasks. (Chen et al., 2017), proposes a inverse autoregressive flow based prior which leads to improvements in complex image generation tasks like CIFAR-10. (Ziegler & Rush, 2019) proposes a prior for VAE based text generation using complex non-linear flows which allows for complex multi-modal priors. While these works focus on unconditional priors, we aim to develop more expressive conditional priors.
+Posterior Collapse. Posterior collapse arises when the latent posterior does not encode useful information. Most prior work (Yang et al., 2017; Dieng et al., 2019; Higgins et al., 2017) concentrate on unconditional VAEs and modify the training objective – the KL divergence term is annealed to prevent collapse to the prior. Liu et al. (2019) extends KL annealing to CVAEs. However, KL annealing does not optimize a true lower bound of the ELBO for most of training. Zhao et al. (2017) also modifies the objective to choose the model with the maximal rate. Razavi et al. (2019) propose anti-causal sequential priors for text modelling tasks. Bowman et al. (2016); Gulrajani et al. (2017) proposes to weaken the decoder so that the latent variables cannot be ignored, however only unconditional VAEs are considered. Wang & Wang (2019) shows the advantage of normalizing flow based posteriors for preventing posterior collapse. In contrast, we study for the first time posterior collapse in conditional models on datasets with minor modes.
+Structured Sequence Prediction. Helbing & Molnar (1995); Robicquet et al. (2016); Alahi et al.
+(2016); Gupta et al. (2018); Zhao et al. (2019); Sadeghian et al. (2019) consider the problem of traffic participant trajectory prediction in a social context. Notably, (Gupta et al., 2018; Zhao et al., 2019;
+Sadeghian et al., 2019) use generative adversarial networks to generate socially compliant trajectories.
+However, the predictions are uni-modal. Starting from Bayer & Osendorfer (2014); Chung et al.
+(2015), more recently Lee et al. (2017); Bhattacharyya et al. (2018); Rhinehart et al. (2018); Deo & Trivedi (2019); Pajouheshgar & Lampert (2018) considers structured (one to many) predictions using – a CVAE, improved CVAE training, pushforward policies for vehicle ego-motion prediction, motion planning, spatio-temporal convolutional network respectively. Kumar et al. (2019) proposes a normalizing flow based model for video sequence prediction, however the sequences considered have very limited diversity compared to the trajectory prediction tasks considered here. Here, we focus on improving structured predictions using conditional normalizing flows based priors.
+# 3 CONDITIONAL FLOW VARIATIONAL AUTOENCODER (CF-VAE)
+Our Conditional Flow Variational Autoencoder is based on the conditional variational autoencoder (Sohn et al., 2015) which is a deep directed graphical model for modeling conditional data distributions $p _ { \theta } ( \mathbf { y } | \mathbf { x } )$ . Here, $\mathbf { X }$ is the sequence up to time $t$ , $\boldsymbol { x } = \left[ x ^ { 1 } , \cdots , x ^ { t } \right]$ and $_ \textrm { y }$ is the sequence to be predicted up to time $T$ , $y = \left[ y ^ { t + 1 } , \cdot \cdot \cdot , y ^ { T } \right]$ . CVAEs factorize the conditional distribution using latent variables z. In detail, $\begin{array} { r } { p _ { \theta } ( \mathbf { y } \vert \mathbf { x } ) = \int p _ { \theta } ( \mathbf { y } \vert \mathbf { z } , \mathbf { x } ) p ( \mathbf { z } \vert \mathbf { x } ) d \mathbf { z } } \end{array}$ , where $p ( \mathbf { z } | \mathbf { x } )$ is the prior on the latent variables. During training, amortized variational inference is used and the posterior distribution $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } )$ is learnt using a recognition network. The ELBO is maximized, given by,
+$$
+\begin{array} { r } { \log ( p _ { \theta } ( \mathbf { y } \vert \mathbf { x } ) ) \geq \mathbb { E } _ { q _ { \phi } ( \mathbf { z } \vert \mathbf { x } , \mathbf { y } ) } \log ( p _ { \theta } ( \mathbf { y } \vert \mathbf { z } , \mathbf { x } ) ) - D _ { \mathrm { K L } } ( q _ { \phi } ( \mathbf { z } \vert \mathbf { x } , \mathbf { y } ) \vert \vert p ( \mathbf { z } \vert \mathbf { x } ) ) . } \end{array}
+$$
+In practice, to simplify learning, simple unconditional standard Gaussian priors are used (Sohn et al., 2015). However, the complexity e.g. the number of modes of the target distributions $p _ { \theta } ( \mathbf { y } | \mathbf { x } )$ , is highly dependent upon the condition $x$ . An unconditional prior demands identical latent distributions irrespective complexity of the target conditional distribution – a very strong constraint on the recognition network. Moreover, the latent variables cannot encode any conditioning information and this leaves the burden of learning the dependence on the condition completely on the decoder.
+Furthermore, on complex conditional multi-modal data, Gaussian priors have been shown to induce a strong model bias (Tomczak & Welling, 2016; Ziegler & Rush, 2019). It becomes increasingly difficult to map complex multi-modal distributions to uni-modal Gaussian distributions, further complicated by the sensitivity of the RNNs encoder/decoders to subtle variations in the hidden states (Bowman et al., 2016). Moreover, the standard closed form estimate of the KL-divergence pushes the encoded latent distributions to the mean of the Gaussian leading to latent variable collapse (Wang et al., 2017; Gu et al., 2018) while discriminator based approaches (Tolstikhin et al., 2017) lead to underestimates of the KL-divergence (Rosca et al., 2017).
+Therefore, we propose conditional priors based on conditional normalizing flows to enable the latent variables to encode conditional information and allow for complex multi-modal latent representations. Next, we introduce our new conditional non-linear normalizing flows followed by our regularized Conditional Flow Variational Autoencoder (CF-VAE) formulation.
+# 3.1 CONDITIONAL NORMALIZING FLOWS
+Recently, normalizing flow (Tabak et al., 2010; Dinh et al., 2015) based priors for VAEs have been proposed (Chen et al., 2017; Ziegler & Rush, 2019). Normalizing flows allows for complex priors by transforming a simple base density e.g. standard Gaussian to a complex multi-modal density through a series of $n$ layers of invertible transformations $f _ { i }$ ,
+$$
+\epsilon \longleftrightarrow { \mathrm { h _ { 1 } } } \longleftrightarrow { \mathrm { h _ { 2 } } } \to { \mathrm { h _ { 2 } } } \cdots \langle ^ { f _ { n } } \rangle { \mathrm { z } } .
+$$
+However, such flows cannot model conditional priors. In contrast to prior work, we utilize conditional normalizing flows to model complex conditional priors. Conditional normalizing flows also consists of a series of $n$ layers of invertible transformations $f _ { i }$ (with parameters $\psi$ ), however we modify the transformations $f _ { i }$ such that they are dependent on the condition $\mathbf { X }$ ,
+$$
+\epsilon | \mathbf { x } \ { \overset { f _ { 1 } | \mathbf { x } } { \longleftrightarrow } } \ \mathbf { h } _ { 1 } | \mathbf { x } \ { \overset { f _ { 2 } | \mathbf { x } } { \longleftrightarrow } } \ \mathbf { h } _ { 2 } | \mathbf { x } \cdot \cdot \cdot \ { \overset { f _ { n } | \mathbf { x } } { \longleftrightarrow } } \ \mathbf { z } | \mathbf { x } .
+$$
+Further, in contrast to prior work (Lu & Huang, 2019; Atanov et al., 2019; Ardizzone et al., 2019) which use affine flows $( f _ { i } )$ , we build upon (Ziegler & Rush, 2019) and introduce conditional nonlinear normalizing flows with split coupling. Split couplings ensure invertibility by applying a flow
+layer $f _ { i }$ on only half of the dimensions at a time. To compute (5), we split the dimensions $\boldsymbol { z } ^ { D }$ of the latent variable into halfs, $\mathbf { z } ^ { L } = \{ 1 , \cdots , D / 2 \}$ and $\mathsf { z } ^ { R } = \{ \overset { \cdot } { D } / 2 , \cdot \cdot \cdot , d \}$ at each invertible layer $f _ { i }$ . Our transformation takes the following form for each dimension $\mathbf { z } ^ { j }$ alternatively from $ { \boldsymbol { z } } ^ { L }$ or $\hat { z ^ { R } }$ ,
+$$
+f _ { i } ^ { - 1 } ( z ^ { j } | z ^ { R } , \mathbf { x } ) = \epsilon ^ { j } = a ( \mathbf { z } ^ { R } , \mathbf { x } ) + b ( \mathbf { z } ^ { R } , \mathbf { x } ) \times \mathbf { z } ^ { j } + \frac { c ( \mathbf { z } ^ { R } , \mathbf { x } ) } { 1 + \big ( d ( \mathbf { z } ^ { R } , \mathbf { x } ) \times \mathbf { z } ^ { j } + g \big ( \mathbf { z } ^ { R } , \mathbf { x } \big ) \big ) ^ { 2 } } .
+$$
+where, $\mathbf { z } ^ { j } \in \mathbf { z } ^ { L }$ . Details of the forward (generating) operation $f _ { i }$ are in Appendix A. To ensure that the generated prior distribution is conditioned on $\mathbf { X }$ , in (4) and in the corresponding forward operation $f _ { i }$ , the coefficients $\{ a , b , c , d , g \} \in \mathbb { R }$ are functions of both the other half of the dimensions of $\mathbf { Z }$ and the condition $\mathbf { X }$ (unlike Ziegler $\&$ Rush (2019)). Finally, due to the expressive power of our conditional non-linear normalizing flows, simple spherical Gaussians base distributions were sufficient.
+# 3.2 VARIATIONAL INFERENCE USING CONDITIONAL NORMALIZING FLOWS BASED PRIORS
+Here, we derive the ELBO (1) for our regularized CF-VAE with our conditional flow based prior. In case of the standard CVAE with the Gaussian prior, the KL divergence term in the ELBO has a simple closed form expression. In case of our conditional flow based prior, we can use the change of variables formula to compute the KL divergence. In detail, given the base density $p ( \epsilon \vert \mathbf { x } )$ and the Jacobian $J _ { i }$ of each layer $i$ of the transformation, the log-likelihood of the latent variable $\mathbf { Z }$ under the prior can be expressed using the change of variables formula,
+$$
+\log ( p _ { \psi } ( \mathbf { \boldsymbol { z } } | \mathbf { \boldsymbol { x } } ) ) = \log ( p ( \boldsymbol { \epsilon } | \mathbf { \boldsymbol { x } } ) ) + \sum _ { i = 1 } ^ { n } \log ( | \operatorname* { d e t } J _ { i } | ) .
+$$
+This change of variables allows us to evaluate the likelihood of latent variable $\mathbf { Z }$ over the base distribution instead of the complex conditional prior and to express the KL divergence as,
+$$
+\begin{array} { r l r } {  { - D _ { \mathrm { K L } } ( q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } ) | | p _ { \psi } ( \mathbf { z } | \mathbf { x } ) ) = - \mathbb { E } _ { q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } ) } \log ( q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } ) ) + \mathbb { E } _ { q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } ) } \log ( p _ { \psi } ( \mathbf { z } | \mathbf { x } ) ) } } \\ & { } & { = \mathcal { H } ( q _ { \phi } ) + \mathbb { E } _ { q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } ) } \log ( p ( \boldsymbol { \epsilon } | \mathbf { x } ) ) + \sum _ { i = 1 } ^ { n } \log ( | \operatorname* { d e t } J _ { i } | ) . } \end{array}
+$$
+where, $\mathcal { H } ( q _ { \phi } )$ is the entropy of the variational distribution. Therefore, the ELBO can be expressed as,
+$$
+\log ( p _ { \theta } ( \mathbf { y } | \mathbf { x } ) ) \geq \mathbb { E } _ { q _ { \phi } ( z | \mathbf { x } , \mathbf { y } ) } \log ( p _ { \theta } ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) ) + \mathcal { H } ( q _ { \phi } ) + \mathbb { E } _ { q _ { \phi } ( z | \mathbf { x } , \mathbf { y } ) } \log ( p ( \boldsymbol { \epsilon } | \mathbf { x } ) ) + \sum _ { i = 1 } ^ { n } \log ( | \operatorname* { d e t } J _ { i } | )
+$$
+To learn complex conditional priors, we alternately optimize both the variational posterior distribution $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } )$ and the conditional prior ${ \dot { p } } _ { \psi } ( { \bf z } | { \bf x } )$ in (7). This would allow the variational posterior $q _ { \theta }$ to match the conditional prior and vice-versa so that the ELBO (7) is maximized. However, in practice we observe instabilities during training and posterior collapse. Next, we introduce our novel regularization schemes to deal with both these problems.
+Posterior Regularization for Stability $\mathbf { \Pi } ( \mathbf { p } \mathbf { R } )$ . The entropy and the log-Jacobian of the CF-VAE objective (7) are at odds with each other. The log-Jacobian favours the contraction of the base density. Therefore, log-Jacobian at the right of (7) is maximized when the conditional flow maps the base distribution $( \epsilon  z$ in Figure 2) to a low entropy conditional prior and thus a low entropy variational distribution $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } )$ . Therefore, in practice we observe instabilities during training. We observe that either the entropy or the log-Jacobian term dominates and the data log-likelihood is fully or partially ignored. Therefore, we regularize the posterior $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } )$ by fixing the variance to C. This leads to a constant entropy term which in turn bounds the maximum possible amount of contraction, thus upper bounding the log-Jacobian. This encourages our model to concentrate on explaining the data and leads better fit to the target data distribution. Note that, although $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } )$
+![](images/86b295e9ae3398cb690828a8b3a03114f9ecb10a4d0d6a2ef3882dfcfed39582.jpg)
+Figure 2: CF-VAE. The decoder is regularized by removing conditioning (grey arrow) to prevent posterior collapse.
+has fixed variance, this does not significantly effect sample quality as the marginal $q _ { \phi } ( \mathbf { z } | \mathbf { x } )$ can be arbitrarily complex due to our conditional flow prior. Moreover, we observe that the LSTM based decoders employed demonstrate robust performance across a wide range of values $\mathbf { C } = [ 0 . 0 5 , 0 . 2 5 ]$
+Condition Regularization for Posterior Collapse (cR). We observe missing modes when the target conditional data distribution has a major mode(s) and one or more minor modes (corresponding to rare events). This is because the condition x on the decoder is already enough to model the main mode(s). If the cost of ignoring the minor modes is out-weighed by the cost of encoding a more complex latent distribution reflecting all modes, the minor modes and the latent variables are ignored. We propose a regularization scheme by removing the additional conditioning $\mathbf { X }$ on the decoder, when the dataset in question has a dominating mode(s). This enabled by our conditional flow prior, which ensures that conditioning information is encoded in the latent space and $p _ { \theta } ( \mathbf { y } | \mathbf { z } )$ can match $p _ { \theta } ( \mathbf { y } | \mathbf { x } , \mathbf { z } )$ . Leading to a simpler factorization, $\begin{array} { r } { p _ { \theta } ( \mathbf { y } | \mathbf { x } ) = \int p _ { \theta } ( \mathbf { y } | \mathbf { z } ) p _ { \psi } ( \mathbf { z } | \mathbf { x } ) d \mathbf { z } } \end{array}$ . Equivalently, this ensures that the latent variable z cannot be ignored by the CF-VAE and thus must encode useful information. Note that this regularization scheme is only possible due to our conditional prior, the unconditional Gaussian prior of CVAE would always need to condition the decoder.
+The parallel work of Klushyn et al. (2019) also proposes a similar regularization scheme. However, we employ this regularization to deal with posterior collapse only in case of distributions with dominant modes. We also provide a more detailed analysis of their proposed prior in Appendix E.
+Finally, we discuss the integration of diverse sources of contextual information into the conditional prior $p _ { \psi } ( { \boldsymbol { \mathbf { z } } } | { \boldsymbol { \mathbf { x } } } )$ for even richer conditional latent distributions of our regularized CF-VAE.
+# 3.3 CONDITIONING PRIORS ON CONTEXTUAL INFORMATION
+For prediction tasks, it is often crucial to integrate sources of contextual information e.g. past trajectories or environmental information for accurate predictions. As these sources are heterogeneous, we employ source specific networks to extract fixed length vectors from each source.
+Past Trajectory. We encode the past trajectories using a LSTM to an fixed length vector $\mathbf { X } _ { t }$ . For efficiency we share the condition encoder between the conditional flow and the CF-VAE decoder.
+Environmental Map. We use a CNN to encode environmental information to a set of region specific feature vectors. We apply attention conditioned on the past trajectory to extract a fixed length conditioning vector $\mathbf { X } _ { m }$ , such that $\mathbf { X } _ { m }$ contains information relevant to the future trajectory.
+Interacting Agents. To encode information of interacting traffic participants/agents, we build on Deo & Trivedi (2018) and propose a fully convolutional social pooling layer. We aggregate information of interacting agents using a grid overlayed on the environment. This grid is represented using a tensor, where the past trajectory information of traffic participants are aggregated into the tensor indexed corresponding to the grid in the environment. In Deo & Trivedi (2018) past trajectory information is aggregated using a LSTM. We aggregate the past trajectory information into the tensor using $1 \times 1$ convolutions as it allows for stable learning and is computationally efficient. Finally, we apply several layers of $k \times k$ convolutions to capture interaction aware contextual features $\mathbf { X } _ { p }$ of traffic participants in the scene.
+Due to the expressive power of our conditional non-linear normalizing flows, simple concatenation into a single vector $\mathbf { x } = \left\{ { \mathbf { x } } _ { t } , { \mathbf { x } } _ { m } , { \mathbf { x } } _ { t } \right\}$ was sufficient to learn powerful conditional priors.
+# 4 EXPERIMENTS
+We evaluate our CF-VAE on three popular and highly multi-modal sequence prediction datasets. We begin with a description of our evaluation metrics and model architecture.
+Evaluation Metrics. In line with prior work (Lee et al., 2017; Bhattacharyya et al., 2018; Pajouheshgar & Lampert, 2018; Deo & Trivedi, 2019; Bhattacharyya et al., 2019), we use the negative conditional log-likelihood (-CLL) and mean Euclidean distances of the oracle Top $n \%$ of $N$ predictions. The oracle Top $n \%$ metric measures not only the coverage of all modes but also discourages random guessing for a reasonably large value of $n$ (e.g. $n = 1 0 \%$ ). This is because, a model can only improve this metric by moving randomly guessed samples from an overestimated mode to the correct modes (detailed analysis in Appendix F).
+![](images/bc15a1a4cd35f188f2ad3cb9c4662d11886de5162e0be0b775766c1ecd61fb15.jpg)
+Figure 3: Random samples clustered using k-means. The number of clusters is set manually to the number of expected digits. The corresponding priors of our $\mathrm { C F - V A E + p R }$ on the right. Note, our 64D CF-VAE latent distribution is (approximately) projected to 2D using tSNE and KDE.
+Conditional Flow Model Architecture. Our conditional flow prior consists of 16 layers of conditional non-linear flows with split coupling. Increasing the number of conditional non-linear flows generally led to “over-fitting” on the training latent distribution.
+# 4.1 MNIST SEQUENCES
+The MNIST Sequence dataset (D. De Jong, 2016) consists of sequences of handwriting strokes of the MNIST digits. The state-of-the-art approach is the “Best-of-Many”-CVAE (Bhattacharyya et al., 2018) with a Gaussian prior. We follow the evaluation protocol of Bhattacharyya et al. (2018) and predict the complete stroke given the first ten steps. We also compare with, 1. A standard CVAE with uni-modal Gaussian prior; 2. A CVAE with a data dependent conditional mixture of Gaussians (MoG) prior; 3. A CF-VAE without any regularization ; 4. A CF-VAE without the conditional non-linear flow layers (CF-VAE-Affine, replaced with affine flows (Lu & Huang, 2019; Atanov et al., 2019)). We also experiment with a conditional MoG prior (see Appendix D and E). We use the same model architecture (Bhattacharyya et al., 2018) across all baselines.
+We report the results in Table 1. We see that our CFVAE with posterior regularization (pR) performs best. It has a performance advantage of over $20 \%$ against the state of the art BMS-CVAE. We see that without regularization $\left( \mathrm { p R } \right)$ $\mathrm { { C } = 0 . 2 }$ ) there is a $40 \%$ drop in performance, highlighting the effectiveness of our proposed regularization scheme. We further illustrate the modes captured and the learnt multi-modal conditional flow priors in Figure 3. We do not use condition regularization here (cR) as we do not observe posterior collapse. In contrast, the BMS-CVAE is unable to fully capture all modes – its predictions are pushed to the mean due to the strong model bias induced by the Gaussian prior. The results improve considerably with the multi-modal MoG prior $M = 3$ components work best). We also experiment with optimizing the standard CVAE architecture. This improves performance only slightly (after increasing LSTM encoder/decoder units to 256 from 48, increasing the number of layers did not help). Moreover, our experiments with a conditional (MoG) AAE/WAE (Gu et al., 2018) based baseline did not improve performance beyond the standard (MoG) CVAE, because the discriminator based KL estimate tends to be an underestimate (Rosca et al., 2017). This illustrates that in practice it is difficult to map highly multi-modal sequences to a Gaussian prior and highlights the need of a data-dependent multi-modal priors. Our CF-VAE still significantly outperforms the MoG-CVAE as normalizing flows are better at learning complex multi-modal distributions (Kingma & Dhariwal, 2018). We also see that affine conditional flow based priors leads to a drop in performance (77.2 vs 74.9 CLL) illustrating the advantage of our non-linear conditional flows.
+Table 1: Evaluation on MNIST Sequences.
+<table><tr><td>Method</td><td>-CLL↓</td></tr><tr><td>CVAE (Sohn et al.,2015)</td><td>96.4</td></tr><tr><td>BMS-CVAE (Bhattacharyya et al., 2018)</td><td>95.6</td></tr><tr><td>CVAE+ increased capacity (Ours)</td><td>94.5</td></tr><tr><td>CVAE + conditional prior (Ours)</td><td>88.9</td></tr><tr><td>MoG-CVAE,M= 3</td><td>84.6</td></tr><tr><td>CF-VAE -no regularization (Ours)</td><td>104.3</td></tr><tr><td>CF-VAE - Affine + pR, C = 0.2 (Ours)</td><td>77.2</td></tr><tr><td>CF-VAE + pR,C= 0.2 (Ours)</td><td>74.9</td></tr></table>
+Sampled Predictions Latent Prior Sampled Predictions Latent Prior Sampled Predictions Latent Prior
+<table><tr><td>Method</td><td>Visual</td><td>Error @1sec</td><td>Error@ 2sec</td><td>Error @ 3sec</td><td>Error@4sec</td><td>-CLL↓</td></tr><tr><td>“Shotgun&quot;(Top 10%)(Pajouheshgar &amp; Lampert,2018)</td><td>None</td><td>0.7</td><td>1.7</td><td>3.0</td><td>4.5</td><td>91.6</td></tr><tr><td>DESIRE-SI-IT4 (Top 10%) (Lee et al.,2017)</td><td>RGB</td><td>1.2</td><td>2.3</td><td>3.4</td><td>5.3</td><td>X</td></tr><tr><td>STCNN (Top 10%)(Pajouheshgar &amp; Lampert, 2018)</td><td>RGB</td><td>1.2</td><td>2.1</td><td>3.3</td><td>4.6</td><td>X</td></tr><tr><td>BMS-CVAE(Top 10%)(Bhattacharyya et al.,2018)</td><td>RGB</td><td>0.8</td><td>1.7</td><td>3.1</td><td>4.6</td><td>126.6</td></tr><tr><td>MoG-CVAE,M=3(Top 10%)</td><td>None</td><td>0.8</td><td>1.7</td><td>2.7</td><td>3.9</td><td>86.1</td></tr><tr><td>CF-VAE- no regularization (Ours,Top 10%)</td><td>None</td><td>0.9</td><td>1.9</td><td>3.3</td><td>4.7</td><td>96.2</td></tr><tr><td>CF-VAE+pR,C= 0.2 (Ours,Top 10%)</td><td>None</td><td>0.7</td><td>1.5</td><td>2.5</td><td>3.6</td><td>84.6</td></tr><tr><td>CF-VAE+ pR,C= 0.2(Ours,Top 10%)</td><td>RGB</td><td>0.7</td><td>1.5</td><td>2.4</td><td>3.5</td><td>84.1</td></tr></table>
+Table 2: Five fold cross validation on the Stanford Drone dataset. Euclidean error at $( 1 / 5 )$ resolution.
+# 4.2 STANFORD DRONE
+![](images/f9410f85f74be21149edc7c0684080d5141c2ddf06f3bb6f7c5f8ff2bdda370c.jpg)
+Figure 4: Randomly sampled predictions of our CF-VAE $^ +$ pR model on the Stanford Drone. We observe that our prediction are highly multi-modal and is reflected by the Conditional Flow Priors. Note, our 64D CF-VAE latent distribution is (approximatly) projected to 2D using tSNE and KDE.
+![](images/fe6f9329e565ee70293a41a0ed330f4a45591301f3759d178dc6f17ec8a71a8b.jpg)
+Figure 5: Comparison of our CF-VAE $^ +$ pR (Red) and the “Shoutgun” baseline (Yellow) of (Pajouheshgar & Lampert, 2018), Groundtruth (Blue). Initial conditioning trajectory in white. Our CF-VAE not only learns to capture the correct modes but also generates more fine-grained predictions.
+The Stanford Drone dataset (Robicquet et al., 2016) consists of multi-model trajectories of traffic participant e.g. pedestrians, bicyclists, cars captured from a drone. Prior works follow two different evaluation protocols, 1. (Lee et al., 2017; Bhattacharyya et al., 2018; Pajouheshgar & Lampert, 2018) use 5 fold cross validation, 2. (Robicquet et al., 2016; Sadeghian et al., 2018; 2019; Deo & Trivedi, 2019) use a single split. We evaluate using the first protocol in Table 2 and the second in Table 3.
+Additionally, Pajouheshgar & Lampert (2018) suggest a “Shotgun” baseline. This baseline extrapolates the trajectory from the last known position and orientation in 10 different ways – 5 orientations: $( 0 ^ { \circ } , \pm 8 ^ { \circ } , \pm 1 5 ^ { \circ } )$ and 5 velocities: None or exponentially weighted over the past with coefficients (0, 0.3, 0.7, 1.0). This baseline obtains results at par with the state-of-the-art because it a good template which covers the most likely possible futures (modes) for traffic participant motion in this dataset. We report the results using 5 fold cross validation in Table 2. We additionally compare to a mixture of Gaussians prior (Appendix D). We use the same model architecture as in Bhattacharyya et al. (2018) and a CNN encoder with attention to extract features from the last observed RGB image (Appendix C). These visual features serve as additional conditioning $\left( \mathbf { { x } } _ { m } \right)$ to our Conditional Flow model. We see that our CF-VAE model with RGB input and posterior regularization $\left( \mathrm { p R } \right)$ performs best – outperforming the state-of-art “Shotgun” and BMS-CVAE by over $20 \%$ (Error $@$ 4sec). We see that our conditional flows are able to utilize visual scene (RGB) information to improve performance (3.5 vs 3.6 Error $@$ 4sec). We also see that the MoG-CVAE and our $\mathrm { C F - V A E + p R }$ outperforms the BMS-CVAE, even without visual scene information. This again reinforces our claim that the standard Gaussian prior induces a strong model bias and data dependent multi-modal priors are needed for best performance. The performance advantage of CF-VAE over the MoG-CVAE again illustrates the advantage of normalizing flows at learning complex conditional multi-modal distributions. The performance advantage over the “Shotgun” baseline shows that our $\mathrm { C F - V A E + p R }$ not only learns to capture the correct modes but also generates more fine-grained predictions. The qualitative examples in Figure 5 shows that our CF-VAE is better able to capture complex trajectories with sharp turns.
+<table><tr><td>Method</td><td>mADE↓</td><td>mFDE↓</td></tr><tr><td>SocialGAN(Gupta et al., 2018)</td><td>27.2</td><td>41.4</td></tr><tr><td>MATF GAN (Zhao et al., 2019)</td><td>22.5</td><td>33.5</td></tr><tr><td>SoPhie (Sadeghian et al., 2019)</td><td>16.2</td><td>29.3</td></tr><tr><td>Goal Prediction (Deo &amp; Trivedi,2019)</td><td>15.7</td><td>28.1</td></tr><tr><td>CF-VAE+pR,C=0.2(Ours)</td><td>12.6</td><td>22.3</td></tr></table>
+Table 3: Evaluation on the Stanford Drone dataset on a single split (see also Table 2).
+We report results using the single train/test split of (Robicquet et al., 2016; Sadeghian et al., 2018; 2019; Deo & Trivedi, 2019) in Table 3. We use the minimum Average Displacement Error (mADE) and minimum Final Displacement Error (mFDE) metrics as in (Deo & Trivedi, 2019). The minimum is over as set of predictions of size $N$ . Although this metric is less robust to random guessing compared to the Top $n \%$ metric, it avoids rewarding random guessing for a small enough value of $N$ . We choose $N = 2 0$ as in (Deo & Trivedi, 2019). Similar to the results with 5 fold cross validation, we observe $20 \%$ improvement over the state-of-the-art.
+# 4.3 HIGHD
+The HighD dataset (Krajewski et al., 2018) consists of vehicle trajectories recorded using a drone over highways. In contrast to other vehicle trajectory datasets e.g. NGSIM it contains minimal false positive trajectory collisions or physically improvable velocities.
+The HighD dataset is challenging because lane changes or interactions are rare $\sim 1 0 \%$ of all trajectories. The distribution of future trajectories contain a single main mode (linear continuations) along with several minor modes. Thus, approaches which predict a single mean trajectory (targeting the main mode) are challenging to outperform. In Table 4, we see that the simple Feed Forward (FF) model performs well and the Graph
+<table><tr><td>Method</td><td>Context</td><td>ADE↓</td><td>FDE↓</td><td>-CLL↓</td></tr><tr><td>Constant Velocity</td><td>None</td><td>1.09</td><td>2.66</td><td>X</td></tr><tr><td>FF (Diehl et al.,2019)</td><td>None</td><td>0.45</td><td>1.09</td><td>X</td></tr><tr><td>GAT (Diehl et al., 2019)</td><td>Yes</td><td>0.47</td><td>1.04</td><td>X</td></tr><tr><td>CVAE(Top 10%)</td><td>None</td><td>0.45</td><td>0.96</td><td>5.32</td></tr><tr><td>CVAE+Cyclic KL(Top 10%)</td><td>None</td><td>0.38</td><td>0.80</td><td>4.80</td></tr><tr><td>CF-VAE + pR,(Ours,Top 10%)</td><td>None</td><td>0.44</td><td>0.94</td><td>4.71</td></tr><tr><td>CF-VAE+{pR,cR},(Ours,Top 10%)</td><td>None</td><td>0.30</td><td>0.57</td><td>3.64</td></tr><tr><td>CF-VAE+{pR.cR},(Ours,Top 10%)</td><td>Yes</td><td>0.29</td><td>0.55</td><td>3.42</td></tr></table>
+Table 4: Evaluation on the HighD dataset.
+Convolutional GAT model of Diehl et al. (2019), which captures interactions, only narrowly outperforms the FF model. This dataset is challenging for CVAE based models as they frequently suffer from posterior collapse when a single mode dominates. This is clearly observed with our CVAE baseline in Table 4. To prevent posterior collapse, we use the cyclic KL annealing scheme proposed in Liu et al. (2019) (using a MoG prior did not help). This already leads to significant improvement over the deterministic FF and GAT baselines. We also observe posterior collapse with our CF-VAE model. Therefore, we regularize by removing additional conditioning (cR). Our $\mathrm { C F - V A E + \{ p R , c R \} }$ with condition regularization significantly outperforms the $\mathrm { C F - V A E + p R }$ and CVAE baselines (with cyclic KL annealing), demonstrating the effectiveness of our condition regularization scheme (cR) in preventing posterior collapse. The addition of contextual information of interacting traffic participants using our convolutional social pooling network with $1 \times 1$ convolutions significantly improves performance (also see Appendix G), demonstrating the effectiveness of our conditional normalizing flow based priors.
+# 5 CONCLUSION
+In this work, we presented the first variational model for learning multi-modal conditional data distributions with Conditional Flow based priors – the Conditional Flow Variational Autoencoder (CF-VAE). Furthermore, we propose two novel regularization techniques – posterior regularization (pR) and condition regularization (cR) – which stabilizes training solutions and prevents posterior collapse leading to better fit to the target distribution. This techniques lead to better match to the target distribution. Our experiments on diverse sequence prediction datasets show that our CF-VAE achieves state-of-the-art results across different performance metrics.
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+# APPENDIX A. CONDITIONAL NON-LINEAR NORMALIZING FLOWS
+In Subsection 3.1 of the main paper, we describe the inverse operation $f _ { i } ^ { - 1 }$ of our non-linear conditional normalizing flows. Here, we describe the forward operation. Note that while the forward operation is necessary to compute the likelihood (3) (in the main paper) during training, the forward operation is necessary to sample from the latent prior distribution of our CF-VAE. The forward operation consists of solving for the roots of the following equation (more details in (Ziegler & Rush, 2019)),
+$$
+\begin{array} { l } { { - b d ^ { 2 } ( \epsilon ^ { j } ) ^ { 3 } + ( ( { \bf z } ^ { j } - a ) d ^ { 2 } - 2 d g b ) ( \epsilon ^ { j } ) ^ { 2 } } } \\ { { + ( 2 d g ( { \bf z } ^ { j } - a ) - b ( { g } ^ { 2 } + 1 ) ) \epsilon ^ { j } + ( ( { \bf z } ^ { j } - a ) ( { g } ^ { 2 } + 1 ) - c ) = 0 } } \end{array}
+$$
+This equation has one real root which can be found analytically (Holmes). As mentioned in the main paper, note that the coefficients $\{ a , b , c , d , g \}$ are also functions of the condition $\mathbf { X }$ (unlike (Ziegler & Rush, 2019)).
+APPENDIX B. ADDITIONAL EVALUATION OF CONDITIONAL NON-LINEAR FLOWS
+<table><tr><td>Given x in,</td><td>p(yx）</td><td>Cond Affine Flow</td><td>Our Cond NL Flow</td></tr><tr><td></td><td>：：</td><td></td><td>：</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr></table>
+We compare conditional affine flows of (Atanov et al., 2019; Lu & Huang, 2019) and our conditional non-linear (Cond NL) flows in Figure 6 and Figure 7. We plot the conditional distribution $p ( \mathbf { y } \vert \mathbf { x } )$ and the corresponding condition x in the second and first columns. We use 8 and 16 layers of flow in case of the densities in Figure 6 and Figure 7 respectively. We see that the estimated density by the conditional affine flows of (Atanov et al., 2019; Lu & Huang, 2019) contains distinctive “tails” in case of Figure 6 and discontinuities in case of Figure 7. In comparison our conditional non-linear flows does not have distinctive “tails” or discontinuities and is able to complex capture the multi-modal distributions better. Note, the “ring”-like distributions in Figure 7 cannot be well captured by more traditional methods like Mixture of Gaussians. We see in Figure 8 that even with 64 mixture components, the learnt density is not smooth in comparison to our conditional non-linear flows. This again demonstrates the advantage of our conditional non-linear flows.
+![](images/48fc7f7e970558434c92488bebd00eb98cf1260c46c8d46969901cbc801ca1f7.jpg)
+Figure 7: Comparison between conditional affine flows of (Atanov et al., 2019; Lu & Huang, 2019) and our conditional non-linear (Cond NL) flows. We see that the conditional affine flows cannot fully capture “ring”-like conditional distributions (note the discontinuity at the top), while our conditional non-linear flows does not have such discontinuities.
+![](images/0e75227c1d8b81b0f6569af3e1d72b60342c5ffd9943119b5a9a35d26b24447e.jpg)
+Figure 8: Comparison between our conditional non-linear (Cond NL) flows and a Mixture of Gaussians (MoG) model. We see that even with 64 mixture components, the learnt density is not smooth in comparison to our conditional non-linear flows.
+# APPENDIX C. ADDITIONAL DETAILS OF OUR MODEL ARCHITECTURES
+Here, we provide details of the model architectures used across the three datasets used in the main paper.
+MNIST Sequences. We use the same model architecture as in Bhattacharyya et al. (2018). The LSTM condition encoder on the input sequence x, the LSTM recognition network $q _ { \theta }$ and the decoder LSTM network has 48 hidden neurons each. Also as in Bhattacharyya et al. (2018), we use a 64 dimensional latent space.
+Stanford Drone. Again, we use the same model architecture as in Bhattacharyya et al. (2018) except for the CNN encoder. The LSTM condition encoder on the input sequence $\mathbf { X }$ and the decoder LSTM network has 64 hidden neurons each. The LSTM recognition network $q _ { \theta }$ has 128 hidden neurons. Also as in Bhattacharyya et al. (2018), we use a 64 dimensional latent space. Our CNN encoder has 6 convolutional layers of size 32, 64, 128, 256, 512 and 512. We predict the attention weights on the final feature vectors using the encoding of the LSTM condition encoder. The attention weighted feature vectors are passed through a final fully connected layer to obtain the final CNN encoding. Furthermore, we found it helpful to additionally encode the past trajectory as an image (as in (Pajouheshgar & Lampert, 2018)) as provide this as an additional channel to the CNN encoder.
+HighD. We use the same model architecture with both the CVAE and CF-VAE models. As in the Stanford drone dataset, we use LSTM condition encoder on the input sequence x and the decoder LSTM network with 64 hidden neurons each and the LSTM recognition network $q _ { \theta }$ with 128 hidden neurons. The contextual information of interacting traffic participants are encoded into a spatial grid tensor of size $1 3 \times 3$ (see Section 3.2 of the main paper). We use a CNN with 5 layers of sizes 64, 128, 256, 256 and 256 to extract contextual features.
+# APPENDIX D. DETAILS OF THE MIXTURE OF GAUSSIANS (MOG) BASELINE
+In the main paper, we include results on the MNIST Sequence and Stanford Drone dataset with a Mixture of Gaussians (MoG) prior. In detail, instead of a normalizing flow, we set the prior to a MoG form,
+$$
+p _ { \xi } ( \mathbf { z } | \mathbf { x } ) = \sum _ { i = 1 } ^ { M } p ( \mathbf { c } _ { i } | \mathbf { x } ) \mathcal { N } ( \mathbf { z } ; \mu _ { i } , \sigma _ { i } | \mathbf { x } ) .
+$$
+We use a simple feed forward neural network that takes in the condition $\mathbf { X }$ (see Section 3.4 of the main paper) and predicts the parameters of the MoG, $\xi = \{ \mathbf { c } _ { 1 } , \mu _ { 1 } , \sigma _ { 1 } , \cdots , \mathbf { c } _ { M } , \mu _ { M } , \sigma _ { M } \}$ . Note, to ensure a reasonable number of parameters, we consider spherical Gaussians. Similar to (5) in the main paper, the ELBO can be expressed as,
+$$
+\begin{array} { r } { \log \bigl ( p _ { \theta } ( \mathbf { y } | \mathbf { x } ) \bigr ) \geq \mathbb { E } _ { q _ { \phi } ( z | \mathbf { x } , \mathbf { y } ) } \log \bigl ( p _ { \theta } ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) \bigr ) + \mathcal { H } ( q _ { \phi } ) + \mathbb { E } _ { q _ { \phi } ( z | \mathbf { x } , \mathbf { y } ) } \log \bigl ( p _ { \xi } ( z | \mathbf { x } ) \bigr ) . } \end{array}
+$$
+Note that we fix the entropy of the posterior distribution $q _ { \phi }$ for stability
+# APPENDIX E. ADDITIONAL EVALUATION ON THE MNIST SEQUENCE DATASET
+Here, we perform a comprehensive evaluation using the MoG prior with varying mixture components, a CVAE with unconditional non-linear flow based prior (NL-CVAE), our CF-VAE with Volumepreserving constant Jacobian conditional NICE flows based on Dinh et al. (2015), a CVAE with the conditional VampPrior (CDV) of (Klushyn et al., 2019), our CF-VAE with varying hyper-parameters $C = [ 0 . 0 5 , 0 . 2 5 ]$ of our posterior regularization (pR) scheme and finally analyze the effect of our posterior regularization (pR) scheme in detail. We report the results in Table 5.
+Table 5: Evaluation on MNIST Sequences (CLL: lower is better).
+<table><tr><td rowspan=1 colspan=4>Method                                     -CLL↓</td></tr><tr><td rowspan=1 colspan=4>NL-CVAE                                107.6±1.2CVAE(M = 1) (Sohn et al., 2015)     96.4±0.2</td></tr><tr><td rowspan=1 colspan=4>MoG-CVAE, M = 2                    85.3±0.4MoG-CVAE, M = 3                     84.6±0.5MoG-CVAE, M = 4                     85.7±0.4MoG-CVAE, M = 5                     86.3±0.6CDV (Klushyn et al., 2019), M = 12   99.4±0.7</td></tr><tr><td rowspan=1 colspan=4>CF-VAE - NICE (Ours)                  78.9±0.2</td></tr><tr><td rowspan=1 colspan=1> CF-VAE+ pR.</td><td rowspan=1 colspan=2>C=0.05,(Ours）</td><td rowspan=1 colspan=1>75.9±0.5</td></tr><tr><td rowspan=3 colspan=2>CF-VAE + pR,(</td><td rowspan=3 colspan=1>,C = 0.10,(Ours)</td><td></td></tr><tr><td rowspan=1 colspan=1>7</td></tr><tr><td rowspan=1 colspan=1>75.4±0.3</td></tr><tr><td rowspan=1 colspan=4>CF-VAE + pR,C: = 0.15, (Ours)        75.1±0.3CF-VAE + pR,C= 0.20,(Ours)        74.9±0.2CF-VAE + pR, C = 0.25,(Ours)        75.8±0.4</td></tr></table>
+MoG Prior. As mentioned in the main paper, we see that the MoG-CVAE outperforms the plain CVAE. This again reinforces our claim that the standard Gaussian prior induces a strong model bias. We see that using $M = 3$ components with the variance of the posterior distribution fixed to $C = 0 . 2$ leads to the best performance. This is expected as 3 is the most frequent number of possible strokes in the MNIST Sequence dataset. Also note that the results with the MoG prior are also relatively robust across $\mathbf { C } = [ 0 . 0 5 , 0 . 2 5 ]$ as we learn the variance of the prior (see the section above). Finally, our $\mathrm { C F - V A E + p R }$ still significantly outperforms the MoG-CVAE (74.9 vs 84.6). This is expected as normalizing flows are more powerful compared to MoG at learning complex multi-modal distributions (Kingma & Dhariwal, 2018) (also see Figure 8).
+![](images/50a15d633cd65996bc46084a5bd7bce523dc1a79afdd807f07ca89c64a1e2b37.jpg)
+Figure 9: Random samples using the CDV Prior of (Klushyn et al., 2019) clustered using $\mathbf { k } .$ -means. The number of clusters is set manually to the number of expected digits. The CDV Prior latent distribution on the right. Note, the 64D latent distribution is (approximately) projected to 2D using tSNE and KDE. In comparison to the samples and latent spaces of our CF-VAE (Figure 3) we see that the latent spaces are more simplistic and samples are of poorer quality.
+NL-CVAE. We also see that using an unconditional non-linear flow based prior actually harms performance (107.6 vs 96.4). This is because the latent distribution is highly dependent upon the condition. Therefore, without conditioning information the non-linear conditional flow learns a global representation of the latent space which leads to out-of-distribution samples at prediction time.
+CF-VAE with conditional NICE flows (Dinh et al., 2015). We have added results with the volume preserving NICE flows in Table 5. We observe that even without our posterior regularization scheme (pR) volume preserving NICE flows (Dinh et al., 2015) performs well – because of the constant Jacobian term. However, our conditional non-linear flows with posterior regularization still perform significantly better (78.9 vs 74.9 -CLL). This is because of the additional expressive power of our conditional non-linear flows combined with the stability offered by our posterior regularization scheme.
+Comparison to Klushyn et al. (2019). We also perform additional experiments with the conditional VampPrior (CDV) of Klushyn et al. (2019) using $M = 1 2$ components. Using more components makes training/inference significantly slower in comparison to plain CVAEs, Mog-CVAE ( $M = 3$ ) or our CF-VAE. Furthermore, with $M = 1 2$ components we observe that it is outperformed by the simpler MoG-CVAE. This is because the mean and variance parameters of the ( $M = 1 2$ ) components are obtained using the recognition network $q _ { \phi }$ . The recognition network $q _ { \phi }$ has to learn to both reconstruct the data and maintain a latent space representative of full conditional data distribution $p ( \mathbf { y } | \mathbf { x } )$ . These objectives are at odds with each other. In practice, we find that this leads to simplistic latent spaces along with lower overall data log-likelihood in comparison with our CF-VAE (Figure 3). This can be seen in the samples and corresponding latent spaces in Figure 9.
+Hyper-parameter analysis of our posterior regularization scheme (pR). We provide additional analysis of our posterior regularization scheme in Table 5. We observe that our CF-VAE is relatively robust across $C = [ 0 . 0 5 , 0 2 5 ]$ , with only small variance in performance. This is because our posterior regularization scheme encourages our CF-VAE to focus on explaining the data well. We explain this further in the following paragraph.
+Analysis of our posterior regularization scheme (pR). We provide additional analysis of our posterior regularization scheme (pR) in Figure 10. We show each term of our objective (7) in Figure 10. First, we see that with our posterior regularization scheme, our CF-VAE focuses on explaining the data well – the data log-likelihood is best with our posterior regularization (pR) scheme Figure 10a, with $C = 0 . 2$ having a advantage over $C = \{ 0 . 0 5 , 0 . 1 \}$ . Furthermore, we see that without our posterior regularization scheme the Jacobian term dominates while entropy term decreases (Figure 10b vs Figure 10d) – the contraction of the base density is favoured. Interestingly, the likelihood under the prior Figure 10c is similar across methods – with our posterior regularization providing additional stability. We also experimented with re-weighting these terms (although its no longer a valid lower bound on the true data log-likelihood). This leads to the opposite behaviour – the entropy term dominates over the Jacobian term at the cost of the data log-likelihood. On the other hand, we observe that all terms of our objective are stable with our posterior regularization scheme, illustrating the advantage of our posterior regularization scheme.
+![](images/ddecc9ab2431b6098f5848ee87462eb50e266afb273c9704a024c0b3a63f769b.jpg)
+Figure 10: Analysis of all four terms of our CF-VAE objective (7) at training time, with $C =$ $\{ 0 . \bar { 0 5 } , 0 . 1 0 , 0 . 2 0 \bar { \} } )$ and without our posterior regularization (pR) scheme. We observe better data log-likelihoods and stable training with our posterior regularization (pR) scheme. Without pR, we observe that the Jacobian term dominates at the cost of data log-likelihood.
+# APPENDIX F. EVALUATION OF THE ROBUSTNESS OF THE TOP $N \%$ METRIC
+We use two simpler uniform “Shotgun” baselines to study the robustness of the Top ${ \mathfrak { n } } \%$ metric against random guessing. In particular, we consider the “Shotgun”- $\mathbf { \nabla } \cdot \mathbf { u } 9 0 ^ { \circ }$ and “Shotgun”- $\mathbf { \cdot u l 3 5 ^ { \circ } }$ baselines which: given a budget of N predictions, it uniformly distributes the predictions between $\left( - 9 0 ^ { \circ } , 9 0 ^ { \circ } \right)$ and $\left( - 1 3 5 ^ { \circ } , 1 3 5 ^ { \circ } \right)$ respectively of the original orientation and using the velocity of the last time-step. In Table 6 we compare the Top 1 (best guess) to Top $10 \%$ metric with $\mathrm { N } = 5 0$ , 100, 500 predictions.
+We see that in case of both the “Shotgun”- $\mathbf { \nabla } \cdot \mathbf { u } 9 0 ^ { \circ }$ and “Shotgun”- $\mathbf { \cdot u l 3 5 ^ { \circ } }$ baselines, the Top 1 (best guess) metric improves with increasing number of guesses. This effect is even more pronounced in case of the “Shotgun”- $\cdot \mathrm { { u 1 3 5 ^ { \circ } } }$ baseline as the random guesses are distributed over a larger spatial range. In contrast, the Top $10 \%$ metric remains remarkably stable. This is because, in order to improve the Top $10 \%$ metric, random guessing is not enough – the predictions have to be on the correct modes. In other words, the only way to improve the Top $10 \%$ metric is move random predictions to any of the correct modes.
+APPENDIX G. QUALITATIVE EXAMPLES ON THE HIGHD DATASET
+<table><tr><td>Method</td><td>K</td><td>Error @1sec</td><td>Error @ 2sec</td><td>Error @ 3sec</td><td>Error @ 4sec</td></tr><tr><td></td><td colspan="5">Top 1 (Best Guess)</td></tr><tr><td>“Shotgun&quot;-u90°</td><td>50</td><td>0.9</td><td>1.9</td><td>3.1</td><td>4.4</td></tr><tr><td>“Shotgun&quot;-u90°</td><td>100</td><td>0.9</td><td>1.9</td><td>3.0</td><td>4.3</td></tr><tr><td>&quot;Shotgun&quot;-u90°</td><td>500</td><td>0.9</td><td>1.9</td><td>3.0</td><td>4.3</td></tr><tr><td></td><td colspan="5">Top 10%</td></tr><tr><td>“Shotgun&quot;-u90°</td><td>50</td><td>1.2</td><td>2.5</td><td>3.9</td><td>5.4</td></tr><tr><td>“Shotgun&quot;-u90°</td><td>100</td><td>1.2</td><td>2.5</td><td>3.9</td><td>5.4</td></tr><tr><td>“Shotgun&quot;-u90°</td><td>500</td><td>1.2</td><td>2.5</td><td>3.9</td><td>5.4</td></tr><tr><td></td><td colspan="5">Top 1 (Best Guess)</td></tr><tr><td>“Shotgun&quot;-u135°</td><td>50</td><td>0.9</td><td>2.0</td><td>3.1</td><td>4.5</td></tr><tr><td>“Shotgun&quot;-u135°</td><td>100</td><td>0.9</td><td>1.9</td><td>3.0</td><td>4.3</td></tr><tr><td>“Shotgun&quot;-u135°</td><td>500</td><td>0.9</td><td>1.9</td><td>3.0</td><td>4.2</td></tr><tr><td></td><td colspan="5">Top 10%</td></tr><tr><td>“Shotgun&quot;-u135°</td><td>50</td><td>1.4</td><td>2.9</td><td>4.5</td><td>6.2</td></tr><tr><td>&quot;Shotgun&quot;-u135°</td><td>100</td><td>1.4</td><td>2.9</td><td>4.5</td><td>6.2</td></tr><tr><td>&quot;Shotgun&quot;-u135°</td><td>500</td><td>1.4</td><td>2.9</td><td>4.5</td><td>6.2</td></tr></table>
+Table 6: Five fold cross validation on the Stanford Drone dataset. Euclidean error at $( 1 / 5 )$ resolution.
+![](images/d834c03a140771003f59337ab88e45dab1c004e269af3abbd0cc11c101285b6d.jpg)
+Figure 11: Predictions on the HighD dataset. Left: 128 random samples from the HighD test set (in yellow). Middle: CVAE predictions (5 samples per test set example). Right: Our CV-VAE $^ +$ $\{ \mathrm { p R } , \mathrm { c R } \}$ predictions (5 samples per test set example). While the predictions by the CVAE are linear continuations, our CF-VAE sample predictions are much more diverse and cover events like lane changes e.g. top most sample track from the test set.
+We show qualitative examples on the HighD dataset in Figure 11. In the left of Figure 11 we show 128 random samples from the HighD test set. In the middle we show predictions on these samples by the CVAE (with cyclic KL annealing (Liu et al., 2019)). We see that even with cyclic KL annealing, we observe posterior collapse. All samples have been pushed towards the mean and the variance in the 5 samples per test set example is minimal. E.g. note the top most sample track from the test set in Figure 11 (left). All CVAE sample predictions are a linear continuation of the trajectory (continuing on the same lane), while there is in fact a turn (change of lanes). In contrast, our $\mathsf { \bar { C } F - V A \bar { E } + \{ p R , c R \} }$ sample predictions are much more diverse and cover such eventualities. This also shows that our $\mathrm { C F - \bar { V } A \bar { E } + \{ p R , c R \} }$ does not suffer from such posterior variable collapse.

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+# DUORC: TOWARDS COMPLEX LANGUAGE UNDER-STANDING WITH PARAPHRASED READING COMPRE-HENSION
+Anonymous authors Paper under double-blind review
+# ABSTRACT
+We propose DuoRC, a novel dataset for Reading Comprehension (RC) that motivates several new challenges for neural approaches in language understanding beyond those offered by existing RC datasets. DuoRC contains 186,089 unique question-answer pairs created from a collection of 7680 pairs of movie plots where each pair in the collection reflects two versions of the same movie - one from Wikipedia and the other from IMDb - written by two different authors. We asked crowdsourced workers to create questions from one version of the plot and a different set of workers to extract or synthesize answers from the other version. This unique characteristic of DuoRC where questions and answers are created from different versions of a document narrating the same underlying story, ensures by design, that there is very little lexical overlap between the questions created from one version and the segments containing the answer in the other version. Further, since the two versions have different levels of plot detail, narration style, vocabulary, etc., answering questions from the second version requires deeper language understanding and incorporating external background knowledge. Additionally, the narrative style of passages arising from movie plots (as opposed to typical descriptive passages in existing datasets) exhibits the need to perform complex reasoning over events across multiple sentences. Indeed, we observe that state-ofthe-art neural RC models which have achieved near human performance on the SQuAD dataset (Rajpurkar et al., 2016b), even when coupled with traditional NLP techniques to address the challenges presented in DuoRC exhibit very poor performance (F1 score of $3 7 . 4 2 \%$ on DuoRC v/s $86 \%$ on SQuAD dataset). This opens up several interesting research avenues wherein DuoRC could complement other RC datasets to explore novel neural approaches for studying language understanding.
+# 1 INTRODUCTION
+Natural Language Understanding is widely accepted to be one of the key capabilities required for AI systems. Scientific progress on this endeavor is measured through multiple tasks such as machine translation, reading comprehension, question-answering, and others, each of which requires the machine to demonstrate the ability to “comprehend” the given textual input (apart from other aspects) and achieve their task-specific goals. In particular, Reading Comprehension (RC) systems are required to “understand” a given text passage as input and then answer questions based on it. It is therefore critical, that the dataset benchmarks established for the RC task keep progressing in complexity to reflect the challenges that arise in true language understanding, thereby enabling the development of models and techniques to solve these challenges.
+For RC in particular, there has been significant progress over the recent years with several benchmark datasets, the most popular of which are the SQuAD dataset (Rajpurkar et al., 2016a), TriviaQA (Joshi et al., 2017), MS MARCO (Nguyen et al., 2016), MovieQA (Tapaswi et al., 2016) and cloze-style datasets(Mostafazadeh et al., 2016; Onishi et al., 2016; Hermann et al., 2015). However, these benchmarks, owing to both the nature of the passages and the question-answer pairs to evaluate the RC task, have 2 primary limitations in studying language understanding: (i) Other than MovieQA, which is a small dataset of 15K QA pairs, all other large-scale RC datasets deal only with factual descriptive passages and not narratives (involving events with causality linkages that require reasoning
+# Movie: Twelve Monkeys
+# Original Plot Synopsis(Wikipedia)
+# Paraphrased Plot Synopsis (IMDB)
+A deadly virus released in 1996..,[James Cole is a prisoner living in a subterranean compound beneath the ruins of Philadelphia $1 ^ { \circ 1 }$ [Cole is selected foramission]Q2
+[Cole arrives in Baltimore]Q3 in 1990, not 1996 as planned...[Goines denies any involvement with the group and says that in 199o Cole originated the idea of wiping out humanity with a virus stolen from Goines' virologist father.jQ4
+Cole convinces himself. Railly confronts him with evidence of his time travel.. [They decide to spend their remaining time together in the Florida Keys before the onset of the plague]Q5 [At the airport, Cole leaves a last message]Q6 .. [He is soon confronted by Jose,an acquaintance from his own time,who gives Cole a handgunjQ7 and ambiguously instructs him to follow orders.At the same time,Raillyspots Dr.Peters..
+Cole forces his way through a security checkpoint... [Peters, aboard theplane with the virus]Q8
+A virus,deliberately released in 1996 .. One such prisoner is [James Cole,who after retrieving samples is given the chance to go back in time to $1 9 9 6 ] ^ { \circ 2 }$ and find information about the group believed responsible, known as "The Army of 12 Monkeys."
+Throughout the ensuing episodes, Cole .. There he meets Jeffrey Goines, ... Cole is now racing against time...he wants to stay in 1996 with Dr. Railly,... They [travel toPhiladelphia]Q1,
+[Jeffrey rambles about how Cole had given him the idea to release a virus that would destroy most of humanity. $| ^ { \circ 4 }$ Cole leaves,...and then posts flyers declaring "We did it!"[Cole realizes that the "Army" isnot the threat, and he leaves a phone message to that effectjQ6.
+[Jose,a fellow "volunteer" from the present,approaches Cole with orders forhimtocompletehismissionand handshima revolverjQ7...Inan airport,while attempting with Cole to elude capture, Dr. Railly recognizes [Dr Peters,a man who worked with Jeffrey Goines's father.... The man goes through airport screening and manages to persuade security that his biological samplesjQ8
+Q1: James Cole is a prisonerliving in a subterranean shelter beneath what city?Philadelphia,Philadelphia Q2:What is the name of the person selected for the mission? James Cole, James Cole Q3:Where did Cole arrive in 1990? Baltimore, - Q4: Who does Goines claim came up with the idea to exterminate humanity? Cole, Cole Q5:Where do Cole and Railly decide to go before the plague? Florida Keys, Q6:Where does Cole leave his message? At the airport， on the phone Q7:Who gives Cole a handgun? Jose， Jose Q8:Peters is aboard the plane with what? Virus, biological samples
+Figure 1: Example QA pairs obtained from the original movie plot and the paraphrased plot. The relevant spans needed for answering the corresponding question are highlighted in blue and red with the respective question numbers. Note that the span highlighting shown here is for illustrative purposes only and is not available in the dataset.
+and background knowledge) which is the case with a lot of real-world content such as story books, movies, news reports, etc. (ii) their questions possess a large lexical overlap with segments of the passage, or have a high noise level in Q/A pairs themselves. As demonstrated by recent work, this makes it easy for even simple keyword matching algorithms to achieve high accuracy (Weissenborn et al., 2017). In fact, these models have been shown to perform poorly in the presence of adversarially inserted sentences which have a high word overlap with the question but do not contain the answer (Jia & Liang, 2017). While this problem does not exist in TriviaQA it is admittedly noisy because of the use of distant supervision. Similarly, for cloze-style datasets, due to the automatic question generation process, it is very easy for current models to reach near human performance (Cui, 2017). This therefore limits the complexity in language understanding that a machine is required to demonstrate to do well on the RC task.
+Motivated by these shortcomings and to push the state-of-the-art in language understanding in RC, in this paper we propose DuoRC, which specifically presents the following challenges beyond the existing datasets:
+1. DuoRC is especially designed to contain a large number of questions with low lexical overlap between questions and their corresponding passages.
+2. It requires the use of background and common-sense knowledge to arrive at the answer and go beyond the content of the passage itself.
+3. It contains narrative passages from movie plots that require complex reasoning across multiple sentences to infer the answer.
+4. Several of the questions in DuoRC, while seeming relevant, cannot actually be answered from the given passage, thereby requiring the machine to detect the unanswerability of questions.
+In order to capture these four challenges, DuoRC contains QA pairs created from pairs of documents describing movie plots which were gathered as follows. Each document in a pair is a different version of the same movie plot written by different authors; one version of the plot is taken from the Wikipedia page of the movie whereas the other from its IMDb page (see Fig. 1 for portions of an example pair of plots from the movie “Twelve Monkeys”). We first showed crowd workers on Amazon Mechanical Turk (AMT) the first version of the plot and asked them to create QA pairs from it. We then showed the second version of the plot along with the questions created from the first version to a different set of workers on AMT and asked them to provide answers by reading the second version only. Since the two versions contain different levels of plot detail, narration style, vocabulary, etc., answering questions from the second version exhibits all of the four challenges mentioned above.
+We now make several interesting observations from the example in Fig. 1. For 4 out of the 8 questions (Q1, Q2, Q4, and Q7), though the answers extracted from the two plots are exactly the same, the analysis required to arrive at this answer is very different in the two cases. In particular, for Q1 even though there is no explicit mention of the prisoner living in a subterranean shelter and hence no lexical overlap with the question, the workers were still able to infer that the answer is Philadelphia because that is the city to which James Cole travels to for his mission. Another interesting characteristic of this dataset is that for a few questions (Q6, Q8) alternative but valid answers are obtained from the second plot. Further, note the kind of complex reasoning required for answering Q8 where the machine needs to resolve coreferences over multiple sentences (that man refers to Dr. Peters) and use common sense knowledge that if an item clears an airport screening, then a person can likely board the plane with it. To re-emphasize, these examples exhibit the need for machines to demonstrate new capabilities in RC such as: (i) employing a knowledge graph (e.g. to know that Philadelphia is a city in Q1), (ii) common-sense knowledge (e.g., clearing airport security implies boarding) (iii) paraphrase/semantic understanding (e.g. revolver is a type of handgun in Q7) (iv) multiple-sentence inferencing across events in the passage including coreference resolution of named entities and nouns, and (v) educated guesswork when the question is not directly answerable but there are subtle hints in the passage (as in Q1). Finally, for quite a few questions, there wasn’t sufficient information in the second plot to obtain their answers. In such cases, the workers marked the question as “unanswerable”. This brings out a very important challenge for machines to exhibit (i.e. detect unanswerability of questions) because a practical system should be able to know when it is not possible for it to answer a particular question given the data available to it, and in such cases, possibly delegate the task to a human instead.
+Current RC systems built using existing datasets are far from possessing these capabilities to solve the above challenges. In Section 4, we seek to establish solid baselines for DuoRC employing state-of-the-art RC models coupled with a collection of standard NLP techniques to address few of the above challenges. Proposing novel neural models that solve all of the challenges in DuoRC is out of the scope of this paper. Our experiments demonstrate that when the existing state-of-the-art RC systems are trained and evaluated on DuoRC they perform poorly leaving a lot of scope for improvement and open new avenues for research in RC. Do note that this dataset is not a substitute for existing RC datasets but can be coupled with them to collectively address a large set of challenges in language understanding with RC (the more the merrier).
+# 2 RELATED WORK
+Over the past few years, there has been a surge in datasets for Reading Comprehension. Most of these datasets differ in the manner in which questions and answers are created. For example, in SQuAD (Rajpurkar et al., 2016a), NewsQA (Trischler et al., 2016), TriviaQA (Joshi et al., 2017) and MovieQA (Tapaswi et al., 2016) the answers correspond to a span in the document. MS-MARCO uses web queries as questions and the answers are synthesized by workers from documents relevant to the query. On the other hand, in most cloze-style datasets (Mostafazadeh et al., 2016; Onishi et al., 2016) the questions are created automatically by deleting a word/entity from a sentence. There are also some datasets for RC with multiple choice questions (Richardson et al., 2013; Berant et al., 2014; Lai et al., 2017) where the task is to select one among $k$ given candidate answers.
+Given that there are already a few datasets for RC, a natural question to ask is “Do we really need any more datasets?”. We believe that the answer to this question is yes. Each new dataset brings in new challenges and contributes towards building better QA systems. It keeps researchers on their toes and prevents research from stagnating once state-of-the-art results are achieved on one dataset. A classic example of this is the CoNLL NER dataset (Tjong Kim Sang & De Meulder, 2003). While several NER systems (Passos et al., 2014) gave close to human performance on this dataset, NER on general web text, domain specific text, noisy social media text is still an unsolved problem (mainly due to the lack of representative datasets which cover the real-world challenges of NER). In this context, DuoRC presents 4 new challenges mentioned earlier which are not exhibited in existing RC datasets and would thus enable exploring novel neural approaches in complex language understanding. The hope is that all these datasets (including ours) will collectively help in addressing a wide range of challenges in QA and prevent stagnation via overfitting on a single dataset.
+# 3 DATASET
+In this section, we elaborate on our dataset collection process which consisted of the following three phrases.
+1. Extracting parallel movie plots: We first collected top 40K movies from IMDb across different genres (crime, drama, comedy, etc.) whose plot synopsis were crawled from Wikipedia as well as IMDb. We retained only 7680 movies for which both the plots were available and longer than 100 words. In general, we found that the IMDb plots were usually longer (avg. length 926 words) and more descriptive than the Wikipedia plots (avg. length 580 words).
+2. Collecting QA pairs from shorter version of the plot (SelfRC): As mentioned earlier, on average the longer version of the plot is almost double the size of the shorter version which is itself usually 500 words long. Intuitively, the longer version should have more details and the questions asked from the shorter version should be answerable from the longer one. Hence, we first showed the shorter version of the plot to workers on AMT and ask them to create QA pairs from it. For the answer, the workers were given freedom to either pick an answer which directly matches a span in the document or synthesize the answer from scratch. This option allowed them to be creative and ask hard questions where possible. We found that in $70 \%$ of the cases the workers picked an answer directly from the document and in $30 \%$ of the cases they synthesized the answer. We thus collected 85,773 such QA pairs along with their corresponding documents. We refer to this as the SelfRC dataset because the answers were derived from the same document from which the questions were asked.
+3. Collecting answers from longer version of the plot (ParaphraseRC): We then paired the questions from the SelfRC dataset with the corresponding longer version of the plot and showed it to a different set of AMT workers asking them to answer these questions from the longer version of the plot. They now have the option of either (a) selecting an answer which matches a span in the longer version, or (b) synthesizing the answer from scratch, or (c) marking the question not-answerable because of lack of information in the given passage. We found that in $50 \%$ of the cases the workers selected an answer which matched a span in the document, whereas in $37 \%$ cases they synthesized the answer and in $13 \%$ cases they said that question was not answerable. The workers were strictly instructed to derive the answer from the plot and not rely on their personal knowledge about the movie (in any case given the large number of movies in our dataset the chance of a worker remembering all the plot details for a given movie is very less). Further, a wait period of 2-3 weeks was deliberately introduced between the two phases of data collection to ensure the availability of a fresh pool of workers as well as to reduce information bias among any worker common to both the tasks. We refer to this dataset, where the questions are taken from one version of the document and the answers are obtained from a different version, as ParaphraseRC dataset. We collected 100,316 such {question, answer, document} triplets.
+Note that the number of unique questions in the ParaphraseRC dataset is the same as that in SelfRC because we do not create any new questions from the longer version of the plot. We end up with a greater number of {question, answer, document} triplets in ParaphraseRC as compared to SelfRC (100,316 v/s 85,773) since movies that are remakes of a previous movie had very little difference in their Wikipedia plots. Therefore, we did not separately collect questions from the Wikipedia plot of the remake. However, the IMDb plots of the two movies are very different and so we have two different longer versions of the movie (one for the original and one for the remake). We can thus pair the questions created from the Wikipedia plot with both the IMDb versions of the plot and hence we end up with more {question, answer, document} triplets.
+Table 1: Statistics regarding the Self and ParaphraseRC Datasets
+<table><tr><td rowspan=1 colspan=2>Question/Answer-Length Statistics</td></tr><tr><td rowspan=1 colspan=1>Avg. Question-Length</td><td rowspan=1 colspan=1>9 words</td></tr><tr><td rowspan=1 colspan=1>Avg.Answer Length (SelfRC Dataset)</td><td rowspan=1 colspan=1>3words</td></tr><tr><td rowspan=1 colspan=1>Avg.AnswerLength (ParaphraseRCDataset)</td><td rowspan=1 colspan=1>5words</td></tr><tr><td rowspan=1 colspan=1>Avg.Number of noun phrases in Question</td><td rowspan=1 colspan=1>4</td></tr><tr><td rowspan=1 colspan=1>Avg.Number of noun phrases in Answers</td><td rowspan=1 colspan=1>1.5</td></tr><tr><td rowspan=1 colspan=1>Comparative Hardness of ParaphraseRC w.r.t SelfRC</td><td rowspan=1 colspan=1>:.t SelfRC</td></tr><tr><td rowspan=1 colspan=1>% of QAs with no noun phrase common between Ques-tion and Answer (SelfRC)</td><td rowspan=1 colspan=1>35.86%</td></tr><tr><td rowspan=1 colspan=1>%of QAs with no noun phrase common between Ques-tion and Answer (ParaphraseRC)</td><td rowspan=1 colspan=1>49.76%</td></tr><tr><td rowspan=1 colspan=1>Avg.Minimum Distance between Named Entities inQuestion and Answer (in the Self and ParaphraseRCPlot)</td><td rowspan=1 colspan=1>Avg distance16wordsmore forParaphraseRC</td></tr><tr><td rowspan=1 colspan=1>% Length of the Longest Common Subsequence ofNon-stop words in Query and SelfRC plot</td><td rowspan=1 colspan=1>38.1%ofthequery</td></tr><tr><td rowspan=1 colspan=1>% Length of the Longest Common Subsequence ofNon-stop words in Query and ParaphraseRC plot</td><td rowspan=1 colspan=1>21.9%ofthequery</td></tr></table>
+![](images/df4e0e5c2b8ec94d99ad7d0345d9174b6ba227def1a974b43ca20c5006eb516b.jpg)
+Figure 2: Analysis of the Question Types
+We refer to this combined dataset containing a total of 186,089 instances as DuoRC. Fig. 2 shows the distribution of different Wh-type questions in our dataset. Some more interesting statistics about the dataset are presented in Table 1 and also in Appendix B.
+Another notable observation is that in many cases the answers to the same question are different in the two versions. Specifically, only $4 0 . 7 \%$ of the questions have the same answer in the two documents. For around $3 7 . 8 \%$ of the questions there is no overlap between the words in the two answers. For the remaining $21 \%$ of the questions there is a partial overlap between the two answers. For e.g., the answer derived from the shorter version could be “using his wife’s gun” and from the longer version could be “with Dana’s handgun” where Dana is the name of the wife. In Appendix A, we provide a few randomly picked examples from our dataset which should convince the reader of the difficulty of ParaphraseRC and its differences with SelfRC.
+# 4 MODELS
+In this section, we describe in detail the various state-of-the-art RC and language generation models along with a collection of traditional NLP techniques employed together that will serve to establish baseline performance on the DuoRC dataset.
+Most of the current state-of-the-art models for RC assume that the answer corresponds to a span in the document and the task of the model is to predict this span. This is indeed true for the SQuAD, TriviaQA and NewsQA datasets. However, in our dataset, in many cases the answers do not correspond to an exact span in the document but are synthesized by humans. Specifically, for the SelfRC version of the dataset around $30 \%$ of the answers are synthesized and do not match a span in the document whereas for the ParaphraseRC task this number is $50 \%$ . Nevertheless, we could still leverage the advances made on the SQuAD dataset and adapt these span prediction models for our task. To do so, we propose to use two models. The first model is a basic span prediction model which we train and evaluate using only those instances in our dataset where the answer matches a span in the document. The purpose of this model is to establish whether even for instances where the answer matches a span in the document, our dataset is harder than the SQuAD dataset or not. Specifically, we want to explore the performance of state-of-the-art models (such as DCN (Xiong et al., 2016)), which exhibit near human results on the SQuAD dataset, on DuoRC (especially, in the ParaphraseRC setup). To do so, we seek to employ a good span prediction model for which (i) the performance is within $3- 5 \%$ of the top performing model on the SQuAD leaderboard (Rajpurkar et al., 2016b) and (ii) the results are reproducible based on the code released by the authors of the paper. Note that the second criteria is important to ensure that the poor performance of the model is not due to incorrect implementation. The Bidirectional Attention Flow (BiDAF) model (Seo et al., 2016) satisfies these criteria and hence we employ this model. Due to space constraints, we do not provide details of the
+BiDAF model here and simply refer the reader to the original paper. In the remainder of this paper we will refer to this model as the SpanModel.
+The second model that we employ is a two stage process which first predicts the span and then synthesizes the answers from the span. Here again, for the first step (i.e., span prediction) we use the BiDAF model (Seo et al., 2016). The job of the second model is to then take the span (mini-document) and question (query) as input and generate the answer. For this, we employ a state-of-the-art query based abstractive summarization model (Nema et al., 2017) as this task is very similar to our task. Specifically, in query based abstractive summarization the training data is of the form {query, document, generated summary} and in our case the training data is of the form {query, mini-document, generated answer}. Once again we refer the reader to the original paper (Nema et al., 2017) for details of the model. We refer to this two stage model as the GenModel.
+Note that Tan et al. (2017) recently proposed an answer generation model for the MS MARCO dataset. However, the authors have not released their code and therefore, in the interest of reproducibility of our work, we omit incorporating this model in this paper.
+Additional NLP pre-processing: Referring back to the example cited in Fig. 1, we reiterate that ideally a good model for ParaphraseRC would require: (i) employing a knowledge graph, (ii) common-sense knowledge (iii) paraphrase/semantic understanding (iv) multiple-sentence inferencing across events in the passage including coreference resolution of named entities and nouns, and (v) educated guesswork when the question is not directly answerable but there are subtle hints in the passage. While addressing all of these challenges in their entirety is beyond the scope of a single paper, in the interest of establishing a good baseline for DuoRC, we additionally seek to address some of these challenges to a certain extent by using standard NLP techniques. Specifically, we look at the problems of paraphrase understanding, coreference resolution and handling long passages.
+To do so, we prune the document and extract only those sentences which are most relevant to the question, so that the span detector does not need to look at the entire 900-word long ParaphraseRC plot. Now, since these relevant sentences are obtained not from the original but the paraphrased version of the document, they may have a very small word overlap with the question. For example, the question might contain the word “hand gun” and the relevant sentence in the document may contain the word “revolver”. Further some of the named entities in the question may not be exactly present in the relevant sentence but may simply be co-referenced. To resolve these coreferences, we first employ the Stanford coreference resolution on the entire document. We then compute the fraction of words in a sentence which match a query word (ignoring stop words). Two words are considered to match if (a) they have the same surface form, or (b) one words is an inflected form of the word (e.g., river and rivers), or (c) the Glove and Skip-thought embeddings of the two words are very close to each other, or (d) the two words appear in the same synset in Wordnet. We consider a sentence to be relevant for the question if at least $50 \%$ of the query words (ignoring stop words) match the words in the sentence. If none of the sentences in the document have atleast $50 \%$ overlap with the question, then we pick sentences having atleast a $30 \%$ overlap with the question.
+# 5 EXPERIMENTAL SETUP
+In the following sub-sections we describe (i) the evaluation metrics, and (ii) the choices considered for augmenting the training data for the answer generation model. Note that when creating the train, validation and test set, we ensure that the test set does not contain question-answer pairs for any movie that was seen during training. We split the movies in such a way that the resulting train, valid, test sets respectively contain $70 \%$ , $15 \%$ and $15 \%$ of the total number of QA pairs.
+Span-Based Test Set and Full Test Set As mentioned earlier, the SpanModel only predicts the span in the document whereas the GenModel generates the answer after predicting the span. Ideally, the SpanModel should only be evaluated on those instances in the test set where the answer matches a span in the document. We refer to this subset of the test set as the Span-based Test Set. Though not ideal, we also evaluate the SpanModel model on the entire test set. We say this is not ideal because we know for sure that there are many answers in the test set which do not correspond to a span in the document whereas the model was only trained to predict spans. We refer to this as the Full Test Set. We also evaluate the GenModel on both the test sets.
+Training Data for the GenModel As mentioned earlier, the GenModel contains two stages; the first stage predicts the span and the second stage then generates an answer from the predicted span. For the first step we plug-in the best performing SpanModel from our earlier exploration. To train the second stage we need training data of the form $\{ x = s p a n , y = a n s w e r \}$ which comes from two types of instances: one where the answer matches a span and the other where the answer is synthesized and the span corresponding to it is not known. In the first case $x { = } y$ and there is nothing interesting for the model to learn (except for copying the input to the output). In the second case $x$ is not known. To overcome this problem, for the second type of instances, we consider various approaches for finding the approximate span from which the answer could have been generated, in order to augment the training data with $\{ x = a p p r o x \_ s p a n , y = a n s w e r \}$ pairs.
+The easiest method was to simply treat the entire document as the true span from which the answer was generated $x =$ document, $y = a n s w e r$ ). The second alternative that we tried was to first extract the named entities, noun phrases and verb phrases from the question and create a lucene query from these components. We then used the lucene search engine to extract the most relevant portions of the document given this query. We then considered this portion of the document as the true span (as opposed to treating the entire document as the true span). Note that lucene could return multiple relevant spans in which case we treat all these $\left\{ x = a p p r o x \ldots s p a n , y = a n s w e r \right.$ as training instances. Another alternative was to find the longest common subsequence (LCS) between the document and the question and treat this subsequence as the span from which the answer was generated. Of these, we found that the model trained using $\{ x = a p p r o x \_ s p a n , y = a n s w e r \}$ pairs created using the LCS based method gave the best results. We report numbers only for this model.
+Evaluation Metrics Similar to Rajpurkar et al. (2016a) we use Accuracy and F-score as the evaluation metric. While accuracy, being a stricter metric, considers a predicted answer to be correct only if it exactly matches the true answer, F-score also gives credit to predictions partially overlapping with the true answer.
+# 6 RESULTS AND DISCUSSIONS
+The results of our experiments are summarized in Tables 2 to 4 which we discuss in the following sub-sections.
+Table 2: Performance of the preprocessing step. Plot compression is the $\%$ size of the extracted plot w.r.t the original plot size
+<table><tr><td rowspan=1 colspan=1>Preprocessing step of Relevant Sub-plot Extraction</td><td rowspan=1 colspan=1>Plot Com-pression</td><td rowspan=1 colspan=1>AnswerRecall</td></tr><tr><td rowspan=1 colspan=1>Using WordNet synonym+Glove basedparaphrase</td><td rowspan=1 colspan=1>30%</td><td rowspan=1 colspan=1>66.51%</td></tr><tr><td rowspan=1 colspan=1>WordNet synonym + Glove based para-phrase on Coref resolved plots</td><td rowspan=1 colspan=1>50%</td><td rowspan=1 colspan=1>84.10%</td></tr><tr><td rowspan=1 colspan=1>WordNet synonym + Glove + Skip-thought based paraphrase on Coref re-solved plots</td><td rowspan=1 colspan=1>48%</td><td rowspan=1 colspan=1>85%</td></tr></table>
+Table 3: Performance of the SpanModel and GenModel on the Span Test subset and the Full Test Set of the Self and ParaphraseRC.
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>Span Test Set</td><td rowspan=1 colspan=2>Full Test Set</td></tr><tr><td rowspan=1 colspan=1>TrainOn</td><td rowspan=1 colspan=1>TestOn</td><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td></tr><tr><td rowspan=3 colspan=1>SelfRC</td><td rowspan=1 colspan=1>SelfRC</td><td rowspan=1 colspan=1>46.14</td><td rowspan=1 colspan=1>57.49</td><td rowspan=1 colspan=1>37.53</td><td rowspan=1 colspan=1>50.56</td></tr><tr><td rowspan=1 colspan=1>Para-phraseRC</td><td rowspan=1 colspan=1>27.85</td><td rowspan=1 colspan=1>36.82</td><td rowspan=1 colspan=1>15.16</td><td rowspan=1 colspan=1>22.70</td></tr><tr><td rowspan=1 colspan=1>SelfRC+ Para-phraseRC</td><td rowspan=1 colspan=1>37.79</td><td rowspan=1 colspan=1>48.05</td><td rowspan=1 colspan=1>25.05</td><td rowspan=1 colspan=1>35.01</td></tr><tr><td rowspan=3 colspan=1>Para-phraseRC</td><td rowspan=1 colspan=1>SelfRC</td><td rowspan=1 colspan=1>34.85</td><td rowspan=1 colspan=1>45.71</td><td rowspan=1 colspan=1>28.25</td><td rowspan=1 colspan=1>40.16</td></tr><tr><td rowspan=1 colspan=1>Para-phraseRC</td><td rowspan=1 colspan=1>19.74</td><td rowspan=1 colspan=1>27.57</td><td rowspan=1 colspan=1>10.78</td><td rowspan=1 colspan=1>17.13</td></tr><tr><td rowspan=1 colspan=1>SelfRC+Para-phraseRC</td><td rowspan=1 colspan=1>27.94</td><td rowspan=1 colspan=1>37.42</td><td rowspan=1 colspan=1>18.50</td><td rowspan=1 colspan=1>27.31</td></tr><tr><td rowspan=3 colspan=1>SelfRC +Para-phraseRC</td><td rowspan=1 colspan=1>SelfRC</td><td rowspan=1 colspan=1>49.66</td><td rowspan=1 colspan=1>61.45</td><td rowspan=1 colspan=1>40.24</td><td rowspan=1 colspan=1>54.04</td></tr><tr><td rowspan=1 colspan=1>Para-phraseRC</td><td rowspan=1 colspan=1>29.88</td><td rowspan=1 colspan=1>39.34</td><td rowspan=1 colspan=1>16.33</td><td rowspan=1 colspan=1>24.25</td></tr><tr><td rowspan=1 colspan=1>Self+Para-phraseRC</td><td rowspan=1 colspan=1>40.62</td><td rowspan=1 colspan=1>51.35</td><td rowspan=1 colspan=1>26.90</td><td rowspan=1 colspan=1>37.42</td></tr></table>
+Table 4: Combined and Cross-Testing between Self and ParaphraseRC Dataset, by taking the best performing SpanModel from Table 3.
+<table><tr><td rowspan=2 colspan=1>SelfRC</td><td rowspan=1 colspan=2>Span Test subset</td><td rowspan=1 colspan=2>Full Test set</td></tr><tr><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td></tr><tr><td rowspan=1 colspan=1>SpanModel</td><td rowspan=1 colspan=1>46.14</td><td rowspan=1 colspan=1>57.49</td><td rowspan=1 colspan=1>37.53</td><td rowspan=1 colspan=1>50.56</td></tr><tr><td rowspan=1 colspan=1>GenModel(withaug-mented training data)</td><td rowspan=1 colspan=1>16.45</td><td rowspan=1 colspan=1>26.97</td><td rowspan=1 colspan=1>15.31</td><td rowspan=1 colspan=1>24.05</td></tr><tr><td rowspan=2 colspan=1>ParaphraseRC</td><td rowspan=1 colspan=2>Span Test subset</td><td rowspan=1 colspan=2>Full Test set</td></tr><tr><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td></tr><tr><td rowspan=1 colspan=1>SpanModel</td><td rowspan=1 colspan=1>17.93</td><td rowspan=1 colspan=1>26.27</td><td rowspan=1 colspan=1>9.78</td><td rowspan=1 colspan=1>16.33</td></tr><tr><td rowspan=1 colspan=1>SpanModel with Prepro-cessed Data</td><td rowspan=1 colspan=1>27.49</td><td rowspan=1 colspan=1>35.10</td><td rowspan=1 colspan=1>14.92</td><td rowspan=1 colspan=1>21.53</td></tr><tr><td rowspan=1 colspan=1>GenModel(withaug-mented training data)</td><td rowspan=1 colspan=1>12.66</td><td rowspan=1 colspan=1>19.48</td><td rowspan=1 colspan=1>5.42</td><td rowspan=1 colspan=1>9.64</td></tr></table>
+• SpanModel v/s GenModel: Comparing the first two rows (SelfRC) and the last two rows (ParaphraseRC) of Table 3 we see that the SpanModel clearly outperforms the GenModel. This is not very surprising for two reasons. First, around $70 \%$ (and $50 \%$ ) of the answers in SelfRC (and ParaphraseRC) respectively, match an exact span in the document so the span based model still has scope to do well on these answers. On the other hand, even if the first stage of the GenModel predicts the span correctly, the second stage could make an error in generating the correct answer from it because generation is a harder problem. For the second stage, it is expected that the GenModel should learn to copy the predicted span to produce the answer output (as is required in most cases) and only occasionally where necessary, generate an answer. However, surprisingly the GenModel fails to even do this. Manual inspection of the generated answers shows that in many cases the generator ends up generating either more or fewer words compared the true answer. This demonstrates that there is clearly scope for the GenModel to perform better.
+• SelfRC v/s ParaphraseRC: Comparing the SelfRC and ParaphraseRC numbers in Table 3, we observe that the performance of the models clearly drops for the latter task, thus validating our hypothesis that ParaphraseRC is a indeed a much harder task.
+• Effect of NLP pre-processing: As mentioned in Section 4, for ParaphraseRC, we first perform a few pre-processing steps to identify relevant sentences in the longer document. In order to evaluate whether the pre-processing method is effective, we compute: (i) the percentage of the document that gets pruned, and (ii) whether the true answer is present in the pruned document (i.e., average recall of the answer). We can compute the recall only for the span-based subset of the data since for the remaining data we do not know the true span. In Table 2, we report these two quantities for the span-based subset using different pruning strategies. Finally, comparing the SpanModel with and without Paraphrasing in Table 3 for ParaphraseRC, we observe that the pre-processing step indeed improves the performance of the Span Detection Model.
+• Effect of oracle pre-processing: As noted in Section 3, the ParaphraseRC plot is almost double in length in comparison to the SelfRC plot, which while adding to the complexities of the former task, is clearly not the primary reason of the model’s poor performance on that. To empirically validate this, we perform an Oracle pre-processing step, where, starting with the knowledge of the span containing the true answer, we extract a subplot around it such that the span is randomly located within that subplot and the average length of the subplot is similar to the SelfRC plots. The SpanModel with this Oracle preprocessed data exhibits a minor improvement in performance over that with rule-based preprocessing ( $1 . 6 \%$ in Accuracy and $4 . 3 \%$ in F1 over the Span Test), still failing to bridge the wide performance gap between the SelfRC and ParaphraseRC task.
+• Cross Testing We wanted to examine whether a model trained on SelfRC performs well on ParaphraseRC and vice-versa. We also wanted to evaluate if merging the two datasets improves the performance of the model. For this we experimented with various combinations of train and test data. The results of these experiments for the SpanModel are summarized in Table 4. We make two main observations. First, training on one dataset and evaluating on the other results in a drop in the performance. Merging the training data from the two datasets exhibits better performance on the individual test sets.
+Based on our experiments and empirical observations we believe that the DuoRC dataset indeed holds a lot of potential for advancing the horizon of complex language understanding by exposing newer challenges in this area.
+# 7 CONCLUSION
+In this paper we introduced DuoRC, a large scale RC dataset of 186K human-generated questionanswer pairs created from 7680 pairs of parallel movie-plots, each pair taken from Wikipedia and IMDb. We then showed that this dataset, by design, ensures very little or no lexical overlap between the questions created from one version and the segments containing the answer in the other version. With this, we hope to introduce the RC community to new research challenges on question-answering requiring external knowledge and common-sense driven reasoning, deeper language understanding and multiple-sentence inferencing. Through our experiments, we show how the state-of-the-art RC models, which have achieved near human performance on the SQuAD dataset, perform poorly on our dataset, thus emphasizing the need to explore further avenues for research.
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+Chuanqi Tan, Furu Wei, Nan Yang, Weifeng Lv, and Ming Zhou. S-net: From answer extraction to answer generation for machine reading comprehension. CoRR, abs/1706.04815, 2017. URL http://arxiv.org/abs/1706.04815.
+Makarand Tapaswi, Yukun Zhu, Rainer Stiefelhagen, Antonio Torralba, Raquel Urtasun, and Sanja Fidler. Movieqa: Understanding stories in movies through question-answering. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.
+Erik F. Tjong Kim Sang and Fien De Meulder. Introduction to the conll-2003 shared task: Languageindependent named entity recognition. In Walter Daelemans and Miles Osborne (eds.), Proceedings of CoNLL-2003, pp. 142–147. Edmonton, Canada, 2003.
+Adam Trischler, Tong Wang, Xingdi Yuan, Justin Harris, Alessandro Sordoni, Philip Bachman, and Kaheer Suleman. Newsqa: A machine comprehension dataset. CoRR, abs/1611.09830, 2016. URL http://arxiv.org/abs/1611.09830.
+Dirk Weissenborn, Georg Wiese, and Laura Seiffe. Making neural QA as simple as possible but not simpler. In Proceedings of the 21st Conference on Computational Natural Language Learning (CoNLL 2017), Vancouver, Canada, August 3-4, 2017, pp. 271–280, 2017. doi: 10.18653/v1/ K17-1028. URL https://doi.org/10.18653/v1/K17-1028.
+Caiming Xiong, Victor Zhong, and Richard Socher. Dynamic coattention networks for question answering. CoRR, abs/1611.01604, 2016. URL http://arxiv.org/abs/1611.01604.
+# APPENDIX A EXAMPLES
+In this appendix, we showcase some examples of plots from which questions are created and answered. Since the questions are created from the smaller plot, answering these questions by the reading the smaller plot (which is named as the SelfRC task) is straightforward. However, answering them by reading the larger plot (i.e. the ParaphraseRC task) is more challenging and requires multi-sentence and sometimes multi-paragraph inferencing.
+Due to shortage of space, we truncate the plot contents and only show snippets from which the questions can be answered. In the smaller plot, blue indicates that an answer can directly be found from the sentence and cyan indicates that the answer spans over multiple sentences. For the larger plot, red and orange are used respectively.
+# A.1 EXAMPLE 1: PALE RIDER (1985)
+# A.1.1 SMALLER PLOT
+In the countryside outside the fictional town of Lahood, California, sometime around 1880, [[thugs working for big-time miner Coy LaHood ride in and destroy the camp of a group of struggling miners]Q1 and their families who have settled in nearby Carbon Canyon and are panning for gold there. In leaving, they also shoot the little dog of fourteen-year-old Megan Wheeler]Q15. As Megan buries her dog in the woods and prays for a miracle, a stranger passes by heading to the town on horseback.
+[Megan’s mother, Sarah]Q16, is being courted by [Hull Barret, the leader of the miners]Q17 . . . [Coy LaHood’s son Josh]Q8 . . . [Club, who with one hammer blow smashes a large rock]Q7 . . . [Coy LaHood has been away in Sacramento]Q9 . . . [[Megan, who has grown fond of the Preacher, goes looking for him, but Josh confronts and attempts to rape her]Q11, while his cohorts look on and encourage him, except for Club, who sees what is happening and moves forward to help Megan]Q13 before Josh can do anything serious. At this moment the [Preacher arrives on horseback armed with a Remington Model 1858 revolver he has recovered from a Wells Fargo office and, after shooting Josh]Q14 . . . [Stockburn, who appears startled and says that he sounds like someone that he once knew, but that couldn’t be, since that man is dead]Q5. [Stockburn and his men gun down Spider Conway] Q4, . . .
+[The Preacher and Hull go to LaHood’s strip mining site and blow it up with dynamite]Q6. [To stop Hull from following him, the Preacher then scares off Hull’s horse]Q3 and rides into town alone. . . [Coy LaHood, watching from his office]Q10, . [snow-covered mountains]Q2. [Megan then drives into town and shouts her love to the Preacher]Q12 and thanks after him. The words echo along the ravine that he is traversing.
+# A.1.2 LARGER PLOT
+Somewhere in California, at the end of the Gold Rush, several horsemen come riding down from the nearby mountains . . . [The horsemen shoot cattle and Megan’s dog]Q4,Q15, and then chase donkeys as they leave . . .
+Hull describes the fight between the stranger and McGill and his men. [Megan’s mother, Sarah]Q16 says he sounds no different from McGill, Tyson, or any of LaHood’s roughnecks . . . Preacher says there is lot of sinners around, that he can’t leave before he finishes his work. [Josh says, ”Club”, who gets down and walks into the stream. Everyone is apprehensive. He rolls down his sleeves, and then. . . quickly grabs Hull’s sledgehammer with one hand and strikes the boulder once, screaming, splitting it]Q7 .
+[A train pulls into the station from Sacramento while Josh and McGill wait. [Josh’s father Coy LaHood]]Q8,Q9 (Richard Dysart) exits the train, and then he goes with Josh and McGill. . .
+Josh asks what she really came for. She replies that she’s just riding, taking a look around. [Josh says he wants to take a look too, at her real close. He pulls her off the horse. She screams as he carries her downhill. . . Josh grabs her hair and kisses her. They both fall to the ground. The men cheer him on while Megan begs him to stop]Q11 . . . a gunshot sounds out. Josh gets up and everyone turns around. [Preacher, on his horse. . . His gun is trained on Josh. Megan sees him and smiles]Q13, . . . [Josh falls to the ground. He reaches for his gun, but Preacher shoots his hand]Q14 . . . LaHood replies, ”Tall. Lean. His eyes. . . his eyes. Something strange about em. That mean something to you?” [Stockburn says that it sounds like a man he knew, but that man is dead]Q5 . . . [LaHood watches through the window]Q10 as they kill Spider, . . .
+Table 5: QA for Pale Rider
+<table><tr><td>Question</td><td></td><td>Shorter Plot Answer</td><td>Larger Plot Answer</td></tr><tr><td>Q1</td><td>For which big-time miner are the thugs who destroyed miners camp in Carbon Canyon working for?</td><td>Coy Lahood</td><td>Coy Lahood</td></tr><tr><td>Q2</td><td>How are the mountains in the film?</td><td>Covered with snow</td><td> snow-capped</td></tr><tr><td>Q3</td><td>How does the Preacher stop Hull from following him?</td><td> Scares Hulls&#x27; horse</td><td>To stop Hull from following him, the Preacher then scares off Hull&#x27;s horse and rides into town alone</td></tr><tr><td>Q4</td><td>In the movie, who do Stockburn and his men gun down?</td><td> Spider Conway</td><td>Megan&#x27;s dog and cattle</td></tr><tr><td>Q5</td><td>In the movie, why does Stockburn say that the Preacher could not be the man he once knew?</td><td> that man is dead</td><td>The man Stockburn once knew is dead</td></tr><tr><td>Q6</td><td>What did they use to blow up the strip mining site?</td><td>Dynamite</td><td>dynamite</td></tr><tr><td>Q7</td><td>What does Club smash?</td><td>A rock</td><td>A Boulder</td></tr><tr><td>Q8</td><td>What is Coy Lahood&#x27;s relation to Josh?</td><td>Father and son</td><td>Father</td></tr><tr><td>Q9</td><td>Where has Coy Lahood been living?</td><td> Sacramento</td><td> Sacramento</td></tr><tr><td>Q10</td><td>Where was Coy watching from?</td><td>Office</td><td> a window</td></tr><tr><td>Q11</td><td> Who attempts to rape Megan?</td><td>Josh</td><td>Josh</td></tr><tr><td>Q12</td><td>Who does megan love?</td><td>The preacher</td><td>The preacher</td></tr><tr><td>Q13</td><td>Who prevents Josh from raping Megan?</td><td>Club</td><td>the preacher The</td></tr><tr><td>Q14</td><td>Who shoots Josh in the hand?</td><td>Preacher</td><td> Preacher</td></tr><tr><td>Q15</td><td>Whose little dog did the thugs shoot?</td><td>Megan Wheeler</td><td> Megan</td></tr><tr><td>Q16</td><td>Who is Megan&#x27;s mother?</td><td> Sarah</td><td> Sarah</td></tr><tr><td>Q17</td><td>Who is the leader of the miners ?</td><td>Hull Barret</td><td>Coy LaHood</td></tr></table>
+Hull insists on going with him so Preacher agrees. [They go to the LaHood camp and blow up their pipes, sluices, tents, and the barracks with dynamite]Q6. [After fooling Hull to dismount, Preacher scares away his horse. He then tells Hull to take care of Sarah and Megan, and rides into town]Q3 . . . Blankenship tells her that the horses are exhausted and she would kill them. [Megan runs to the end of town and shouts out thank you to Preacher, that they love him, that she loves him]Q12 . . . The final shot of the movie shows Preacher riding through the [snow in the mountains]Q2.
+# A.2 EXAMPLE 2: BIG JAKE (1971)
+# A.2.1 SMALLER PLOT
+[In 1909]Q6, [there is a raid on the McCandles family . . . Martha, the head of the family . . . [In consequence, she sends for her estranged husband, the aging Jacob ”Big Jake” McCandles]Q9, . . . [the ransom to the kidnappers, a million dollars]Q4
+. . . [The Texas Ranger captain is present and offers the services of his men]Q11, . . . Jake, preferring the old ways, has followed on horseback, accompanied by an old Apache associate, Sam Sharpnose. [He is now joined by his sons, Michael and James]Q2, . . . Knowing that they have been followed by another gang intent on stealing the strongbox, [Jake sets a trap for them and they are all killed]Q16. [During the attack, the chest is blasted open]Q1, [revealing clipped bundles of newspaper instead of money] Q5
+A thunderstorm breaks and [Pop Dawson, one of the outlaws, arrives to give them the details of the exchange]Q7 . . . [Jake arranges for Michael to follow after them to take care of the sharp] . . . [Jake tosses the key of the chest to Fain, who opens it up to discover that he has been tricked]Q12. [Fain orders his brother Will to kill the boy]Q13 but he is shot by Jake. [Dog is wounded by the sniper]Q15 and Jake is wounded in the leg before Michael kills him. Jake tells the boy to escape but Little Jake is hunted by the machete wielding [John Goodfellow, who has already hacked Sam to death]Q10 . . . [With Little Jake rescued, and the broken family bonded, they prepare to head home]Q3.
+# A.2.2 LARGER PLOT
+[[Jacob McCandles (John Wayne) is a big man with a bigger reputation. A successful rancher and landowner]Q14, his many businesses keep him conveniently away from his home and estranged wife Martha (Maureen O’Hara)]Q9. . . , [and is demanding one million dollars for his safe return]Q4.
+[The local sheriff has convened a posse complete with then state-of-the-art automobiles. [Two of Jake’s sons, the passionate, gunslinging James (Patrick Wayne) and the motorcycle-riding, sharpshooting Michael (Christopher Mitchum) $] ^ { Q 2 }$ elect to go with the sheriff’s posse. Big Jake decides to set off across the rough terrain on his horse with his Dog at his side, and soon meets up with his Native American friend, Sam Sharpnose (Bruce Cabot), who has brought additional horses and supplies]Q11.
+[They then devise their strategy: James will go have a good time in the saloon, Big Jake will head to the barbershop for a shower, Sam will secrete himself on the roof of the hotel, seemingly leaving Michael alone protecting the strong box. Big Jake tells Sam to listen for a ”disturbance” in the street, and use the distraction to join Michael in the hotel room to protect the strong box. As Big Jake predicted, the gang tries to hit the strong box when it looks most vulnerable. Fain and another of his gang members start a fight with James in the saloon, one keeps a gun on Big Jake in the barbershop, and two others come up the hotel stairs and toward the room. Big Jake dispatches his captor in the barbershop, James fights his way out of the saloon with Jake’s help, and the two head to the hotel. At the hotel, once Sam hears the fight in the saloon, he climbs over the roof and slips in the window to aid Michael in protecting the strong box. Shotguns blast as the gang hits the hotel room. When James and Jake arrive they find Sam, Michael and the Dog unharmed, [but the strong box has suffered damage. To their horror, James and Michael realize they’ve been risking their lives to protect a box of newspaper clippings!]]Q1,Q5,Q16 .
+[Big Jake takes the few moments he has to plan with his sons. He tells Michael of the sharpshooter and instructs him to find a high position and take him out whenever he can. Big Jake takes the Dog and goes to the meet as instructed, while the others follow discreetly behind]Q8 . . . [As Fain unlocks the strong box, he realizes hes been had ´ ]Q12. Big Jake whispers to him that no matter what happens, Fain will be the first one to die. [Fain screams his command to kill the boy ]Q13,
+[Dog giving his life protecting Little Jake from one of Fain’s machete-wielding gang]Q15. . . Sam points him toward James at the exit, [who helps Little Jake escape. Fain and Big Jake are in a duel to the death, when Michael takes a fatal shot at Fain, saving his father and Little Jake. After a harrowing journey and a risky gamble, the family leaves, happy to be together]Q3.
+Table 6: QA for Big Jake
+<table><tr><td>Question</td><td></td><td>Shorter Plot Answer</td><td>Larger Plot Answer</td></tr><tr><td>Q1</td><td>How was the strongbox opened?</td><td>It was blasted during an attack</td><td>it was damaged during the fight</td></tr><tr><td>Q2</td><td>What are the names of Jake&#x27;s sons?</td><td>Jake&#x27;s sons are Michael and James</td><td>James and Michael</td></tr><tr><td>Q3</td><td>What did the family prepare to do once Jake had been rescued?</td><td>head home</td><td>Leave</td></tr><tr><td>Q4</td><td>What is the amount of the ransom?</td><td>The ransom amount is a million dollars</td><td> one million dollars</td></tr><tr><td>Q5</td><td>What was in the strongbox?</td><td>Clipped bundles of newspaper</td><td> newspaper clippings</td></tr><tr><td>Q6</td><td>What year does the movie take place?</td><td>1909</td><td> No Answer</td></tr><tr><td>Q7</td><td>Which outlaw gives details of the exchange to the others?</td><td>Pop Dawson</td><td> No Answer</td></tr><tr><td>Q8</td><td>Who does Jake arrange to follow the rest of the group?</td><td>Michael</td><td>Michael</td></tr><tr><td>Q9</td><td>Who is married to Big Jake?</td><td>Martha</td><td>Martha</td></tr><tr><td>Q10</td><td>Who killed Sam?</td><td>John Goodfellow</td><td> No Answer</td></tr><tr><td>Q11</td><td>Who offers his services to help Jake combat the kidnappers?</td><td>The Texas ranger captain offers the services of men</td><td>the posse, native American friend and his two sons</td></tr><tr><td>Q12</td><td>Who opens the chest to discover he has been tricked?</td><td>Fain</td><td>Fain</td></tr><tr><td>Q13</td><td>Who orders Will to kill the boy?</td><td>Fain</td><td>Fain</td></tr><tr><td>Q14</td><td>Who owns the ranch?</td><td>McCandles family</td><td> McCandles family</td></tr><tr><td>Q15</td><td>Who wounded the dog?</td><td>A sniper</td><td>Fain&#x27;s machete-wielding gang</td></tr><tr><td>Q16</td><td>Why does Jake set a trap and kill another gang?</td><td>on stealing the strongbox</td><td>to protect the strongbox</td></tr></table>
+# APPENDIX B DATA ANALYSIS
+We conducted a manual verification of 100 question-answer pairs where the SelfRC and ParaphraseRC were different or the latter was marked as non-answerable. As noted in Fig. 3, the chief reason behind getting No Answer from the Paraphrase plot is lack of information and at times, need for an educated guesswork or missing general knowledge (e.g. Philadelphia is a city) or missing movie meta-data (e.g. to answer questions like ‘Where did Julia Roberts’ character work in the movie?’). On the other hand, SelfRC and ParaphraseRC answers are occasionally seen to have partial or no overlap, mainly because of the following causes; phrasal paraphrases or subjective questions (e.g. Why and How type questions) or different valid answers to objective questions (e.g. ‘Where did Jane work?’ is answered by one worker as ‘Bloomberg�� and other as ‘New York City’) or differently spelt names in the answers (e.g. ‘Rebeca’ as opposed to ‘Rebecca’).
+![](images/cc758b5c05b95d333ecb70264727ad69aa0622190ab33fdd35c3f0f51c68a706.jpg)
+Figure 3: Manual Analysis of 100 Questions and their corresponding answers from the SelfRC and ParaphraseRC Dataset to understand the various reasons behind these two answers being different or the latter being non-answerable
+# APPENDIX C MODEL ARCHITECTURE
+Fig. 4 illustrates the 5-step process of answering a question from the comprehension, by optionally pre-processing the input passage in Step 2 and 3, then using the BiDirectional Attention Flow (BiDAF) model for Span identification, and finally generating the answer text from the identified span by employing a state-of-the-art query-based Abstractive Summarization (qBAS) model.
+![](images/bbf4e4186cba1284a210e98de5e53be59cef477dc4238c76a15317654ae61e4e.jpg)
+Figure 4: Model architecture
+Question: Peters is aboard the plane with what?
+# APPENDIX D PERFORMANCE ANALYSIS
+In Fig. 5 we show a performance analysis of the SelfRC and ParaphraseRC tasks when evaluated on the Span Test Subset and the Full Test Set, over different question types and plots of different length.
+![](images/dc5087c0dbcf25d98d448d4fcd1a74b4dfda8d170bea4b4bfb36212da7cd6e05.jpg)
+Figure 5: Performance Analysis of the Self and ParaphraseRC on different plot-lengths or different questiontypes

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+        "text": "DUORC: TOWARDS COMPLEX LANGUAGE UNDER-STANDING WITH PARAPHRASED READING COMPRE-HENSION",
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+        "text": "Anonymous authors Paper under double-blind review ",
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+        "text": "ABSTRACT ",
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+        "text": "We propose DuoRC, a novel dataset for Reading Comprehension (RC) that motivates several new challenges for neural approaches in language understanding beyond those offered by existing RC datasets. DuoRC contains 186,089 unique question-answer pairs created from a collection of 7680 pairs of movie plots where each pair in the collection reflects two versions of the same movie - one from Wikipedia and the other from IMDb - written by two different authors. We asked crowdsourced workers to create questions from one version of the plot and a different set of workers to extract or synthesize answers from the other version. This unique characteristic of DuoRC where questions and answers are created from different versions of a document narrating the same underlying story, ensures by design, that there is very little lexical overlap between the questions created from one version and the segments containing the answer in the other version. Further, since the two versions have different levels of plot detail, narration style, vocabulary, etc., answering questions from the second version requires deeper language understanding and incorporating external background knowledge. Additionally, the narrative style of passages arising from movie plots (as opposed to typical descriptive passages in existing datasets) exhibits the need to perform complex reasoning over events across multiple sentences. Indeed, we observe that state-ofthe-art neural RC models which have achieved near human performance on the SQuAD dataset (Rajpurkar et al., 2016b), even when coupled with traditional NLP techniques to address the challenges presented in DuoRC exhibit very poor performance (F1 score of $3 7 . 4 2 \\%$ on DuoRC v/s $86 \\%$ on SQuAD dataset). This opens up several interesting research avenues wherein DuoRC could complement other RC datasets to explore novel neural approaches for studying language understanding. ",
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+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "text": "Natural Language Understanding is widely accepted to be one of the key capabilities required for AI systems. Scientific progress on this endeavor is measured through multiple tasks such as machine translation, reading comprehension, question-answering, and others, each of which requires the machine to demonstrate the ability to “comprehend” the given textual input (apart from other aspects) and achieve their task-specific goals. In particular, Reading Comprehension (RC) systems are required to “understand” a given text passage as input and then answer questions based on it. It is therefore critical, that the dataset benchmarks established for the RC task keep progressing in complexity to reflect the challenges that arise in true language understanding, thereby enabling the development of models and techniques to solve these challenges. ",
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+        "text": "For RC in particular, there has been significant progress over the recent years with several benchmark datasets, the most popular of which are the SQuAD dataset (Rajpurkar et al., 2016a), TriviaQA (Joshi et al., 2017), MS MARCO (Nguyen et al., 2016), MovieQA (Tapaswi et al., 2016) and cloze-style datasets(Mostafazadeh et al., 2016; Onishi et al., 2016; Hermann et al., 2015). However, these benchmarks, owing to both the nature of the passages and the question-answer pairs to evaluate the RC task, have 2 primary limitations in studying language understanding: (i) Other than MovieQA, which is a small dataset of 15K QA pairs, all other large-scale RC datasets deal only with factual descriptive passages and not narratives (involving events with causality linkages that require reasoning ",
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+        "text": "Movie: Twelve Monkeys ",
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+        "text": "Original Plot Synopsis(Wikipedia) ",
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+        "text": "A deadly virus released in 1996..,[James Cole is a prisoner living in a subterranean compound beneath the ruins of Philadelphia $1 ^ { \\circ 1 }$ [Cole is selected foramission]Q2 ",
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+        "text": "[Cole arrives in Baltimore]Q3 in 1990, not 1996 as planned...[Goines denies any involvement with the group and says that in 199o Cole originated the idea of wiping out humanity with a virus stolen from Goines' virologist father.jQ4 ",
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+        "text": "Cole forces his way through a security checkpoint... [Peters, aboard theplane with the virus]Q8 ",
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+        "text": "A virus,deliberately released in 1996 .. One such prisoner is [James Cole,who after retrieving samples is given the chance to go back in time to $1 9 9 6 ] ^ { \\circ 2 }$ and find information about the group believed responsible, known as \"The Army of 12 Monkeys.\" ",
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+        "text": "[Jeffrey rambles about how Cole had given him the idea to release a virus that would destroy most of humanity. $| ^ { \\circ 4 }$ Cole leaves,...and then posts flyers declaring \"We did it!\"[Cole realizes that the \"Army\" isnot the threat, and he leaves a phone message to that effectjQ6. ",
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+        "text": "[Jose,a fellow \"volunteer\" from the present,approaches Cole with orders forhimtocompletehismissionand handshima revolverjQ7...Inan airport,while attempting with Cole to elude capture, Dr. Railly recognizes [Dr Peters,a man who worked with Jeffrey Goines's father.... The man goes through airport screening and manages to persuade security that his biological samplesjQ8 ",
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+        "text": "Q1: James Cole is a prisonerliving in a subterranean shelter beneath what city?Philadelphia,Philadelphia Q2:What is the name of the person selected for the mission? James Cole, James Cole Q3:Where did Cole arrive in 1990? Baltimore, - Q4: Who does Goines claim came up with the idea to exterminate humanity? Cole, Cole Q5:Where do Cole and Railly decide to go before the plague? Florida Keys, Q6:Where does Cole leave his message? At the airport， on the phone Q7:Who gives Cole a handgun? Jose， Jose Q8:Peters is aboard the plane with what? Virus, biological samples ",
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+        "type": "text",
+        "text": "Figure 1: Example QA pairs obtained from the original movie plot and the paraphrased plot. The relevant spans needed for answering the corresponding question are highlighted in blue and red with the respective question numbers. Note that the span highlighting shown here is for illustrative purposes only and is not available in the dataset. ",
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+        "text": "and background knowledge) which is the case with a lot of real-world content such as story books, movies, news reports, etc. (ii) their questions possess a large lexical overlap with segments of the passage, or have a high noise level in Q/A pairs themselves. As demonstrated by recent work, this makes it easy for even simple keyword matching algorithms to achieve high accuracy (Weissenborn et al., 2017). In fact, these models have been shown to perform poorly in the presence of adversarially inserted sentences which have a high word overlap with the question but do not contain the answer (Jia & Liang, 2017). While this problem does not exist in TriviaQA it is admittedly noisy because of the use of distant supervision. Similarly, for cloze-style datasets, due to the automatic question generation process, it is very easy for current models to reach near human performance (Cui, 2017). This therefore limits the complexity in language understanding that a machine is required to demonstrate to do well on the RC task. ",
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+        "type": "text",
+        "text": "Motivated by these shortcomings and to push the state-of-the-art in language understanding in RC, in this paper we propose DuoRC, which specifically presents the following challenges beyond the existing datasets: ",
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+        "text": "1. DuoRC is especially designed to contain a large number of questions with low lexical overlap between questions and their corresponding passages.   \n2. It requires the use of background and common-sense knowledge to arrive at the answer and go beyond the content of the passage itself.   \n3. It contains narrative passages from movie plots that require complex reasoning across multiple sentences to infer the answer.   \n4. Several of the questions in DuoRC, while seeming relevant, cannot actually be answered from the given passage, thereby requiring the machine to detect the unanswerability of questions. ",
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+        "text": "In order to capture these four challenges, DuoRC contains QA pairs created from pairs of documents describing movie plots which were gathered as follows. Each document in a pair is a different version of the same movie plot written by different authors; one version of the plot is taken from the Wikipedia page of the movie whereas the other from its IMDb page (see Fig. 1 for portions of an example pair of plots from the movie “Twelve Monkeys”). We first showed crowd workers on Amazon Mechanical Turk (AMT) the first version of the plot and asked them to create QA pairs from it. We then showed the second version of the plot along with the questions created from the first version to a different set of workers on AMT and asked them to provide answers by reading the second version only. Since the two versions contain different levels of plot detail, narration style, vocabulary, etc., answering questions from the second version exhibits all of the four challenges mentioned above. ",
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+        "type": "text",
+        "text": "We now make several interesting observations from the example in Fig. 1. For 4 out of the 8 questions (Q1, Q2, Q4, and Q7), though the answers extracted from the two plots are exactly the same, the analysis required to arrive at this answer is very different in the two cases. In particular, for Q1 even though there is no explicit mention of the prisoner living in a subterranean shelter and hence no lexical overlap with the question, the workers were still able to infer that the answer is Philadelphia because that is the city to which James Cole travels to for his mission. Another interesting characteristic of this dataset is that for a few questions (Q6, Q8) alternative but valid answers are obtained from the second plot. Further, note the kind of complex reasoning required for answering Q8 where the machine needs to resolve coreferences over multiple sentences (that man refers to Dr. Peters) and use common sense knowledge that if an item clears an airport screening, then a person can likely board the plane with it. To re-emphasize, these examples exhibit the need for machines to demonstrate new capabilities in RC such as: (i) employing a knowledge graph (e.g. to know that Philadelphia is a city in Q1), (ii) common-sense knowledge (e.g., clearing airport security implies boarding) (iii) paraphrase/semantic understanding (e.g. revolver is a type of handgun in Q7) (iv) multiple-sentence inferencing across events in the passage including coreference resolution of named entities and nouns, and (v) educated guesswork when the question is not directly answerable but there are subtle hints in the passage (as in Q1). Finally, for quite a few questions, there wasn’t sufficient information in the second plot to obtain their answers. In such cases, the workers marked the question as “unanswerable”. This brings out a very important challenge for machines to exhibit (i.e. detect unanswerability of questions) because a practical system should be able to know when it is not possible for it to answer a particular question given the data available to it, and in such cases, possibly delegate the task to a human instead. ",
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+        "type": "text",
+        "text": "Current RC systems built using existing datasets are far from possessing these capabilities to solve the above challenges. In Section 4, we seek to establish solid baselines for DuoRC employing state-of-the-art RC models coupled with a collection of standard NLP techniques to address few of the above challenges. Proposing novel neural models that solve all of the challenges in DuoRC is out of the scope of this paper. Our experiments demonstrate that when the existing state-of-the-art RC systems are trained and evaluated on DuoRC they perform poorly leaving a lot of scope for improvement and open new avenues for research in RC. Do note that this dataset is not a substitute for existing RC datasets but can be coupled with them to collectively address a large set of challenges in language understanding with RC (the more the merrier). ",
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+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Over the past few years, there has been a surge in datasets for Reading Comprehension. Most of these datasets differ in the manner in which questions and answers are created. For example, in SQuAD (Rajpurkar et al., 2016a), NewsQA (Trischler et al., 2016), TriviaQA (Joshi et al., 2017) and MovieQA (Tapaswi et al., 2016) the answers correspond to a span in the document. MS-MARCO uses web queries as questions and the answers are synthesized by workers from documents relevant to the query. On the other hand, in most cloze-style datasets (Mostafazadeh et al., 2016; Onishi et al., 2016) the questions are created automatically by deleting a word/entity from a sentence. There are also some datasets for RC with multiple choice questions (Richardson et al., 2013; Berant et al., 2014; Lai et al., 2017) where the task is to select one among $k$ given candidate answers. ",
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+        "type": "text",
+        "text": "Given that there are already a few datasets for RC, a natural question to ask is “Do we really need any more datasets?”. We believe that the answer to this question is yes. Each new dataset brings in new challenges and contributes towards building better QA systems. It keeps researchers on their toes and prevents research from stagnating once state-of-the-art results are achieved on one dataset. A classic example of this is the CoNLL NER dataset (Tjong Kim Sang & De Meulder, 2003). While several NER systems (Passos et al., 2014) gave close to human performance on this dataset, NER on general web text, domain specific text, noisy social media text is still an unsolved problem (mainly due to the lack of representative datasets which cover the real-world challenges of NER). In this context, DuoRC presents 4 new challenges mentioned earlier which are not exhibited in existing RC datasets and would thus enable exploring novel neural approaches in complex language understanding. The hope is that all these datasets (including ours) will collectively help in addressing a wide range of challenges in QA and prevent stagnation via overfitting on a single dataset. ",
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+        "type": "text",
+        "text": "3 DATASET ",
+        "text_level": 1,
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+        "text": "In this section, we elaborate on our dataset collection process which consisted of the following three phrases. ",
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+        "text": "1. Extracting parallel movie plots: We first collected top 40K movies from IMDb across different genres (crime, drama, comedy, etc.) whose plot synopsis were crawled from Wikipedia as well as IMDb. We retained only 7680 movies for which both the plots were available and longer than 100 words. In general, we found that the IMDb plots were usually longer (avg. length 926 words) and more descriptive than the Wikipedia plots (avg. length 580 words). ",
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+        "type": "text",
+        "text": "2. Collecting QA pairs from shorter version of the plot (SelfRC): As mentioned earlier, on average the longer version of the plot is almost double the size of the shorter version which is itself usually 500 words long. Intuitively, the longer version should have more details and the questions asked from the shorter version should be answerable from the longer one. Hence, we first showed the shorter version of the plot to workers on AMT and ask them to create QA pairs from it. For the answer, the workers were given freedom to either pick an answer which directly matches a span in the document or synthesize the answer from scratch. This option allowed them to be creative and ask hard questions where possible. We found that in $70 \\%$ of the cases the workers picked an answer directly from the document and in $30 \\%$ of the cases they synthesized the answer. We thus collected 85,773 such QA pairs along with their corresponding documents. We refer to this as the SelfRC dataset because the answers were derived from the same document from which the questions were asked. ",
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+        "type": "text",
+        "text": "3. Collecting answers from longer version of the plot (ParaphraseRC): We then paired the questions from the SelfRC dataset with the corresponding longer version of the plot and showed it to a different set of AMT workers asking them to answer these questions from the longer version of the plot. They now have the option of either (a) selecting an answer which matches a span in the longer version, or (b) synthesizing the answer from scratch, or (c) marking the question not-answerable because of lack of information in the given passage. We found that in $50 \\%$ of the cases the workers selected an answer which matched a span in the document, whereas in $37 \\%$ cases they synthesized the answer and in $13 \\%$ cases they said that question was not answerable. The workers were strictly instructed to derive the answer from the plot and not rely on their personal knowledge about the movie (in any case given the large number of movies in our dataset the chance of a worker remembering all the plot details for a given movie is very less). Further, a wait period of 2-3 weeks was deliberately introduced between the two phases of data collection to ensure the availability of a fresh pool of workers as well as to reduce information bias among any worker common to both the tasks. We refer to this dataset, where the questions are taken from one version of the document and the answers are obtained from a different version, as ParaphraseRC dataset. We collected 100,316 such {question, answer, document} triplets. ",
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+        "type": "text",
+        "text": "Note that the number of unique questions in the ParaphraseRC dataset is the same as that in SelfRC because we do not create any new questions from the longer version of the plot. We end up with a greater number of {question, answer, document} triplets in ParaphraseRC as compared to SelfRC (100,316 v/s 85,773) since movies that are remakes of a previous movie had very little difference in their Wikipedia plots. Therefore, we did not separately collect questions from the Wikipedia plot of the remake. However, the IMDb plots of the two movies are very different and so we have two different longer versions of the movie (one for the original and one for the remake). We can thus pair the questions created from the Wikipedia plot with both the IMDb versions of the plot and hence we end up with more {question, answer, document} triplets. ",
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+    {
+        "type": "table",
+        "img_path": "images/bbfe2796f9091d7f7515a9fad82460881ad9bf8f8359dd1f9663a011c57ce0c4.jpg",
+        "table_caption": [
+            "Table 1: Statistics regarding the Self and ParaphraseRC Datasets "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=2>Question/Answer-Length Statistics</td></tr><tr><td rowspan=1 colspan=1>Avg. Question-Length</td><td rowspan=1 colspan=1>9 words</td></tr><tr><td rowspan=1 colspan=1>Avg.Answer Length (SelfRC Dataset)</td><td rowspan=1 colspan=1>3words</td></tr><tr><td rowspan=1 colspan=1>Avg.AnswerLength (ParaphraseRCDataset)</td><td rowspan=1 colspan=1>5words</td></tr><tr><td rowspan=1 colspan=1>Avg.Number of noun phrases in Question</td><td rowspan=1 colspan=1>4</td></tr><tr><td rowspan=1 colspan=1>Avg.Number of noun phrases in Answers</td><td rowspan=1 colspan=1>1.5</td></tr><tr><td rowspan=1 colspan=1>Comparative Hardness of ParaphraseRC w.r.t SelfRC</td><td rowspan=1 colspan=1>:.t SelfRC</td></tr><tr><td rowspan=1 colspan=1>% of QAs with no noun phrase common between Ques-tion and Answer (SelfRC)</td><td rowspan=1 colspan=1>35.86%</td></tr><tr><td rowspan=1 colspan=1>%of QAs with no noun phrase common between Ques-tion and Answer (ParaphraseRC)</td><td rowspan=1 colspan=1>49.76%</td></tr><tr><td rowspan=1 colspan=1>Avg.Minimum Distance between Named Entities inQuestion and Answer (in the Self and ParaphraseRCPlot)</td><td rowspan=1 colspan=1>Avg distance16wordsmore forParaphraseRC</td></tr><tr><td rowspan=1 colspan=1>% Length of the Longest Common Subsequence ofNon-stop words in Query and SelfRC plot</td><td rowspan=1 colspan=1>38.1%ofthequery</td></tr><tr><td rowspan=1 colspan=1>% Length of the Longest Common Subsequence ofNon-stop words in Query and ParaphraseRC plot</td><td rowspan=1 colspan=1>21.9%ofthequery</td></tr></table>",
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+    {
+        "type": "image",
+        "img_path": "images/df4e0e5c2b8ec94d99ad7d0345d9174b6ba227def1a974b43ca20c5006eb516b.jpg",
+        "image_caption": [
+            "Figure 2: Analysis of the Question Types "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "We refer to this combined dataset containing a total of 186,089 instances as DuoRC. Fig. 2 shows the distribution of different Wh-type questions in our dataset. Some more interesting statistics about the dataset are presented in Table 1 and also in Appendix B. ",
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+        "type": "text",
+        "text": "Another notable observation is that in many cases the answers to the same question are different in the two versions. Specifically, only $4 0 . 7 \\%$ of the questions have the same answer in the two documents. For around $3 7 . 8 \\%$ of the questions there is no overlap between the words in the two answers. For the remaining $21 \\%$ of the questions there is a partial overlap between the two answers. For e.g., the answer derived from the shorter version could be “using his wife’s gun” and from the longer version could be “with Dana’s handgun” where Dana is the name of the wife. In Appendix A, we provide a few randomly picked examples from our dataset which should convince the reader of the difficulty of ParaphraseRC and its differences with SelfRC. ",
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+        "type": "text",
+        "text": "4 MODELS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we describe in detail the various state-of-the-art RC and language generation models along with a collection of traditional NLP techniques employed together that will serve to establish baseline performance on the DuoRC dataset. ",
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+        "type": "text",
+        "text": "Most of the current state-of-the-art models for RC assume that the answer corresponds to a span in the document and the task of the model is to predict this span. This is indeed true for the SQuAD, TriviaQA and NewsQA datasets. However, in our dataset, in many cases the answers do not correspond to an exact span in the document but are synthesized by humans. Specifically, for the SelfRC version of the dataset around $30 \\%$ of the answers are synthesized and do not match a span in the document whereas for the ParaphraseRC task this number is $50 \\%$ . Nevertheless, we could still leverage the advances made on the SQuAD dataset and adapt these span prediction models for our task. To do so, we propose to use two models. The first model is a basic span prediction model which we train and evaluate using only those instances in our dataset where the answer matches a span in the document. The purpose of this model is to establish whether even for instances where the answer matches a span in the document, our dataset is harder than the SQuAD dataset or not. Specifically, we want to explore the performance of state-of-the-art models (such as DCN (Xiong et al., 2016)), which exhibit near human results on the SQuAD dataset, on DuoRC (especially, in the ParaphraseRC setup). To do so, we seek to employ a good span prediction model for which (i) the performance is within $3- 5 \\%$ of the top performing model on the SQuAD leaderboard (Rajpurkar et al., 2016b) and (ii) the results are reproducible based on the code released by the authors of the paper. Note that the second criteria is important to ensure that the poor performance of the model is not due to incorrect implementation. The Bidirectional Attention Flow (BiDAF) model (Seo et al., 2016) satisfies these criteria and hence we employ this model. Due to space constraints, we do not provide details of the ",
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+        "type": "text",
+        "text": "BiDAF model here and simply refer the reader to the original paper. In the remainder of this paper we will refer to this model as the SpanModel. ",
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+        "type": "text",
+        "text": "The second model that we employ is a two stage process which first predicts the span and then synthesizes the answers from the span. Here again, for the first step (i.e., span prediction) we use the BiDAF model (Seo et al., 2016). The job of the second model is to then take the span (mini-document) and question (query) as input and generate the answer. For this, we employ a state-of-the-art query based abstractive summarization model (Nema et al., 2017) as this task is very similar to our task. Specifically, in query based abstractive summarization the training data is of the form {query, document, generated summary} and in our case the training data is of the form {query, mini-document, generated answer}. Once again we refer the reader to the original paper (Nema et al., 2017) for details of the model. We refer to this two stage model as the GenModel. ",
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+        "type": "text",
+        "text": "Note that Tan et al. (2017) recently proposed an answer generation model for the MS MARCO dataset. However, the authors have not released their code and therefore, in the interest of reproducibility of our work, we omit incorporating this model in this paper. ",
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+        "type": "text",
+        "text": "Additional NLP pre-processing: Referring back to the example cited in Fig. 1, we reiterate that ideally a good model for ParaphraseRC would require: (i) employing a knowledge graph, (ii) common-sense knowledge (iii) paraphrase/semantic understanding (iv) multiple-sentence inferencing across events in the passage including coreference resolution of named entities and nouns, and (v) educated guesswork when the question is not directly answerable but there are subtle hints in the passage. While addressing all of these challenges in their entirety is beyond the scope of a single paper, in the interest of establishing a good baseline for DuoRC, we additionally seek to address some of these challenges to a certain extent by using standard NLP techniques. Specifically, we look at the problems of paraphrase understanding, coreference resolution and handling long passages. ",
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+        "type": "text",
+        "text": "To do so, we prune the document and extract only those sentences which are most relevant to the question, so that the span detector does not need to look at the entire 900-word long ParaphraseRC plot. Now, since these relevant sentences are obtained not from the original but the paraphrased version of the document, they may have a very small word overlap with the question. For example, the question might contain the word “hand gun” and the relevant sentence in the document may contain the word “revolver”. Further some of the named entities in the question may not be exactly present in the relevant sentence but may simply be co-referenced. To resolve these coreferences, we first employ the Stanford coreference resolution on the entire document. We then compute the fraction of words in a sentence which match a query word (ignoring stop words). Two words are considered to match if (a) they have the same surface form, or (b) one words is an inflected form of the word (e.g., river and rivers), or (c) the Glove and Skip-thought embeddings of the two words are very close to each other, or (d) the two words appear in the same synset in Wordnet. We consider a sentence to be relevant for the question if at least $50 \\%$ of the query words (ignoring stop words) match the words in the sentence. If none of the sentences in the document have atleast $50 \\%$ overlap with the question, then we pick sentences having atleast a $30 \\%$ overlap with the question. ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTAL SETUP ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In the following sub-sections we describe (i) the evaluation metrics, and (ii) the choices considered for augmenting the training data for the answer generation model. Note that when creating the train, validation and test set, we ensure that the test set does not contain question-answer pairs for any movie that was seen during training. We split the movies in such a way that the resulting train, valid, test sets respectively contain $70 \\%$ , $15 \\%$ and $15 \\%$ of the total number of QA pairs. ",
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+        "type": "text",
+        "text": "Span-Based Test Set and Full Test Set As mentioned earlier, the SpanModel only predicts the span in the document whereas the GenModel generates the answer after predicting the span. Ideally, the SpanModel should only be evaluated on those instances in the test set where the answer matches a span in the document. We refer to this subset of the test set as the Span-based Test Set. Though not ideal, we also evaluate the SpanModel model on the entire test set. We say this is not ideal because we know for sure that there are many answers in the test set which do not correspond to a span in the document whereas the model was only trained to predict spans. We refer to this as the Full Test Set. We also evaluate the GenModel on both the test sets. ",
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+        "type": "text",
+        "text": "Training Data for the GenModel As mentioned earlier, the GenModel contains two stages; the first stage predicts the span and the second stage then generates an answer from the predicted span. For the first step we plug-in the best performing SpanModel from our earlier exploration. To train the second stage we need training data of the form $\\{ x = s p a n , y = a n s w e r \\}$ which comes from two types of instances: one where the answer matches a span and the other where the answer is synthesized and the span corresponding to it is not known. In the first case $x { = } y$ and there is nothing interesting for the model to learn (except for copying the input to the output). In the second case $x$ is not known. To overcome this problem, for the second type of instances, we consider various approaches for finding the approximate span from which the answer could have been generated, in order to augment the training data with $\\{ x = a p p r o x \\_ s p a n , y = a n s w e r \\}$ pairs. ",
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+    {
+        "type": "text",
+        "text": "The easiest method was to simply treat the entire document as the true span from which the answer was generated $x =$ document, $y = a n s w e r$ ). The second alternative that we tried was to first extract the named entities, noun phrases and verb phrases from the question and create a lucene query from these components. We then used the lucene search engine to extract the most relevant portions of the document given this query. We then considered this portion of the document as the true span (as opposed to treating the entire document as the true span). Note that lucene could return multiple relevant spans in which case we treat all these $\\left\\{ x = a p p r o x \\ldots s p a n , y = a n s w e r \\right.$ as training instances. Another alternative was to find the longest common subsequence (LCS) between the document and the question and treat this subsequence as the span from which the answer was generated. Of these, we found that the model trained using $\\{ x = a p p r o x \\_ s p a n , y = a n s w e r \\}$ pairs created using the LCS based method gave the best results. We report numbers only for this model. ",
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+    {
+        "type": "text",
+        "text": "Evaluation Metrics Similar to Rajpurkar et al. (2016a) we use Accuracy and F-score as the evaluation metric. While accuracy, being a stricter metric, considers a predicted answer to be correct only if it exactly matches the true answer, F-score also gives credit to predictions partially overlapping with the true answer. ",
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+    {
+        "type": "text",
+        "text": "6 RESULTS AND DISCUSSIONS ",
+        "text_level": 1,
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+        "text": "The results of our experiments are summarized in Tables 2 to 4 which we discuss in the following sub-sections. ",
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+        "type": "table",
+        "img_path": "images/d16c156d5687d94c9d15c29514e0d6f3601ab6fa88c1442c786843b864275fbd.jpg",
+        "table_caption": [
+            "Table 2: Performance of the preprocessing step. Plot compression is the $\\%$ size of the extracted plot w.r.t the original plot size "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Preprocessing step of Relevant Sub-plot Extraction</td><td rowspan=1 colspan=1>Plot Com-pression</td><td rowspan=1 colspan=1>AnswerRecall</td></tr><tr><td rowspan=1 colspan=1>Using WordNet synonym+Glove basedparaphrase</td><td rowspan=1 colspan=1>30%</td><td rowspan=1 colspan=1>66.51%</td></tr><tr><td rowspan=1 colspan=1>WordNet synonym + Glove based para-phrase on Coref resolved plots</td><td rowspan=1 colspan=1>50%</td><td rowspan=1 colspan=1>84.10%</td></tr><tr><td rowspan=1 colspan=1>WordNet synonym + Glove + Skip-thought based paraphrase on Coref re-solved plots</td><td rowspan=1 colspan=1>48%</td><td rowspan=1 colspan=1>85%</td></tr></table>",
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+        "table_caption": [
+            "Table 3: Performance of the SpanModel and GenModel on the Span Test subset and the Full Test Set of the Self and ParaphraseRC. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>Span Test Set</td><td rowspan=1 colspan=2>Full Test Set</td></tr><tr><td rowspan=1 colspan=1>TrainOn</td><td rowspan=1 colspan=1>TestOn</td><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td></tr><tr><td rowspan=3 colspan=1>SelfRC</td><td rowspan=1 colspan=1>SelfRC</td><td rowspan=1 colspan=1>46.14</td><td rowspan=1 colspan=1>57.49</td><td rowspan=1 colspan=1>37.53</td><td rowspan=1 colspan=1>50.56</td></tr><tr><td rowspan=1 colspan=1>Para-phraseRC</td><td rowspan=1 colspan=1>27.85</td><td rowspan=1 colspan=1>36.82</td><td rowspan=1 colspan=1>15.16</td><td rowspan=1 colspan=1>22.70</td></tr><tr><td rowspan=1 colspan=1>SelfRC+ Para-phraseRC</td><td rowspan=1 colspan=1>37.79</td><td rowspan=1 colspan=1>48.05</td><td rowspan=1 colspan=1>25.05</td><td rowspan=1 colspan=1>35.01</td></tr><tr><td rowspan=3 colspan=1>Para-phraseRC</td><td rowspan=1 colspan=1>SelfRC</td><td rowspan=1 colspan=1>34.85</td><td rowspan=1 colspan=1>45.71</td><td rowspan=1 colspan=1>28.25</td><td rowspan=1 colspan=1>40.16</td></tr><tr><td rowspan=1 colspan=1>Para-phraseRC</td><td rowspan=1 colspan=1>19.74</td><td rowspan=1 colspan=1>27.57</td><td rowspan=1 colspan=1>10.78</td><td rowspan=1 colspan=1>17.13</td></tr><tr><td rowspan=1 colspan=1>SelfRC+Para-phraseRC</td><td rowspan=1 colspan=1>27.94</td><td rowspan=1 colspan=1>37.42</td><td rowspan=1 colspan=1>18.50</td><td rowspan=1 colspan=1>27.31</td></tr><tr><td rowspan=3 colspan=1>SelfRC +Para-phraseRC</td><td rowspan=1 colspan=1>SelfRC</td><td rowspan=1 colspan=1>49.66</td><td rowspan=1 colspan=1>61.45</td><td rowspan=1 colspan=1>40.24</td><td rowspan=1 colspan=1>54.04</td></tr><tr><td rowspan=1 colspan=1>Para-phraseRC</td><td rowspan=1 colspan=1>29.88</td><td rowspan=1 colspan=1>39.34</td><td rowspan=1 colspan=1>16.33</td><td rowspan=1 colspan=1>24.25</td></tr><tr><td rowspan=1 colspan=1>Self+Para-phraseRC</td><td rowspan=1 colspan=1>40.62</td><td rowspan=1 colspan=1>51.35</td><td rowspan=1 colspan=1>26.90</td><td rowspan=1 colspan=1>37.42</td></tr></table>",
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+    },
+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 4: Combined and Cross-Testing between Self and ParaphraseRC Dataset, by taking the best performing SpanModel from Table 3. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=2 colspan=1>SelfRC</td><td rowspan=1 colspan=2>Span Test subset</td><td rowspan=1 colspan=2>Full Test set</td></tr><tr><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td></tr><tr><td rowspan=1 colspan=1>SpanModel</td><td rowspan=1 colspan=1>46.14</td><td rowspan=1 colspan=1>57.49</td><td rowspan=1 colspan=1>37.53</td><td rowspan=1 colspan=1>50.56</td></tr><tr><td rowspan=1 colspan=1>GenModel(withaug-mented training data)</td><td rowspan=1 colspan=1>16.45</td><td rowspan=1 colspan=1>26.97</td><td rowspan=1 colspan=1>15.31</td><td rowspan=1 colspan=1>24.05</td></tr><tr><td rowspan=2 colspan=1>ParaphraseRC</td><td rowspan=1 colspan=2>Span Test subset</td><td rowspan=1 colspan=2>Full Test set</td></tr><tr><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td><td rowspan=1 colspan=1>Accur.</td><td rowspan=1 colspan=1>F1</td></tr><tr><td rowspan=1 colspan=1>SpanModel</td><td rowspan=1 colspan=1>17.93</td><td rowspan=1 colspan=1>26.27</td><td rowspan=1 colspan=1>9.78</td><td rowspan=1 colspan=1>16.33</td></tr><tr><td rowspan=1 colspan=1>SpanModel with Prepro-cessed Data</td><td rowspan=1 colspan=1>27.49</td><td rowspan=1 colspan=1>35.10</td><td rowspan=1 colspan=1>14.92</td><td rowspan=1 colspan=1>21.53</td></tr><tr><td rowspan=1 colspan=1>GenModel(withaug-mented training data)</td><td rowspan=1 colspan=1>12.66</td><td rowspan=1 colspan=1>19.48</td><td rowspan=1 colspan=1>5.42</td><td rowspan=1 colspan=1>9.64</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "• SpanModel v/s GenModel: Comparing the first two rows (SelfRC) and the last two rows (ParaphraseRC) of Table 3 we see that the SpanModel clearly outperforms the GenModel. This is not very surprising for two reasons. First, around $70 \\%$ (and $50 \\%$ ) of the answers in SelfRC (and ParaphraseRC) respectively, match an exact span in the document so the span based model still has scope to do well on these answers. On the other hand, even if the first stage of the GenModel predicts the span correctly, the second stage could make an error in generating the correct answer from it because generation is a harder problem. For the second stage, it is expected that the GenModel should learn to copy the predicted span to produce the answer output (as is required in most cases) and only occasionally where necessary, generate an answer. However, surprisingly the GenModel fails to even do this. Manual inspection of the generated answers shows that in many cases the generator ends up generating either more or fewer words compared the true answer. This demonstrates that there is clearly scope for the GenModel to perform better. ",
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+    {
+        "type": "text",
+        "text": "• SelfRC v/s ParaphraseRC: Comparing the SelfRC and ParaphraseRC numbers in Table 3, we observe that the performance of the models clearly drops for the latter task, thus validating our hypothesis that ParaphraseRC is a indeed a much harder task. ",
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+    },
+    {
+        "type": "text",
+        "text": "• Effect of NLP pre-processing: As mentioned in Section 4, for ParaphraseRC, we first perform a few pre-processing steps to identify relevant sentences in the longer document. In order to evaluate whether the pre-processing method is effective, we compute: (i) the percentage of the document that gets pruned, and (ii) whether the true answer is present in the pruned document (i.e., average recall of the answer). We can compute the recall only for the span-based subset of the data since for the remaining data we do not know the true span. In Table 2, we report these two quantities for the span-based subset using different pruning strategies. Finally, comparing the SpanModel with and without Paraphrasing in Table 3 for ParaphraseRC, we observe that the pre-processing step indeed improves the performance of the Span Detection Model. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "• Effect of oracle pre-processing: As noted in Section 3, the ParaphraseRC plot is almost double in length in comparison to the SelfRC plot, which while adding to the complexities of the former task, is clearly not the primary reason of the model’s poor performance on that. To empirically validate this, we perform an Oracle pre-processing step, where, starting with the knowledge of the span containing the true answer, we extract a subplot around it such that the span is randomly located within that subplot and the average length of the subplot is similar to the SelfRC plots. The SpanModel with this Oracle preprocessed data exhibits a minor improvement in performance over that with rule-based preprocessing ( $1 . 6 \\%$ in Accuracy and $4 . 3 \\%$ in F1 over the Span Test), still failing to bridge the wide performance gap between the SelfRC and ParaphraseRC task. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "• Cross Testing We wanted to examine whether a model trained on SelfRC performs well on ParaphraseRC and vice-versa. We also wanted to evaluate if merging the two datasets improves the performance of the model. For this we experimented with various combinations of train and test data. The results of these experiments for the SpanModel are summarized in Table 4. We make two main observations. First, training on one dataset and evaluating on the other results in a drop in the performance. Merging the training data from the two datasets exhibits better performance on the individual test sets. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Based on our experiments and empirical observations we believe that the DuoRC dataset indeed holds a lot of potential for advancing the horizon of complex language understanding by exposing newer challenges in this area. ",
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+    {
+        "type": "text",
+        "text": "7 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+            318,
+            784
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper we introduced DuoRC, a large scale RC dataset of 186K human-generated questionanswer pairs created from 7680 pairs of parallel movie-plots, each pair taken from Wikipedia and IMDb. We then showed that this dataset, by design, ensures very little or no lexical overlap between the questions created from one version and the segments containing the answer in the other version. With this, we hope to introduce the RC community to new research challenges on question-answering requiring external knowledge and common-sense driven reasoning, deeper language understanding and multiple-sentence inferencing. Through our experiments, we show how the state-of-the-art RC models, which have achieved near human performance on the SQuAD dataset, perform poorly on our dataset, thus emphasizing the need to explore further avenues for research. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "APPENDIX A EXAMPLES ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In this appendix, we showcase some examples of plots from which questions are created and answered. Since the questions are created from the smaller plot, answering these questions by the reading the smaller plot (which is named as the SelfRC task) is straightforward. However, answering them by reading the larger plot (i.e. the ParaphraseRC task) is more challenging and requires multi-sentence and sometimes multi-paragraph inferencing. ",
+        "bbox": [
+            174,
+            132,
+            825,
+            202
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Due to shortage of space, we truncate the plot contents and only show snippets from which the questions can be answered. In the smaller plot, blue indicates that an answer can directly be found from the sentence and cyan indicates that the answer spans over multiple sentences. For the larger plot, red and orange are used respectively. ",
+        "bbox": [
+            174,
+            208,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1 EXAMPLE 1: PALE RIDER (1985) ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            277,
+            449,
+            292
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1.1 SMALLER PLOT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            304,
+            341,
+            319
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In the countryside outside the fictional town of Lahood, California, sometime around 1880, [[thugs working for big-time miner Coy LaHood ride in and destroy the camp of a group of struggling miners]Q1 and their families who have settled in nearby Carbon Canyon and are panning for gold there. In leaving, they also shoot the little dog of fourteen-year-old Megan Wheeler]Q15. As Megan buries her dog in the woods and prays for a miracle, a stranger passes by heading to the town on horseback. ",
+        "bbox": [
+            174,
+            332,
+            825,
+            416
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[Megan’s mother, Sarah]Q16, is being courted by [Hull Barret, the leader of the miners]Q17 . . . [Coy LaHood’s son Josh]Q8 . . . [Club, who with one hammer blow smashes a large rock]Q7 . . . [Coy LaHood has been away in Sacramento]Q9 . . . [[Megan, who has grown fond of the Preacher, goes looking for him, but Josh confronts and attempts to rape her]Q11, while his cohorts look on and encourage him, except for Club, who sees what is happening and moves forward to help Megan]Q13 before Josh can do anything serious. At this moment the [Preacher arrives on horseback armed with a Remington Model 1858 revolver he has recovered from a Wells Fargo office and, after shooting Josh]Q14 . . . [Stockburn, who appears startled and says that he sounds like someone that he once knew, but that couldn’t be, since that man is dead]Q5. [Stockburn and his men gun down Spider Conway] Q4, . . . ",
+        "bbox": [
+            174,
+            421,
+            825,
+            563
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[The Preacher and Hull go to LaHood’s strip mining site and blow it up with dynamite]Q6. [To stop Hull from following him, the Preacher then scares off Hull’s horse]Q3 and rides into town alone. . . [Coy LaHood, watching from his office]Q10, . [snow-covered mountains]Q2. [Megan then drives into town and shouts her love to the Preacher]Q12 and thanks after him. The words echo along the ravine that he is traversing. ",
+        "bbox": [
+            174,
+            568,
+            825,
+            638
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1.2 LARGER PLOT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            651,
+            333,
+            666
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Somewhere in California, at the end of the Gold Rush, several horsemen come riding down from the nearby mountains . . . [The horsemen shoot cattle and Megan’s dog]Q4,Q15, and then chase donkeys as they leave . . . ",
+        "bbox": [
+            176,
+            679,
+            821,
+            720
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Hull describes the fight between the stranger and McGill and his men. [Megan’s mother, Sarah]Q16 says he sounds no different from McGill, Tyson, or any of LaHood’s roughnecks . . . Preacher says there is lot of sinners around, that he can’t leave before he finishes his work. [Josh says, ”Club”, who gets down and walks into the stream. Everyone is apprehensive. He rolls down his sleeves, and then. . . quickly grabs Hull’s sledgehammer with one hand and strikes the boulder once, screaming, splitting it]Q7 . ",
+        "bbox": [
+            174,
+            728,
+            825,
+            813
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[A train pulls into the station from Sacramento while Josh and McGill wait. [Josh’s father Coy LaHood]]Q8,Q9 (Richard Dysart) exits the train, and then he goes with Josh and McGill. . . ",
+        "bbox": [
+            173,
+            819,
+            825,
+            848
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Josh asks what she really came for. She replies that she’s just riding, taking a look around. [Josh says he wants to take a look too, at her real close. He pulls her off the horse. She screams as he carries her downhill. . . Josh grabs her hair and kisses her. They both fall to the ground. The men cheer him on while Megan begs him to stop]Q11 . . . a gunshot sounds out. Josh gets up and everyone turns around. [Preacher, on his horse. . . His gun is trained on Josh. Megan sees him and smiles]Q13, . . . [Josh falls to the ground. He reaches for his gun, but Preacher shoots his hand]Q14 . . . LaHood replies, ”Tall. Lean. His eyes. . . his eyes. Something strange about em. That mean something to you?” [Stockburn says that it sounds like a man he knew, but that man is dead]Q5 . . . [LaHood watches through the window]Q10 as they kill Spider, . . . ",
+        "bbox": [
+            174,
+            854,
+            825,
+            924
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/03c13a7bee9156b102eee198b55e4f611e8193a89e2ef763021e06942a30f4c6.jpg",
+        "table_caption": [
+            "Table 5: QA for Pale Rider "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Question</td><td></td><td>Shorter Plot Answer</td><td>Larger Plot Answer</td></tr><tr><td>Q1</td><td>For which big-time miner are the thugs who destroyed miners camp in Carbon Canyon working for?</td><td>Coy Lahood</td><td>Coy Lahood</td></tr><tr><td>Q2</td><td>How are the mountains in the film?</td><td>Covered with snow</td><td> snow-capped</td></tr><tr><td>Q3</td><td>How does the Preacher stop Hull from following him?</td><td> Scares Hulls&#x27; horse</td><td>To stop Hull from following him, the Preacher then scares off Hull&#x27;s horse and rides into town alone</td></tr><tr><td>Q4</td><td>In the movie, who do Stockburn and his men gun down?</td><td> Spider Conway</td><td>Megan&#x27;s dog and cattle</td></tr><tr><td>Q5</td><td>In the movie, why does Stockburn say that the Preacher could not be the man he once knew?</td><td> that man is dead</td><td>The man Stockburn once knew is dead</td></tr><tr><td>Q6</td><td>What did they use to blow up the strip mining site?</td><td>Dynamite</td><td>dynamite</td></tr><tr><td>Q7</td><td>What does Club smash?</td><td>A rock</td><td>A Boulder</td></tr><tr><td>Q8</td><td>What is Coy Lahood&#x27;s relation to Josh?</td><td>Father and son</td><td>Father</td></tr><tr><td>Q9</td><td>Where has Coy Lahood been living?</td><td> Sacramento</td><td> Sacramento</td></tr><tr><td>Q10</td><td>Where was Coy watching from?</td><td>Office</td><td> a window</td></tr><tr><td>Q11</td><td> Who attempts to rape Megan?</td><td>Josh</td><td>Josh</td></tr><tr><td>Q12</td><td>Who does megan love?</td><td>The preacher</td><td>The preacher</td></tr><tr><td>Q13</td><td>Who prevents Josh from raping Megan?</td><td>Club</td><td>the preacher The</td></tr><tr><td>Q14</td><td>Who shoots Josh in the hand?</td><td>Preacher</td><td> Preacher</td></tr><tr><td>Q15</td><td>Whose little dog did the thugs shoot?</td><td>Megan Wheeler</td><td> Megan</td></tr><tr><td>Q16</td><td>Who is Megan&#x27;s mother?</td><td> Sarah</td><td> Sarah</td></tr><tr><td>Q17</td><td>Who is the leader of the miners ?</td><td>Hull Barret</td><td>Coy LaHood</td></tr></table>",
+        "bbox": [
+            171,
+            90,
+            821,
+            731
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            776,
+            825,
+            833
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Hull insists on going with him so Preacher agrees. [They go to the LaHood camp and blow up their pipes, sluices, tents, and the barracks with dynamite]Q6. [After fooling Hull to dismount, Preacher scares away his horse. He then tells Hull to take care of Sarah and Megan, and rides into town]Q3 . . . Blankenship tells her that the horses are exhausted and she would kill them. [Megan runs to the end of town and shouts out thank you to Preacher, that they love him, that she loves him]Q12 . . . The final shot of the movie shows Preacher riding through the [snow in the mountains]Q2. ",
+        "bbox": [
+            173,
+            840,
+            825,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.2 EXAMPLE 2: BIG JAKE (1971) ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            431,
+            118
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.2.1 SMALLER PLOT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            130,
+            343,
+            145
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "[In 1909]Q6, [there is a raid on the McCandles family . . . Martha, the head of the family . . . [In consequence, she sends for her estranged husband, the aging Jacob ”Big Jake” McCandles]Q9, . . . [the ransom to the kidnappers, a million dollars]Q4 ",
+        "bbox": [
+            174,
+            159,
+            825,
+            202
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": ". . . [The Texas Ranger captain is present and offers the services of his men]Q11, . . . Jake, preferring the old ways, has followed on horseback, accompanied by an old Apache associate, Sam Sharpnose. [He is now joined by his sons, Michael and James]Q2, . . . Knowing that they have been followed by another gang intent on stealing the strongbox, [Jake sets a trap for them and they are all killed]Q16. [During the attack, the chest is blasted open]Q1, [revealing clipped bundles of newspaper instead of money] Q5 ",
+        "bbox": [
+            174,
+            208,
+            825,
+            292
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A thunderstorm breaks and [Pop Dawson, one of the outlaws, arrives to give them the details of the exchange]Q7 . . . [Jake arranges for Michael to follow after them to take care of the sharp] . . . [Jake tosses the key of the chest to Fain, who opens it up to discover that he has been tricked]Q12. [Fain orders his brother Will to kill the boy]Q13 but he is shot by Jake. [Dog is wounded by the sniper]Q15 and Jake is wounded in the leg before Michael kills him. Jake tells the boy to escape but Little Jake is hunted by the machete wielding [John Goodfellow, who has already hacked Sam to death]Q10 . . . [With Little Jake rescued, and the broken family bonded, they prepare to head home]Q3. ",
+        "bbox": [
+            173,
+            299,
+            825,
+            397
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.2.2 LARGER PLOT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            409,
+            333,
+            422
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "[[Jacob McCandles (John Wayne) is a big man with a bigger reputation. A successful rancher and landowner]Q14, his many businesses keep him conveniently away from his home and estranged wife Martha (Maureen O’Hara)]Q9. . . , [and is demanding one million dollars for his safe return]Q4. ",
+        "bbox": [
+            174,
+            435,
+            825,
+            478
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "[The local sheriff has convened a posse complete with then state-of-the-art automobiles. [Two of Jake’s sons, the passionate, gunslinging James (Patrick Wayne) and the motorcycle-riding, sharpshooting Michael (Christopher Mitchum) $] ^ { Q 2 }$ elect to go with the sheriff’s posse. Big Jake decides to set off across the rough terrain on his horse with his Dog at his side, and soon meets up with his Native American friend, Sam Sharpnose (Bruce Cabot), who has brought additional horses and supplies]Q11. ",
+        "bbox": [
+            174,
+            484,
+            826,
+            569
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "[They then devise their strategy: James will go have a good time in the saloon, Big Jake will head to the barbershop for a shower, Sam will secrete himself on the roof of the hotel, seemingly leaving Michael alone protecting the strong box. Big Jake tells Sam to listen for a ”disturbance” in the street, and use the distraction to join Michael in the hotel room to protect the strong box. As Big Jake predicted, the gang tries to hit the strong box when it looks most vulnerable. Fain and another of his gang members start a fight with James in the saloon, one keeps a gun on Big Jake in the barbershop, and two others come up the hotel stairs and toward the room. Big Jake dispatches his captor in the barbershop, James fights his way out of the saloon with Jake’s help, and the two head to the hotel. At the hotel, once Sam hears the fight in the saloon, he climbs over the roof and slips in the window to aid Michael in protecting the strong box. Shotguns blast as the gang hits the hotel room. When James and Jake arrive they find Sam, Michael and the Dog unharmed, [but the strong box has suffered damage. To their horror, James and Michael realize they’ve been risking their lives to protect a box of newspaper clippings!]]Q1,Q5,Q16 . ",
+        "bbox": [
+            173,
+            575,
+            826,
+            756
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "[Big Jake takes the few moments he has to plan with his sons. He tells Michael of the sharpshooter and instructs him to find a high position and take him out whenever he can. Big Jake takes the Dog and goes to the meet as instructed, while the others follow discreetly behind]Q8 . . . [As Fain unlocks the strong box, he realizes hes been had ´ ]Q12. Big Jake whispers to him that no matter what happens, Fain will be the first one to die. [Fain screams his command to kill the boy ]Q13, ",
+        "bbox": [
+            174,
+            762,
+            825,
+            833
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "[Dog giving his life protecting Little Jake from one of Fain’s machete-wielding gang]Q15. . . Sam points him toward James at the exit, [who helps Little Jake escape. Fain and Big Jake are in a duel to the death, when Michael takes a fatal shot at Fain, saving his father and Little Jake. After a harrowing journey and a risky gamble, the family leaves, happy to be together]Q3. ",
+        "bbox": [
+            174,
+            839,
+            825,
+            896
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/9211cb7a85fcdfa743946ae90dcd26b6dba1f4da820771eb03a33193bfecf504.jpg",
+        "table_caption": [
+            "Table 6: QA for Big Jake "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Question</td><td></td><td>Shorter Plot Answer</td><td>Larger Plot Answer</td></tr><tr><td>Q1</td><td>How was the strongbox opened?</td><td>It was blasted during an attack</td><td>it was damaged during the fight</td></tr><tr><td>Q2</td><td>What are the names of Jake&#x27;s sons?</td><td>Jake&#x27;s sons are Michael and James</td><td>James and Michael</td></tr><tr><td>Q3</td><td>What did the family prepare to do once Jake had been rescued?</td><td>head home</td><td>Leave</td></tr><tr><td>Q4</td><td>What is the amount of the ransom?</td><td>The ransom amount is a million dollars</td><td> one million dollars</td></tr><tr><td>Q5</td><td>What was in the strongbox?</td><td>Clipped bundles of newspaper</td><td> newspaper clippings</td></tr><tr><td>Q6</td><td>What year does the movie take place?</td><td>1909</td><td> No Answer</td></tr><tr><td>Q7</td><td>Which outlaw gives details of the exchange to the others?</td><td>Pop Dawson</td><td> No Answer</td></tr><tr><td>Q8</td><td>Who does Jake arrange to follow the rest of the group?</td><td>Michael</td><td>Michael</td></tr><tr><td>Q9</td><td>Who is married to Big Jake?</td><td>Martha</td><td>Martha</td></tr><tr><td>Q10</td><td>Who killed Sam?</td><td>John Goodfellow</td><td> No Answer</td></tr><tr><td>Q11</td><td>Who offers his services to help Jake combat the kidnappers?</td><td>The Texas ranger captain offers the services of men</td><td>the posse, native American friend and his two sons</td></tr><tr><td>Q12</td><td>Who opens the chest to discover he has been tricked?</td><td>Fain</td><td>Fain</td></tr><tr><td>Q13</td><td>Who orders Will to kill the boy?</td><td>Fain</td><td>Fain</td></tr><tr><td>Q14</td><td>Who owns the ranch?</td><td>McCandles family</td><td> McCandles family</td></tr><tr><td>Q15</td><td>Who wounded the dog?</td><td>A sniper</td><td>Fain&#x27;s machete-wielding gang</td></tr><tr><td>Q16</td><td>Why does Jake set a trap and kill another gang?</td><td>on stealing the strongbox</td><td>to protect the strongbox</td></tr></table>",
+        "bbox": [
+            171,
+            198,
+            821,
+            796
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX B DATA ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            439,
+            118
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We conducted a manual verification of 100 question-answer pairs where the SelfRC and ParaphraseRC were different or the latter was marked as non-answerable. As noted in Fig. 3, the chief reason behind getting No Answer from the Paraphrase plot is lack of information and at times, need for an educated guesswork or missing general knowledge (e.g. Philadelphia is a city) or missing movie meta-data (e.g. to answer questions like ‘Where did Julia Roberts’ character work in the movie?’). On the other hand, SelfRC and ParaphraseRC answers are occasionally seen to have partial or no overlap, mainly because of the following causes; phrasal paraphrases or subjective questions (e.g. Why and How type questions) or different valid answers to objective questions (e.g. ‘Where did Jane work?’ is answered by one worker as ‘Bloomberg’ and other as ‘New York City’) or differently spelt names in the answers (e.g. ‘Rebeca’ as opposed to ‘Rebecca’). ",
+        "bbox": [
+            173,
+            132,
+            825,
+            271
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/cc758b5c05b95d333ecb70264727ad69aa0622190ab33fdd35c3f0f51c68a706.jpg",
+        "image_caption": [
+            "Figure 3: Manual Analysis of 100 Questions and their corresponding answers from the SelfRC and ParaphraseRC Dataset to understand the various reasons behind these two answers being different or the latter being non-answerable "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            210,
+            284,
+            787,
+            507
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX C MODEL ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            504,
+            118
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Fig. 4 illustrates the 5-step process of answering a question from the comprehension, by optionally pre-processing the input passage in Step 2 and 3, then using the BiDirectional Attention Flow (BiDAF) model for Span identification, and finally generating the answer text from the identified span by employing a state-of-the-art query-based Abstractive Summarization (qBAS) model. ",
+        "bbox": [
+            173,
+            132,
+            826,
+            188
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/bbf4e4186cba1284a210e98de5e53be59cef477dc4238c76a15317654ae61e4e.jpg",
+        "image_caption": [
+            "Figure 4: Model architecture "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            195,
+            821,
+            521
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Question: Peters is aboard the plane with what? ",
+        "bbox": [
+            625,
+            525,
+            797,
+            532
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX D PERFORMANCE ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            522,
+            118
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "In Fig. 5 we show a performance analysis of the SelfRC and ParaphraseRC tasks when evaluated on the Span Test Subset and the Full Test Set, over different question types and plots of different length. ",
+        "bbox": [
+            173,
+            131,
+            825,
+            160
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/dc5087c0dbcf25d98d448d4fcd1a74b4dfda8d170bea4b4bfb36212da7cd6e05.jpg",
+        "image_caption": [
+            "Figure 5: Performance Analysis of the Self and ParaphraseRC on different plot-lengths or different questiontypes "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            176,
+            818,
+            559
+        ],
+        "page_idx": 16
+    }
+]

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+# Exploiting the Intrinsic Neighborhood Structure for Source-free Domain Adaptation
+Shiqi Yang1, Yaxing Wang1,2∗, Joost van de Weijer1, Luis Herranz1, Shangling Jui3 1 Computer Vision Center, Universitat Autonoma de Barcelona, Barcelona, Spain 2 PCALab, Nanjing University of Science and Technology, China 3 Huawei Kirin Solution, Shanghai, China
+{syang,yaxing,joost,lherranz}@cvc.uab.es, jui.shangling@huawei.com
+# Abstract
+Domain adaptation (DA) aims to alleviate the domain shift between source domain and target domain. Most DA methods require access to the source data, but often that is not possible (e.g. due to data privacy or intellectual property). In this paper, we address the challenging source-free domain adaptation (SFDA) problem, where the source pretrained model is adapted to the target domain in the absence of source data. Our method is based on the observation that target data, which might no longer align with the source domain classifier, still forms clear clusters. We capture this intrinsic structure by defining local affinity of the target data, and encourage label consistency among data with high local affinity. We observe that higher affinity should be assigned to reciprocal neighbors, and propose a self regularization loss to decrease the negative impact of noisy neighbors. Furthermore, to aggregate information with more context, we consider expanded neighborhoods with small affinity values. In the experimental results we verify that the inherent structure of the target features is an important source of information for domain adaptation. We demonstrate that this local structure can be efficiently captured by considering the local neighbors, the reciprocal neighbors, and the expanded neighborhood. Finally, we achieve state-of-the-art performance on several 2D image and 3D point cloud recognition datasets. Code is available in https://github.com/Albert0147/SFDA_neighbors.
+# 1 Introduction
+Most deep learning methods rely on training on large amount of labeled data, while they cannot generalize well to a related yet different domain. One research direction to address this issue is Domain Adaptation (DA), which aims to transfer learned knowledge from a source to a target domain. Most existing DA methods demand labeled source data during the adaptation period, however, it is often not practical that source data are always accessible, such as when applied on data with privacy or property restrictions. Therefore, recently, there have emerged a few works [16, 17, 20, 21] tackling a new challenging DA scenario where instead of source data only the source pretrained model is available for adapting, i.e., source-free domain adaptation (SFDA). Among these methods, USFDA [16] addresses universal DA [57] and SF [17] addresses open-set DA [36]. In both universal and open-set DA the label set is different for source and target domains. SHOT [21] and 3C-GAN [20] are for closed-set DA where source and target domains have the same categories. 3C-GAN [20] is based on target-style image generation with a conditional GAN, and SHOT [21] is based on mutual information maximization and pseudo labeling. Finally, BAIT [56] extends MCD [35] to the SFDA setting. However, these methods ignore the intrinsic neighborhood structure of the target data in feature space which can be very valuable to tackle SFDA.
+![](images/343b4b429f7a34d25d762b61bf6977f13ba8eaac4be276860b5d2170fa2f18be.jpg)
+Figure 1: (a) t-SNE visualization of target features by source model. (b) Ratio of different type of nearest neighbor features of which: the predicted label is the same as the feature, K is the number of nearest neighbors. The features in (a) and (b) are on task $\mathrm { A r } {  } \mathrm { R w }$ of Office-Home. (c) Illustration of our method. In the left shows we distinguish reciprocal and non-reciprocal neighbors. The adaptation is achieved by pushed the features towards reciprocal neighbors heavily.
+In this paper, we focus on closed-set source-free domain adaptation. Our main observation is that current DA methods do not exploit the intrinsic neighborhood structure of the target data. We use this term to refer to the fact that, even though the target data might have shifted in the feature space (due to the covariance shift), target data of the same class is still expected to form a cluster in the embedding space. This can be implied to some degree from the t-SNE visualization of target features on the source model which suggests that significant cluster structure is preserved (see Fig. 1 (a)). This assumption is implicitly adopted by most DA methods, as instantiated by a recent DA work [42]. A well-established way to assess the structure of points in high-dimensional spaces is by considering the nearest neighbors of points, which are expected to belong to the same class. However, this assumption is not true for all points; the blue curve in Figure 1(b) shows that around $7 5 \%$ of the nearest neighbors has the correct label. In this paper, we observe that this problem can be mitigated by considering reciprocal nearest neighbors (RNN); the reciprocal neighbors of a point have the point as their neighbor. Reciprocal neighbors have been studied before in different contexts [14, 31, 60]. The reason why reciprocal neighbors are more trustworthy is illustrated in Fig. 1(c). Fig. 1(b) shows the ratio of neighbors which have the correct prediction for different kinds of nearest neighbors. The curves show that reciprocal neighbors indeed have more chances to predict the true label than non-reciprocal nearest neighbors (nRNN).
+The above observation and analysis motivate us to assign different weights to the supervision from nearest neighbors. Our method, called Neighborhood Reciprocity Clustering (NRC), achieves sourcefree domain adaptation by encouraging reciprocal neighbors to concord in their label prediction. In addition, we will also consider a weaker connection to the non-reciprocal neighbors. We define affinity values to describe the degree of connectivity between each data point and its neighbors, which is also utilized to encourage class-consistency between neighbors, and we propose to use a self-regularization to decrease the negative impact of potential noisy neighbors. Furthermore, inspired by recent graph based methods [1, 3, 61] which show that the higher order neighbors can provide relevant context, and also considering neighbors of neighbors is more likely to provide datapoints that are close on the data manifold [43]. Thus, to aggregate wider local information, we further retrieve the expanded neighbors, i.e, neighbor of the nearest neighbors, for auxiliary supervision.
+Our contributions can be summarized as follows, to achieve source-free domain adaptation: (i) we explicitly exploit the fact that same-class data forms cluster in the target embedding space, we do this by considering the predictions of neighbors and reciprocal neighbors, (ii) we further show that considering an extended neighborhood of data points further improves results (iii) the experiments results on three 2D image datasets and one 3D point cloud dataset show that our method achieves state-of-the-art performance compared with related methods.
+# 2 Related Work
+Domain Adaptation. Most DA methods tackle domain shift by aligning the feature distributions. Early DA methods such as [23, 41, 45] adopt moment matching to align feature distributions. And in recent years, plenty of works have emerged that achieve alignment by adversarial training. DANN [7] formulates domain adaptation as an adversarial two-player game. The adversarial training of CDAN [24] is conditioned on several sources of information. DIRT-T [40] performs domain adversarial training with an added term that penalizes violations of the cluster assumption. Additionally, [18, 26, 35] adopts prediction diversity between multiple learnable classifiers to achieve local or category-level feature alignment between source and target domains. AFN [52] shows that the erratic discrimination of target features stems from much smaller norms than those found in the source features. SRDC [42] proposes to directly uncover the intrinsic target discrimination via discriminative clustering to achieve adaptation. More related, [27] resorts to K-means clustering for open-set adaptation while considering global structure. Our method instead only focuses on nearest neighbors (local structure) for source-free adaptation.
+Source-free Domain Adaptation. Source-present methods need supervision from the source domain during adaptation. Recently, there are several methods investigating source-free domain adaptation. USFDA [16] and FS [17] explore source-free universal DA [57] and open-set DA [36], and they propose to synthesize extra training samples to make the decision boundary compact, thereby allowing to recognise the open classes. For closed-set DA setting. SHOT [21] proposes to fix the source classifier and match the target features to the fixed classifier by maximizing mutual information and a proposed pseudo label strategy which considers global structure. 3C-GAN [20] synthesizes labeled target-style training images based on the conditional GAN to provide supervision for adaptation. Finally, SFDA [22] is for segmentation based on synthesizing fake source samples.
+Graph Clustering. Our method shares some similarities with graph clustering work such as [38, 48, 54, 55] by utilizing neighborhood information. However, our methods are fundamentally different. Unlike those works which require labeled data to train the graph network for estimating the affinity, we instead adopt reciprocity to assign affinity.
+# 3 Method
+Notation. We denote the labeled source domain data with $n _ { s }$ samples as $\mathcal { D } _ { s } = \{ ( x _ { i } ^ { s } , y _ { i } ^ { s } ) \} _ { i = 1 } ^ { n _ { s } }$ , where $y _ { i } ^ { s }$ orresponding label of . Both domains have t $x _ { i } ^ { s }$ , andsame e unlabeled target domain data with classes (closed-set setting). Under the $n _ { t }$ samples asFDA setting $\mathcal { D } _ { t } \overset { \vartriangle } { = } \{ x _ { j } ^ { t } \} _ { j = 1 } ^ { n _ { t } }$ $C$ $\mathcal { D } _ { s }$ is only available for model pretraining. Our method is based on a neural network, which we split into two parts: a feature extractor $f$ , and a classifier $g$ . The feature output by the feature extractor is denoted as $z ( x ) = f \left( x \right)$ , the output of network is denoted as $p ( x ) = \bar { \delta } ( g ( \dot { z } ) ) \in \mathcal { R } ^ { C }$ where $\delta$ is the softmax function, for readability we will abandon the input and use $z , p$ in the following sections.
+Overview. We assume that the source pretrained model has already been trained. As discusses in the introduction, the target features output by the source model form clusters. We exploit this intrinsic structure of the target data for SFDA by considering the neighborhood information, and the adaptation is achieved with the following objective:
+$$
+\mathcal { L } = - \frac { 1 } { n _ { t } } \sum _ { x _ { i } \in \mathcal { D } _ { t } } \sum _ { x _ { j } \in \mathrm { N e i g h } ( x _ { i } ) } \frac { D _ { s i m } ( p _ { i } , p _ { j } ) } { D _ { d i s } ( x _ { i } , x _ { j } ) }
+$$
+where the $\mathrm { { N e i g h } } ( x _ { i } )$ means the nearest neighbors of $x _ { i }$ , $D _ { s i m }$ computes the similarity between predictions, and $D _ { d i s }$ is a constant measuring the semantic distance (dissimilarity) between data. The principle behind the objective is to push the data towards their semantically close neighbors by encouraging similar predictions. In the next sections, we will define $D _ { s i m }$ and $D _ { d i s }$ .
+# 3.1 Encouraging Class-Consistency with Neighborhood Affinity
+To achieve adaptation without source data, we use the prediction of the nearest neighbor to encourage prediction consistency. While the target features from the source model are not necessarily totally intrinsic discriminative, meaning some neighbors belong to different class and will provide the wrong supervision. To decrease the potentially negative impact of those neighbors, we propose to weigh the supervision from neighbors according to the connectivity (semantic similarity). We define affinity values to signify the connectivity between the neighbor and the feature, which corresponds to the $\frac { 1 } { D _ { d i s } }$ in Eq. 1 indicating the semantic similarity.
+To retrieve the nearest neighbors for batch training, similar to [33, 50, 62], we build two memory banks: $\mathcal { F }$ stores all target features, and $s$ stores corresponding prediction scores:
+$$
+\mathcal { F } = [ z _ { 1 } , z _ { 2 } , \dotsc , z _ { n _ { t } } ] \mathrm { a n d } \ S = [ p _ { 1 } , p _ { 2 } , \dotsc , p _ { n _ { t } } ]
+$$
+We use the cosine similarity for nearest neighbors retrieving. The difference between ours and [33, 50] lies in the fact that we utilize the memory bank to retrieve nearest neighbors while [33, 50] adopts the memory bank to compute the instance discrimination loss. Before every mini-batch training, we simply update the old items in the memory banks corresponding to current mini-batch. Note that updating the memory bank is only done to replace the old low-dimension vectors with new ones computed by the model, and does not require any additional computation.
+We then use the prediction of the neighbors to supervise the training weighted by the affinity values, with the following objective adapted from Eq. 1:
+$$
+\mathcal { L } _ { \mathcal { N } } = - \frac { 1 } { n _ { t } } \sum _ { i } \sum _ { k \in \mathcal { N } _ { K } ^ { i } } A _ { i k } \boldsymbol { S } _ { k } ^ { \top } \boldsymbol { p } _ { i }
+$$
+where we use the dot product to compute the similarity between predictions, corresponding to $D _ { s i m }$ in Eq.1, the $k$ is the index of the $k$ -th nearest neighbors of $z _ { i }$ , $\scriptstyle { S _ { k } }$ is the $k$ -th item in memory bank $s$ , $A _ { i k }$ is the affinity value of $k$ -th nearest neighbors of feature $z _ { i }$ . Here the $\mathcal { N } _ { K } ^ { i }$ is the index $\mathrm { { \dot { s e t } } } ^ { 2 }$ of the $K$ -nearest neighbors of feature $z _ { i }$ . Note that all neighbors are retrieved from the feature bank $\mathcal { F }$ . With the affinity value as weight, this objective pushes the features to their neighbors with strong connectivity and to a lesser degree to those with weak connectivity.
+To assign larger affinity values to semantic similar neighbors, we divide the nearest neighbors retrieved into two groups: reciprocal nearest neighbors (RNN) and non-reciprocal nearest neighbors (nRNN). The feature $z _ { j }$ is regarded as the RNN of the feature $z _ { i }$ if it meets the following condition:
+$$
+j \in \mathcal { N } _ { K } ^ { i } \wedge i \in \mathcal { N } _ { M } ^ { j }
+$$
+Other neighbors which do not meet the above condition are nRNN. Note that the normal definition of reciprocal nearest neighbors [31] applies $K = M$ , while in this paper $K$ and $M$ can be different. We find that reciprocal neighbors have a higher potential to belong to the same cluster as the feature (Fig. 1(b)). Thus, we assign a high affinity value to the RNN features. Specifically for feature $z _ { i }$ , the affinity value of its $j$ -th $\mathrm { K }$ -nearest neighbor is defined as:
+$$
+A _ { i , j } = { \left\{ \begin{array} { l l } { 1 } & { { \mathrm { i f ~ } } j \in { \mathcal { N } } _ { K } ^ { i } \land i \in { \mathcal { N } } _ { M } ^ { j } } \\ { r } & { { \mathrm { o t h e r w i s e . } } } \end{array} \right. }
+$$
+where $r$ is a hyperparameter. If not specified $r$ is set to 0.1.
+To further reduce the potential impact of noisy neighbors in $\mathcal { N } _ { K }$ , which belong to the different class but still are RNN, we propose a simply yet effective way dubbed self-regularization, that is, to not ignore the current prediction of ego feature:
+$$
+\mathcal { L } _ { s e l f } = - \frac { 1 } { n _ { t } } \sum _ { i } ^ { n _ { t } } S _ { i } ^ { \top } p _ { i }
+$$
+where $s _ { i }$ means the stored prediction in the memory bank, note this term is a constant vector and is identical to the $p _ { i }$ since we update the memory banks before the training, here the loss is only back-propagated for variable $p _ { i }$ .
+Require: $\mathcal { D } _ { s }$ (only for source model training), $\mathcal { D } _ { t }$
+1: Pre-train model on $\mathcal { D } _ { s }$
+2: Build feature bank $\mathcal { F }$ and score bank $s$ for $\mathcal { D } _ { t }$
+3: while Adaptation do
+4: Sample batch $\tau$ from $\mathcal { D } _ { t }$
+5: Update $\mathcal { F }$ and $s$ corresponding to current batch $\tau$
+6: Retrieve nearest neighbors $\mathcal { N }$ for each of $\tau$
+7: Compute affinity value $A$
+8: Retrieve expanded neighborhoods $E$ for each of $\mathcal { N }$
+9: Compute loss and update the model
+10: end while
+. Eq.5 . Eq. 9
+To avoid the degenerated solution [8, 39] where the model predicts all data as some specific classes (and does not predict other classes for any of the target data), we encourage the prediction to be balanced. We adopt the prediction diversity loss which is widely used in clustering [8, 9, 13] and also in several domain adaptation works [21, 39, 42]:
+$$
+\mathcal { L } _ { d i v } = \sum _ { c = 1 } ^ { C } \mathrm { K L } ( \bar { p } _ { c } | | q _ { c } ) , \mathrm { w i t h } \bar { p } _ { c } = \frac { 1 } { n _ { t } } \sum _ { i } p _ { i } ^ { ( c ) } , \mathrm { a n d } q _ { \{ c = 1 , . . , C \} } = \frac { 1 } { C }
+$$
+where the $p _ { i } ^ { ( c ) }$ is the score of the $c$ -th class and $\bar { p } _ { c }$ is the empirical label distribution, it represents the predicted possibility of class $c$ and q is a uniform distribution.
+# 3.2 Expanded Neighborhood Affinity
+As mentioned in Sec. 1, a simple way to achieve the aggregation of more information is by considering more nearest neighbors. However, a drawback is that larger neighborhoods are expected to contain more datapoint from multiple classes, defying the purpose of class consistency. A better way to include more target features is by considering the $M$ -nearest neighbor of each neighbor in $\mathcal { N } _ { K }$ of $z _ { i }$ in Eq. 4, i.e., the expanded neighbors. These target features are expected to be closer on the target data manifold than the features that are included by considering a larger number of nearest neighbors [43]. The expanded neighbors of feature $z _ { i }$ are defined as $\bar { E _ { M } } ( z _ { i } ) \bar { = } \mathcal { N } _ { M } ( z _ { j } ) \forall j \in \mathcal { N } _ { K } ( z _ { i } \bar { ) }$ , note that $E _ { M } ( z _ { i } )$ is still an index set and $i$ (ego feature) $\not \in E _ { M } ( z _ { i } )$ . We directly assign a small affinity value $r$ to those expanded neighbors, since they are further than nearest neighbors and may contain noise. We utilize the prediction of those expanded neighborhoods for training:
+$$
+\mathcal { L } _ { E } = - \frac { 1 } { n _ { t } } \sum _ { i } \sum _ { k \in \mathcal { N } _ { K } ^ { i } } \sum _ { m \in E _ { M } ^ { k } } r \mathcal { S } _ { m } ^ { \top } p _ { i }
+$$
+where $E _ { M } ^ { k }$ contain the $M$ -nearest neighbors of neighbor $k$ in $\mathcal { N } _ { K }$
+Although the affinity values of all expanded neighbors are the same, it does not necessarily mean that they have equal importance. Taking a closer look at the expanded neighbors $E _ { M } ( z _ { i } )$ , some neighbors will show up more than once, for example $z _ { m }$ can be the nearest neighbor of both $z _ { h }$ and $z _ { j }$ where $h , j \in \mathcal N _ { K } ( \bar { z } _ { i } )$ , and the nearest neighbors can also serve as expanded neighbor. It implies that those neighbors form compact cluster, and we posit that those duplicated expanded neighbors have potential to be semantically closer to the ego-feature $z _ { i }$ . Thus, we do not remove duplicated features in $E _ { M } ( z _ { i } )$ , as those can lead to actually larger affinity value for those expanded neighbors. This is one advantage of utilizing expanded neighbors instead of more nearest neighbors, we will verify the importance of maintaining the duplicated features in the experimental section.
+Final objective. Our method, called Neighborhood Reciprocity Clustering (NRC), is illustrated in Algorithm. 1. The final objective for adaptation is:
+$$
+\mathcal { L } = \mathcal { L } _ { d i v } + \mathcal { L } _ { \mathcal { N } } + \mathcal { L } _ { E } + \mathcal { L } _ { s e l f } .
+$$
+# 4 Experiments
+Datasets. We use three 2D image benchmark datasets and a 3D point cloud recognition dataset.
+Office-31 [32] contains 3 domains (Amazon, Webcam, DSLR) with 31 classes and 4,652 images.
+Table 1: Accuracies $( \% )$ on Office-31 for ResNet50-based methods.
+<table><tr><td>Method</td><td>SF</td><td>A→D</td><td>A→W</td><td>D→W</td><td>W→D</td><td>D→A</td><td>W→A</td><td>Avg</td></tr><tr><td>MCD [35]</td><td>X</td><td>92.2</td><td>88.6</td><td>98.5</td><td>100.0</td><td>69.5</td><td>69.7</td><td>86.5</td></tr><tr><td>CDAN [24]</td><td>X</td><td>92.9</td><td>94.1</td><td>98.6</td><td>100.0</td><td>71.0</td><td>69.3</td><td>87.7</td></tr><tr><td>MDD [59]</td><td>X</td><td>90.4</td><td>90.4</td><td>98.7</td><td>99.9</td><td>75.0</td><td>73.7</td><td>88.0</td></tr><tr><td>BNM[4]</td><td>X</td><td>90.3</td><td>91.5</td><td>98.5</td><td>100.0</td><td>70.9</td><td>71.6</td><td>87.1</td></tr><tr><td>DMRL [49]</td><td>X</td><td>93.4</td><td>90.8</td><td>99.0</td><td>100.0</td><td>73.0</td><td>71.2</td><td>87.9</td></tr><tr><td>BDG[53]</td><td>X</td><td>93.6</td><td>93.6</td><td>99.0</td><td>100.0</td><td>73.2</td><td>72.0</td><td>88.5</td></tr><tr><td>MCC[15]</td><td>X</td><td>95.6</td><td>95.4</td><td>98.6</td><td>100.0</td><td>72.6</td><td>73.9</td><td>89.4</td></tr><tr><td>SRDC[42]</td><td>X</td><td>95.8</td><td>95.7</td><td>99.2</td><td>100.0</td><td>76.7</td><td>77.1</td><td>90.8</td></tr><tr><td>RWOT[51]</td><td>X</td><td>94.5</td><td>95.1</td><td>99.5</td><td>100.0</td><td>77.5</td><td>77.9</td><td>90.8</td></tr><tr><td>RSDA-MSTN[10]</td><td>X</td><td>95.8</td><td>96.1</td><td>99.3</td><td>100.0</td><td>77.4</td><td>78.9</td><td>91.1</td></tr><tr><td>SHOT [21]</td><td>√</td><td>94.0</td><td>90.1</td><td>98.4</td><td>99.9</td><td>74.7</td><td>74.3</td><td>88.6</td></tr><tr><td>3C-GAN[20]</td><td>【</td><td>92.7</td><td>93.7</td><td>98.5</td><td>99.8</td><td>75.3</td><td>77.8</td><td>89.6</td></tr><tr><td>NRC</td><td></td><td>96.0</td><td>90.8</td><td>99.0</td><td>100.0</td><td>75.3</td><td>75.0</td><td>89.4</td></tr></table>
+Table 2: Accuracies $( \% )$ on Office-Home for ResNet50-based methods.
+<table><tr><td>Method</td><td></td><td>SFAr-&gt;CIAr-→PrAr-→RwC1-→ArCI-→PrCI-→&gt;RwPr-→ArPr-→&gt;CIPr-→RwRw-→ArRw-→CIRw-→PrAvg</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MCD [35]</td><td>xxxxxxxxxx</td><td>48.9 68.3</td><td>74.6</td><td>61.3</td><td>67.6</td><td>68.8</td><td>57.0</td><td>47.1</td><td>75.1</td><td>69.1</td><td>52.2</td><td>79.6</td><td>64.1</td></tr><tr><td>CDAN [24]</td><td></td><td>50.7</td><td>70.6 76.0</td><td>57.6</td><td>70.0</td><td>70.0</td><td>57.4</td><td>50.9</td><td>77.3</td><td>70.9</td><td>56.7</td><td>81.6</td><td>65.8</td></tr><tr><td>SAFN [52]</td><td></td><td>52.0</td><td>71.7 76.3</td><td>64.2</td><td>69.9</td><td>71.9</td><td>63.7</td><td>51.4</td><td>77.1</td><td>70.9</td><td>57.1</td><td>81.5</td><td>67.3</td></tr><tr><td>Symnets [58]</td><td></td><td>47.7 72.9</td><td>78.5</td><td>64.2</td><td>71.3</td><td>74.2</td><td>64.2</td><td>48.8</td><td>79.5</td><td>74.5</td><td>52.6</td><td>82.7</td><td>67.6</td></tr><tr><td>MDD [59]</td><td></td><td>54.9 73.7</td><td>77.8</td><td>60.0</td><td>71.4</td><td>71.8</td><td>61.2</td><td>53.6</td><td>78.1</td><td>72.5</td><td>60.2</td><td>82.3</td><td>68.1</td></tr><tr><td>TADA [47]</td><td></td><td>53.1</td><td>72.3 77.2</td><td>59.1</td><td>71.2</td><td>72.1</td><td>59.7</td><td>53.1</td><td>78.4</td><td>72.4</td><td>60.0</td><td>82.9</td><td>67.6</td></tr><tr><td>BNM[4]</td><td></td><td>52.3</td><td>73.9 80.0</td><td>63.3</td><td>72.9</td><td>74.9</td><td>61.7</td><td>49.5</td><td>79.7</td><td>70.5</td><td>53.6</td><td>82.2</td><td>67.9</td></tr><tr><td>BDG [53]</td><td></td><td>51.5 73.4</td><td>78.7</td><td>65.3</td><td>71.5</td><td>73.7</td><td>65.1</td><td>49.7</td><td>81.1</td><td>74.6</td><td>55.1</td><td>84.8</td><td>68.7</td></tr><tr><td>SRDC [42]</td><td></td><td>52.3 76.3</td><td>81.0</td><td>69.5</td><td>76.2</td><td>78.0</td><td>68.7</td><td>53.8</td><td>81.7</td><td>76.3</td><td>57.1</td><td>85.0</td><td>71.3</td></tr><tr><td>RSDA-MSTN[10]</td><td></td><td>53.2</td><td>77.7 81.3</td><td>66.4</td><td>74.0</td><td>76.5</td><td>67.9</td><td>53.0</td><td>82.0</td><td>75.8</td><td>57.8</td><td>85.4</td><td>70.9</td></tr><tr><td>SHOT [21]</td><td></td><td>57.1</td><td>78.1 81.5</td><td>68.0</td><td>78.2</td><td>78.1</td><td>67.4</td><td>54.9</td><td>82.2</td><td>73.3</td><td>58.8</td><td>84.3</td><td>71.8</td></tr><tr><td>NRC</td><td>区</td><td>57.7</td><td>80.3 82.0</td><td>68.1</td><td>79.8</td><td>78.6</td><td>65.3</td><td>56.4</td><td>83.0</td><td>71.0</td><td>58.6</td><td>85.6</td><td>72.2</td></tr></table>
+Office-Home [46] contains 4 domains (Real, Clipart, Art, Product) with 65 classes and a total of 15,500 images. VisDA [28] is a more challenging dataset, with 12-class synthetic-to-real object recognition tasks, its source domain contains of $1 5 2 \mathrm { k }$ synthetic images while the target domain has 55k real object images. PointDA-10 [30] is the first 3D point cloud benchmark specifically designed for domain adaptation, it has 3 domains with 10 classes, denoted as ModelNet-10, ShapeNet-10 and ScanNet-10, containing approximately $2 7 . 7 \mathrm { k }$ training and 5.1k testing images together.
+Evaluation. We compare with existing source-present and source-free DA methods. All results are the average on three random runs. SF in the tables denotes source-free.
+Model details. For fair comparison with related methods, we also adopt the backbone of ResNet-50 [11] for Office-Home and ResNet-101 for VisDA, and PointNet [29] for PointDA10. Specifically, for 2D image datasets, we use the same network architecture as SHOT [21], i.e., the final part of the network is: fully connected layer − Batch Normalization [12] − fully connected layer with weight normalization [37]. And for PointDA-10 [29], we use the code released by the authors for fair comparison with PointDAN [29], and only use the backbone without any of their proposed modules. To train the source model, we also adopt label smoothing as SHOT does. We adopt SGD with momentum 0.9 and batch size of 64 for all 2D datasets, and Adam for PointDA-10. The learning rate for Office-31 and Office-Home is set to 1e-3 for all layers, except for the last two newly added fc layers, where we apply 1e-2. Learning rates are set 10 times smaller for VisDA. Learning rate for PointDA-10 is set to 1e-6. We train 30 epochs for Office-31 and OfficeHome while 15 epochs for VisDA, and 100 for PointDA-10. For the number of nearest neighbors (K) and expanded neighborhoods (M), we use 3,2 for Office-31, Office-Home and PointDA-10, since VisDA is much larger we set K, M to 5. Experiments are conducted on a TITAN Xp.
+# 4.1 Results
+2D image datasets. We first evaluate the target performance of our method compared with existing DA and SFDA methods on three 2D image datasets. As shown in Table 1-3, the top part shows results for the source-present methods with access to source data during adaptation. The bottom shows results for the source-free DA methods. On Office-31, our method gets similar results compared with source-free method 3C-GAN and lower than source-present method RSDA-MSTN. And our method achieves state-of-the-art performance on Office-Home and VisDA, especially on VisDA our method surpasses the source-free method SHOT and source-present method RWOT by a wide margin $3 \%$ and $1 . 9 \%$ respectively). The reported results clearly demonstrate the efficiency of the proposed method for source-free domain adaptation. Interestingly, like already observed in the SHOT paper, source-free methods outperform methods that have access to source data during adaptation.
+Table 3: Accuracies $( \% )$ on VisDA-C (Synthesis Real) for ResNet101-based methods.
+<table><tr><td rowspan=1 colspan=1>Method</td><td rowspan=1 colspan=1>SF</td><td rowspan=1 colspan=1>[SF|plane bcycl bus car horse knife mcycl person plant sktbrd train truck Per-class</td></tr><tr><td rowspan=5 colspan=1>ADR [34]CDAN [24]CDAN+BSP[2]SAFN [52]SWD[19]MDD [59]DMRL [49]MCC[15]STAR [26]RWOT[51]</td><td rowspan=1 colspan=1>X</td><td rowspan=1 colspan=1>94.248.584.0 72.990.174.292.6 72.580.861.882.2 28.8  73.5</td></tr><tr><td rowspan=1 colspan=1>X</td><td rowspan=1 colspan=1>85.266.983.0 50.884.274.988.1 74.583.476.081.9 38.0  73.9</td></tr><tr><td rowspan=3 colspan=1>×</td><td rowspan=2 colspan=1>61.081.0 57.5 89.080.690.1 77.084.277.982.1 38.4  75.9</td></tr><tr><td rowspan=1 colspan=1>92.493.690.8</td></tr><tr><td rowspan=1 colspan=1>93.661.384.1 70.6 94.179.091.8 79.689.955.689.0 24.4  76.190.882.5 81.7 70.5 91.769.586.3 77.587.463.685.6 29.2  76.4-    1    1   1   1   1    1     1    1    -    1   1    74.6-                =     =     =     =     =     =     =          =    75.588.780.3 80.5 71.5 90.1 93.285.0 71.689.473.8 85.0 36.9  78.895.084.084.6 73.0 91.691.885.9 78.494.484.787.0 42.2  82.795.180.383.7 90.092.468.092.5 82.287.978.490.4 68.2  84.0</td></tr><tr><td rowspan=3 colspan=1>3C-GAN [20]SHOT[21]NRC</td><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=1>94.873.468.8 74.893.195.488.6 84.7 89.184.783.5 48.1  81.6</td></tr><tr><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=1>94.388.580.1 57.3 93.194.980.7 80.391.589.186.3 58.2  82.9</td></tr><tr><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=1>96.891.382.4 62.4 96.295.986.1 80.694.894.190.4 59.7  85.9</td></tr></table>
+Table 4: Accuracies $( \% )$ on PointDA-10. The results except ours are from PointDAN [30].
+<table><tr><td colspan="2"></td><td colspan="4">|SF|Model-→Shape Model-→Scan Shape-→Model Shape-&gt;Scan Scan→Model Scan-→Shape Avg</td></tr><tr><td>MMD [25]</td><td></td><td>57.5 27.9</td><td>40.7</td><td>26.7</td><td>47.3</td><td>54.8</td><td>42.5</td></tr><tr><td>DANN [6]</td><td>xxxxx</td><td>58.7 29.4</td><td>42.3</td><td>30.5</td><td>48.1</td><td>56.7</td><td>44.2</td></tr><tr><td>ADDA [44]</td><td></td><td>61.0 30.5</td><td>40.4</td><td>29.3</td><td>48.9</td><td>51.1</td><td>43.5</td></tr><tr><td>MCD [35]</td><td></td><td>62.0 31.0</td><td>41.4</td><td>31.3</td><td>46.8</td><td>59.3</td><td>45.3</td></tr><tr><td>PointDAN [30]</td><td></td><td>64.2 33.0</td><td>47.6</td><td>33.9</td><td>49.1</td><td>64.1</td><td>48.7</td></tr><tr><td>Source-only</td><td></td><td>43.1</td><td>17.3 40.0</td><td>15.0</td><td>33.9</td><td>47.1</td><td>32.7</td></tr><tr><td>NRC</td><td>&lt;</td><td>64.8</td><td>25.8 59.8</td><td>26.9</td><td>70.1</td><td>68.1</td><td>52.6</td></tr></table>
+3D point cloud dataset. We also report the result for the PointDA-10. As shown in Table 4, our method outperforms PointDA [30], which demands source data for adaptation and is specifically tailored for point cloud data with extra attention modules, by a large margin $(4 \% )$ .
+# 4.2 Analysis
+Ablation study on neighbors $\mathcal { N }$ , $E$ and affinity $A$ . In the first two tables of Table 5, we conduct the ablation study on Office-Home and VisDA. The 1-st row contains results from the source model and the 2-nd row from only training with the diversity loss $\mathcal { L } _ { d i v }$ . From the remaining rows, several conclusions can be drawn.
+First, the original supervision, which considers all neighbors equally can lead to a decent performance (67.1 on Office-Home). Second, considering higher affinity values for reciprocal neighbors leads to a large performance gain (69.1 on Office-Home). Last but not the least, the expanded neighborhoods can also be helpful, but only when combined with the affinity values $A$ (72.2 on Office-Home). Using expanded neighborhoods without affinity obtains bad performance (65,2 on Office-Home). We conjecture that those expanded neighborhoods, especially those neighbors of nRNN, may be noisy as discussed in Sec. 3.2. Removing the affinity $A$ means we treat all those neighbors equally, which is not reasonable.
+Table 5: Ablation study of different modules on Office-Home (left) and VisDA (middle), comparison between using expanded neighbors and larger nearest neighbors (right).
+<table><tr><td>Ldiv</td><td>LN</td><td>LE LEA</td><td>Avg</td><td>Ldiv</td><td>LN</td><td></td><td>LE LEA</td><td></td><td>Acc</td></tr><tr><td></td><td></td><td></td><td>59.5</td><td></td><td></td><td></td><td></td><td></td><td>44.6</td></tr><tr><td></td><td></td><td></td><td>62.1</td><td></td><td></td><td></td><td></td><td></td><td>47.8</td></tr><tr><td></td><td></td><td></td><td>67.1</td><td></td><td></td><td></td><td></td><td></td><td>74.6</td></tr><tr><td></td><td></td><td></td><td>√ 69.1</td><td></td><td></td><td></td><td></td><td>√</td><td>81.5</td></tr><tr><td></td><td></td><td></td><td>65.2</td><td></td><td></td><td></td><td></td><td></td><td>61.2</td></tr><tr><td></td><td></td><td></td><td>72.2</td><td></td><td></td><td></td><td></td><td>！</td><td>85.9</td></tr><tr><td></td><td></td><td></td><td>69.1 [</td><td></td><td></td><td></td><td></td><td></td><td>82.0</td></tr></table>
+<table><tr><td rowspan=1 colspan=1>Method&amp;Dataset</td><td rowspan=1 colspan=1>Acc</td></tr><tr><td rowspan=1 colspan=1>VisDA (K=M=5)VisDA w/o E (K=30)</td><td rowspan=1 colspan=1>85.984.0</td></tr><tr><td rowspan=1 colspan=1>OH(K=3,M=2)OH w/o E (K=9)</td><td rowspan=1 colspan=1>72.269.5</td></tr></table>
+Table 6: Runtime analysis on SHOT and our method. For SHOT, pseudo labels are computed at each epoch. $20 \%$ , $10 \%$ and $5 \%$ denote the percentage of target features which are stored in the memory bank.
+<table><tr><td>VisDA</td><td colspan="2">Runtime (s/epoch)Per-class (%)</td></tr><tr><td>SHOT</td><td>618.82</td><td>82.9</td></tr><tr><td>NRC</td><td>540.89</td><td>85.9</td></tr><tr><td>NRC(20%) 6formemorybank)</td><td>507.15</td><td>85.3</td></tr><tr><td>NRC(10% for memory bank)</td><td>499.49</td><td>85.2</td></tr><tr><td>NRC(5% for memory bank)</td><td>499.28</td><td>85.1</td></tr></table>
+![](images/e1748829bba37f8f3b6d43d90dfdbea6be91a7b5cbb5e87bd18f0bf9bd522aa6.jpg)
+Figure 2: (Left and middle) Ablation study of $\mathcal { L } _ { s e l f }$ on Office-Home and VisDA respectively. (Right) Performance with different $r$ on VisDA.
+We also show that duplication in the expanded neighbors is important in the last row of Table 5, where the $\mathcal { L } _ { \hat { E } }$ means we remove duplication in Eq. 8. The results show that the performance will degrade significantly when removing them, implying that the duplicated expanded neighbors are indeed more important than others.
+Next we ablate the importance of the expanded neighborhood in the right of Table5. We show that if we increase the number of datapoints considered for class-consistency by simply considering a larger K, we obtain significantly lower scores. We have chosen $K$ so that the total number of points considered is equal to our method (i.e. $5 { + } 5 ^ { * } 5 { = } 3 0$ and $3 + 3 ^ { * } 2 { = } 9 ,$ ). Considering neighbors of neighbors is more likely to provide datapoints that are close on the data manifold [43], and are therefore more likely to share the class label with the ego feature.
+Runtime analysis. Instead of storing all feature vectors in the memory bank, we follow the same memory bank setting as in [5] which is for nearest neighbor retrieval. The method only stores a fixed number of target features, we update the memory bank at the end of each iteration by taking the $n$ (batch size) embeddings from the current training iteration and concatenating them at the end of the memory bank, and discard the oldest $n$ elements from the memory bank. We report the results with this type of memory bank of different buffer size in the Table 6. The results show that indeed this could be an efficient way to reduce computation on very large datasets.
+Ablation study on self-regularization. In the left and middle of Fig 2, we show the results with and without self-regularization $\mathcal { L } _ { s e l f }$ . The $\mathcal { L } _ { s e l f }$ can improve the performance when adopting only nearest neighbors $\mathcal { N }$ or all neighbors $\mathcal { N } + E$ . The results imply that self-regularization can effectively reduce the negative impact of the potential noisy neighbors, especially on the Office-Home dataset.
+Sensitivity to hyperparameter. There are three hyperparameters in our method: K and M which are the number of nearest neighbors and expanded neighbors, $r$ which is the affinity value assigned to nRNN. We show the results with different $r$ in the right of Fig. 2. Note we keep the affinity of expanded neighbors as 0.1. $r = 1$ means no affinity. $r = - 1$ means treating supervision of nRNN feature as totally wrong, which is not always the case and will lead to quite lower result. $r = 0$ can also achieve good performance, signifying RNN can already work well. Results with $r = 0 . 1 / 0 . 1 5 / 0 . 2$ show that our method is not sensitive to the choice of a reasonable $r$ . Note in DA, there is no validation set for hyperparameter tuning, we show the results varying the number of neighbors in the right of Tab. 3, demonstrating the robustness to the choice of $K$ and $M$ .
+![](images/52c51cde4275a75094e8c62c8d4fd77f70977cdffb6dcc8e5fcf1796cfa99e42.jpg)
+Figure 3: (Left) The three curves are (on VisDA): target accuracy (Blue), ratio of features which have 5-nearest neighbors all sharing the same predicted label (dashed Red), and ratio of features which have 5-nearest neighbors all sharing the same and correct predicted label (dashed Black). (Right) Ablation study on choice of K and M on VisDA.
+![](images/fd8c9cc81f0a4968ed7f3124861b6deeb77a38f4952bd4cbfedaa30cfe215f98.jpg)
+Figure 4: (Left) Ratio of different type of nearest neighbor features which have the correct predicted label, before and after adaptation. (Right) Visualization of target features after adaptation.
+Training curve. We show the evolution of several statistics during adaptation on VisDA in the left of Tab. 3. The blue curve is the target accuracy. The dashed red and black curves are the ratio of features which have 5-nearest neighbors all sharing the same (dashed Red), or the same and also correct (dashed Black) predicted label. The curves show that the target features are clustering during the training. Another interesting finding is that the curve ’Per Shared’ correlates with the accuracy curve, which might therefore be used to determine training convergence.
+Accuracy of supervision from neighbors. We also show the accuracy of supervision from neighbors on task $\mathrm { A r } {  } \mathrm { R w }$ of Office-Home in Fig. 4(left). It shows that after adaptation, the ratio of all types of neighbors having more correct predicted label, proving the effectiveness of the method.
+t-SNE visualization. We show the t-SNE feature visualization on task $\mathrm { A r } {  } \mathrm { R w }$ of target features before (Fig. 1(a)) and after (Fig. 4(right)) adaptation. After adaptation, the features are more compactly clustered.
+# 5 Conclusions
+We introduce a source-free domain adaptation (SFDA) method by uncovering the intrinsic target data structure. We propose to achieve the adaptation by encouraging label consistency among local target features. We differentiate between nearest neighbors, reciprocal neighbors and expanded neighborhood. Experimental results verify the importance of considering the local structure of the target features. Finally, our experimental results on both 2D image and 3D point cloud datasets testify the efficacy of our method.
+Acknowledgement We acknowledge the support from Huawei Kirin Solution, and the project PID2019-104174GB-I00 (MINECO, Spain) and RTI2018-102285-A-I00 (MICINN, Spain), Ramón y Cajal fellowship RYC2019-027020-I, and the CERCA Programme of Generalitat de Catalunya.
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+[61] Jiong Zhu, Yujun Yan, Lingxiao Zhao, Mark Heimann, Leman Akoglu, and Danai Koutra. Beyond homophily in graph neural networks: Current limitations and effective designs. Advances in Neural Information Processing Systems, 33, 2020.
+[62] Chengxu Zhuang, Alex Lin Zhai, and Daniel Yamins. Local aggregation for unsupervised learning of visual embeddings. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6002–6012, 2019.
+# Checklist
+1. For all authors...
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]
+(b) Did you describe the limitations of your work? [No]
+(c) Did you discuss any potential negative societal impacts of your work? [No]
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+2. If you are including theoretical results...
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+3. If you ran experiments...
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] We attach the code in the supplemental material.
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] As in the model details in Sec.4
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] All main results are average over three running with random seeds.
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes]
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+(a) If your work uses existing assets, did you cite the creators? [Yes]
+(b) Did you mention the license of the assets? [No]
+(c) Did you include any new assets either in the supplemental material or as a URL? [No]
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [No]
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [No]
+5. If you used crowdsourcing or conducted research with human subjects...
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

parse/train/ueGDv64HmO/ueGDv64HmO_content_list.json ADDED Viewed

	@@ -0,0 +1,1193 @@

+[
+    {
+        "type": "text",
+        "text": "Exploiting the Intrinsic Neighborhood Structure for Source-free Domain Adaptation ",
+        "text_level": 1,
+        "bbox": [
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+            122,
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+            172
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Shiqi Yang1, Yaxing Wang1,2∗, Joost van de Weijer1, Luis Herranz1, Shangling Jui3 1 Computer Vision Center, Universitat Autonoma de Barcelona, Barcelona, Spain 2 PCALab, Nanjing University of Science and Technology, China 3 Huawei Kirin Solution, Shanghai, China   \n{syang,yaxing,joost,lherranz}@cvc.uab.es, jui.shangling@huawei.com ",
+        "bbox": [
+            207,
+            224,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            333,
+            535,
+            349
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Domain adaptation (DA) aims to alleviate the domain shift between source domain and target domain. Most DA methods require access to the source data, but often that is not possible (e.g. due to data privacy or intellectual property). In this paper, we address the challenging source-free domain adaptation (SFDA) problem, where the source pretrained model is adapted to the target domain in the absence of source data. Our method is based on the observation that target data, which might no longer align with the source domain classifier, still forms clear clusters. We capture this intrinsic structure by defining local affinity of the target data, and encourage label consistency among data with high local affinity. We observe that higher affinity should be assigned to reciprocal neighbors, and propose a self regularization loss to decrease the negative impact of noisy neighbors. Furthermore, to aggregate information with more context, we consider expanded neighborhoods with small affinity values. In the experimental results we verify that the inherent structure of the target features is an important source of information for domain adaptation. We demonstrate that this local structure can be efficiently captured by considering the local neighbors, the reciprocal neighbors, and the expanded neighborhood. Finally, we achieve state-of-the-art performance on several 2D image and 3D point cloud recognition datasets. Code is available in https://github.com/Albert0147/SFDA_neighbors. ",
+        "bbox": [
+            232,
+            366,
+            766,
+            627
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            657,
+            310,
+            675
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Most deep learning methods rely on training on large amount of labeled data, while they cannot generalize well to a related yet different domain. One research direction to address this issue is Domain Adaptation (DA), which aims to transfer learned knowledge from a source to a target domain. Most existing DA methods demand labeled source data during the adaptation period, however, it is often not practical that source data are always accessible, such as when applied on data with privacy or property restrictions. Therefore, recently, there have emerged a few works [16, 17, 20, 21] tackling a new challenging DA scenario where instead of source data only the source pretrained model is available for adapting, i.e., source-free domain adaptation (SFDA). Among these methods, USFDA [16] addresses universal DA [57] and SF [17] addresses open-set DA [36]. In both universal and open-set DA the label set is different for source and target domains. SHOT [21] and 3C-GAN [20] are for closed-set DA where source and target domains have the same categories. 3C-GAN [20] is based on target-style image generation with a conditional GAN, and SHOT [21] is based on mutual information maximization and pseudo labeling. Finally, BAIT [56] extends MCD [35] to the SFDA setting. However, these methods ignore the intrinsic neighborhood structure of the target data in feature space which can be very valuable to tackle SFDA. ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/343b4b429f7a34d25d762b61bf6977f13ba8eaac4be276860b5d2170fa2f18be.jpg",
+        "image_caption": [
+            "Figure 1: (a) t-SNE visualization of target features by source model. (b) Ratio of different type of nearest neighbor features of which: the predicted label is the same as the feature, K is the number of nearest neighbors. The features in (a) and (b) are on task $\\mathrm { A r } {  } \\mathrm { R w }$ of Office-Home. (c) Illustration of our method. In the left shows we distinguish reciprocal and non-reciprocal neighbors. The adaptation is achieved by pushed the features towards reciprocal neighbors heavily. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            209,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we focus on closed-set source-free domain adaptation. Our main observation is that current DA methods do not exploit the intrinsic neighborhood structure of the target data. We use this term to refer to the fact that, even though the target data might have shifted in the feature space (due to the covariance shift), target data of the same class is still expected to form a cluster in the embedding space. This can be implied to some degree from the t-SNE visualization of target features on the source model which suggests that significant cluster structure is preserved (see Fig. 1 (a)). This assumption is implicitly adopted by most DA methods, as instantiated by a recent DA work [42]. A well-established way to assess the structure of points in high-dimensional spaces is by considering the nearest neighbors of points, which are expected to belong to the same class. However, this assumption is not true for all points; the blue curve in Figure 1(b) shows that around $7 5 \\%$ of the nearest neighbors has the correct label. In this paper, we observe that this problem can be mitigated by considering reciprocal nearest neighbors (RNN); the reciprocal neighbors of a point have the point as their neighbor. Reciprocal neighbors have been studied before in different contexts [14, 31, 60]. The reason why reciprocal neighbors are more trustworthy is illustrated in Fig. 1(c). Fig. 1(b) shows the ratio of neighbors which have the correct prediction for different kinds of nearest neighbors. The curves show that reciprocal neighbors indeed have more chances to predict the true label than non-reciprocal nearest neighbors (nRNN). ",
+        "bbox": [
+            174,
+            484,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The above observation and analysis motivate us to assign different weights to the supervision from nearest neighbors. Our method, called Neighborhood Reciprocity Clustering (NRC), achieves sourcefree domain adaptation by encouraging reciprocal neighbors to concord in their label prediction. In addition, we will also consider a weaker connection to the non-reciprocal neighbors. We define affinity values to describe the degree of connectivity between each data point and its neighbors, which is also utilized to encourage class-consistency between neighbors, and we propose to use a self-regularization to decrease the negative impact of potential noisy neighbors. Furthermore, inspired by recent graph based methods [1, 3, 61] which show that the higher order neighbors can provide relevant context, and also considering neighbors of neighbors is more likely to provide datapoints that are close on the data manifold [43]. Thus, to aggregate wider local information, we further retrieve the expanded neighbors, i.e, neighbor of the nearest neighbors, for auxiliary supervision. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contributions can be summarized as follows, to achieve source-free domain adaptation: (i) we explicitly exploit the fact that same-class data forms cluster in the target embedding space, we do this by considering the predictions of neighbors and reciprocal neighbors, (ii) we further show that considering an extended neighborhood of data points further improves results (iii) the experiments results on three 2D image datasets and one 3D point cloud dataset show that our method achieves state-of-the-art performance compared with related methods. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            170,
+            321,
+            186
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Domain Adaptation. Most DA methods tackle domain shift by aligning the feature distributions. Early DA methods such as [23, 41, 45] adopt moment matching to align feature distributions. And in recent years, plenty of works have emerged that achieve alignment by adversarial training. DANN [7] formulates domain adaptation as an adversarial two-player game. The adversarial training of CDAN [24] is conditioned on several sources of information. DIRT-T [40] performs domain adversarial training with an added term that penalizes violations of the cluster assumption. Additionally, [18, 26, 35] adopts prediction diversity between multiple learnable classifiers to achieve local or category-level feature alignment between source and target domains. AFN [52] shows that the erratic discrimination of target features stems from much smaller norms than those found in the source features. SRDC [42] proposes to directly uncover the intrinsic target discrimination via discriminative clustering to achieve adaptation. More related, [27] resorts to K-means clustering for open-set adaptation while considering global structure. Our method instead only focuses on nearest neighbors (local structure) for source-free adaptation. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Source-free Domain Adaptation. Source-present methods need supervision from the source domain during adaptation. Recently, there are several methods investigating source-free domain adaptation. USFDA [16] and FS [17] explore source-free universal DA [57] and open-set DA [36], and they propose to synthesize extra training samples to make the decision boundary compact, thereby allowing to recognise the open classes. For closed-set DA setting. SHOT [21] proposes to fix the source classifier and match the target features to the fixed classifier by maximizing mutual information and a proposed pseudo label strategy which considers global structure. 3C-GAN [20] synthesizes labeled target-style training images based on the conditional GAN to provide supervision for adaptation. Finally, SFDA [22] is for segmentation based on synthesizing fake source samples. ",
+        "bbox": [
+            174,
+            388,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Graph Clustering. Our method shares some similarities with graph clustering work such as [38, 48, 54, 55] by utilizing neighborhood information. However, our methods are fundamentally different. Unlike those works which require labeled data to train the graph network for estimating the affinity, we instead adopt reciprocity to assign affinity. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Method ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            599,
+            271,
+            616
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Notation. We denote the labeled source domain data with $n _ { s }$ samples as $\\mathcal { D } _ { s } = \\{ ( x _ { i } ^ { s } , y _ { i } ^ { s } ) \\} _ { i = 1 } ^ { n _ { s } }$ , where $y _ { i } ^ { s }$ orresponding label of . Both domains have t $x _ { i } ^ { s }$ , andsame e unlabeled target domain data with classes (closed-set setting). Under the $n _ { t }$ samples asFDA setting $\\mathcal { D } _ { t } \\overset { \\vartriangle } { = } \\{ x _ { j } ^ { t } \\} _ { j = 1 } ^ { n _ { t } }$ $C$ $\\mathcal { D } _ { s }$ is only available for model pretraining. Our method is based on a neural network, which we split into two parts: a feature extractor $f$ , and a classifier $g$ . The feature output by the feature extractor is denoted as $z ( x ) = f \\left( x \\right)$ , the output of network is denoted as $p ( x ) = \\bar { \\delta } ( g ( \\dot { z } ) ) \\in \\mathcal { R } ^ { C }$ where $\\delta$ is the softmax function, for readability we will abandon the input and use $z , p$ in the following sections. ",
+        "bbox": [
+            173,
+            632,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Overview. We assume that the source pretrained model has already been trained. As discusses in the introduction, the target features output by the source model form clusters. We exploit this intrinsic structure of the target data for SFDA by considering the neighborhood information, and the adaptation is achieved with the following objective: ",
+        "bbox": [
+            174,
+            738,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f5201ec763543d11770c0d5cb15e97a623ee3202a252898dd2e123a078de00d7.jpg",
+        "text": "$$\n\\mathcal { L } = - \\frac { 1 } { n _ { t } } \\sum _ { x _ { i } \\in \\mathcal { D } _ { t } } \\sum _ { x _ { j } \\in \\mathrm { N e i g h } ( x _ { i } ) } \\frac { D _ { s i m } ( p _ { i } , p _ { j } ) } { D _ { d i s } ( x _ { i } , x _ { j } ) }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            343,
+            803,
+            620,
+            844
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where the $\\mathrm { { N e i g h } } ( x _ { i } )$ means the nearest neighbors of $x _ { i }$ , $D _ { s i m }$ computes the similarity between predictions, and $D _ { d i s }$ is a constant measuring the semantic distance (dissimilarity) between data. The principle behind the objective is to push the data towards their semantically close neighbors by encouraging similar predictions. In the next sections, we will define $D _ { s i m }$ and $D _ { d i s }$ . ",
+        "bbox": [
+            174,
+            854,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Encouraging Class-Consistency with Neighborhood Affinity ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            90,
+            629,
+            106
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To achieve adaptation without source data, we use the prediction of the nearest neighbor to encourage prediction consistency. While the target features from the source model are not necessarily totally intrinsic discriminative, meaning some neighbors belong to different class and will provide the wrong supervision. To decrease the potentially negative impact of those neighbors, we propose to weigh the supervision from neighbors according to the connectivity (semantic similarity). We define affinity values to signify the connectivity between the neighbor and the feature, which corresponds to the $\\frac { 1 } { D _ { d i s } }$ in Eq. 1 indicating the semantic similarity. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To retrieve the nearest neighbors for batch training, similar to [33, 50, 62], we build two memory banks: $\\mathcal { F }$ stores all target features, and $s$ stores corresponding prediction scores: ",
+        "bbox": [
+            173,
+            220,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/77d28a00bc4b339a6c125a9e814ebeed0f4f2af38733b940ab6aa2d9c7ee636a.jpg",
+        "text": "$$\n\\mathcal { F } = [ z _ { 1 } , z _ { 2 } , \\dotsc , z _ { n _ { t } } ] \\mathrm { a n d } \\ S = [ p _ { 1 } , p _ { 2 } , \\dotsc , p _ { n _ { t } } ]\n$$",
+        "text_format": "latex",
+        "bbox": [
+            326,
+            256,
+            638,
+            273
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We use the cosine similarity for nearest neighbors retrieving. The difference between ours and [33, 50] lies in the fact that we utilize the memory bank to retrieve nearest neighbors while [33, 50] adopts the memory bank to compute the instance discrimination loss. Before every mini-batch training, we simply update the old items in the memory banks corresponding to current mini-batch. Note that updating the memory bank is only done to replace the old low-dimension vectors with new ones computed by the model, and does not require any additional computation. ",
+        "bbox": [
+            173,
+            279,
+            825,
+            363
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We then use the prediction of the neighbors to supervise the training weighted by the affinity values, with the following objective adapted from Eq. 1: ",
+        "bbox": [
+            171,
+            368,
+            823,
+            397
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ba2c563d21377f4062e4a0eb8b3c9ea39a500ab7b58d34337af1aa5687d187a1.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathcal { N } } = - \\frac { 1 } { n _ { t } } \\sum _ { i } \\sum _ { k \\in \\mathcal { N } _ { K } ^ { i } } A _ { i k } \\boldsymbol { S } _ { k } ^ { \\top } \\boldsymbol { p } _ { i }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            375,
+            402,
+            588,
+            444
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where we use the dot product to compute the similarity between predictions, corresponding to $D _ { s i m }$ in Eq.1, the $k$ is the index of the $k$ -th nearest neighbors of $z _ { i }$ , $\\scriptstyle { S _ { k } }$ is the $k$ -th item in memory bank $s$ , $A _ { i k }$ is the affinity value of $k$ -th nearest neighbors of feature $z _ { i }$ . Here the $\\mathcal { N } _ { K } ^ { i }$ is the index $\\mathrm { { \\dot { s e t } } } ^ { 2 }$ of the $K$ -nearest neighbors of feature $z _ { i }$ . Note that all neighbors are retrieved from the feature bank $\\mathcal { F }$ . With the affinity value as weight, this objective pushes the features to their neighbors with strong connectivity and to a lesser degree to those with weak connectivity. ",
+        "bbox": [
+            173,
+            449,
+            825,
+            535
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To assign larger affinity values to semantic similar neighbors, we divide the nearest neighbors retrieved into two groups: reciprocal nearest neighbors (RNN) and non-reciprocal nearest neighbors (nRNN). The feature $z _ { j }$ is regarded as the RNN of the feature $z _ { i }$ if it meets the following condition: ",
+        "bbox": [
+            173,
+            539,
+            825,
+            582
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a9d9b4a442e9d237d920ac30ca38baaa15d164bc7139d9d474453e1248ee9ec9.jpg",
+        "text": "$$\nj \\in \\mathcal { N } _ { K } ^ { i } \\wedge i \\in \\mathcal { N } _ { M } ^ { j }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            418,
+            589,
+            547,
+            608
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Other neighbors which do not meet the above condition are nRNN. Note that the normal definition of reciprocal nearest neighbors [31] applies $K = M$ , while in this paper $K$ and $M$ can be different. We find that reciprocal neighbors have a higher potential to belong to the same cluster as the feature (Fig. 1(b)). Thus, we assign a high affinity value to the RNN features. Specifically for feature $z _ { i }$ , the affinity value of its $j$ -th $\\mathrm { K }$ -nearest neighbor is defined as: ",
+        "bbox": [
+            173,
+            613,
+            825,
+            684
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7c68533c93cb96b6505a8381ce377b48d20e35c00d1231df58593a8ccd6a27f2.jpg",
+        "text": "$$\nA _ { i , j } = { \\left\\{ \\begin{array} { l l } { 1 } & { { \\mathrm { i f ~ } } j \\in { \\mathcal { N } } _ { K } ^ { i } \\land i \\in { \\mathcal { N } } _ { M } ^ { j } } \\\\ { r } & { { \\mathrm { o t h e r w i s e . } } } \\end{array} \\right. }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            374,
+            690,
+            589,
+            724
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $r$ is a hyperparameter. If not specified $r$ is set to 0.1. ",
+        "bbox": [
+            173,
+            729,
+            560,
+            744
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To further reduce the potential impact of noisy neighbors in $\\mathcal { N } _ { K }$ , which belong to the different class but still are RNN, we propose a simply yet effective way dubbed self-regularization, that is, to not ignore the current prediction of ego feature: ",
+        "bbox": [
+            173,
+            751,
+            825,
+            792
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/06558638152092a6f3c523e045df68d43ae228dd6b46d434df06a6d7d21bf3ce.jpg",
+        "text": "$$\n\\mathcal { L } _ { s e l f } = - \\frac { 1 } { n _ { t } } \\sum _ { i } ^ { n _ { t } } S _ { i } ^ { \\top } p _ { i }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            401,
+            799,
+            562,
+            839
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $s _ { i }$ means the stored prediction in the memory bank, note this term is a constant vector and is identical to the $p _ { i }$ since we update the memory banks before the training, here the loss is only back-propagated for variable $p _ { i }$ . ",
+        "bbox": [
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+            845,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Require: $\\mathcal { D } _ { s }$ (only for source model training), $\\mathcal { D } _ { t }$ ",
+        "bbox": [
+            176,
+            111,
+            472,
+            123
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "1: Pre-train model on $\\mathcal { D } _ { s }$   \n2: Build feature bank $\\mathcal { F }$ and score bank $s$ for $\\mathcal { D } _ { t }$   \n3: while Adaptation do   \n4: Sample batch $\\tau$ from $\\mathcal { D } _ { t }$   \n5: Update $\\mathcal { F }$ and $s$ corresponding to current batch $\\tau$   \n6: Retrieve nearest neighbors $\\mathcal { N }$ for each of $\\tau$   \n7: Compute affinity value $A$   \n8: Retrieve expanded neighborhoods $E$ for each of $\\mathcal { N }$   \n9: Compute loss and update the model   \n10: end while ",
+        "bbox": [
+            178,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": ". Eq.5 . Eq. 9 ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To avoid the degenerated solution [8, 39] where the model predicts all data as some specific classes (and does not predict other classes for any of the target data), we encourage the prediction to be balanced. We adopt the prediction diversity loss which is widely used in clustering [8, 9, 13] and also in several domain adaptation works [21, 39, 42]: ",
+        "bbox": [
+            173,
+            273,
+            825,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/573d90daac2f84185a8ae91be8ed3864534da43c9506209ed0e2158432214e91.jpg",
+        "text": "$$\n\\mathcal { L } _ { d i v } = \\sum _ { c = 1 } ^ { C } \\mathrm { K L } ( \\bar { p } _ { c } | | q _ { c } ) , \\mathrm { w i t h } \\bar { p } _ { c } = \\frac { 1 } { n _ { t } } \\sum _ { i } p _ { i } ^ { ( c ) } , \\mathrm { a n d } q _ { \\{ c = 1 , . . , C \\} } = \\frac { 1 } { C }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            256,
+            333,
+            709,
+            376
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the $p _ { i } ^ { ( c ) }$ is the score of the $c$ -th class and $\\bar { p } _ { c }$ is the empirical label distribution, it represents the predicted possibility of class $c$ and q is a uniform distribution. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 Expanded Neighborhood Affinity ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            419,
+            444,
+            434
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As mentioned in Sec. 1, a simple way to achieve the aggregation of more information is by considering more nearest neighbors. However, a drawback is that larger neighborhoods are expected to contain more datapoint from multiple classes, defying the purpose of class consistency. A better way to include more target features is by considering the $M$ -nearest neighbor of each neighbor in $\\mathcal { N } _ { K }$ of $z _ { i }$ in Eq. 4, i.e., the expanded neighbors. These target features are expected to be closer on the target data manifold than the features that are included by considering a larger number of nearest neighbors [43]. The expanded neighbors of feature $z _ { i }$ are defined as $\\bar { E _ { M } } ( z _ { i } ) \\bar { = } \\mathcal { N } _ { M } ( z _ { j } ) \\forall j \\in \\mathcal { N } _ { K } ( z _ { i } \\bar { ) }$ , note that $E _ { M } ( z _ { i } )$ is still an index set and $i$ (ego feature) $\\not \\in E _ { M } ( z _ { i } )$ . We directly assign a small affinity value $r$ to those expanded neighbors, since they are further than nearest neighbors and may contain noise. We utilize the prediction of those expanded neighborhoods for training: ",
+        "bbox": [
+            173,
+            444,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/191bdd0d5b01784262feba9ccaf69858692f4d6b2b63d4147a304c98893c147e.jpg",
+        "text": "$$\n\\mathcal { L } _ { E } = - \\frac { 1 } { n _ { t } } \\sum _ { i } \\sum _ { k \\in \\mathcal { N } _ { K } ^ { i } } \\sum _ { m \\in E _ { M } ^ { k } } r \\mathcal { S } _ { m } ^ { \\top } p _ { i }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            364,
+            585,
+            602,
+            627
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $E _ { M } ^ { k }$ contain the $M$ -nearest neighbors of neighbor $k$ in $\\mathcal { N } _ { K }$ ",
+        "bbox": [
+            173,
+            631,
+            606,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Although the affinity values of all expanded neighbors are the same, it does not necessarily mean that they have equal importance. Taking a closer look at the expanded neighbors $E _ { M } ( z _ { i } )$ , some neighbors will show up more than once, for example $z _ { m }$ can be the nearest neighbor of both $z _ { h }$ and $z _ { j }$ where $h , j \\in \\mathcal N _ { K } ( \\bar { z } _ { i } )$ , and the nearest neighbors can also serve as expanded neighbor. It implies that those neighbors form compact cluster, and we posit that those duplicated expanded neighbors have potential to be semantically closer to the ego-feature $z _ { i }$ . Thus, we do not remove duplicated features in $E _ { M } ( z _ { i } )$ , as those can lead to actually larger affinity value for those expanded neighbors. This is one advantage of utilizing expanded neighbors instead of more nearest neighbors, we will verify the importance of maintaining the duplicated features in the experimental section. ",
+        "bbox": [
+            173,
+            651,
+            825,
+            777
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Final objective. Our method, called Neighborhood Reciprocity Clustering (NRC), is illustrated in Algorithm. 1. The final objective for adaptation is: ",
+        "bbox": [
+            171,
+            782,
+            821,
+            810
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ae8aa11a8013cac6ffb5c6ceca6f5aefe7cec77b25048817ebdc48852e90b837.jpg",
+        "text": "$$\n\\mathcal { L } = \\mathcal { L } _ { d i v } + \\mathcal { L } _ { \\mathcal { N } } + \\mathcal { L } _ { E } + \\mathcal { L } _ { s e l f } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            852,
+            312,
+            869
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We use three 2D image benchmark datasets and a 3D point cloud recognition dataset.   \nOffice-31 [32] contains 3 domains (Amazon, Webcam, DSLR) with 31 classes and 4,652 images. ",
+        "bbox": [
+            173,
+            882,
+            825,
+            911
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/d30542c42975f40b60b9b182d2926ef49a24c6a1af57e99813de1d1fb8002c91.jpg",
+        "table_caption": [
+            "Table 1: Accuracies $( \\% )$ on Office-31 for ResNet50-based methods. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>SF</td><td>A→D</td><td>A→W</td><td>D→W</td><td>W→D</td><td>D→A</td><td>W→A</td><td>Avg</td></tr><tr><td>MCD [35]</td><td>X</td><td>92.2</td><td>88.6</td><td>98.5</td><td>100.0</td><td>69.5</td><td>69.7</td><td>86.5</td></tr><tr><td>CDAN [24]</td><td>X</td><td>92.9</td><td>94.1</td><td>98.6</td><td>100.0</td><td>71.0</td><td>69.3</td><td>87.7</td></tr><tr><td>MDD [59]</td><td>X</td><td>90.4</td><td>90.4</td><td>98.7</td><td>99.9</td><td>75.0</td><td>73.7</td><td>88.0</td></tr><tr><td>BNM[4]</td><td>X</td><td>90.3</td><td>91.5</td><td>98.5</td><td>100.0</td><td>70.9</td><td>71.6</td><td>87.1</td></tr><tr><td>DMRL [49]</td><td>X</td><td>93.4</td><td>90.8</td><td>99.0</td><td>100.0</td><td>73.0</td><td>71.2</td><td>87.9</td></tr><tr><td>BDG[53]</td><td>X</td><td>93.6</td><td>93.6</td><td>99.0</td><td>100.0</td><td>73.2</td><td>72.0</td><td>88.5</td></tr><tr><td>MCC[15]</td><td>X</td><td>95.6</td><td>95.4</td><td>98.6</td><td>100.0</td><td>72.6</td><td>73.9</td><td>89.4</td></tr><tr><td>SRDC[42]</td><td>X</td><td>95.8</td><td>95.7</td><td>99.2</td><td>100.0</td><td>76.7</td><td>77.1</td><td>90.8</td></tr><tr><td>RWOT[51]</td><td>X</td><td>94.5</td><td>95.1</td><td>99.5</td><td>100.0</td><td>77.5</td><td>77.9</td><td>90.8</td></tr><tr><td>RSDA-MSTN[10]</td><td>X</td><td>95.8</td><td>96.1</td><td>99.3</td><td>100.0</td><td>77.4</td><td>78.9</td><td>91.1</td></tr><tr><td>SHOT [21]</td><td>√</td><td>94.0</td><td>90.1</td><td>98.4</td><td>99.9</td><td>74.7</td><td>74.3</td><td>88.6</td></tr><tr><td>3C-GAN[20]</td><td>【</td><td>92.7</td><td>93.7</td><td>98.5</td><td>99.8</td><td>75.3</td><td>77.8</td><td>89.6</td></tr><tr><td>NRC</td><td></td><td>96.0</td><td>90.8</td><td>99.0</td><td>100.0</td><td>75.3</td><td>75.0</td><td>89.4</td></tr></table>",
+        "bbox": [
+            209,
+            116,
+            789,
+            292
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/0cdd1c9003321317d28d8b4559d03bcd25da016f57b307b23642e9f94c25ffba.jpg",
+        "table_caption": [
+            "Table 2: Accuracies $( \\% )$ on Office-Home for ResNet50-based methods. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td></td><td>SFAr-&gt;CIAr-→PrAr-→RwC1-→ArCI-→PrCI-→&gt;RwPr-→ArPr-→&gt;CIPr-→RwRw-→ArRw-→CIRw-→PrAvg</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MCD [35]</td><td>xxxxxxxxxx</td><td>48.9 68.3</td><td>74.6</td><td>61.3</td><td>67.6</td><td>68.8</td><td>57.0</td><td>47.1</td><td>75.1</td><td>69.1</td><td>52.2</td><td>79.6</td><td>64.1</td></tr><tr><td>CDAN [24]</td><td></td><td>50.7</td><td>70.6 76.0</td><td>57.6</td><td>70.0</td><td>70.0</td><td>57.4</td><td>50.9</td><td>77.3</td><td>70.9</td><td>56.7</td><td>81.6</td><td>65.8</td></tr><tr><td>SAFN [52]</td><td></td><td>52.0</td><td>71.7 76.3</td><td>64.2</td><td>69.9</td><td>71.9</td><td>63.7</td><td>51.4</td><td>77.1</td><td>70.9</td><td>57.1</td><td>81.5</td><td>67.3</td></tr><tr><td>Symnets [58]</td><td></td><td>47.7 72.9</td><td>78.5</td><td>64.2</td><td>71.3</td><td>74.2</td><td>64.2</td><td>48.8</td><td>79.5</td><td>74.5</td><td>52.6</td><td>82.7</td><td>67.6</td></tr><tr><td>MDD [59]</td><td></td><td>54.9 73.7</td><td>77.8</td><td>60.0</td><td>71.4</td><td>71.8</td><td>61.2</td><td>53.6</td><td>78.1</td><td>72.5</td><td>60.2</td><td>82.3</td><td>68.1</td></tr><tr><td>TADA [47]</td><td></td><td>53.1</td><td>72.3 77.2</td><td>59.1</td><td>71.2</td><td>72.1</td><td>59.7</td><td>53.1</td><td>78.4</td><td>72.4</td><td>60.0</td><td>82.9</td><td>67.6</td></tr><tr><td>BNM[4]</td><td></td><td>52.3</td><td>73.9 80.0</td><td>63.3</td><td>72.9</td><td>74.9</td><td>61.7</td><td>49.5</td><td>79.7</td><td>70.5</td><td>53.6</td><td>82.2</td><td>67.9</td></tr><tr><td>BDG [53]</td><td></td><td>51.5 73.4</td><td>78.7</td><td>65.3</td><td>71.5</td><td>73.7</td><td>65.1</td><td>49.7</td><td>81.1</td><td>74.6</td><td>55.1</td><td>84.8</td><td>68.7</td></tr><tr><td>SRDC [42]</td><td></td><td>52.3 76.3</td><td>81.0</td><td>69.5</td><td>76.2</td><td>78.0</td><td>68.7</td><td>53.8</td><td>81.7</td><td>76.3</td><td>57.1</td><td>85.0</td><td>71.3</td></tr><tr><td>RSDA-MSTN[10]</td><td></td><td>53.2</td><td>77.7 81.3</td><td>66.4</td><td>74.0</td><td>76.5</td><td>67.9</td><td>53.0</td><td>82.0</td><td>75.8</td><td>57.8</td><td>85.4</td><td>70.9</td></tr><tr><td>SHOT [21]</td><td></td><td>57.1</td><td>78.1 81.5</td><td>68.0</td><td>78.2</td><td>78.1</td><td>67.4</td><td>54.9</td><td>82.2</td><td>73.3</td><td>58.8</td><td>84.3</td><td>71.8</td></tr><tr><td>NRC</td><td>区</td><td>57.7</td><td>80.3 82.0</td><td>68.1</td><td>79.8</td><td>78.6</td><td>65.3</td><td>56.4</td><td>83.0</td><td>71.0</td><td>58.6</td><td>85.6</td><td>72.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Office-Home [46] contains 4 domains (Real, Clipart, Art, Product) with 65 classes and a total of 15,500 images. VisDA [28] is a more challenging dataset, with 12-class synthetic-to-real object recognition tasks, its source domain contains of $1 5 2 \\mathrm { k }$ synthetic images while the target domain has 55k real object images. PointDA-10 [30] is the first 3D point cloud benchmark specifically designed for domain adaptation, it has 3 domains with 10 classes, denoted as ModelNet-10, ShapeNet-10 and ScanNet-10, containing approximately $2 7 . 7 \\mathrm { k }$ training and 5.1k testing images together. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation. We compare with existing source-present and source-free DA methods. All results are the average on three random runs. SF in the tables denotes source-free. ",
+        "bbox": [
+            174,
+            583,
+            821,
+            611
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Model details. For fair comparison with related methods, we also adopt the backbone of ResNet-50 [11] for Office-Home and ResNet-101 for VisDA, and PointNet [29] for PointDA10. Specifically, for 2D image datasets, we use the same network architecture as SHOT [21], i.e., the final part of the network is: fully connected layer − Batch Normalization [12] − fully connected layer with weight normalization [37]. And for PointDA-10 [29], we use the code released by the authors for fair comparison with PointDAN [29], and only use the backbone without any of their proposed modules. To train the source model, we also adopt label smoothing as SHOT does. We adopt SGD with momentum 0.9 and batch size of 64 for all 2D datasets, and Adam for PointDA-10. The learning rate for Office-31 and Office-Home is set to 1e-3 for all layers, except for the last two newly added fc layers, where we apply 1e-2. Learning rates are set 10 times smaller for VisDA. Learning rate for PointDA-10 is set to 1e-6. We train 30 epochs for Office-31 and OfficeHome while 15 epochs for VisDA, and 100 for PointDA-10. For the number of nearest neighbors (K) and expanded neighborhoods (M), we use 3,2 for Office-31, Office-Home and PointDA-10, since VisDA is much larger we set K, M to 5. Experiments are conducted on a TITAN Xp. ",
+        "bbox": [
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+            617,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1 Results ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            829,
+            263,
+            843
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "2D image datasets. We first evaluate the target performance of our method compared with existing DA and SFDA methods on three 2D image datasets. As shown in Table 1-3, the top part shows results for the source-present methods with access to source data during adaptation. The bottom shows results for the source-free DA methods. On Office-31, our method gets similar results compared with source-free method 3C-GAN and lower than source-present method RSDA-MSTN. And our method achieves state-of-the-art performance on Office-Home and VisDA, especially on VisDA our method surpasses the source-free method SHOT and source-present method RWOT by a wide margin $3 \\%$ and $1 . 9 \\%$ respectively). The reported results clearly demonstrate the efficiency of the proposed method for source-free domain adaptation. Interestingly, like already observed in the SHOT paper, source-free methods outperform methods that have access to source data during adaptation. ",
+        "bbox": [
+            176,
+            856,
+            823,
+            911
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/6a311b2328d40c53ef20883419217b4dd44bd0f693fb7b8a722536b379b6e88c.jpg",
+        "table_caption": [
+            "Table 3: Accuracies $( \\% )$ on VisDA-C (Synthesis Real) for ResNet101-based methods. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Method</td><td rowspan=1 colspan=1>SF</td><td rowspan=1 colspan=1>[SF|plane bcycl bus car horse knife mcycl person plant sktbrd train truck Per-class</td></tr><tr><td rowspan=5 colspan=1>ADR [34]CDAN [24]CDAN+BSP[2]SAFN [52]SWD[19]MDD [59]DMRL [49]MCC[15]STAR [26]RWOT[51]</td><td rowspan=1 colspan=1>X</td><td rowspan=1 colspan=1>94.248.584.0 72.990.174.292.6 72.580.861.882.2 28.8  73.5</td></tr><tr><td rowspan=1 colspan=1>X</td><td rowspan=1 colspan=1>85.266.983.0 50.884.274.988.1 74.583.476.081.9 38.0  73.9</td></tr><tr><td rowspan=3 colspan=1>×</td><td rowspan=2 colspan=1>61.081.0 57.5 89.080.690.1 77.084.277.982.1 38.4  75.9</td></tr><tr><td rowspan=1 colspan=1>92.493.690.8</td></tr><tr><td rowspan=1 colspan=1>93.661.384.1 70.6 94.179.091.8 79.689.955.689.0 24.4  76.190.882.5 81.7 70.5 91.769.586.3 77.587.463.685.6 29.2  76.4-    1    1   1   1   1    1     1    1    -    1   1    74.6-                =     =     =     =     =     =     =          =    75.588.780.3 80.5 71.5 90.1 93.285.0 71.689.473.8 85.0 36.9  78.895.084.084.6 73.0 91.691.885.9 78.494.484.787.0 42.2  82.795.180.383.7 90.092.468.092.5 82.287.978.490.4 68.2  84.0</td></tr><tr><td rowspan=3 colspan=1>3C-GAN [20]SHOT[21]NRC</td><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=1>94.873.468.8 74.893.195.488.6 84.7 89.184.783.5 48.1  81.6</td></tr><tr><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=1>94.388.580.1 57.3 93.194.980.7 80.391.589.186.3 58.2  82.9</td></tr><tr><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=1>96.891.382.4 62.4 96.295.986.1 80.694.894.190.4 59.7  85.9</td></tr></table>",
+        "bbox": [
+            179,
+            116,
+            818,
+            308
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/332a783b5902ad7cfa38d86058bd58c58d53c04b7c617a4ab838c6053a0fe857.jpg",
+        "table_caption": [
+            "Table 4: Accuracies $( \\% )$ on PointDA-10. The results except ours are from PointDAN [30]. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td colspan=\"4\">|SF|Model-→Shape Model-→Scan Shape-→Model Shape-&gt;Scan Scan→Model Scan-→Shape Avg</td></tr><tr><td>MMD [25]</td><td></td><td>57.5 27.9</td><td>40.7</td><td>26.7</td><td>47.3</td><td>54.8</td><td>42.5</td></tr><tr><td>DANN [6]</td><td>xxxxx</td><td>58.7 29.4</td><td>42.3</td><td>30.5</td><td>48.1</td><td>56.7</td><td>44.2</td></tr><tr><td>ADDA [44]</td><td></td><td>61.0 30.5</td><td>40.4</td><td>29.3</td><td>48.9</td><td>51.1</td><td>43.5</td></tr><tr><td>MCD [35]</td><td></td><td>62.0 31.0</td><td>41.4</td><td>31.3</td><td>46.8</td><td>59.3</td><td>45.3</td></tr><tr><td>PointDAN [30]</td><td></td><td>64.2 33.0</td><td>47.6</td><td>33.9</td><td>49.1</td><td>64.1</td><td>48.7</td></tr><tr><td>Source-only</td><td></td><td>43.1</td><td>17.3 40.0</td><td>15.0</td><td>33.9</td><td>47.1</td><td>32.7</td></tr><tr><td>NRC</td><td>&lt;</td><td>64.8</td><td>25.8 59.8</td><td>26.9</td><td>70.1</td><td>68.1</td><td>52.6</td></tr></table>",
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+        "text": "3D point cloud dataset. We also report the result for the PointDA-10. As shown in Table 4, our method outperforms PointDA [30], which demands source data for adaptation and is specifically tailored for point cloud data with extra attention modules, by a large margin $(4 \\% )$ . ",
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+        "type": "text",
+        "text": "4.2 Analysis ",
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+        "text": "Ablation study on neighbors $\\mathcal { N }$ , $E$ and affinity $A$ . In the first two tables of Table 5, we conduct the ablation study on Office-Home and VisDA. The 1-st row contains results from the source model and the 2-nd row from only training with the diversity loss $\\mathcal { L } _ { d i v }$ . From the remaining rows, several conclusions can be drawn. ",
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+        "type": "text",
+        "text": "First, the original supervision, which considers all neighbors equally can lead to a decent performance (67.1 on Office-Home). Second, considering higher affinity values for reciprocal neighbors leads to a large performance gain (69.1 on Office-Home). Last but not the least, the expanded neighborhoods can also be helpful, but only when combined with the affinity values $A$ (72.2 on Office-Home). Using expanded neighborhoods without affinity obtains bad performance (65,2 on Office-Home). We conjecture that those expanded neighborhoods, especially those neighbors of nRNN, may be noisy as discussed in Sec. 3.2. Removing the affinity $A$ means we treat all those neighbors equally, which is not reasonable. ",
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+        "type": "table",
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+        "table_caption": [
+            "Table 5: Ablation study of different modules on Office-Home (left) and VisDA (middle), comparison between using expanded neighbors and larger nearest neighbors (right). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Ldiv</td><td>LN</td><td>LE LEA</td><td>Avg</td><td>Ldiv</td><td>LN</td><td></td><td>LE LEA</td><td></td><td>Acc</td></tr><tr><td></td><td></td><td></td><td>59.5</td><td></td><td></td><td></td><td></td><td></td><td>44.6</td></tr><tr><td></td><td></td><td></td><td>62.1</td><td></td><td></td><td></td><td></td><td></td><td>47.8</td></tr><tr><td></td><td></td><td></td><td>67.1</td><td></td><td></td><td></td><td></td><td></td><td>74.6</td></tr><tr><td></td><td></td><td></td><td>√ 69.1</td><td></td><td></td><td></td><td></td><td>√</td><td>81.5</td></tr><tr><td></td><td></td><td></td><td>65.2</td><td></td><td></td><td></td><td></td><td></td><td>61.2</td></tr><tr><td></td><td></td><td></td><td>72.2</td><td></td><td></td><td></td><td></td><td>！</td><td>85.9</td></tr><tr><td></td><td></td><td></td><td>69.1 [</td><td></td><td></td><td></td><td></td><td></td><td>82.0</td></tr></table>",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Method&amp;Dataset</td><td rowspan=1 colspan=1>Acc</td></tr><tr><td rowspan=1 colspan=1>VisDA (K=M=5)VisDA w/o E (K=30)</td><td rowspan=1 colspan=1>85.984.0</td></tr><tr><td rowspan=1 colspan=1>OH(K=3,M=2)OH w/o E (K=9)</td><td rowspan=1 colspan=1>72.269.5</td></tr></table>",
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+        "table_caption": [
+            "Table 6: Runtime analysis on SHOT and our method. For SHOT, pseudo labels are computed at each epoch. $20 \\%$ , $10 \\%$ and $5 \\%$ denote the percentage of target features which are stored in the memory bank. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>VisDA</td><td colspan=\"2\">Runtime (s/epoch)Per-class (%)</td></tr><tr><td>SHOT</td><td>618.82</td><td>82.9</td></tr><tr><td>NRC</td><td>540.89</td><td>85.9</td></tr><tr><td>NRC(20%) 6formemorybank)</td><td>507.15</td><td>85.3</td></tr><tr><td>NRC(10% for memory bank)</td><td>499.49</td><td>85.2</td></tr><tr><td>NRC(5% for memory bank)</td><td>499.28</td><td>85.1</td></tr></table>",
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+        "image_caption": [
+            "Figure 2: (Left and middle) Ablation study of $\\mathcal { L } _ { s e l f }$ on Office-Home and VisDA respectively. (Right) Performance with different $r$ on VisDA. "
+        ],
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+        "type": "text",
+        "text": "We also show that duplication in the expanded neighbors is important in the last row of Table 5, where the $\\mathcal { L } _ { \\hat { E } }$ means we remove duplication in Eq. 8. The results show that the performance will degrade significantly when removing them, implying that the duplicated expanded neighbors are indeed more important than others. ",
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+    {
+        "type": "text",
+        "text": "Next we ablate the importance of the expanded neighborhood in the right of Table5. We show that if we increase the number of datapoints considered for class-consistency by simply considering a larger K, we obtain significantly lower scores. We have chosen $K$ so that the total number of points considered is equal to our method (i.e. $5 { + } 5 ^ { * } 5 { = } 3 0$ and $3 + 3 ^ { * } 2 { = } 9 ,$ ). Considering neighbors of neighbors is more likely to provide datapoints that are close on the data manifold [43], and are therefore more likely to share the class label with the ego feature. ",
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+        "type": "text",
+        "text": "Runtime analysis. Instead of storing all feature vectors in the memory bank, we follow the same memory bank setting as in [5] which is for nearest neighbor retrieval. The method only stores a fixed number of target features, we update the memory bank at the end of each iteration by taking the $n$ (batch size) embeddings from the current training iteration and concatenating them at the end of the memory bank, and discard the oldest $n$ elements from the memory bank. We report the results with this type of memory bank of different buffer size in the Table 6. The results show that indeed this could be an efficient way to reduce computation on very large datasets. ",
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+    {
+        "type": "text",
+        "text": "Ablation study on self-regularization. In the left and middle of Fig 2, we show the results with and without self-regularization $\\mathcal { L } _ { s e l f }$ . The $\\mathcal { L } _ { s e l f }$ can improve the performance when adopting only nearest neighbors $\\mathcal { N }$ or all neighbors $\\mathcal { N } + E$ . The results imply that self-regularization can effectively reduce the negative impact of the potential noisy neighbors, especially on the Office-Home dataset. ",
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+    {
+        "type": "text",
+        "text": "Sensitivity to hyperparameter. There are three hyperparameters in our method: K and M which are the number of nearest neighbors and expanded neighbors, $r$ which is the affinity value assigned to nRNN. We show the results with different $r$ in the right of Fig. 2. Note we keep the affinity of expanded neighbors as 0.1. $r = 1$ means no affinity. $r = - 1$ means treating supervision of nRNN feature as totally wrong, which is not always the case and will lead to quite lower result. $r = 0$ can also achieve good performance, signifying RNN can already work well. Results with $r = 0 . 1 / 0 . 1 5 / 0 . 2$ show that our method is not sensitive to the choice of a reasonable $r$ . Note in DA, there is no validation set for hyperparameter tuning, we show the results varying the number of neighbors in the right of Tab. 3, demonstrating the robustness to the choice of $K$ and $M$ . ",
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+        "img_path": "images/52c51cde4275a75094e8c62c8d4fd77f70977cdffb6dcc8e5fcf1796cfa99e42.jpg",
+        "image_caption": [
+            "Figure 3: (Left) The three curves are (on VisDA): target accuracy (Blue), ratio of features which have 5-nearest neighbors all sharing the same predicted label (dashed Red), and ratio of features which have 5-nearest neighbors all sharing the same and correct predicted label (dashed Black). (Right) Ablation study on choice of K and M on VisDA. "
+        ],
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+        "image_caption": [
+            "Figure 4: (Left) Ratio of different type of nearest neighbor features which have the correct predicted label, before and after adaptation. (Right) Visualization of target features after adaptation. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Training curve. We show the evolution of several statistics during adaptation on VisDA in the left of Tab. 3. The blue curve is the target accuracy. The dashed red and black curves are the ratio of features which have 5-nearest neighbors all sharing the same (dashed Red), or the same and also correct (dashed Black) predicted label. The curves show that the target features are clustering during the training. Another interesting finding is that the curve ’Per Shared’ correlates with the accuracy curve, which might therefore be used to determine training convergence. ",
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+    {
+        "type": "text",
+        "text": "Accuracy of supervision from neighbors. We also show the accuracy of supervision from neighbors on task $\\mathrm { A r } {  } \\mathrm { R w }$ of Office-Home in Fig. 4(left). It shows that after adaptation, the ratio of all types of neighbors having more correct predicted label, proving the effectiveness of the method. ",
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+    {
+        "type": "text",
+        "text": "t-SNE visualization. We show the t-SNE feature visualization on task $\\mathrm { A r } {  } \\mathrm { R w }$ of target features before (Fig. 1(a)) and after (Fig. 4(right)) adaptation. After adaptation, the features are more compactly clustered. ",
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+    {
+        "type": "text",
+        "text": "5 Conclusions ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We introduce a source-free domain adaptation (SFDA) method by uncovering the intrinsic target data structure. We propose to achieve the adaptation by encouraging label consistency among local target features. We differentiate between nearest neighbors, reciprocal neighbors and expanded neighborhood. Experimental results verify the importance of considering the local structure of the target features. Finally, our experimental results on both 2D image and 3D point cloud datasets testify the efficacy of our method. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgement We acknowledge the support from Huawei Kirin Solution, and the project PID2019-104174GB-I00 (MINECO, Spain) and RTI2018-102285-A-I00 (MICINN, Spain), Ramón y Cajal fellowship RYC2019-027020-I, and the CERCA Programme of Generalitat de Catalunya. ",
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
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