| Method Linear classifier | Error % (Full) | Error % (Path) | Params. (Full) | Params. (Path) | Ensemble Size |
| JSINN | Random Forests (Breiman, 2001) Compact Multi-Class Boosted Trees (Ponomareva et al., 2017) Alternating Decision Forest (Schulter et al., 2013) Neural Decision Tree (Xiao,2017) ANT-MNIST-C MLP with 2 hidden layers (Simard et al., 2003) LeNet-5† (LeCun et al.,1998) | 7.91 3.21 | N/A 3.21 | 7,840 | N/A 1 | 1 200 |
| 2.88 2.71 | 1 2.71 | 1 1 | 1 | 100 |
| 2.10 1.62 | 1.68 N/A | 1 1,773,130 | 1 502,170 7,956 | 20 1 |
| 39,670 | |
| 1.40 0.82 | 1,275,200 431,000 | 1 N/A 1 1 |
| ANT-MNIST-A | gcForest (Zhou & Feng,2017) ANT-MNIST-B Neural Decision Forest (Kontschieder et al., 2015) | 0.74 0.72 | N/A 0.74 0.73 | 1 | N/A 1 | 500 |
| 0.70 | 1 | 76,703 544,600 | 50,653 463,180 | 1 10 |
|
| 0.64 | 0.69 | 100,596 | 84,935 | 1 |
| CapsNet (Sabour et al., 2017) | 0.25 | 1 | 8.2M | N/A | 1 |
| Compact Multi-ClassBoosted Trees (Ponomareva et al.,2017) Random Forests (Breiman,2001) | 52.31 50.17 | 1 50.17 | 1 1 | 1 | 100 |
| CEIPAII1 | gcForest (Zhou& Feng,2017) | 38.22 | 38.22 | 1 | 1 | 2000 500 |
| 1 |
| MaxOut (Goodfellow et al., 2013) ANT-CIFAR10-C | 9.38 9.31 | N/A 9.34 | 6M 0.7M | N/A 0.5M | 1 1 |
| ANT-CIFAR10-B Network in Network (Lin et al.,2014) | 9.15 8.81 | 9.18 N/A | 0.9M 1M | 0.6M N/A | 1 1 |
| All-CNN+(Springenberg et al.,2015) ANT-CIFAR10-A | 8.71 | N/A | 1.4M | N/A | 1 |
| ANT-CIFAR10-A* | 8.31 6.72 | 8.32 6.74 | 1.4M 1.3M | 1.0M 0.8M | 1 |
| ResNet-110 (He et al., 2016) | 6.43 | N/A | 1.7M | N/A | 1 |
| DenseNet-BC (k=40) (Huang et al.,2017) | 3.46 | N/A | 25.6M | N/A | 1 1 |
+
+# 5.1 PERFORMANCE ON IMAGE CLASSIFICATION
+
+We train ANTs with a range of primitive modules (Tab. 2) and compare against relevant DT and NN models (Tab. 3). In general, DT methods without feature learning, such as RFs (Breiman, 2001; Zhou & Feng, 2017) and GBTs (Ponomareva et al., 2017), perform poorly on complex image data (Krizhevsky & Hinton, 2009). In comparison with CNNs without shortcut connections (LeCun et al., 1998; Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015), different ANTs balance between strong performance with comparable numbers of trainable parameters, and reasonable performance with a relatively small amount of parameters. At the other end of the spectrum, state-of-the-art NNs (Sabour et al., 2017; Huang et al., 2017) contain significantly more parameters.
+
+For simplicity, we define primitive modules based on three types of NN layers: convolutional, global-average-pooling (GAP) and fully-connected (FC). Solver modules are fixed as linear classifiers (LC) with a softmax output. Router modules are binary classifiers with a sigmoid output. All convolutional and FC layer are followed by ReLUs, except in the last layers of solvers and routers. We also apply $2 \times 2$ max-pooling to feature maps after every $d$ transformer modules where $d$ is the downsample frequency. We balance the number of parameters in the router and transformer modules to be of the same order of magnitude to avoid favouring either partitioning the data or learning more expressive features. We hold out $1 0 \%$ of training images as a validation set, on which the best performing model is selected. Full training details, including training times, are provided in the supplementary material.
+
+Two inference schemes: for each ANT, classification is performed in two ways: multi-path inference with the full predictive distribution (eq. equation 1), and single-path inference based on the greedily-selected leaf node (Sec. 3.2). We observed that with our training scheme the splitting probabilities in the routers tend to be very confident, being close to 0 or 1 (see histograms in blue in Fig. 2(b)). This means that single path inference gives a good approximation of the multi-path inference but is more efficient to compute. We show this holds empirically in Tab. 3, where the largest difference between Error (Full) and Error (Path) is $0 . 0 6 \%$ while number of parameters is reduced from Params (Full) to Params (Path) across all ANT models.
+
+Patience-based local optimisation: in the growth phase the parameters for the new modules are trained until convergence, as determined by patience-based early stopping on the validation set. We observe that very low or high patience levels result in new modules underfitting or overfitting locally, respectively, thus preventing meaningful further growth. We tuned this hyperparameter using the validation sets, and set the patience level to 5, which produced consistently good performance on both MNIST and CIFAR-10 datasets across different specifications of primitive modules. A quantitative evaluation is given in the supplementary (Sec. E).
+
+MNIST digit classification: we observe that ANT-MNIST-A outperforms state-of-the-art GBT (Ponomareva et al., 2017) and RF (Zhou & Feng, 2017) methods in accuracy. This performance is attained despite the use of a single tree, while RF methods operate with ensembles of classifiers (the size shown in Tab. 2). In particular, the NDF (Kontschieder et al., 2015) has a pre-specified architecture where LeNet-5 (LeCun et al., 1998) is used as the root transformer module, and 10 trees of fixed depth 5 are constructed from this base feature extractor. On the other hand, ANT-MNISTA is constructed in a data-driven manner from primitive modules, and displays an improvement over the NDF both in terms of accuracy and number of parameters. In addition, reducing the size of convolution kernels (ANT-MNIST-B) reduces the total number of parameters by $2 5 \%$ and the path-wise average by almost $4 0 \%$ while only increasing absolute error by $< 0 . 1 \%$ .
+
+We also compare against the LeNet-5 CNN (LeCun et al., 1998), comprised of the same types of operations used in our primitive modules (i.e. convolutional, max-pooling and FC layers). For a fair comparison, the network is trained with the same protocol as that of the ANT refinement phase, achieving an error rate of $0 . 8 2 \%$ (lower than the reported value of $0 . 8 7 \%$ ) on the test set. Both ANT-MNIST-A and ANT-MNIST-B attain better accuracy with a smaller number of parameters than LeNet-5. The current state-of-the-art, capsule networks (CapsNets) (Sabour et al., 2017), have more parameters than ANT-MNIST-A by almost two orders of magnitude.1 By ensembling ANTs we can reach similar performance $( 0 . 2 9 \%$ versus $0 . 2 5 \%$ ; see Tab. 9) with an order of magnitude less parameters (see Tab. 10).
+
+Lastly, we highlight the observation that ANT-MNIST-C, with the simplest primitive modules, achieves an error rate of $1 . 6 8 \%$ with single-path inference, which is significantly better than that of the linear classifier $( 7 . 9 1 \% )$ , while engaging almost the same number of parameters (7, 956 vs. 7, 840) on average. To isolate the benefit of convolutions, we took one of the root-to-path CNNs on ANT-MNIST-C and increased the number of kernels to adjust the number of parameters to the same value. We observe a higher error rate of $3 . 5 5 \%$ , which indicates that while convolutions are beneficial, data partitioning has additional benefits in improving accuracy. This result demonstrates the potential of ANT growth protocol for constructing performant models with lightweight inference. See Sec. G in the supplementary materials for the architecture of ANT-MNIST-C.
+
+CIFAR-10 object recognition: we see that variants of ANTs outperform the state-of-the-art DT method, gcForest (Zhou & Feng, 2017) by a large margin, achieving over $90 \%$ accuracy, demonstrating the benefit of representation learning in tree-structured models. Secondly, with fewer number of parameters in single-path inference, ANT-CIFAR-A achieves higher accuracy than CNN models without shortcut connections (Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015) that held the state-of-the-art performance at the time of publication. With simpler primitive modules we learn more compact models (ANT-MNIST-B and -C) with a marginal compromise in accuracy. In addition, initialising the parameters of transformers and routers from a pre-trained single-path CNN further reduced the error rate of ANT-MNIST-A by $20 \%$ (see ANT-MNIST- $\mathbf { A } ^ { * }$ in Tab. 3), which indicates room for improvement in our proposed optimisation method.
+
+Shortcut connections (Fahlman & Lebiere, 1990) have recently lead to leaps in performance in deep CNNs (He et al., 2016; Huang et al., 2017). We observe that our best network, ANT-MNIST- $A ^ { * }$ , has a comparable error rate and half the parameter count (with single-path inference) to the bestperforming residual network, ResNet-110 (He et al., 2016). Densely connected networks leads to substantially better accuracy, but with an order of magnitude more parameters (Huang et al., 2017). We expect that shortcut connections could also improve ANT performance, and leave integrating them to future work.
+
+
+Figure 2: Visualisation of class distributions (red) and path probabilities (blue) at respective nodes of an example ANT (a) before and (b) after the refinement phase. (a) shows that the learned model captures an interpretable hierarchy, grouping semantically similar images on the same branches. (b) shows that the refinement phase polarises path probabilities, pruning a branch.
+
+Ablation study: we lastly compare the classification errors of different variants of ANTs in cases where the options for adding transformer or router modules are disabled (see Tab. 4). In this experiment, patience levels are tuned separately for respective models. In the first case, the resulting models are equivalent to SDTs (Suarez & Lutsko, 1999) or HMEs (Jordan & Jacobs, 1994) with lo- ´ cally grown architectures, while the second case is equivalent to standard CNNs, grown adaptively layer by layer. We observe that either ablation consistently leads to higher classification errors across different module configurations.
+
+Table 4: Ablation study to compare the effects of different components of ANTs on classification performance. “CNN” refers to the case where the ANT is grown without routers while “SDT/HME” refers to the case where transformer modules on the edges are disabled.
+
+| Algorithm1ANT Optimisation | |
| Initialise topology T and parameters O | >T is set to a root node with one solver and one transformer |
| Optimise parameters in O via gradient descent on NLL Set the root node “suboptimal" | Learning root classifier |
| while true do Freeze all parameters O | Growth of T begins |
| Pick next“suboptimal"leaf node l ∈Nteaf in the breadth-first order | |
| Add(1) router to l and train new parameters | Split data |
| Add (2) transformer to the incoming edge of l and train new parameters | Deepen transform |
| Add (1)or (2) permanently to T if validation error decreases,otherwise leaf is set to “optimal" |
| Add any new modules to O | |
| if no “suboptimal’ leaves remain then | |
| Break Unfreeze and train all parameters in O | |
+
+# B ADDITIONAL RELATED WORK
+
+The tree-structure of ANTs naturally performs conditional computation. We can also view the proposed tree-building algorithm as a form of neural architecture search. Here we provide surveys of these areas and their relations to ANTs.
+
+Conditional Computation: In NNs, computation of each sample engages every parameter of the model. In contrast, DTs route each sample to a single path, only activating a small fraction of the model. Bengio Bengio (2013) advocated for this notion of conditional computation to be integrated into NNs, and this has become a topic of growing interest. Rationales for using conditional computation ranges from attaining better capacity-to-computation ratio (Bengio et al., 2013; Davis & Arel, 2013; Bengio et al., 2015; Shazeer et al., 2017) to adapting the required computation to the difficulty of the input and task (Bengio et al., 2015; Almahairi et al., 2016; Teerapittayanon et al., 2016; Graves, 2016; Figurnov et al., 2017; Veit & Belongie, 2017). We view the growth procedure of ANTs as having a similar motivation with the latter—processing raw pixels is suboptimal for computer vision tasks, but we have no reason to believe that the hundreds of convolutional layers in current state-of-the-art architectures (He et al., 2016; Huang et al., 2017) are necessary either. Growing ANTs adapts the architecture complexity to the dataset as a whole, with routers determining the computation needed on a per-sample basis.
+
+Neural Architecture Search: The ANT growing procedure is related to the progressive growing of NNs (Fahlman & Lebiere, 1990; Hinton et al., 2006; Xiao et al., 2014; Chen et al., 2016; Srivastava et al., 2015; Lee et al., 2017; Cai et al., 2018; ˙Irsoy & Alpaydın, 2018), or more broadly, the field of neural architecture search (Zoph & Le, 2017; Brock et al., 2017; Cortes et al., 2017). This approach, mainly via greedy layerwise training, has historically been one solution to optimising NNs (Fahlman & Lebiere, 1990; Hinton et al., 2006). However, nowadays it is possible to train NNs in an end-toend fashion. One area which still uses progressive growing is lifelong learning, in which a model needs to adapt to new tasks while retaining performance on previous ones (Xiao et al., 2014; Lee et al., 2017). In particular, (Xiao et al., 2014) introduced a method that grows a tree-shaped network to accommodate new classes. However, their method never transforms the data before passing it to the children classifiers, and hence never benefit from the parent’s representations.
+
+Whilst we learn the architecture of an ANT in a greedy, layerwise fashion, several other methods search globally. Based on a variety of techniques, including evolutionary algorithms (Stanley & Miikkulainen, 2002; Real et al., 2017), reinforcement learning (Zoph & Le, 2017), sequential optimisation (Liu et al., 2017) and boosting (Cortes et al., 2017), these methods find extremely high-performance yet complex architectures. In our case, we constrain the search space to simple tree-structured NNs, retaining desirable properties of DTs such as data-dependent computation and interpretable structures, while keeping the space and time requirement of architecture search tractable thanks to the locality of our growth procedure.
+
+# C TRAINING DETAILS
+
+We perform our experiments on the MNIST digit classification task (LeCun et al., 1998) and CIFAR10 object recognition task (Krizhevsky & Hinton, 2009). The MNIST dataset consists of 60, 000 training and $1 0 , 0 0 0$ testing examples, all of which are $2 8 \times 2 8$ grayscale images of digits from 0 to 9 (10 classes). The dataset is preprocessed by subtracting the mean, but no data augmentation is used. The CIFAR-10 dataset consists of 50, 000 training and 10, 000 testing examples, all of which are $3 2 \times 3 2$ coloured natural images drawn from 10 classes. We adopt an augmentation scheme widely used in the literature (Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015; He et al., 2016; Huang et al., 2017) where images are zero-padded with 4 pixels on each side, randomly cropped and horizontally mirrored.
+
+For both datasets, we hold out $1 0 \%$ of training images as a validation set. The best model is selected based on the validation accuracy over the course of ANT training, spanning both the growth phase and the refinement phase, and its accuracy on the testing set is reported. The hyperparameters are also selected based on the validation performance alone.
+
+Both the growth and refinement phase of ANTs takes up to 2 hours on a single Titan X GPU on both datasets. For all the experiments in this paper, we employ the following training protocol: (1) optimize parameters using Adam (Kingma & Ba, 2014) with initial learning rate of $\bar { 1 0 } ^ { - 3 }$ and $\beta = \left. 0 . 9 , 0 . 9 \bar { 9 } 9 \right.$ , with minibatches of size 512; (2) during the growth phase, employ early stopping with a patience of 5, that is, training is stopped after 5 epochs of no progress on the validation set; (3) during the refinement phase, train for 100 epochs for MNIST and 200 epochs for CIFAR-10, decreasing the learning rate by a factor of 10 at every multiple of 50.
+
+# D TRAINING TIMES
+
+Tab. 5 summarises the time taken on a single Titan X GPU for the growth phase and refinement phase of various ANTs, and compares against the training time of All-CNN (Springenberg et al., 2015). Local optimisation during the growth phase means that the gradient computation is constrained to the newly added component of the graph, allowing us to grow a good candidate model under 2 hours on a single GPU.
+
+Table 5: Training time comparison. Time and number of epochs taken for the growth and refinement phase are shown. along with the time required to train the baseline, All-CNN (Springenberg et al., 2015).
+
+ | Method Linear classifier | Error % (Full) | Error % (Path) | Params. (Full) | Params. (Path) | Ensemble Size |
| JSINN | Random Forests (Breiman, 2001) Compact Multi-Class Boosted Trees (Ponomareva et al., 2017) Alternating Decision Forest (Schulter et al., 2013) Neural Decision Tree (Xiao,2017) ANT-MNIST-C MLP with 2 hidden layers (Simard et al., 2003) LeNet-5† (LeCun et al.,1998) | 7.91 3.21 | N/A 3.21 | 7,840 | N/A 1 | 1 200 |
| 2.88 2.71 | 1 2.71 | 1 1 | 1 | 100 |
| 2.10 1.62 | 1.68 N/A | 1 1,773,130 | 1 502,170 7,956 | 20 1 |
| 39,670 | |
| 1.40 0.82 | 1,275,200 431,000 | 1 N/A 1 1 |
| ANT-MNIST-A | gcForest (Zhou & Feng,2017) ANT-MNIST-B Neural Decision Forest (Kontschieder et al., 2015) | 0.74 0.72 | N/A 0.74 0.73 | 1 | N/A 1 | 500 |
| 0.70 | 1 | 76,703 544,600 | 50,653 463,180 | 1 10 |
|
| 0.64 | 0.69 | 100,596 | 84,935 | 1 |
| CapsNet (Sabour et al., 2017) | 0.25 | 1 | 8.2M | N/A | 1 |
| Compact Multi-ClassBoosted Trees (Ponomareva et al.,2017) Random Forests (Breiman,2001) | 52.31 50.17 | 1 50.17 | 1 1 | 1 | 100 |
| CEIPAII1 | gcForest (Zhou& Feng,2017) | 38.22 | 38.22 | 1 | 1 | 2000 500 |
| 1 |
| MaxOut (Goodfellow et al., 2013) ANT-CIFAR10-C | 9.38 9.31 | N/A 9.34 | 6M 0.7M | N/A 0.5M | 1 1 |
| ANT-CIFAR10-B Network in Network (Lin et al.,2014) | 9.15 8.81 | 9.18 N/A | 0.9M 1M | 0.6M N/A | 1 1 |
| All-CNN+(Springenberg et al.,2015) ANT-CIFAR10-A | 8.71 | N/A | 1.4M | N/A | 1 |
| ANT-CIFAR10-A* | 8.31 6.72 | 8.32 6.74 | 1.4M 1.3M | 1.0M 0.8M | 1 |
| ResNet-110 (He et al., 2016) | 6.43 | N/A | 1.7M | N/A | 1 |
| DenseNet-BC (k=40) (Huang et al.,2017) | 3.46 | N/A | 25.6M | N/A | 1 1 |
",
+ "bbox": [
+ 178,
+ 202,
+ 816,
+ 492
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "5.1 PERFORMANCE ON IMAGE CLASSIFICATION ",
+ "text_level": 1,
+ "bbox": [
+ 174,
+ 518,
+ 516,
+ 532
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "We train ANTs with a range of primitive modules (Tab. 2) and compare against relevant DT and NN models (Tab. 3). In general, DT methods without feature learning, such as RFs (Breiman, 2001; Zhou & Feng, 2017) and GBTs (Ponomareva et al., 2017), perform poorly on complex image data (Krizhevsky & Hinton, 2009). In comparison with CNNs without shortcut connections (LeCun et al., 1998; Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015), different ANTs balance between strong performance with comparable numbers of trainable parameters, and reasonable performance with a relatively small amount of parameters. At the other end of the spectrum, state-of-the-art NNs (Sabour et al., 2017; Huang et al., 2017) contain significantly more parameters. ",
+ "bbox": [
+ 174,
+ 547,
+ 825,
+ 660
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "For simplicity, we define primitive modules based on three types of NN layers: convolutional, global-average-pooling (GAP) and fully-connected (FC). Solver modules are fixed as linear classifiers (LC) with a softmax output. Router modules are binary classifiers with a sigmoid output. All convolutional and FC layer are followed by ReLUs, except in the last layers of solvers and routers. We also apply $2 \\times 2$ max-pooling to feature maps after every $d$ transformer modules where $d$ is the downsample frequency. We balance the number of parameters in the router and transformer modules to be of the same order of magnitude to avoid favouring either partitioning the data or learning more expressive features. We hold out $1 0 \\%$ of training images as a validation set, on which the best performing model is selected. Full training details, including training times, are provided in the supplementary material. ",
+ "bbox": [
+ 174,
+ 666,
+ 825,
+ 805
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "Two inference schemes: for each ANT, classification is performed in two ways: multi-path inference with the full predictive distribution (eq. equation 1), and single-path inference based on the greedily-selected leaf node (Sec. 3.2). We observed that with our training scheme the splitting probabilities in the routers tend to be very confident, being close to 0 or 1 (see histograms in blue in Fig. 2(b)). This means that single path inference gives a good approximation of the multi-path inference but is more efficient to compute. We show this holds empirically in Tab. 3, where the largest difference between Error (Full) and Error (Path) is $0 . 0 6 \\%$ while number of parameters is reduced from Params (Full) to Params (Path) across all ANT models. ",
+ "bbox": [
+ 174,
+ 811,
+ 825,
+ 924
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "Patience-based local optimisation: in the growth phase the parameters for the new modules are trained until convergence, as determined by patience-based early stopping on the validation set. We observe that very low or high patience levels result in new modules underfitting or overfitting locally, respectively, thus preventing meaningful further growth. We tuned this hyperparameter using the validation sets, and set the patience level to 5, which produced consistently good performance on both MNIST and CIFAR-10 datasets across different specifications of primitive modules. A quantitative evaluation is given in the supplementary (Sec. E). ",
+ "bbox": [
+ 174,
+ 103,
+ 825,
+ 202
+ ],
+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "MNIST digit classification: we observe that ANT-MNIST-A outperforms state-of-the-art GBT (Ponomareva et al., 2017) and RF (Zhou & Feng, 2017) methods in accuracy. This performance is attained despite the use of a single tree, while RF methods operate with ensembles of classifiers (the size shown in Tab. 2). In particular, the NDF (Kontschieder et al., 2015) has a pre-specified architecture where LeNet-5 (LeCun et al., 1998) is used as the root transformer module, and 10 trees of fixed depth 5 are constructed from this base feature extractor. On the other hand, ANT-MNISTA is constructed in a data-driven manner from primitive modules, and displays an improvement over the NDF both in terms of accuracy and number of parameters. In addition, reducing the size of convolution kernels (ANT-MNIST-B) reduces the total number of parameters by $2 5 \\%$ and the path-wise average by almost $4 0 \\%$ while only increasing absolute error by $< 0 . 1 \\%$ . ",
+ "bbox": [
+ 173,
+ 208,
+ 825,
+ 347
+ ],
+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "We also compare against the LeNet-5 CNN (LeCun et al., 1998), comprised of the same types of operations used in our primitive modules (i.e. convolutional, max-pooling and FC layers). For a fair comparison, the network is trained with the same protocol as that of the ANT refinement phase, achieving an error rate of $0 . 8 2 \\%$ (lower than the reported value of $0 . 8 7 \\%$ ) on the test set. Both ANT-MNIST-A and ANT-MNIST-B attain better accuracy with a smaller number of parameters than LeNet-5. The current state-of-the-art, capsule networks (CapsNets) (Sabour et al., 2017), have more parameters than ANT-MNIST-A by almost two orders of magnitude.1 By ensembling ANTs we can reach similar performance $( 0 . 2 9 \\%$ versus $0 . 2 5 \\%$ ; see Tab. 9) with an order of magnitude less parameters (see Tab. 10). ",
+ "bbox": [
+ 174,
+ 354,
+ 825,
+ 479
+ ],
+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "Lastly, we highlight the observation that ANT-MNIST-C, with the simplest primitive modules, achieves an error rate of $1 . 6 8 \\%$ with single-path inference, which is significantly better than that of the linear classifier $( 7 . 9 1 \\% )$ , while engaging almost the same number of parameters (7, 956 vs. 7, 840) on average. To isolate the benefit of convolutions, we took one of the root-to-path CNNs on ANT-MNIST-C and increased the number of kernels to adjust the number of parameters to the same value. We observe a higher error rate of $3 . 5 5 \\%$ , which indicates that while convolutions are beneficial, data partitioning has additional benefits in improving accuracy. This result demonstrates the potential of ANT growth protocol for constructing performant models with lightweight inference. See Sec. G in the supplementary materials for the architecture of ANT-MNIST-C. ",
+ "bbox": [
+ 174,
+ 486,
+ 825,
+ 611
+ ],
+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "CIFAR-10 object recognition: we see that variants of ANTs outperform the state-of-the-art DT method, gcForest (Zhou & Feng, 2017) by a large margin, achieving over $90 \\%$ accuracy, demonstrating the benefit of representation learning in tree-structured models. Secondly, with fewer number of parameters in single-path inference, ANT-CIFAR-A achieves higher accuracy than CNN models without shortcut connections (Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015) that held the state-of-the-art performance at the time of publication. With simpler primitive modules we learn more compact models (ANT-MNIST-B and -C) with a marginal compromise in accuracy. In addition, initialising the parameters of transformers and routers from a pre-trained single-path CNN further reduced the error rate of ANT-MNIST-A by $20 \\%$ (see ANT-MNIST- $\\mathbf { A } ^ { * }$ in Tab. 3), which indicates room for improvement in our proposed optimisation method. ",
+ "bbox": [
+ 174,
+ 618,
+ 825,
+ 757
+ ],
+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "Shortcut connections (Fahlman & Lebiere, 1990) have recently lead to leaps in performance in deep CNNs (He et al., 2016; Huang et al., 2017). We observe that our best network, ANT-MNIST- $A ^ { * }$ , has a comparable error rate and half the parameter count (with single-path inference) to the bestperforming residual network, ResNet-110 (He et al., 2016). Densely connected networks leads to substantially better accuracy, but with an order of magnitude more parameters (Huang et al., 2017). We expect that shortcut connections could also improve ANT performance, and leave integrating them to future work. ",
+ "bbox": [
+ 174,
+ 763,
+ 825,
+ 861
+ ],
+ "page_idx": 7
+ },
+ {
+ "type": "image",
+ "img_path": "images/5f73aa9624e4814beed4d4eb917fb6338b459bb521c58052eba5994febfd81f2.jpg",
+ "image_caption": [
+ "Figure 2: Visualisation of class distributions (red) and path probabilities (blue) at respective nodes of an example ANT (a) before and (b) after the refinement phase. (a) shows that the learned model captures an interpretable hierarchy, grouping semantically similar images on the same branches. (b) shows that the refinement phase polarises path probabilities, pruning a branch. "
+ ],
+ "image_footnote": [],
+ "bbox": [
+ 189,
+ 78,
+ 807,
+ 247
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "text",
+ "text": "Ablation study: we lastly compare the classification errors of different variants of ANTs in cases where the options for adding transformer or router modules are disabled (see Tab. 4). In this experiment, patience levels are tuned separately for respective models. In the first case, the resulting models are equivalent to SDTs (Suarez & Lutsko, 1999) or HMEs (Jordan & Jacobs, 1994) with lo- ´ cally grown architectures, while the second case is equivalent to standard CNNs, grown adaptively layer by layer. We observe that either ablation consistently leads to higher classification errors across different module configurations. ",
+ "bbox": [
+ 174,
+ 321,
+ 825,
+ 419
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "table",
+ "img_path": "images/043c26baa00d09d69a6ac9753d784a9a0d88c386cdfdcae5b24098ce53412c4a.jpg",
+ "table_caption": [
+ "Table 4: Ablation study to compare the effects of different components of ANTs on classification performance. “CNN” refers to the case where the ANT is grown without routers while “SDT/HME” refers to the case where transformer modules on the edges are disabled. "
+ ],
+ "table_footnote": [],
+ "table_body": "| Algorithm1ANT Optimisation | |
| Initialise topology T and parameters O | >T is set to a root node with one solver and one transformer |
| Optimise parameters in O via gradient descent on NLL Set the root node “suboptimal" | Learning root classifier |
| while true do Freeze all parameters O | Growth of T begins |
| Pick next“suboptimal"leaf node l ∈Nteaf in the breadth-first order | |
| Add(1) router to l and train new parameters | Split data |
| Add (2) transformer to the incoming edge of l and train new parameters | Deepen transform |
| Add (1)or (2) permanently to T if validation error decreases,otherwise leaf is set to “optimal" |
| Add any new modules to O | |
| if no “suboptimal’ leaves remain then | |
| Break Unfreeze and train all parameters in O | |
",
+ "bbox": [
+ 173,
+ 176,
+ 826,
+ 368
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "B ADDITIONAL RELATED WORK ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 386,
+ 454,
+ 400
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "The tree-structure of ANTs naturally performs conditional computation. We can also view the proposed tree-building algorithm as a form of neural architecture search. Here we provide surveys of these areas and their relations to ANTs. ",
+ "bbox": [
+ 176,
+ 416,
+ 823,
+ 458
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "Conditional Computation: In NNs, computation of each sample engages every parameter of the model. In contrast, DTs route each sample to a single path, only activating a small fraction of the model. Bengio Bengio (2013) advocated for this notion of conditional computation to be integrated into NNs, and this has become a topic of growing interest. Rationales for using conditional computation ranges from attaining better capacity-to-computation ratio (Bengio et al., 2013; Davis & Arel, 2013; Bengio et al., 2015; Shazeer et al., 2017) to adapting the required computation to the difficulty of the input and task (Bengio et al., 2015; Almahairi et al., 2016; Teerapittayanon et al., 2016; Graves, 2016; Figurnov et al., 2017; Veit & Belongie, 2017). We view the growth procedure of ANTs as having a similar motivation with the latter—processing raw pixels is suboptimal for computer vision tasks, but we have no reason to believe that the hundreds of convolutional layers in current state-of-the-art architectures (He et al., 2016; Huang et al., 2017) are necessary either. Growing ANTs adapts the architecture complexity to the dataset as a whole, with routers determining the computation needed on a per-sample basis. ",
+ "bbox": [
+ 173,
+ 465,
+ 825,
+ 645
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "Neural Architecture Search: The ANT growing procedure is related to the progressive growing of NNs (Fahlman & Lebiere, 1990; Hinton et al., 2006; Xiao et al., 2014; Chen et al., 2016; Srivastava et al., 2015; Lee et al., 2017; Cai et al., 2018; ˙Irsoy & Alpaydın, 2018), or more broadly, the field of neural architecture search (Zoph & Le, 2017; Brock et al., 2017; Cortes et al., 2017). This approach, mainly via greedy layerwise training, has historically been one solution to optimising NNs (Fahlman & Lebiere, 1990; Hinton et al., 2006). However, nowadays it is possible to train NNs in an end-toend fashion. One area which still uses progressive growing is lifelong learning, in which a model needs to adapt to new tasks while retaining performance on previous ones (Xiao et al., 2014; Lee et al., 2017). In particular, (Xiao et al., 2014) introduced a method that grows a tree-shaped network to accommodate new classes. However, their method never transforms the data before passing it to the children classifiers, and hence never benefit from the parent’s representations. ",
+ "bbox": [
+ 173,
+ 652,
+ 825,
+ 805
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "Whilst we learn the architecture of an ANT in a greedy, layerwise fashion, several other methods search globally. Based on a variety of techniques, including evolutionary algorithms (Stanley & Miikkulainen, 2002; Real et al., 2017), reinforcement learning (Zoph & Le, 2017), sequential optimisation (Liu et al., 2017) and boosting (Cortes et al., 2017), these methods find extremely high-performance yet complex architectures. In our case, we constrain the search space to simple tree-structured NNs, retaining desirable properties of DTs such as data-dependent computation and interpretable structures, while keeping the space and time requirement of architecture search tractable thanks to the locality of our growth procedure. ",
+ "bbox": [
+ 174,
+ 811,
+ 823,
+ 924
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "C TRAINING DETAILS ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 102,
+ 370,
+ 117
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "text",
+ "text": "We perform our experiments on the MNIST digit classification task (LeCun et al., 1998) and CIFAR10 object recognition task (Krizhevsky & Hinton, 2009). The MNIST dataset consists of 60, 000 training and $1 0 , 0 0 0$ testing examples, all of which are $2 8 \\times 2 8$ grayscale images of digits from 0 to 9 (10 classes). The dataset is preprocessed by subtracting the mean, but no data augmentation is used. The CIFAR-10 dataset consists of 50, 000 training and 10, 000 testing examples, all of which are $3 2 \\times 3 2$ coloured natural images drawn from 10 classes. We adopt an augmentation scheme widely used in the literature (Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015; He et al., 2016; Huang et al., 2017) where images are zero-padded with 4 pixels on each side, randomly cropped and horizontally mirrored. ",
+ "bbox": [
+ 174,
+ 132,
+ 825,
+ 258
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "text",
+ "text": "For both datasets, we hold out $1 0 \\%$ of training images as a validation set. The best model is selected based on the validation accuracy over the course of ANT training, spanning both the growth phase and the refinement phase, and its accuracy on the testing set is reported. The hyperparameters are also selected based on the validation performance alone. ",
+ "bbox": [
+ 174,
+ 265,
+ 825,
+ 321
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "text",
+ "text": "Both the growth and refinement phase of ANTs takes up to 2 hours on a single Titan X GPU on both datasets. For all the experiments in this paper, we employ the following training protocol: (1) optimize parameters using Adam (Kingma & Ba, 2014) with initial learning rate of $\\bar { 1 0 } ^ { - 3 }$ and $\\beta = \\left. 0 . 9 , 0 . 9 \\bar { 9 } 9 \\right.$ , with minibatches of size 512; (2) during the growth phase, employ early stopping with a patience of 5, that is, training is stopped after 5 epochs of no progress on the validation set; (3) during the refinement phase, train for 100 epochs for MNIST and 200 epochs for CIFAR-10, decreasing the learning rate by a factor of 10 at every multiple of 50. ",
+ "bbox": [
+ 173,
+ 328,
+ 825,
+ 426
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "text",
+ "text": "D TRAINING TIMES ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 445,
+ 352,
+ 463
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "text",
+ "text": "Tab. 5 summarises the time taken on a single Titan X GPU for the growth phase and refinement phase of various ANTs, and compares against the training time of All-CNN (Springenberg et al., 2015). Local optimisation during the growth phase means that the gradient computation is constrained to the newly added component of the graph, allowing us to grow a good candidate model under 2 hours on a single GPU. ",
+ "bbox": [
+ 173,
+ 477,
+ 825,
+ 547
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "table",
+ "img_path": "images/81cbc566ba964074307d79aa8d5e8c7ede51e3f3088021d99a62a1f30e5dcd92.jpg",
+ "table_caption": [
+ "Table 5: Training time comparison. Time and number of epochs taken for the growth and refinement phase are shown. along with the time required to train the baseline, All-CNN (Springenberg et al., 2015). "
+ ],
+ "table_footnote": [],
+ "table_body": " | Method Linear classifier | Error % (Full) | Error % (Path) | Params. (Full) | Params. (Path) | Ensemble Size |
| JSINN | Random Forests (Breiman, 2001) Compact Multi-Class Boosted Trees (Ponomareva et al., 2017) Alternating Decision Forest (Schulter et al., 2013) Neural Decision Tree (Xiao,2017) ANT-MNIST-C MLP with 2 hidden layers (Simard et al., 2003) LeNet-5† (LeCun et al.,1998) | 7.91 3.21 | N/A 3.21 | 7,840 | N/A 1 | 1 200 |
| 2.88 2.71 | 1 2.71 | 1 1 | 1 | 100 |
| 2.10 1.62 | 1.68 N/A | 1 1,773,130 | 1 502,170 7,956 | 20 1 |
| 39,670 | |
| 1.40 0.82 | 1,275,200 431,000 | 1 N/A 1 1 |
| ANT-MNIST-A | gcForest (Zhou & Feng,2017) ANT-MNIST-B Neural Decision Forest (Kontschieder et al., 2015) | 0.74 0.72 | N/A 0.74 0.73 | 1 | N/A 1 | 500 |
| 0.70 | 1 | 76,703 544,600 | 50,653 463,180 | 1 10 |
|
| 0.64 | 0.69 | 100,596 | 84,935 | 1 |
| CapsNet (Sabour et al., 2017) | 0.25 | 1 | 8.2M | N/A | 1 |
| Compact Multi-ClassBoosted Trees (Ponomareva et al.,2017) Random Forests (Breiman,2001) | 52.31 50.17 | 1 50.17 | 1 1 | 1 | 100 |
| CEIPAII1 | gcForest (Zhou& Feng,2017) | 38.22 | 38.22 | 1 | 1 | 2000 500 |
| 1 |
| MaxOut (Goodfellow et al., 2013) ANT-CIFAR10-C | 9.38 9.31 | N/A 9.34 | 6M 0.7M | N/A 0.5M | 1 1 |
| ANT-CIFAR10-B Network in Network (Lin et al.,2014) | 9.15 8.81 | 9.18 N/A | 0.9M 1M | 0.6M N/A | 1 1 |
| All-CNN+(Springenberg et al.,2015) ANT-CIFAR10-A | 8.71 | N/A | 1.4M | N/A | 1 |
| ANT-CIFAR10-A* | 8.31 6.72 | 8.32 6.74 | 1.4M 1.3M | 1.0M 0.8M | 1 |
| ResNet-110 (He et al., 2016) | 6.43 | N/A | 1.7M | N/A | 1 |
| DenseNet-BC (k=40) (Huang et al.,2017) | 3.46 | N/A | 25.6M | N/A | 1 1 |
",
+ "type": "table",
+ "image_path": "a9c2e06dc017496739eebef0d3c53a7bb6014a08e0c1a1517a1500ec07af67d4.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 9,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 109,
+ 160,
+ 500,
+ 236.66666666666669
+ ],
+ "spans": [],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 109,
+ 236.66666666666669,
+ 500,
+ 313.33333333333337
+ ],
+ "spans": [],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 109,
+ 313.33333333333337,
+ 500,
+ 390.00000000000006
+ ],
+ "spans": [],
+ "index": 10
+ }
+ ]
+ }
+ ],
+ "index": 9
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 107,
+ 411,
+ 316,
+ 422
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 411,
+ 317,
+ 424
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 411,
+ 317,
+ 424
+ ],
+ "score": 1.0,
+ "content": "5.1 PERFORMANCE ON IMAGE CLASSIFICATION",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ }
+ ],
+ "index": 11
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 434,
+ 505,
+ 523
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 434,
+ 505,
+ 447
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 434,
+ 505,
+ 447
+ ],
+ "score": 1.0,
+ "content": "We train ANTs with a range of primitive modules (Tab. 2) and compare against relevant DT and",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 446,
+ 505,
+ 458
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 446,
+ 505,
+ 458
+ ],
+ "score": 1.0,
+ "content": "NN models (Tab. 3). In general, DT methods without feature learning, such as RFs (Breiman,",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 106,
+ 456,
+ 505,
+ 469
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 456,
+ 505,
+ 469
+ ],
+ "score": 1.0,
+ "content": "2001; Zhou & Feng, 2017) and GBTs (Ponomareva et al., 2017), perform poorly on complex image",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 106,
+ 467,
+ 504,
+ 479
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 467,
+ 504,
+ 479
+ ],
+ "score": 1.0,
+ "content": "data (Krizhevsky & Hinton, 2009). In comparison with CNNs without shortcut connections (LeCun",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 479,
+ 505,
+ 491
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 479,
+ 505,
+ 491
+ ],
+ "score": 1.0,
+ "content": "et al., 1998; Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015), different ANTs",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 489,
+ 505,
+ 502
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 489,
+ 505,
+ 502
+ ],
+ "score": 1.0,
+ "content": "balance between strong performance with comparable numbers of trainable parameters, and reason-",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 106,
+ 500,
+ 505,
+ 513
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 500,
+ 505,
+ 513
+ ],
+ "score": 1.0,
+ "content": "able performance with a relatively small amount of parameters. At the other end of the spectrum,",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 511,
+ 505,
+ 524
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 511,
+ 505,
+ 524
+ ],
+ "score": 1.0,
+ "content": "state-of-the-art NNs (Sabour et al., 2017; Huang et al., 2017) contain significantly more parameters.",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ }
+ ],
+ "index": 15.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 528,
+ 505,
+ 638
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 528,
+ 504,
+ 540
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 528,
+ 504,
+ 540
+ ],
+ "score": 1.0,
+ "content": "For simplicity, we define primitive modules based on three types of NN layers: convolutional,",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 105,
+ 540,
+ 505,
+ 552
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 540,
+ 505,
+ 552
+ ],
+ "score": 1.0,
+ "content": "global-average-pooling (GAP) and fully-connected (FC). Solver modules are fixed as linear clas-",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 550,
+ 505,
+ 563
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 550,
+ 505,
+ 563
+ ],
+ "score": 1.0,
+ "content": "sifiers (LC) with a softmax output. Router modules are binary classifiers with a sigmoid output. All",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 561,
+ 505,
+ 574
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 561,
+ 505,
+ 574
+ ],
+ "score": 1.0,
+ "content": "convolutional and FC layer are followed by ReLUs, except in the last layers of solvers and routers.",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 106,
+ 572,
+ 505,
+ 585
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 572,
+ 165,
+ 585
+ ],
+ "score": 1.0,
+ "content": "We also apply",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 165,
+ 573,
+ 189,
+ 583
+ ],
+ "score": 0.89,
+ "content": "2 \\times 2",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 190,
+ 572,
+ 353,
+ 585
+ ],
+ "score": 1.0,
+ "content": "max-pooling to feature maps after every",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 353,
+ 573,
+ 360,
+ 582
+ ],
+ "score": 0.76,
+ "content": "d",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 360,
+ 572,
+ 473,
+ 585
+ ],
+ "score": 1.0,
+ "content": "transformer modules where",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 473,
+ 573,
+ 480,
+ 582
+ ],
+ "score": 0.78,
+ "content": "d",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 480,
+ 572,
+ 505,
+ 585
+ ],
+ "score": 1.0,
+ "content": "is the",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 106,
+ 583,
+ 504,
+ 595
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 583,
+ 504,
+ 595
+ ],
+ "score": 1.0,
+ "content": "downsample frequency. We balance the number of parameters in the router and transformer mod-",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 592,
+ 506,
+ 608
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 592,
+ 506,
+ 608
+ ],
+ "score": 1.0,
+ "content": "ules to be of the same order of magnitude to avoid favouring either partitioning the data or learning",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 605,
+ 505,
+ 618
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 605,
+ 269,
+ 618
+ ],
+ "score": 1.0,
+ "content": "more expressive features. We hold out",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 270,
+ 605,
+ 289,
+ 615
+ ],
+ "score": 0.88,
+ "content": "1 0 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 290,
+ 605,
+ 505,
+ 618
+ ],
+ "score": 1.0,
+ "content": "of training images as a validation set, on which the",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 616,
+ 506,
+ 629
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 616,
+ 506,
+ 629
+ ],
+ "score": 1.0,
+ "content": "best performing model is selected. Full training details, including training times, are provided in the",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 627,
+ 206,
+ 639
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 627,
+ 206,
+ 639
+ ],
+ "score": 1.0,
+ "content": "supplementary material.",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ }
+ ],
+ "index": 24.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 643,
+ 505,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 644,
+ 505,
+ 656
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 644,
+ 505,
+ 656
+ ],
+ "score": 1.0,
+ "content": "Two inference schemes: for each ANT, classification is performed in two ways: multi-path infer-",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 655,
+ 505,
+ 667
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 655,
+ 505,
+ 667
+ ],
+ "score": 1.0,
+ "content": "ence with the full predictive distribution (eq. equation 1), and single-path inference based on the",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "score": 1.0,
+ "content": "greedily-selected leaf node (Sec. 3.2). We observed that with our training scheme the splitting prob-",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 105,
+ 675,
+ 505,
+ 690
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 675,
+ 505,
+ 690
+ ],
+ "score": 1.0,
+ "content": "abilities in the routers tend to be very confident, being close to 0 or 1 (see histograms in blue in Fig.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 687,
+ 506,
+ 701
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 687,
+ 506,
+ 701
+ ],
+ "score": 1.0,
+ "content": "2(b)). This means that single path inference gives a good approximation of the multi-path inference",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "score": 1.0,
+ "content": "but is more efficient to compute. We show this holds empirically in Tab. 3, where the largest dif-",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 709,
+ 505,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 709,
+ 298,
+ 722
+ ],
+ "score": 1.0,
+ "content": "ference between Error (Full) and Error (Path) is",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 298,
+ 709,
+ 325,
+ 720
+ ],
+ "score": 0.89,
+ "content": "0 . 0 6 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 326,
+ 709,
+ 505,
+ 722
+ ],
+ "score": 1.0,
+ "content": "while number of parameters is reduced from",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 106,
+ 721,
+ 328,
+ 732
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 721,
+ 328,
+ 732
+ ],
+ "score": 1.0,
+ "content": "Params (Full) to Params (Path) across all ANT models.",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ }
+ ],
+ "index": 33.5
+ }
+ ],
+ "page_idx": 6,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 308,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 107,
+ 26,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 26,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 303,
+ 751,
+ 309,
+ 759
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 302,
+ 750,
+ 309,
+ 762
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 302,
+ 750,
+ 309,
+ 762
+ ],
+ "score": 1.0,
+ "content": "7",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 62,
+ 505,
+ 151
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 63,
+ 505,
+ 75
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 63,
+ 505,
+ 75
+ ],
+ "score": 1.0,
+ "content": "Table 3: Comparison of performance of different models on MNIST and CIFAR-10. The columns",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 106,
+ 73,
+ 505,
+ 86
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 73,
+ 505,
+ 86
+ ],
+ "score": 1.0,
+ "content": "“Error (Full)” and “Error (Path)” indicate the classification error of predictions based on the full",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 106,
+ 85,
+ 504,
+ 97
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 85,
+ 504,
+ 97
+ ],
+ "score": 1.0,
+ "content": "distribution and the single-path inference. The columns “Params. (Full)” and “Params. (Path)”",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 104,
+ 96,
+ 506,
+ 109
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 96,
+ 506,
+ 109
+ ],
+ "score": 1.0,
+ "content": "respectively show the total number of parameters in the model and the average number of parameters",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 106,
+ 107,
+ 505,
+ 119
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 107,
+ 505,
+ 119
+ ],
+ "score": 1.0,
+ "content": "utilised during single-path inference. “Ensemble Size” indicates the size of ensemble used to attain",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 105,
+ 118,
+ 505,
+ 130
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 118,
+ 505,
+ 130
+ ],
+ "score": 1.0,
+ "content": "the reported accuracy. An entry of “–” indicates that no value was reported. Methods marked with †",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 106,
+ 129,
+ 505,
+ 142
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 129,
+ 505,
+ 142
+ ],
+ "score": 1.0,
+ "content": "are from our implementations trained in the same experimental setup. * indicates that the parameters",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 106,
+ 140,
+ 262,
+ 153
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 140,
+ 262,
+ 153
+ ],
+ "score": 1.0,
+ "content": "are initialised with a pre-trained CNN.",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ }
+ ],
+ "index": 3.5,
+ "bbox_fs": [
+ 104,
+ 63,
+ 506,
+ 153
+ ]
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 109,
+ 160,
+ 500,
+ 390
+ ],
+ "blocks": [
+ {
+ "type": "table_body",
+ "bbox": [
+ 109,
+ 160,
+ 500,
+ 390
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 109,
+ 160,
+ 500,
+ 390
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 109,
+ 160,
+ 500,
+ 390
+ ],
+ "score": 0.985,
+ "html": " | Method Linear classifier | Error % (Full) | Error % (Path) | Params. (Full) | Params. (Path) | Ensemble Size |
| JSINN | Random Forests (Breiman, 2001) Compact Multi-Class Boosted Trees (Ponomareva et al., 2017) Alternating Decision Forest (Schulter et al., 2013) Neural Decision Tree (Xiao,2017) ANT-MNIST-C MLP with 2 hidden layers (Simard et al., 2003) LeNet-5† (LeCun et al.,1998) | 7.91 3.21 | N/A 3.21 | 7,840 | N/A 1 | 1 200 |
| 2.88 2.71 | 1 2.71 | 1 1 | 1 | 100 |
| 2.10 1.62 | 1.68 N/A | 1 1,773,130 | 1 502,170 7,956 | 20 1 |
| 39,670 | |
| 1.40 0.82 | 1,275,200 431,000 | 1 N/A 1 1 |
| ANT-MNIST-A | gcForest (Zhou & Feng,2017) ANT-MNIST-B Neural Decision Forest (Kontschieder et al., 2015) | 0.74 0.72 | N/A 0.74 0.73 | 1 | N/A 1 | 500 |
| 0.70 | 1 | 76,703 544,600 | 50,653 463,180 | 1 10 |
|
| 0.64 | 0.69 | 100,596 | 84,935 | 1 |
| CapsNet (Sabour et al., 2017) | 0.25 | 1 | 8.2M | N/A | 1 |
| Compact Multi-ClassBoosted Trees (Ponomareva et al.,2017) Random Forests (Breiman,2001) | 52.31 50.17 | 1 50.17 | 1 1 | 1 | 100 |
| CEIPAII1 | gcForest (Zhou& Feng,2017) | 38.22 | 38.22 | 1 | 1 | 2000 500 |
| 1 |
| MaxOut (Goodfellow et al., 2013) ANT-CIFAR10-C | 9.38 9.31 | N/A 9.34 | 6M 0.7M | N/A 0.5M | 1 1 |
| ANT-CIFAR10-B Network in Network (Lin et al.,2014) | 9.15 8.81 | 9.18 N/A | 0.9M 1M | 0.6M N/A | 1 1 |
| All-CNN+(Springenberg et al.,2015) ANT-CIFAR10-A | 8.71 | N/A | 1.4M | N/A | 1 |
| ANT-CIFAR10-A* | 8.31 6.72 | 8.32 6.74 | 1.4M 1.3M | 1.0M 0.8M | 1 |
| ResNet-110 (He et al., 2016) | 6.43 | N/A | 1.7M | N/A | 1 |
| DenseNet-BC (k=40) (Huang et al.,2017) | 3.46 | N/A | 25.6M | N/A | 1 1 |
",
+ "type": "table",
+ "image_path": "a9c2e06dc017496739eebef0d3c53a7bb6014a08e0c1a1517a1500ec07af67d4.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 9,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 109,
+ 160,
+ 500,
+ 236.66666666666669
+ ],
+ "spans": [],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 109,
+ 236.66666666666669,
+ 500,
+ 313.33333333333337
+ ],
+ "spans": [],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 109,
+ 313.33333333333337,
+ 500,
+ 390.00000000000006
+ ],
+ "spans": [],
+ "index": 10
+ }
+ ]
+ }
+ ],
+ "index": 9
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 107,
+ 411,
+ 316,
+ 422
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 411,
+ 317,
+ 424
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 411,
+ 317,
+ 424
+ ],
+ "score": 1.0,
+ "content": "5.1 PERFORMANCE ON IMAGE CLASSIFICATION",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ }
+ ],
+ "index": 11
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 434,
+ 505,
+ 523
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 434,
+ 505,
+ 447
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 434,
+ 505,
+ 447
+ ],
+ "score": 1.0,
+ "content": "We train ANTs with a range of primitive modules (Tab. 2) and compare against relevant DT and",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 446,
+ 505,
+ 458
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 446,
+ 505,
+ 458
+ ],
+ "score": 1.0,
+ "content": "NN models (Tab. 3). In general, DT methods without feature learning, such as RFs (Breiman,",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 106,
+ 456,
+ 505,
+ 469
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 456,
+ 505,
+ 469
+ ],
+ "score": 1.0,
+ "content": "2001; Zhou & Feng, 2017) and GBTs (Ponomareva et al., 2017), perform poorly on complex image",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 106,
+ 467,
+ 504,
+ 479
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 467,
+ 504,
+ 479
+ ],
+ "score": 1.0,
+ "content": "data (Krizhevsky & Hinton, 2009). In comparison with CNNs without shortcut connections (LeCun",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 479,
+ 505,
+ 491
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 479,
+ 505,
+ 491
+ ],
+ "score": 1.0,
+ "content": "et al., 1998; Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015), different ANTs",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 489,
+ 505,
+ 502
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 489,
+ 505,
+ 502
+ ],
+ "score": 1.0,
+ "content": "balance between strong performance with comparable numbers of trainable parameters, and reason-",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 106,
+ 500,
+ 505,
+ 513
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 500,
+ 505,
+ 513
+ ],
+ "score": 1.0,
+ "content": "able performance with a relatively small amount of parameters. At the other end of the spectrum,",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 511,
+ 505,
+ 524
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 511,
+ 505,
+ 524
+ ],
+ "score": 1.0,
+ "content": "state-of-the-art NNs (Sabour et al., 2017; Huang et al., 2017) contain significantly more parameters.",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ }
+ ],
+ "index": 15.5,
+ "bbox_fs": [
+ 105,
+ 434,
+ 505,
+ 524
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 528,
+ 505,
+ 638
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 528,
+ 504,
+ 540
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 528,
+ 504,
+ 540
+ ],
+ "score": 1.0,
+ "content": "For simplicity, we define primitive modules based on three types of NN layers: convolutional,",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 105,
+ 540,
+ 505,
+ 552
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 540,
+ 505,
+ 552
+ ],
+ "score": 1.0,
+ "content": "global-average-pooling (GAP) and fully-connected (FC). Solver modules are fixed as linear clas-",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 550,
+ 505,
+ 563
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 550,
+ 505,
+ 563
+ ],
+ "score": 1.0,
+ "content": "sifiers (LC) with a softmax output. Router modules are binary classifiers with a sigmoid output. All",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 561,
+ 505,
+ 574
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 561,
+ 505,
+ 574
+ ],
+ "score": 1.0,
+ "content": "convolutional and FC layer are followed by ReLUs, except in the last layers of solvers and routers.",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 106,
+ 572,
+ 505,
+ 585
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 572,
+ 165,
+ 585
+ ],
+ "score": 1.0,
+ "content": "We also apply",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 165,
+ 573,
+ 189,
+ 583
+ ],
+ "score": 0.89,
+ "content": "2 \\times 2",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 190,
+ 572,
+ 353,
+ 585
+ ],
+ "score": 1.0,
+ "content": "max-pooling to feature maps after every",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 353,
+ 573,
+ 360,
+ 582
+ ],
+ "score": 0.76,
+ "content": "d",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 360,
+ 572,
+ 473,
+ 585
+ ],
+ "score": 1.0,
+ "content": "transformer modules where",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 473,
+ 573,
+ 480,
+ 582
+ ],
+ "score": 0.78,
+ "content": "d",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 480,
+ 572,
+ 505,
+ 585
+ ],
+ "score": 1.0,
+ "content": "is the",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 106,
+ 583,
+ 504,
+ 595
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 583,
+ 504,
+ 595
+ ],
+ "score": 1.0,
+ "content": "downsample frequency. We balance the number of parameters in the router and transformer mod-",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 592,
+ 506,
+ 608
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 592,
+ 506,
+ 608
+ ],
+ "score": 1.0,
+ "content": "ules to be of the same order of magnitude to avoid favouring either partitioning the data or learning",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 605,
+ 505,
+ 618
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 605,
+ 269,
+ 618
+ ],
+ "score": 1.0,
+ "content": "more expressive features. We hold out",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 270,
+ 605,
+ 289,
+ 615
+ ],
+ "score": 0.88,
+ "content": "1 0 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 290,
+ 605,
+ 505,
+ 618
+ ],
+ "score": 1.0,
+ "content": "of training images as a validation set, on which the",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 616,
+ 506,
+ 629
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 616,
+ 506,
+ 629
+ ],
+ "score": 1.0,
+ "content": "best performing model is selected. Full training details, including training times, are provided in the",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 627,
+ 206,
+ 639
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 627,
+ 206,
+ 639
+ ],
+ "score": 1.0,
+ "content": "supplementary material.",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ }
+ ],
+ "index": 24.5,
+ "bbox_fs": [
+ 105,
+ 528,
+ 506,
+ 639
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 643,
+ 505,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 644,
+ 505,
+ 656
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 644,
+ 505,
+ 656
+ ],
+ "score": 1.0,
+ "content": "Two inference schemes: for each ANT, classification is performed in two ways: multi-path infer-",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 655,
+ 505,
+ 667
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 655,
+ 505,
+ 667
+ ],
+ "score": 1.0,
+ "content": "ence with the full predictive distribution (eq. equation 1), and single-path inference based on the",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "score": 1.0,
+ "content": "greedily-selected leaf node (Sec. 3.2). We observed that with our training scheme the splitting prob-",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 105,
+ 675,
+ 505,
+ 690
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 675,
+ 505,
+ 690
+ ],
+ "score": 1.0,
+ "content": "abilities in the routers tend to be very confident, being close to 0 or 1 (see histograms in blue in Fig.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 687,
+ 506,
+ 701
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 687,
+ 506,
+ 701
+ ],
+ "score": 1.0,
+ "content": "2(b)). This means that single path inference gives a good approximation of the multi-path inference",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "score": 1.0,
+ "content": "but is more efficient to compute. We show this holds empirically in Tab. 3, where the largest dif-",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 709,
+ 505,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 709,
+ 298,
+ 722
+ ],
+ "score": 1.0,
+ "content": "ference between Error (Full) and Error (Path) is",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 298,
+ 709,
+ 325,
+ 720
+ ],
+ "score": 0.89,
+ "content": "0 . 0 6 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 326,
+ 709,
+ 505,
+ 722
+ ],
+ "score": 1.0,
+ "content": "while number of parameters is reduced from",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 106,
+ 721,
+ 328,
+ 732
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 721,
+ 328,
+ 732
+ ],
+ "score": 1.0,
+ "content": "Params (Full) to Params (Path) across all ANT models.",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ }
+ ],
+ "index": 33.5,
+ "bbox_fs": [
+ 105,
+ 644,
+ 506,
+ 732
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 82,
+ 505,
+ 160
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 82,
+ 505,
+ 95
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 82,
+ 505,
+ 95
+ ],
+ "score": 1.0,
+ "content": "Patience-based local optimisation: in the growth phase the parameters for the new modules are",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 105,
+ 94,
+ 505,
+ 106
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 94,
+ 505,
+ 106
+ ],
+ "score": 1.0,
+ "content": "trained until convergence, as determined by patience-based early stopping on the validation set.",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 105,
+ 104,
+ 505,
+ 118
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 104,
+ 505,
+ 118
+ ],
+ "score": 1.0,
+ "content": "We observe that very low or high patience levels result in new modules underfitting or overfitting",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 105,
+ 114,
+ 505,
+ 129
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 114,
+ 505,
+ 129
+ ],
+ "score": 1.0,
+ "content": "locally, respectively, thus preventing meaningful further growth. We tuned this hyperparameter using",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 126,
+ 505,
+ 139
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 126,
+ 505,
+ 139
+ ],
+ "score": 1.0,
+ "content": "the validation sets, and set the patience level to 5, which produced consistently good performance",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 105,
+ 137,
+ 505,
+ 150
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 137,
+ 505,
+ 150
+ ],
+ "score": 1.0,
+ "content": "on both MNIST and CIFAR-10 datasets across different specifications of primitive modules. A",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 149,
+ 356,
+ 161
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 149,
+ 356,
+ 161
+ ],
+ "score": 1.0,
+ "content": "quantitative evaluation is given in the supplementary (Sec. E).",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ }
+ ],
+ "index": 3
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 165,
+ 505,
+ 275
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 165,
+ 505,
+ 176
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 165,
+ 505,
+ 176
+ ],
+ "score": 1.0,
+ "content": "MNIST digit classification: we observe that ANT-MNIST-A outperforms state-of-the-art GBT",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 175,
+ 505,
+ 189
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 175,
+ 505,
+ 189
+ ],
+ "score": 1.0,
+ "content": "(Ponomareva et al., 2017) and RF (Zhou & Feng, 2017) methods in accuracy. This performance",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 186,
+ 505,
+ 199
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 186,
+ 505,
+ 199
+ ],
+ "score": 1.0,
+ "content": "is attained despite the use of a single tree, while RF methods operate with ensembles of classifiers",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 198,
+ 505,
+ 210
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 198,
+ 505,
+ 210
+ ],
+ "score": 1.0,
+ "content": "(the size shown in Tab. 2). In particular, the NDF (Kontschieder et al., 2015) has a pre-specified",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 106,
+ 210,
+ 505,
+ 221
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 210,
+ 505,
+ 221
+ ],
+ "score": 1.0,
+ "content": "architecture where LeNet-5 (LeCun et al., 1998) is used as the root transformer module, and 10 trees",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 106,
+ 220,
+ 505,
+ 232
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 220,
+ 505,
+ 232
+ ],
+ "score": 1.0,
+ "content": "of fixed depth 5 are constructed from this base feature extractor. On the other hand, ANT-MNIST-",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 230,
+ 506,
+ 244
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 230,
+ 506,
+ 244
+ ],
+ "score": 1.0,
+ "content": "A is constructed in a data-driven manner from primitive modules, and displays an improvement",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 242,
+ 505,
+ 254
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 242,
+ 505,
+ 254
+ ],
+ "score": 1.0,
+ "content": "over the NDF both in terms of accuracy and number of parameters. In addition, reducing the size",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 253,
+ 505,
+ 266
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 253,
+ 450,
+ 266
+ ],
+ "score": 1.0,
+ "content": "of convolution kernels (ANT-MNIST-B) reduces the total number of parameters by",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 451,
+ 253,
+ 470,
+ 263
+ ],
+ "score": 0.88,
+ "content": "2 5 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 471,
+ 253,
+ 505,
+ 266
+ ],
+ "score": 1.0,
+ "content": "and the",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 264,
+ 438,
+ 276
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 264,
+ 222,
+ 276
+ ],
+ "score": 1.0,
+ "content": "path-wise average by almost",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 222,
+ 264,
+ 242,
+ 275
+ ],
+ "score": 0.87,
+ "content": "4 0 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 243,
+ 264,
+ 401,
+ 276
+ ],
+ "score": 1.0,
+ "content": "while only increasing absolute error by",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 401,
+ 264,
+ 434,
+ 275
+ ],
+ "score": 0.92,
+ "content": "< 0 . 1 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 434,
+ 264,
+ 438,
+ 276
+ ],
+ "score": 1.0,
+ "content": ".",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ }
+ ],
+ "index": 11.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 281,
+ 505,
+ 380
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 280,
+ 506,
+ 294
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 280,
+ 506,
+ 294
+ ],
+ "score": 1.0,
+ "content": "We also compare against the LeNet-5 CNN (LeCun et al., 1998), comprised of the same types of",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 106,
+ 292,
+ 506,
+ 304
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 292,
+ 506,
+ 304
+ ],
+ "score": 1.0,
+ "content": "operations used in our primitive modules (i.e. convolutional, max-pooling and FC layers). For a",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 303,
+ 506,
+ 316
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 303,
+ 506,
+ 316
+ ],
+ "score": 1.0,
+ "content": "fair comparison, the network is trained with the same protocol as that of the ANT refinement phase,",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 313,
+ 505,
+ 326
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 313,
+ 214,
+ 326
+ ],
+ "score": 1.0,
+ "content": "achieving an error rate of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 215,
+ 313,
+ 243,
+ 325
+ ],
+ "score": 0.9,
+ "content": "0 . 8 2 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 243,
+ 313,
+ 383,
+ 326
+ ],
+ "score": 1.0,
+ "content": "(lower than the reported value of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 384,
+ 313,
+ 412,
+ 325
+ ],
+ "score": 0.87,
+ "content": "0 . 8 7 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 412,
+ 313,
+ 505,
+ 326
+ ],
+ "score": 1.0,
+ "content": ") on the test set. Both",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 106,
+ 325,
+ 505,
+ 337
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 325,
+ 505,
+ 337
+ ],
+ "score": 1.0,
+ "content": "ANT-MNIST-A and ANT-MNIST-B attain better accuracy with a smaller number of parameters",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 335,
+ 505,
+ 348
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 335,
+ 505,
+ 348
+ ],
+ "score": 1.0,
+ "content": "than LeNet-5. The current state-of-the-art, capsule networks (CapsNets) (Sabour et al., 2017), have",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 345,
+ 504,
+ 359
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 345,
+ 504,
+ 359
+ ],
+ "score": 1.0,
+ "content": "more parameters than ANT-MNIST-A by almost two orders of magnitude.1 By ensembling ANTs",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 356,
+ 505,
+ 371
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 356,
+ 244,
+ 371
+ ],
+ "score": 1.0,
+ "content": "we can reach similar performance",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 245,
+ 357,
+ 273,
+ 369
+ ],
+ "score": 0.86,
+ "content": "( 0 . 2 9 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 274,
+ 356,
+ 302,
+ 371
+ ],
+ "score": 1.0,
+ "content": "versus",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 302,
+ 357,
+ 329,
+ 369
+ ],
+ "score": 0.88,
+ "content": "0 . 2 5 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 330,
+ 356,
+ 505,
+ 371
+ ],
+ "score": 1.0,
+ "content": "; see Tab. 9) with an order of magnitude less",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 369,
+ 208,
+ 380
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 369,
+ 208,
+ 380
+ ],
+ "score": 1.0,
+ "content": "parameters (see Tab. 10).",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ }
+ ],
+ "index": 21
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 385,
+ 505,
+ 484
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 384,
+ 505,
+ 398
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 384,
+ 505,
+ 398
+ ],
+ "score": 1.0,
+ "content": "Lastly, we highlight the observation that ANT-MNIST-C, with the simplest primitive modules,",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 396,
+ 506,
+ 409
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 396,
+ 209,
+ 409
+ ],
+ "score": 1.0,
+ "content": "achieves an error rate of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 209,
+ 396,
+ 237,
+ 407
+ ],
+ "score": 0.89,
+ "content": "1 . 6 8 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 237,
+ 396,
+ 506,
+ 409
+ ],
+ "score": 1.0,
+ "content": "with single-path inference, which is significantly better than that",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 406,
+ 506,
+ 420
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 406,
+ 198,
+ 420
+ ],
+ "score": 1.0,
+ "content": "of the linear classifier",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 198,
+ 407,
+ 230,
+ 418
+ ],
+ "score": 0.86,
+ "content": "( 7 . 9 1 \\% )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 230,
+ 406,
+ 506,
+ 420
+ ],
+ "score": 1.0,
+ "content": ", while engaging almost the same number of parameters (7, 956 vs.",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 417,
+ 505,
+ 431
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 417,
+ 505,
+ 431
+ ],
+ "score": 1.0,
+ "content": "7, 840) on average. To isolate the benefit of convolutions, we took one of the root-to-path CNNs on",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 105,
+ 428,
+ 506,
+ 442
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 428,
+ 506,
+ 442
+ ],
+ "score": 1.0,
+ "content": "ANT-MNIST-C and increased the number of kernels to adjust the number of parameters to the same",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 440,
+ 505,
+ 453
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 440,
+ 271,
+ 453
+ ],
+ "score": 1.0,
+ "content": "value. We observe a higher error rate of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 272,
+ 440,
+ 299,
+ 451
+ ],
+ "score": 0.89,
+ "content": "3 . 5 5 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 299,
+ 440,
+ 505,
+ 453
+ ],
+ "score": 1.0,
+ "content": ", which indicates that while convolutions are bene-",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 106,
+ 452,
+ 505,
+ 463
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 452,
+ 505,
+ 463
+ ],
+ "score": 1.0,
+ "content": "ficial, data partitioning has additional benefits in improving accuracy. This result demonstrates the",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 105,
+ 461,
+ 506,
+ 475
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 461,
+ 506,
+ 475
+ ],
+ "score": 1.0,
+ "content": "potential of ANT growth protocol for constructing performant models with lightweight inference.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 473,
+ 434,
+ 485
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 473,
+ 434,
+ 485
+ ],
+ "score": 1.0,
+ "content": "See Sec. G in the supplementary materials for the architecture of ANT-MNIST-C.",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ }
+ ],
+ "index": 30
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 490,
+ 505,
+ 600
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 489,
+ 505,
+ 502
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 489,
+ 505,
+ 502
+ ],
+ "score": 1.0,
+ "content": "CIFAR-10 object recognition: we see that variants of ANTs outperform the state-of-the-art DT",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 106,
+ 501,
+ 504,
+ 513
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 501,
+ 395,
+ 513
+ ],
+ "score": 1.0,
+ "content": "method, gcForest (Zhou & Feng, 2017) by a large margin, achieving over",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 396,
+ 501,
+ 415,
+ 511
+ ],
+ "score": 0.86,
+ "content": "90 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 415,
+ 501,
+ 504,
+ 513
+ ],
+ "score": 1.0,
+ "content": "accuracy, demonstrat-",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 512,
+ 506,
+ 525
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 512,
+ 506,
+ 525
+ ],
+ "score": 1.0,
+ "content": "ing the benefit of representation learning in tree-structured models. Secondly, with fewer number",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 523,
+ 506,
+ 535
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 523,
+ 506,
+ 535
+ ],
+ "score": 1.0,
+ "content": "of parameters in single-path inference, ANT-CIFAR-A achieves higher accuracy than CNN models",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 106,
+ 534,
+ 505,
+ 546
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 534,
+ 505,
+ 546
+ ],
+ "score": 1.0,
+ "content": "without shortcut connections (Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015)",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 544,
+ 505,
+ 557
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 544,
+ 505,
+ 557
+ ],
+ "score": 1.0,
+ "content": "that held the state-of-the-art performance at the time of publication. With simpler primitive modules",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 555,
+ 505,
+ 569
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 555,
+ 505,
+ 569
+ ],
+ "score": 1.0,
+ "content": "we learn more compact models (ANT-MNIST-B and -C) with a marginal compromise in accuracy.",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 105,
+ 566,
+ 505,
+ 579
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 566,
+ 505,
+ 579
+ ],
+ "score": 1.0,
+ "content": "In addition, initialising the parameters of transformers and routers from a pre-trained single-path",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 577,
+ 505,
+ 590
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 577,
+ 344,
+ 590
+ ],
+ "score": 1.0,
+ "content": "CNN further reduced the error rate of ANT-MNIST-A by",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 345,
+ 578,
+ 365,
+ 588
+ ],
+ "score": 0.86,
+ "content": "20 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 577,
+ 442,
+ 590
+ ],
+ "score": 1.0,
+ "content": "(see ANT-MNIST-",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 443,
+ 578,
+ 456,
+ 588
+ ],
+ "score": 0.61,
+ "content": "\\mathbf { A } ^ { * }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 457,
+ 577,
+ 505,
+ 590
+ ],
+ "score": 1.0,
+ "content": "in Tab. 3),",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 105,
+ 589,
+ 416,
+ 601
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 589,
+ 416,
+ 601
+ ],
+ "score": 1.0,
+ "content": "which indicates room for improvement in our proposed optimisation method.",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ }
+ ],
+ "index": 39.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 605,
+ 505,
+ 682
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 604,
+ 505,
+ 619
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 604,
+ 505,
+ 619
+ ],
+ "score": 1.0,
+ "content": "Shortcut connections (Fahlman & Lebiere, 1990) have recently lead to leaps in performance in deep",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ },
+ {
+ "bbox": [
+ 106,
+ 616,
+ 505,
+ 629
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 616,
+ 488,
+ 629
+ ],
+ "score": 1.0,
+ "content": "CNNs (He et al., 2016; Huang et al., 2017). We observe that our best network, ANT-MNIST-",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 488,
+ 617,
+ 501,
+ 627
+ ],
+ "score": 0.33,
+ "content": "A ^ { * }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 501,
+ 616,
+ 505,
+ 629
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 105,
+ 628,
+ 505,
+ 640
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 628,
+ 505,
+ 640
+ ],
+ "score": 1.0,
+ "content": "has a comparable error rate and half the parameter count (with single-path inference) to the best-",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 105,
+ 639,
+ 505,
+ 650
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 639,
+ 505,
+ 650
+ ],
+ "score": 1.0,
+ "content": "performing residual network, ResNet-110 (He et al., 2016). Densely connected networks leads to",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ },
+ {
+ "bbox": [
+ 105,
+ 649,
+ 505,
+ 662
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 649,
+ 505,
+ 662
+ ],
+ "score": 1.0,
+ "content": "substantially better accuracy, but with an order of magnitude more parameters (Huang et al., 2017).",
+ "type": "text"
+ }
+ ],
+ "index": 49
+ },
+ {
+ "bbox": [
+ 105,
+ 660,
+ 505,
+ 673
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 660,
+ 505,
+ 673
+ ],
+ "score": 1.0,
+ "content": "We expect that shortcut connections could also improve ANT performance, and leave integrating",
+ "type": "text"
+ }
+ ],
+ "index": 50
+ },
+ {
+ "bbox": [
+ 105,
+ 671,
+ 191,
+ 684
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 671,
+ 191,
+ 684
+ ],
+ "score": 1.0,
+ "content": "them to future work.",
+ "type": "text"
+ }
+ ],
+ "index": 51
+ }
+ ],
+ "index": 48
+ }
+ ],
+ "page_idx": 7,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 108,
+ 711,
+ 505,
+ 731
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 118,
+ 709,
+ 506,
+ 724
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 118,
+ 709,
+ 506,
+ 724
+ ],
+ "score": 1.0,
+ "content": "1Notably, CapsNets also feature a routing mechanism, but with a significantly different mechanism and",
+ "type": "text"
+ }
+ ]
+ },
+ {
+ "bbox": [
+ 106,
+ 721,
+ 150,
+ 732
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 721,
+ 150,
+ 732
+ ],
+ "score": 1.0,
+ "content": "motivation.",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 302,
+ 752,
+ 308,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 301,
+ 750,
+ 310,
+ 762
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 301,
+ 750,
+ 310,
+ 762
+ ],
+ "score": 1.0,
+ "content": "",
+ "type": "text",
+ "height": 12,
+ "width": 9
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 308,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 107,
+ 25,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 25,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 82,
+ 505,
+ 160
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 82,
+ 505,
+ 95
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 82,
+ 505,
+ 95
+ ],
+ "score": 1.0,
+ "content": "Patience-based local optimisation: in the growth phase the parameters for the new modules are",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 105,
+ 94,
+ 505,
+ 106
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 94,
+ 505,
+ 106
+ ],
+ "score": 1.0,
+ "content": "trained until convergence, as determined by patience-based early stopping on the validation set.",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 105,
+ 104,
+ 505,
+ 118
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 104,
+ 505,
+ 118
+ ],
+ "score": 1.0,
+ "content": "We observe that very low or high patience levels result in new modules underfitting or overfitting",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 105,
+ 114,
+ 505,
+ 129
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 114,
+ 505,
+ 129
+ ],
+ "score": 1.0,
+ "content": "locally, respectively, thus preventing meaningful further growth. We tuned this hyperparameter using",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 126,
+ 505,
+ 139
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 126,
+ 505,
+ 139
+ ],
+ "score": 1.0,
+ "content": "the validation sets, and set the patience level to 5, which produced consistently good performance",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 105,
+ 137,
+ 505,
+ 150
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 137,
+ 505,
+ 150
+ ],
+ "score": 1.0,
+ "content": "on both MNIST and CIFAR-10 datasets across different specifications of primitive modules. A",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 149,
+ 356,
+ 161
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 149,
+ 356,
+ 161
+ ],
+ "score": 1.0,
+ "content": "quantitative evaluation is given in the supplementary (Sec. E).",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ }
+ ],
+ "index": 3,
+ "bbox_fs": [
+ 105,
+ 82,
+ 505,
+ 161
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 165,
+ 505,
+ 275
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 165,
+ 505,
+ 176
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 165,
+ 505,
+ 176
+ ],
+ "score": 1.0,
+ "content": "MNIST digit classification: we observe that ANT-MNIST-A outperforms state-of-the-art GBT",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 175,
+ 505,
+ 189
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 175,
+ 505,
+ 189
+ ],
+ "score": 1.0,
+ "content": "(Ponomareva et al., 2017) and RF (Zhou & Feng, 2017) methods in accuracy. This performance",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 186,
+ 505,
+ 199
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 186,
+ 505,
+ 199
+ ],
+ "score": 1.0,
+ "content": "is attained despite the use of a single tree, while RF methods operate with ensembles of classifiers",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 198,
+ 505,
+ 210
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 198,
+ 505,
+ 210
+ ],
+ "score": 1.0,
+ "content": "(the size shown in Tab. 2). In particular, the NDF (Kontschieder et al., 2015) has a pre-specified",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 106,
+ 210,
+ 505,
+ 221
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 210,
+ 505,
+ 221
+ ],
+ "score": 1.0,
+ "content": "architecture where LeNet-5 (LeCun et al., 1998) is used as the root transformer module, and 10 trees",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 106,
+ 220,
+ 505,
+ 232
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 220,
+ 505,
+ 232
+ ],
+ "score": 1.0,
+ "content": "of fixed depth 5 are constructed from this base feature extractor. On the other hand, ANT-MNIST-",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 230,
+ 506,
+ 244
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 230,
+ 506,
+ 244
+ ],
+ "score": 1.0,
+ "content": "A is constructed in a data-driven manner from primitive modules, and displays an improvement",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 242,
+ 505,
+ 254
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 242,
+ 505,
+ 254
+ ],
+ "score": 1.0,
+ "content": "over the NDF both in terms of accuracy and number of parameters. In addition, reducing the size",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 253,
+ 505,
+ 266
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 253,
+ 450,
+ 266
+ ],
+ "score": 1.0,
+ "content": "of convolution kernels (ANT-MNIST-B) reduces the total number of parameters by",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 451,
+ 253,
+ 470,
+ 263
+ ],
+ "score": 0.88,
+ "content": "2 5 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 471,
+ 253,
+ 505,
+ 266
+ ],
+ "score": 1.0,
+ "content": "and the",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 264,
+ 438,
+ 276
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 264,
+ 222,
+ 276
+ ],
+ "score": 1.0,
+ "content": "path-wise average by almost",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 222,
+ 264,
+ 242,
+ 275
+ ],
+ "score": 0.87,
+ "content": "4 0 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 243,
+ 264,
+ 401,
+ 276
+ ],
+ "score": 1.0,
+ "content": "while only increasing absolute error by",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 401,
+ 264,
+ 434,
+ 275
+ ],
+ "score": 0.92,
+ "content": "< 0 . 1 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 434,
+ 264,
+ 438,
+ 276
+ ],
+ "score": 1.0,
+ "content": ".",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ }
+ ],
+ "index": 11.5,
+ "bbox_fs": [
+ 105,
+ 165,
+ 506,
+ 276
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 281,
+ 505,
+ 380
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 280,
+ 506,
+ 294
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 280,
+ 506,
+ 294
+ ],
+ "score": 1.0,
+ "content": "We also compare against the LeNet-5 CNN (LeCun et al., 1998), comprised of the same types of",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 106,
+ 292,
+ 506,
+ 304
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 292,
+ 506,
+ 304
+ ],
+ "score": 1.0,
+ "content": "operations used in our primitive modules (i.e. convolutional, max-pooling and FC layers). For a",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 303,
+ 506,
+ 316
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 303,
+ 506,
+ 316
+ ],
+ "score": 1.0,
+ "content": "fair comparison, the network is trained with the same protocol as that of the ANT refinement phase,",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 313,
+ 505,
+ 326
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 313,
+ 214,
+ 326
+ ],
+ "score": 1.0,
+ "content": "achieving an error rate of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 215,
+ 313,
+ 243,
+ 325
+ ],
+ "score": 0.9,
+ "content": "0 . 8 2 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 243,
+ 313,
+ 383,
+ 326
+ ],
+ "score": 1.0,
+ "content": "(lower than the reported value of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 384,
+ 313,
+ 412,
+ 325
+ ],
+ "score": 0.87,
+ "content": "0 . 8 7 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 412,
+ 313,
+ 505,
+ 326
+ ],
+ "score": 1.0,
+ "content": ") on the test set. Both",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 106,
+ 325,
+ 505,
+ 337
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 325,
+ 505,
+ 337
+ ],
+ "score": 1.0,
+ "content": "ANT-MNIST-A and ANT-MNIST-B attain better accuracy with a smaller number of parameters",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 335,
+ 505,
+ 348
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 335,
+ 505,
+ 348
+ ],
+ "score": 1.0,
+ "content": "than LeNet-5. The current state-of-the-art, capsule networks (CapsNets) (Sabour et al., 2017), have",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 345,
+ 504,
+ 359
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 345,
+ 504,
+ 359
+ ],
+ "score": 1.0,
+ "content": "more parameters than ANT-MNIST-A by almost two orders of magnitude.1 By ensembling ANTs",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 356,
+ 505,
+ 371
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 356,
+ 244,
+ 371
+ ],
+ "score": 1.0,
+ "content": "we can reach similar performance",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 245,
+ 357,
+ 273,
+ 369
+ ],
+ "score": 0.86,
+ "content": "( 0 . 2 9 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 274,
+ 356,
+ 302,
+ 371
+ ],
+ "score": 1.0,
+ "content": "versus",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 302,
+ 357,
+ 329,
+ 369
+ ],
+ "score": 0.88,
+ "content": "0 . 2 5 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 330,
+ 356,
+ 505,
+ 371
+ ],
+ "score": 1.0,
+ "content": "; see Tab. 9) with an order of magnitude less",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 369,
+ 208,
+ 380
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 369,
+ 208,
+ 380
+ ],
+ "score": 1.0,
+ "content": "parameters (see Tab. 10).",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ }
+ ],
+ "index": 21,
+ "bbox_fs": [
+ 105,
+ 280,
+ 506,
+ 380
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 385,
+ 505,
+ 484
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 384,
+ 505,
+ 398
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 384,
+ 505,
+ 398
+ ],
+ "score": 1.0,
+ "content": "Lastly, we highlight the observation that ANT-MNIST-C, with the simplest primitive modules,",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 396,
+ 506,
+ 409
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 396,
+ 209,
+ 409
+ ],
+ "score": 1.0,
+ "content": "achieves an error rate of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 209,
+ 396,
+ 237,
+ 407
+ ],
+ "score": 0.89,
+ "content": "1 . 6 8 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 237,
+ 396,
+ 506,
+ 409
+ ],
+ "score": 1.0,
+ "content": "with single-path inference, which is significantly better than that",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 406,
+ 506,
+ 420
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 406,
+ 198,
+ 420
+ ],
+ "score": 1.0,
+ "content": "of the linear classifier",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 198,
+ 407,
+ 230,
+ 418
+ ],
+ "score": 0.86,
+ "content": "( 7 . 9 1 \\% )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 230,
+ 406,
+ 506,
+ 420
+ ],
+ "score": 1.0,
+ "content": ", while engaging almost the same number of parameters (7, 956 vs.",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 417,
+ 505,
+ 431
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 417,
+ 505,
+ 431
+ ],
+ "score": 1.0,
+ "content": "7, 840) on average. To isolate the benefit of convolutions, we took one of the root-to-path CNNs on",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 105,
+ 428,
+ 506,
+ 442
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 428,
+ 506,
+ 442
+ ],
+ "score": 1.0,
+ "content": "ANT-MNIST-C and increased the number of kernels to adjust the number of parameters to the same",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 440,
+ 505,
+ 453
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 440,
+ 271,
+ 453
+ ],
+ "score": 1.0,
+ "content": "value. We observe a higher error rate of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 272,
+ 440,
+ 299,
+ 451
+ ],
+ "score": 0.89,
+ "content": "3 . 5 5 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 299,
+ 440,
+ 505,
+ 453
+ ],
+ "score": 1.0,
+ "content": ", which indicates that while convolutions are bene-",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 106,
+ 452,
+ 505,
+ 463
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 452,
+ 505,
+ 463
+ ],
+ "score": 1.0,
+ "content": "ficial, data partitioning has additional benefits in improving accuracy. This result demonstrates the",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 105,
+ 461,
+ 506,
+ 475
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 461,
+ 506,
+ 475
+ ],
+ "score": 1.0,
+ "content": "potential of ANT growth protocol for constructing performant models with lightweight inference.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 473,
+ 434,
+ 485
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 473,
+ 434,
+ 485
+ ],
+ "score": 1.0,
+ "content": "See Sec. G in the supplementary materials for the architecture of ANT-MNIST-C.",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ }
+ ],
+ "index": 30,
+ "bbox_fs": [
+ 105,
+ 384,
+ 506,
+ 485
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 490,
+ 505,
+ 600
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 489,
+ 505,
+ 502
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 489,
+ 505,
+ 502
+ ],
+ "score": 1.0,
+ "content": "CIFAR-10 object recognition: we see that variants of ANTs outperform the state-of-the-art DT",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 106,
+ 501,
+ 504,
+ 513
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 501,
+ 395,
+ 513
+ ],
+ "score": 1.0,
+ "content": "method, gcForest (Zhou & Feng, 2017) by a large margin, achieving over",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 396,
+ 501,
+ 415,
+ 511
+ ],
+ "score": 0.86,
+ "content": "90 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 415,
+ 501,
+ 504,
+ 513
+ ],
+ "score": 1.0,
+ "content": "accuracy, demonstrat-",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 512,
+ 506,
+ 525
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 512,
+ 506,
+ 525
+ ],
+ "score": 1.0,
+ "content": "ing the benefit of representation learning in tree-structured models. Secondly, with fewer number",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 523,
+ 506,
+ 535
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 523,
+ 506,
+ 535
+ ],
+ "score": 1.0,
+ "content": "of parameters in single-path inference, ANT-CIFAR-A achieves higher accuracy than CNN models",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 106,
+ 534,
+ 505,
+ 546
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 534,
+ 505,
+ 546
+ ],
+ "score": 1.0,
+ "content": "without shortcut connections (Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015)",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 544,
+ 505,
+ 557
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 544,
+ 505,
+ 557
+ ],
+ "score": 1.0,
+ "content": "that held the state-of-the-art performance at the time of publication. With simpler primitive modules",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 555,
+ 505,
+ 569
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 555,
+ 505,
+ 569
+ ],
+ "score": 1.0,
+ "content": "we learn more compact models (ANT-MNIST-B and -C) with a marginal compromise in accuracy.",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 105,
+ 566,
+ 505,
+ 579
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 566,
+ 505,
+ 579
+ ],
+ "score": 1.0,
+ "content": "In addition, initialising the parameters of transformers and routers from a pre-trained single-path",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 577,
+ 505,
+ 590
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 577,
+ 344,
+ 590
+ ],
+ "score": 1.0,
+ "content": "CNN further reduced the error rate of ANT-MNIST-A by",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 345,
+ 578,
+ 365,
+ 588
+ ],
+ "score": 0.86,
+ "content": "20 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 577,
+ 442,
+ 590
+ ],
+ "score": 1.0,
+ "content": "(see ANT-MNIST-",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 443,
+ 578,
+ 456,
+ 588
+ ],
+ "score": 0.61,
+ "content": "\\mathbf { A } ^ { * }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 457,
+ 577,
+ 505,
+ 590
+ ],
+ "score": 1.0,
+ "content": "in Tab. 3),",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 105,
+ 589,
+ 416,
+ 601
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 589,
+ 416,
+ 601
+ ],
+ "score": 1.0,
+ "content": "which indicates room for improvement in our proposed optimisation method.",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ }
+ ],
+ "index": 39.5,
+ "bbox_fs": [
+ 105,
+ 489,
+ 506,
+ 601
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 605,
+ 505,
+ 682
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 604,
+ 505,
+ 619
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 604,
+ 505,
+ 619
+ ],
+ "score": 1.0,
+ "content": "Shortcut connections (Fahlman & Lebiere, 1990) have recently lead to leaps in performance in deep",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ },
+ {
+ "bbox": [
+ 106,
+ 616,
+ 505,
+ 629
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 616,
+ 488,
+ 629
+ ],
+ "score": 1.0,
+ "content": "CNNs (He et al., 2016; Huang et al., 2017). We observe that our best network, ANT-MNIST-",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 488,
+ 617,
+ 501,
+ 627
+ ],
+ "score": 0.33,
+ "content": "A ^ { * }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 501,
+ 616,
+ 505,
+ 629
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 105,
+ 628,
+ 505,
+ 640
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 628,
+ 505,
+ 640
+ ],
+ "score": 1.0,
+ "content": "has a comparable error rate and half the parameter count (with single-path inference) to the best-",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 105,
+ 639,
+ 505,
+ 650
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 639,
+ 505,
+ 650
+ ],
+ "score": 1.0,
+ "content": "performing residual network, ResNet-110 (He et al., 2016). Densely connected networks leads to",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ },
+ {
+ "bbox": [
+ 105,
+ 649,
+ 505,
+ 662
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 649,
+ 505,
+ 662
+ ],
+ "score": 1.0,
+ "content": "substantially better accuracy, but with an order of magnitude more parameters (Huang et al., 2017).",
+ "type": "text"
+ }
+ ],
+ "index": 49
+ },
+ {
+ "bbox": [
+ 105,
+ 660,
+ 505,
+ 673
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 660,
+ 505,
+ 673
+ ],
+ "score": 1.0,
+ "content": "We expect that shortcut connections could also improve ANT performance, and leave integrating",
+ "type": "text"
+ }
+ ],
+ "index": 50
+ },
+ {
+ "bbox": [
+ 105,
+ 671,
+ 191,
+ 684
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 671,
+ 191,
+ 684
+ ],
+ "score": 1.0,
+ "content": "them to future work.",
+ "type": "text"
+ }
+ ],
+ "index": 51
+ }
+ ],
+ "index": 48,
+ "bbox_fs": [
+ 105,
+ 604,
+ 505,
+ 684
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "image",
+ "bbox": [
+ 116,
+ 62,
+ 494,
+ 196
+ ],
+ "blocks": [
+ {
+ "type": "image_body",
+ "bbox": [
+ 116,
+ 62,
+ 494,
+ 196
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 116,
+ 62,
+ 494,
+ 196
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 62,
+ 494,
+ 196
+ ],
+ "score": 0.966,
+ "type": "image",
+ "image_path": "5f73aa9624e4814beed4d4eb917fb6338b459bb521c58052eba5994febfd81f2.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 1,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 116,
+ 62,
+ 494,
+ 106.66666666666666
+ ],
+ "spans": [],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 116,
+ 106.66666666666666,
+ 494,
+ 151.33333333333331
+ ],
+ "spans": [],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 116,
+ 151.33333333333331,
+ 494,
+ 195.99999999999997
+ ],
+ "spans": [],
+ "index": 2
+ }
+ ]
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 106,
+ 200,
+ 505,
+ 244
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 200,
+ 505,
+ 212
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 200,
+ 505,
+ 212
+ ],
+ "score": 1.0,
+ "content": "Figure 2: Visualisation of class distributions (red) and path probabilities (blue) at respective nodes",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 211,
+ 506,
+ 224
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 211,
+ 506,
+ 224
+ ],
+ "score": 1.0,
+ "content": "of an example ANT (a) before and (b) after the refinement phase. (a) shows that the learned model",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 105,
+ 222,
+ 506,
+ 235
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 222,
+ 506,
+ 235
+ ],
+ "score": 1.0,
+ "content": "captures an interpretable hierarchy, grouping semantically similar images on the same branches. (b)",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 232,
+ 421,
+ 246
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 232,
+ 421,
+ 246
+ ],
+ "score": 1.0,
+ "content": "shows that the refinement phase polarises path probabilities, pruning a branch.",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ }
+ ],
+ "index": 4.5
+ }
+ ],
+ "index": 2.75
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 255,
+ 505,
+ 332
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 255,
+ 505,
+ 268
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 255,
+ 505,
+ 268
+ ],
+ "score": 1.0,
+ "content": "Ablation study: we lastly compare the classification errors of different variants of ANTs in cases",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 106,
+ 267,
+ 505,
+ 278
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 267,
+ 505,
+ 278
+ ],
+ "score": 1.0,
+ "content": "where the options for adding transformer or router modules are disabled (see Tab. 4). In this ex-",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 277,
+ 505,
+ 290
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 277,
+ 505,
+ 290
+ ],
+ "score": 1.0,
+ "content": "periment, patience levels are tuned separately for respective models. In the first case, the resulting",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 288,
+ 505,
+ 300
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 288,
+ 505,
+ 300
+ ],
+ "score": 1.0,
+ "content": "models are equivalent to SDTs (Suarez & Lutsko, 1999) or HMEs (Jordan & Jacobs, 1994) with lo- ´",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 105,
+ 299,
+ 505,
+ 312
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 299,
+ 505,
+ 312
+ ],
+ "score": 1.0,
+ "content": "cally grown architectures, while the second case is equivalent to standard CNNs, grown adaptively",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 105,
+ 309,
+ 505,
+ 322
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 309,
+ 505,
+ 322
+ ],
+ "score": 1.0,
+ "content": "layer by layer. We observe that either ablation consistently leads to higher classification errors across",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 106,
+ 321,
+ 237,
+ 333
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 321,
+ 237,
+ 333
+ ],
+ "score": 1.0,
+ "content": "different module configurations.",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ }
+ ],
+ "index": 10
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 131,
+ 377,
+ 478,
+ 452
+ ],
+ "blocks": [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 107,
+ 343,
+ 505,
+ 376
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 343,
+ 505,
+ 356
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 343,
+ 505,
+ 356
+ ],
+ "score": 1.0,
+ "content": "Table 4: Ablation study to compare the effects of different components of ANTs on classification",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 354,
+ 505,
+ 366
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 354,
+ 505,
+ 366
+ ],
+ "score": 1.0,
+ "content": "performance. “CNN” refers to the case where the ANT is grown without routers while “SDT/HME”",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 106,
+ 366,
+ 393,
+ 378
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 366,
+ 393,
+ 378
+ ],
+ "score": 1.0,
+ "content": "refers to the case where transformer modules on the edges are disabled.",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ }
+ ],
+ "index": 15
+ },
+ {
+ "type": "table_body",
+ "bbox": [
+ 131,
+ 377,
+ 478,
+ 452
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 131,
+ 377,
+ 478,
+ 452
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 131,
+ 377,
+ 478,
+ 452
+ ],
+ "score": 0.98,
+ "html": "| Algorithm1ANT Optimisation | |
| Initialise topology T and parameters O | >T is set to a root node with one solver and one transformer |
| Optimise parameters in O via gradient descent on NLL Set the root node “suboptimal" | Learning root classifier |
| while true do Freeze all parameters O | Growth of T begins |
| Pick next“suboptimal"leaf node l ∈Nteaf in the breadth-first order | |
| Add(1) router to l and train new parameters | Split data |
| Add (2) transformer to the incoming edge of l and train new parameters | Deepen transform |
| Add (1)or (2) permanently to T if validation error decreases,otherwise leaf is set to “optimal" |
| Add any new modules to O | |
| if no “suboptimal’ leaves remain then | |
| Break Unfreeze and train all parameters in O | |
",
+ "type": "table",
+ "image_path": "6313870878ad71db30f0a9e6812ac0224220b7bd947328516a4b20fa93c31d33.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 3,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 106,
+ 140,
+ 506,
+ 190.66666666666666
+ ],
+ "spans": [],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 106,
+ 190.66666666666666,
+ 506,
+ 241.33333333333331
+ ],
+ "spans": [],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 106,
+ 241.33333333333331,
+ 506,
+ 292.0
+ ],
+ "spans": [],
+ "index": 4
+ }
+ ]
+ }
+ ],
+ "index": 3
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 306,
+ 278,
+ 317
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 304,
+ 280,
+ 319
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 304,
+ 280,
+ 319
+ ],
+ "score": 1.0,
+ "content": "B ADDITIONAL RELATED WORK",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ }
+ ],
+ "index": 5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 330,
+ 504,
+ 363
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 330,
+ 505,
+ 342
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 330,
+ 505,
+ 342
+ ],
+ "score": 1.0,
+ "content": "The tree-structure of ANTs naturally performs conditional computation. We can also view the pro-",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 340,
+ 506,
+ 353
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 340,
+ 506,
+ 353
+ ],
+ "score": 1.0,
+ "content": "posed tree-building algorithm as a form of neural architecture search. Here we provide surveys of",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 106,
+ 352,
+ 266,
+ 363
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 352,
+ 266,
+ 363
+ ],
+ "score": 1.0,
+ "content": "these areas and their relations to ANTs.",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ }
+ ],
+ "index": 7
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 369,
+ 505,
+ 511
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 368,
+ 506,
+ 382
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 368,
+ 506,
+ 382
+ ],
+ "score": 1.0,
+ "content": "Conditional Computation: In NNs, computation of each sample engages every parameter of the",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 380,
+ 506,
+ 393
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 380,
+ 506,
+ 393
+ ],
+ "score": 1.0,
+ "content": "model. In contrast, DTs route each sample to a single path, only activating a small fraction of the",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 105,
+ 390,
+ 505,
+ 403
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 390,
+ 505,
+ 403
+ ],
+ "score": 1.0,
+ "content": "model. Bengio Bengio (2013) advocated for this notion of conditional computation to be integrated",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 105,
+ 402,
+ 505,
+ 415
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 402,
+ 505,
+ 415
+ ],
+ "score": 1.0,
+ "content": "into NNs, and this has become a topic of growing interest. Rationales for using conditional com-",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 413,
+ 505,
+ 425
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 413,
+ 505,
+ 425
+ ],
+ "score": 1.0,
+ "content": "putation ranges from attaining better capacity-to-computation ratio (Bengio et al., 2013; Davis &",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 424,
+ 506,
+ 437
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 424,
+ 506,
+ 437
+ ],
+ "score": 1.0,
+ "content": "Arel, 2013; Bengio et al., 2015; Shazeer et al., 2017) to adapting the required computation to the",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 434,
+ 505,
+ 448
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 434,
+ 505,
+ 448
+ ],
+ "score": 1.0,
+ "content": "difficulty of the input and task (Bengio et al., 2015; Almahairi et al., 2016; Teerapittayanon et al.,",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 445,
+ 505,
+ 459
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 445,
+ 505,
+ 459
+ ],
+ "score": 1.0,
+ "content": "2016; Graves, 2016; Figurnov et al., 2017; Veit & Belongie, 2017). We view the growth procedure",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 456,
+ 505,
+ 469
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 456,
+ 505,
+ 469
+ ],
+ "score": 1.0,
+ "content": "of ANTs as having a similar motivation with the latter—processing raw pixels is suboptimal for",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 105,
+ 467,
+ 505,
+ 480
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 467,
+ 505,
+ 480
+ ],
+ "score": 1.0,
+ "content": "computer vision tasks, but we have no reason to believe that the hundreds of convolutional layers in",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 478,
+ 505,
+ 491
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 478,
+ 505,
+ 491
+ ],
+ "score": 1.0,
+ "content": "current state-of-the-art architectures (He et al., 2016; Huang et al., 2017) are necessary either. Grow-",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 106,
+ 488,
+ 505,
+ 501
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 488,
+ 505,
+ 501
+ ],
+ "score": 1.0,
+ "content": "ing ANTs adapts the architecture complexity to the dataset as a whole, with routers determining the",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 106,
+ 500,
+ 280,
+ 513
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 500,
+ 280,
+ 513
+ ],
+ "score": 1.0,
+ "content": "computation needed on a per-sample basis.",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ }
+ ],
+ "index": 15
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 517,
+ 505,
+ 638
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 516,
+ 506,
+ 530
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 516,
+ 506,
+ 530
+ ],
+ "score": 1.0,
+ "content": "Neural Architecture Search: The ANT growing procedure is related to the progressive growing of",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 527,
+ 506,
+ 541
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 527,
+ 506,
+ 541
+ ],
+ "score": 1.0,
+ "content": "NNs (Fahlman & Lebiere, 1990; Hinton et al., 2006; Xiao et al., 2014; Chen et al., 2016; Srivastava",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 539,
+ 506,
+ 551
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 539,
+ 506,
+ 551
+ ],
+ "score": 1.0,
+ "content": "et al., 2015; Lee et al., 2017; Cai et al., 2018; ˙Irsoy & Alpaydın, 2018), or more broadly, the field of",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 104,
+ 549,
+ 505,
+ 564
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 549,
+ 505,
+ 564
+ ],
+ "score": 1.0,
+ "content": "neural architecture search (Zoph & Le, 2017; Brock et al., 2017; Cortes et al., 2017). This approach,",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 561,
+ 505,
+ 574
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 561,
+ 505,
+ 574
+ ],
+ "score": 1.0,
+ "content": "mainly via greedy layerwise training, has historically been one solution to optimising NNs (Fahlman",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 106,
+ 572,
+ 505,
+ 585
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 572,
+ 505,
+ 585
+ ],
+ "score": 1.0,
+ "content": "& Lebiere, 1990; Hinton et al., 2006). However, nowadays it is possible to train NNs in an end-to-",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 582,
+ 506,
+ 596
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 582,
+ 506,
+ 596
+ ],
+ "score": 1.0,
+ "content": "end fashion. One area which still uses progressive growing is lifelong learning, in which a model",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 594,
+ 505,
+ 606
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 594,
+ 505,
+ 606
+ ],
+ "score": 1.0,
+ "content": "needs to adapt to new tasks while retaining performance on previous ones (Xiao et al., 2014; Lee",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 106,
+ 605,
+ 505,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 605,
+ 505,
+ 617
+ ],
+ "score": 1.0,
+ "content": "et al., 2017). In particular, (Xiao et al., 2014) introduced a method that grows a tree-shaped network",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 616,
+ 506,
+ 629
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 616,
+ 506,
+ 629
+ ],
+ "score": 1.0,
+ "content": "to accommodate new classes. However, their method never transforms the data before passing it to",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 626,
+ 433,
+ 639
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 626,
+ 433,
+ 639
+ ],
+ "score": 1.0,
+ "content": "the children classifiers, and hence never benefit from the parent’s representations.",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ }
+ ],
+ "index": 27
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 643,
+ 504,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 643,
+ 505,
+ 656
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 643,
+ 505,
+ 656
+ ],
+ "score": 1.0,
+ "content": "Whilst we learn the architecture of an ANT in a greedy, layerwise fashion, several other meth-",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 655,
+ 504,
+ 667
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 655,
+ 504,
+ 667
+ ],
+ "score": 1.0,
+ "content": "ods search globally. Based on a variety of techniques, including evolutionary algorithms (Stanley",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "score": 1.0,
+ "content": "& Miikkulainen, 2002; Real et al., 2017), reinforcement learning (Zoph & Le, 2017), sequential",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 677,
+ 504,
+ 689
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 677,
+ 504,
+ 689
+ ],
+ "score": 1.0,
+ "content": "optimisation (Liu et al., 2017) and boosting (Cortes et al., 2017), these methods find extremely",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "score": 1.0,
+ "content": "high-performance yet complex architectures. In our case, we constrain the search space to sim-",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 698,
+ 506,
+ 712
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 698,
+ 506,
+ 712
+ ],
+ "score": 1.0,
+ "content": "ple tree-structured NNs, retaining desirable properties of DTs such as data-dependent computation",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 105,
+ 710,
+ 506,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 710,
+ 506,
+ 722
+ ],
+ "score": 1.0,
+ "content": "and interpretable structures, while keeping the space and time requirement of architecture search",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 721,
+ 330,
+ 733
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 721,
+ 330,
+ 733
+ ],
+ "score": 1.0,
+ "content": "tractable thanks to the locality of our growth procedure.",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ }
+ ],
+ "index": 36.5
+ }
+ ],
+ "page_idx": 14,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 308,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 25,
+ 309,
+ 39
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 25,
+ 309,
+ 39
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 301,
+ 751,
+ 311,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 312,
+ 764
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 312,
+ 764
+ ],
+ "score": 1.0,
+ "content": "",
+ "type": "text",
+ "height": 14,
+ "width": 13
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "title",
+ "bbox": [
+ 126,
+ 78,
+ 485,
+ 98
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 124,
+ 77,
+ 487,
+ 100
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 124,
+ 77,
+ 487,
+ 100
+ ],
+ "score": 1.0,
+ "content": "Adaptive Neural Trees: Supplementary Material",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ }
+ ],
+ "index": 0
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 112,
+ 248,
+ 125
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 112,
+ 249,
+ 127
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 112,
+ 249,
+ 127
+ ],
+ "score": 1.0,
+ "content": "A TRAINING ALGORITHM",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 1,
+ "bbox_fs": [
+ 106,
+ 112,
+ 249,
+ 127
+ ]
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 106,
+ 140,
+ 506,
+ 292
+ ],
+ "blocks": [
+ {
+ "type": "table_body",
+ "bbox": [
+ 106,
+ 140,
+ 506,
+ 292
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 140,
+ 506,
+ 292
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 140,
+ 506,
+ 292
+ ],
+ "score": 0.958,
+ "html": "| Algorithm1ANT Optimisation | |
| Initialise topology T and parameters O | >T is set to a root node with one solver and one transformer |
| Optimise parameters in O via gradient descent on NLL Set the root node “suboptimal" | Learning root classifier |
| while true do Freeze all parameters O | Growth of T begins |
| Pick next“suboptimal"leaf node l ∈Nteaf in the breadth-first order | |
| Add(1) router to l and train new parameters | Split data |
| Add (2) transformer to the incoming edge of l and train new parameters | Deepen transform |
| Add (1)or (2) permanently to T if validation error decreases,otherwise leaf is set to “optimal" |
| Add any new modules to O | |
| if no “suboptimal’ leaves remain then | |
| Break Unfreeze and train all parameters in O | |
",
+ "type": "table",
+ "image_path": "6313870878ad71db30f0a9e6812ac0224220b7bd947328516a4b20fa93c31d33.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 3,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 106,
+ 140,
+ 506,
+ 190.66666666666666
+ ],
+ "spans": [],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 106,
+ 190.66666666666666,
+ 506,
+ 241.33333333333331
+ ],
+ "spans": [],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 106,
+ 241.33333333333331,
+ 506,
+ 292.0
+ ],
+ "spans": [],
+ "index": 4
+ }
+ ]
+ }
+ ],
+ "index": 3
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 306,
+ 278,
+ 317
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 304,
+ 280,
+ 319
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 304,
+ 280,
+ 319
+ ],
+ "score": 1.0,
+ "content": "B ADDITIONAL RELATED WORK",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ }
+ ],
+ "index": 5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 330,
+ 504,
+ 363
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 330,
+ 505,
+ 342
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 330,
+ 505,
+ 342
+ ],
+ "score": 1.0,
+ "content": "The tree-structure of ANTs naturally performs conditional computation. We can also view the pro-",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 340,
+ 506,
+ 353
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 340,
+ 506,
+ 353
+ ],
+ "score": 1.0,
+ "content": "posed tree-building algorithm as a form of neural architecture search. Here we provide surveys of",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 106,
+ 352,
+ 266,
+ 363
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 352,
+ 266,
+ 363
+ ],
+ "score": 1.0,
+ "content": "these areas and their relations to ANTs.",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ }
+ ],
+ "index": 7,
+ "bbox_fs": [
+ 105,
+ 330,
+ 506,
+ 363
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 369,
+ 505,
+ 511
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 368,
+ 506,
+ 382
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 368,
+ 506,
+ 382
+ ],
+ "score": 1.0,
+ "content": "Conditional Computation: In NNs, computation of each sample engages every parameter of the",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 380,
+ 506,
+ 393
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 380,
+ 506,
+ 393
+ ],
+ "score": 1.0,
+ "content": "model. In contrast, DTs route each sample to a single path, only activating a small fraction of the",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 105,
+ 390,
+ 505,
+ 403
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 390,
+ 505,
+ 403
+ ],
+ "score": 1.0,
+ "content": "model. Bengio Bengio (2013) advocated for this notion of conditional computation to be integrated",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 105,
+ 402,
+ 505,
+ 415
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 402,
+ 505,
+ 415
+ ],
+ "score": 1.0,
+ "content": "into NNs, and this has become a topic of growing interest. Rationales for using conditional com-",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 413,
+ 505,
+ 425
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 413,
+ 505,
+ 425
+ ],
+ "score": 1.0,
+ "content": "putation ranges from attaining better capacity-to-computation ratio (Bengio et al., 2013; Davis &",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 424,
+ 506,
+ 437
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 424,
+ 506,
+ 437
+ ],
+ "score": 1.0,
+ "content": "Arel, 2013; Bengio et al., 2015; Shazeer et al., 2017) to adapting the required computation to the",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 434,
+ 505,
+ 448
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 434,
+ 505,
+ 448
+ ],
+ "score": 1.0,
+ "content": "difficulty of the input and task (Bengio et al., 2015; Almahairi et al., 2016; Teerapittayanon et al.,",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 445,
+ 505,
+ 459
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 445,
+ 505,
+ 459
+ ],
+ "score": 1.0,
+ "content": "2016; Graves, 2016; Figurnov et al., 2017; Veit & Belongie, 2017). We view the growth procedure",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 456,
+ 505,
+ 469
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 456,
+ 505,
+ 469
+ ],
+ "score": 1.0,
+ "content": "of ANTs as having a similar motivation with the latter—processing raw pixels is suboptimal for",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 105,
+ 467,
+ 505,
+ 480
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 467,
+ 505,
+ 480
+ ],
+ "score": 1.0,
+ "content": "computer vision tasks, but we have no reason to believe that the hundreds of convolutional layers in",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 478,
+ 505,
+ 491
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 478,
+ 505,
+ 491
+ ],
+ "score": 1.0,
+ "content": "current state-of-the-art architectures (He et al., 2016; Huang et al., 2017) are necessary either. Grow-",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 106,
+ 488,
+ 505,
+ 501
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 488,
+ 505,
+ 501
+ ],
+ "score": 1.0,
+ "content": "ing ANTs adapts the architecture complexity to the dataset as a whole, with routers determining the",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 106,
+ 500,
+ 280,
+ 513
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 500,
+ 280,
+ 513
+ ],
+ "score": 1.0,
+ "content": "computation needed on a per-sample basis.",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ }
+ ],
+ "index": 15,
+ "bbox_fs": [
+ 105,
+ 368,
+ 506,
+ 513
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 517,
+ 505,
+ 638
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 516,
+ 506,
+ 530
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 516,
+ 506,
+ 530
+ ],
+ "score": 1.0,
+ "content": "Neural Architecture Search: The ANT growing procedure is related to the progressive growing of",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 527,
+ 506,
+ 541
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 527,
+ 506,
+ 541
+ ],
+ "score": 1.0,
+ "content": "NNs (Fahlman & Lebiere, 1990; Hinton et al., 2006; Xiao et al., 2014; Chen et al., 2016; Srivastava",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 539,
+ 506,
+ 551
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 539,
+ 506,
+ 551
+ ],
+ "score": 1.0,
+ "content": "et al., 2015; Lee et al., 2017; Cai et al., 2018; ˙Irsoy & Alpaydın, 2018), or more broadly, the field of",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 104,
+ 549,
+ 505,
+ 564
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 549,
+ 505,
+ 564
+ ],
+ "score": 1.0,
+ "content": "neural architecture search (Zoph & Le, 2017; Brock et al., 2017; Cortes et al., 2017). This approach,",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 561,
+ 505,
+ 574
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 561,
+ 505,
+ 574
+ ],
+ "score": 1.0,
+ "content": "mainly via greedy layerwise training, has historically been one solution to optimising NNs (Fahlman",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 106,
+ 572,
+ 505,
+ 585
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 572,
+ 505,
+ 585
+ ],
+ "score": 1.0,
+ "content": "& Lebiere, 1990; Hinton et al., 2006). However, nowadays it is possible to train NNs in an end-to-",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 582,
+ 506,
+ 596
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 582,
+ 506,
+ 596
+ ],
+ "score": 1.0,
+ "content": "end fashion. One area which still uses progressive growing is lifelong learning, in which a model",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 594,
+ 505,
+ 606
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 594,
+ 505,
+ 606
+ ],
+ "score": 1.0,
+ "content": "needs to adapt to new tasks while retaining performance on previous ones (Xiao et al., 2014; Lee",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 106,
+ 605,
+ 505,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 605,
+ 505,
+ 617
+ ],
+ "score": 1.0,
+ "content": "et al., 2017). In particular, (Xiao et al., 2014) introduced a method that grows a tree-shaped network",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 616,
+ 506,
+ 629
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 616,
+ 506,
+ 629
+ ],
+ "score": 1.0,
+ "content": "to accommodate new classes. However, their method never transforms the data before passing it to",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 626,
+ 433,
+ 639
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 626,
+ 433,
+ 639
+ ],
+ "score": 1.0,
+ "content": "the children classifiers, and hence never benefit from the parent’s representations.",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ }
+ ],
+ "index": 27,
+ "bbox_fs": [
+ 104,
+ 516,
+ 506,
+ 639
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 643,
+ 504,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 643,
+ 505,
+ 656
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 643,
+ 505,
+ 656
+ ],
+ "score": 1.0,
+ "content": "Whilst we learn the architecture of an ANT in a greedy, layerwise fashion, several other meth-",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 655,
+ 504,
+ 667
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 655,
+ 504,
+ 667
+ ],
+ "score": 1.0,
+ "content": "ods search globally. Based on a variety of techniques, including evolutionary algorithms (Stanley",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "score": 1.0,
+ "content": "& Miikkulainen, 2002; Real et al., 2017), reinforcement learning (Zoph & Le, 2017), sequential",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 677,
+ 504,
+ 689
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 677,
+ 504,
+ 689
+ ],
+ "score": 1.0,
+ "content": "optimisation (Liu et al., 2017) and boosting (Cortes et al., 2017), these methods find extremely",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "score": 1.0,
+ "content": "high-performance yet complex architectures. In our case, we constrain the search space to sim-",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 698,
+ 506,
+ 712
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 698,
+ 506,
+ 712
+ ],
+ "score": 1.0,
+ "content": "ple tree-structured NNs, retaining desirable properties of DTs such as data-dependent computation",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 105,
+ 710,
+ 506,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 710,
+ 506,
+ 722
+ ],
+ "score": 1.0,
+ "content": "and interpretable structures, while keeping the space and time requirement of architecture search",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 721,
+ 330,
+ 733
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 721,
+ 330,
+ 733
+ ],
+ "score": 1.0,
+ "content": "tractable thanks to the locality of our growth procedure.",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ }
+ ],
+ "index": 36.5,
+ "bbox_fs": [
+ 105,
+ 643,
+ 506,
+ 733
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 81,
+ 227,
+ 93
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 80,
+ 229,
+ 97
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 80,
+ 229,
+ 97
+ ],
+ "score": 1.0,
+ "content": "C TRAINING DETAILS",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ }
+ ],
+ "index": 0
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 105,
+ 505,
+ 205
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 106,
+ 505,
+ 119
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 106,
+ 505,
+ 119
+ ],
+ "score": 1.0,
+ "content": "We perform our experiments on the MNIST digit classification task (LeCun et al., 1998) and CIFAR-",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 106,
+ 116,
+ 505,
+ 130
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 116,
+ 505,
+ 130
+ ],
+ "score": 1.0,
+ "content": "10 object recognition task (Krizhevsky & Hinton, 2009). The MNIST dataset consists of 60, 000",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 105,
+ 128,
+ 506,
+ 141
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 128,
+ 158,
+ 141
+ ],
+ "score": 1.0,
+ "content": "training and",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 158,
+ 128,
+ 189,
+ 139
+ ],
+ "score": 0.27,
+ "content": "1 0 , 0 0 0",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 189,
+ 128,
+ 330,
+ 141
+ ],
+ "score": 1.0,
+ "content": "testing examples, all of which are",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 330,
+ 128,
+ 365,
+ 139
+ ],
+ "score": 0.9,
+ "content": "2 8 \\times 2 8",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 366,
+ 128,
+ 506,
+ 141
+ ],
+ "score": 1.0,
+ "content": "grayscale images of digits from 0",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 139,
+ 506,
+ 152
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 139,
+ 506,
+ 152
+ ],
+ "score": 1.0,
+ "content": "to 9 (10 classes). The dataset is preprocessed by subtracting the mean, but no data augmentation is",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 105,
+ 150,
+ 506,
+ 163
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 150,
+ 506,
+ 163
+ ],
+ "score": 1.0,
+ "content": "used. The CIFAR-10 dataset consists of 50, 000 training and 10, 000 testing examples, all of which",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 160,
+ 505,
+ 174
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 160,
+ 122,
+ 174
+ ],
+ "score": 1.0,
+ "content": "are",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 122,
+ 161,
+ 157,
+ 172
+ ],
+ "score": 0.9,
+ "content": "3 2 \\times 3 2",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 158,
+ 160,
+ 505,
+ 174
+ ],
+ "score": 1.0,
+ "content": "coloured natural images drawn from 10 classes. We adopt an augmentation scheme",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 106,
+ 172,
+ 505,
+ 184
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 172,
+ 505,
+ 184
+ ],
+ "score": 1.0,
+ "content": "widely used in the literature (Goodfellow et al., 2013; Lin et al., 2014; Springenberg et al., 2015; He",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 182,
+ 505,
+ 196
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 182,
+ 505,
+ 196
+ ],
+ "score": 1.0,
+ "content": "et al., 2016; Huang et al., 2017) where images are zero-padded with 4 pixels on each side, randomly",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 106,
+ 194,
+ 248,
+ 206
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 194,
+ 248,
+ 206
+ ],
+ "score": 1.0,
+ "content": "cropped and horizontally mirrored.",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ }
+ ],
+ "index": 5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 210,
+ 505,
+ 255
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 210,
+ 505,
+ 222
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 211,
+ 227,
+ 222
+ ],
+ "score": 1.0,
+ "content": "For both datasets, we hold out",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 228,
+ 210,
+ 247,
+ 221
+ ],
+ "score": 0.88,
+ "content": "1 0 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 248,
+ 211,
+ 505,
+ 222
+ ],
+ "score": 1.0,
+ "content": "of training images as a validation set. The best model is selected",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 105,
+ 222,
+ 505,
+ 234
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 222,
+ 505,
+ 234
+ ],
+ "score": 1.0,
+ "content": "based on the validation accuracy over the course of ANT training, spanning both the growth phase",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 106,
+ 232,
+ 505,
+ 245
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 232,
+ 505,
+ 245
+ ],
+ "score": 1.0,
+ "content": "and the refinement phase, and its accuracy on the testing set is reported. The hyperparameters are",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 244,
+ 334,
+ 256
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 244,
+ 334,
+ 256
+ ],
+ "score": 1.0,
+ "content": "also selected based on the validation performance alone.",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ }
+ ],
+ "index": 11.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 260,
+ 505,
+ 338
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 104,
+ 259,
+ 505,
+ 274
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 259,
+ 505,
+ 274
+ ],
+ "score": 1.0,
+ "content": "Both the growth and refinement phase of ANTs takes up to 2 hours on a single Titan X GPU on",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 271,
+ 505,
+ 285
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 271,
+ 505,
+ 285
+ ],
+ "score": 1.0,
+ "content": "both datasets. For all the experiments in this paper, we employ the following training protocol:",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 282,
+ 505,
+ 295
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 282,
+ 464,
+ 295
+ ],
+ "score": 1.0,
+ "content": "(1) optimize parameters using Adam (Kingma & Ba, 2014) with initial learning rate of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 464,
+ 282,
+ 486,
+ 293
+ ],
+ "score": 0.9,
+ "content": "\\bar { 1 0 } ^ { - 3 }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 487,
+ 282,
+ 505,
+ 295
+ ],
+ "score": 1.0,
+ "content": "and",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 107,
+ 292,
+ 505,
+ 307
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 293,
+ 172,
+ 306
+ ],
+ "score": 0.88,
+ "content": "\\beta = \\left. 0 . 9 , 0 . 9 \\bar { 9 } 9 \\right.",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 173,
+ 292,
+ 505,
+ 307
+ ],
+ "score": 1.0,
+ "content": ", with minibatches of size 512; (2) during the growth phase, employ early stopping",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 105,
+ 303,
+ 505,
+ 318
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 303,
+ 505,
+ 318
+ ],
+ "score": 1.0,
+ "content": "with a patience of 5, that is, training is stopped after 5 epochs of no progress on the validation set;",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 315,
+ 505,
+ 329
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 315,
+ 505,
+ 329
+ ],
+ "score": 1.0,
+ "content": "(3) during the refinement phase, train for 100 epochs for MNIST and 200 epochs for CIFAR-10,",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 326,
+ 383,
+ 339
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 326,
+ 383,
+ 339
+ ],
+ "score": 1.0,
+ "content": "decreasing the learning rate by a factor of 10 at every multiple of 50.",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ }
+ ],
+ "index": 17
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 353,
+ 216,
+ 367
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 352,
+ 217,
+ 369
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 352,
+ 217,
+ 369
+ ],
+ "score": 1.0,
+ "content": "D TRAINING TIMES",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ }
+ ],
+ "index": 21
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 378,
+ 505,
+ 434
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 378,
+ 505,
+ 391
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 378,
+ 505,
+ 391
+ ],
+ "score": 1.0,
+ "content": "Tab. 5 summarises the time taken on a single Titan X GPU for the growth phase and refinement phase",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 106,
+ 390,
+ 504,
+ 402
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 390,
+ 504,
+ 402
+ ],
+ "score": 1.0,
+ "content": "of various ANTs, and compares against the training time of All-CNN (Springenberg et al., 2015).",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 400,
+ 506,
+ 414
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 400,
+ 506,
+ 414
+ ],
+ "score": 1.0,
+ "content": "Local optimisation during the growth phase means that the gradient computation is constrained to",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 411,
+ 505,
+ 425
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 411,
+ 505,
+ 425
+ ],
+ "score": 1.0,
+ "content": "the newly added component of the graph, allowing us to grow a good candidate model under 2 hours",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 423,
+ 177,
+ 435
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 423,
+ 177,
+ 435
+ ],
+ "score": 1.0,
+ "content": "on a single GPU.",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ }
+ ],
+ "index": 24
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 175,
+ 486,
+ 436,
+ 556
+ ],
+ "blocks": [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 106,
+ 438,
+ 504,
+ 472
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 438,
+ 505,
+ 452
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 438,
+ 505,
+ 452
+ ],
+ "score": 1.0,
+ "content": "Table 5: Training time comparison. Time and number of epochs taken for the growth and refinement",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 449,
+ 505,
+ 463
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 449,
+ 505,
+ 463
+ ],
+ "score": 1.0,
+ "content": "phase are shown. along with the time required to train the baseline, All-CNN (Springenberg et al.,",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 104,
+ 458,
+ 137,
+ 475
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 458,
+ 137,
+ 475
+ ],
+ "score": 1.0,
+ "content": "2015).",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ }
+ ],
+ "index": 28
+ },
+ {
+ "type": "table_body",
+ "bbox": [
+ 175,
+ 486,
+ 436,
+ 556
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 175,
+ 486,
+ 436,
+ 556
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 175,
+ 486,
+ 436,
+ 556
+ ],
+ "score": 0.979,
+ "html": " | Method Linear classifier | Error % (Full) | Error % (Path) | Params. (Full) | Params. (Path) | Ensemble Size |
| JSINN | Random Forests (Breiman, 2001) Compact Multi-Class Boosted Trees (Ponomareva et al., 2017) Alternating Decision Forest (Schulter et al., 2013) Neural Decision Tree (Xiao,2017) ANT-MNIST-C MLP with 2 hidden layers (Simard et al., 2003) LeNet-5† (LeCun et al.,1998) | 7.91 3.21 | N/A 3.21 | 7,840 | N/A 1 | 1 200 |
| 2.88 2.71 | 1 2.71 | 1 1 | 1 | 100 |
| 2.10 1.62 | 1.68 N/A | 1 1,773,130 | 1 502,170 7,956 | 20 1 |
| 39,670 | |
| 1.40 0.82 | 1,275,200 431,000 | 1 N/A 1 1 |
| ANT-MNIST-A | gcForest (Zhou & Feng,2017) ANT-MNIST-B Neural Decision Forest (Kontschieder et al., 2015) | 0.74 0.72 | N/A 0.74 0.73 | 1 | N/A 1 | 500 |
| 0.70 | 1 | 76,703 544,600 | 50,653 463,180 | 1 10 |
|
| 0.64 | 0.69 | 100,596 | 84,935 | 1 |
| CapsNet (Sabour et al., 2017) | 0.25 | 1 | 8.2M | N/A | 1 |
| Compact Multi-ClassBoosted Trees (Ponomareva et al.,2017) Random Forests (Breiman,2001) | 52.31 50.17 | 1 50.17 | 1 1 | 1 | 100 |
| CEIPAII1 | gcForest (Zhou& Feng,2017) | 38.22 | 38.22 | 1 | 1 | 2000 500 |
| 1 |
| MaxOut (Goodfellow et al., 2013) ANT-CIFAR10-C | 9.38 9.31 | N/A 9.34 | 6M 0.7M | N/A 0.5M | 1 1 |
| ANT-CIFAR10-B Network in Network (Lin et al.,2014) | 9.15 8.81 | 9.18 N/A | 0.9M 1M | 0.6M N/A | 1 1 |
| All-CNN+(Springenberg et al.,2015) ANT-CIFAR10-A | 8.71 | N/A | 1.4M | N/A | 1 |
| ANT-CIFAR10-A* | 8.31 6.72 | 8.32 6.74 | 1.4M 1.3M | 1.0M 0.8M | 1 |
| ResNet-110 (He et al., 2016) | 6.43 | N/A | 1.7M | N/A | 1 |
| DenseNet-BC (k=40) (Huang et al.,2017) | 3.46 | N/A | 25.6M | N/A | 1 1 |
"
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1467,
+ 1404,
+ 1467,
+ 1404,
+ 1774,
+ 298,
+ 1774
+ ],
+ "score": 0.983
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1206,
+ 1404,
+ 1206,
+ 1404,
+ 1453,
+ 298,
+ 1453
+ ],
+ "score": 0.98
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1788,
+ 1403,
+ 1788,
+ 1403,
+ 2034,
+ 298,
+ 2034
+ ],
+ "score": 0.979
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 298,
+ 1144,
+ 878,
+ 1144,
+ 878,
+ 1174,
+ 298,
+ 1174
+ ],
+ "score": 0.918
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 298,
+ 76,
+ 857,
+ 76,
+ 857,
+ 104,
+ 298,
+ 104
+ ],
+ "score": 0.886
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 174,
+ 1404,
+ 174,
+ 1404,
+ 422,
+ 297,
+ 422
+ ],
+ "score": 0.877
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 842,
+ 2088,
+ 858,
+ 2088,
+ 858,
+ 2111,
+ 842,
+ 2111
+ ],
+ "score": 0.644
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 842,
+ 2088,
+ 859,
+ 2088,
+ 859,
+ 2111,
+ 842,
+ 2111
+ ],
+ "score": 0.271
+ },
+ {
+ "category_id": 6,
+ "poly": [
+ 297,
+ 174,
+ 1404,
+ 174,
+ 1404,
+ 422,
+ 297,
+ 422
+ ],
+ "score": 0.171
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 829,
+ 1972,
+ 905,
+ 1972,
+ 905,
+ 2002,
+ 829,
+ 2002
+ ],
+ "score": 0.89,
+ "latex": "0 . 0 6 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 461,
+ 1592,
+ 527,
+ 1592,
+ 527,
+ 1620,
+ 461,
+ 1620
+ ],
+ "score": 0.89,
+ "latex": "2 \\times 2"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 750,
+ 1681,
+ 805,
+ 1681,
+ 805,
+ 1711,
+ 750,
+ 1711
+ ],
+ "score": 0.88,
+ "latex": "1 0 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1316,
+ 1592,
+ 1335,
+ 1592,
+ 1335,
+ 1618,
+ 1316,
+ 1618
+ ],
+ "score": 0.78,
+ "latex": "d"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 983,
+ 1592,
+ 1001,
+ 1592,
+ 1001,
+ 1618,
+ 983,
+ 1618
+ ],
+ "score": 0.76,
+ "latex": "d"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 428,
+ 676,
+ 450,
+ 676,
+ 450,
+ 700,
+ 428,
+ 700
+ ],
+ "score": 0.61,
+ "latex": "{ \\cdot } 5 ^ { \\dagger }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 490,
+ 1059,
+ 540,
+ 1059,
+ 540,
+ 1080,
+ 490,
+ 1080
+ ],
+ "score": 0.38,
+ "latex": "( \\mathrm { k } { = } 4 0 )"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1142.0,
+ 881.0,
+ 1142.0,
+ 881.0,
+ 1178.0,
+ 294.0,
+ 1178.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 298.0,
+ 73.0,
+ 858.0,
+ 73.0,
+ 858.0,
+ 108.0,
+ 298.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 840.0,
+ 2086.0,
+ 860.0,
+ 2086.0,
+ 860.0,
+ 2119.0,
+ 840.0,
+ 2119.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 840.0,
+ 2087.0,
+ 861.0,
+ 2087.0,
+ 861.0,
+ 2119.0,
+ 840.0,
+ 2119.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 176.0,
+ 1404.0,
+ 176.0,
+ 1404.0,
+ 210.0,
+ 295.0,
+ 210.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 205.0,
+ 1405.0,
+ 205.0,
+ 1405.0,
+ 241.0,
+ 295.0,
+ 241.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 238.0,
+ 1402.0,
+ 238.0,
+ 1402.0,
+ 271.0,
+ 295.0,
+ 271.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 268.0,
+ 1406.0,
+ 268.0,
+ 1406.0,
+ 304.0,
+ 291.0,
+ 304.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 299.0,
+ 1405.0,
+ 299.0,
+ 1405.0,
+ 333.0,
+ 295.0,
+ 333.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 328.0,
+ 1405.0,
+ 328.0,
+ 1405.0,
+ 363.0,
+ 292.0,
+ 363.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 361.0,
+ 1405.0,
+ 361.0,
+ 1405.0,
+ 395.0,
+ 295.0,
+ 395.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 391.0,
+ 730.0,
+ 391.0,
+ 730.0,
+ 425.0,
+ 295.0,
+ 425.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1469.0,
+ 1402.0,
+ 1469.0,
+ 1402.0,
+ 1501.0,
+ 296.0,
+ 1501.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1500.0,
+ 1404.0,
+ 1500.0,
+ 1404.0,
+ 1535.0,
+ 294.0,
+ 1535.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1528.0,
+ 1405.0,
+ 1528.0,
+ 1405.0,
+ 1565.0,
+ 293.0,
+ 1565.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1559.0,
+ 1404.0,
+ 1559.0,
+ 1404.0,
+ 1595.0,
+ 294.0,
+ 1595.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1590.0,
+ 460.0,
+ 1590.0,
+ 460.0,
+ 1626.0,
+ 296.0,
+ 1626.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 528.0,
+ 1590.0,
+ 982.0,
+ 1590.0,
+ 982.0,
+ 1626.0,
+ 528.0,
+ 1626.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1002.0,
+ 1590.0,
+ 1315.0,
+ 1590.0,
+ 1315.0,
+ 1626.0,
+ 1002.0,
+ 1626.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1336.0,
+ 1590.0,
+ 1405.0,
+ 1590.0,
+ 1405.0,
+ 1626.0,
+ 1336.0,
+ 1626.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1622.0,
+ 1402.0,
+ 1622.0,
+ 1402.0,
+ 1654.0,
+ 296.0,
+ 1654.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1647.0,
+ 1406.0,
+ 1647.0,
+ 1406.0,
+ 1691.0,
+ 292.0,
+ 1691.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1682.0,
+ 749.0,
+ 1682.0,
+ 749.0,
+ 1717.0,
+ 293.0,
+ 1717.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 806.0,
+ 1682.0,
+ 1405.0,
+ 1682.0,
+ 1405.0,
+ 1717.0,
+ 806.0,
+ 1717.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1712.0,
+ 1406.0,
+ 1712.0,
+ 1406.0,
+ 1748.0,
+ 294.0,
+ 1748.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1744.0,
+ 573.0,
+ 1744.0,
+ 573.0,
+ 1777.0,
+ 293.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1207.0,
+ 1405.0,
+ 1207.0,
+ 1405.0,
+ 1243.0,
+ 295.0,
+ 1243.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1239.0,
+ 1404.0,
+ 1239.0,
+ 1404.0,
+ 1274.0,
+ 293.0,
+ 1274.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1268.0,
+ 1404.0,
+ 1268.0,
+ 1404.0,
+ 1305.0,
+ 295.0,
+ 1305.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1299.0,
+ 1402.0,
+ 1299.0,
+ 1402.0,
+ 1333.0,
+ 296.0,
+ 1333.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1331.0,
+ 1404.0,
+ 1331.0,
+ 1404.0,
+ 1364.0,
+ 294.0,
+ 1364.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1360.0,
+ 1404.0,
+ 1360.0,
+ 1404.0,
+ 1396.0,
+ 293.0,
+ 1396.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1391.0,
+ 1404.0,
+ 1391.0,
+ 1404.0,
+ 1427.0,
+ 295.0,
+ 1427.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1421.0,
+ 1404.0,
+ 1421.0,
+ 1404.0,
+ 1457.0,
+ 293.0,
+ 1457.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1790.0,
+ 1403.0,
+ 1790.0,
+ 1403.0,
+ 1823.0,
+ 296.0,
+ 1823.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1821.0,
+ 1405.0,
+ 1821.0,
+ 1405.0,
+ 1855.0,
+ 294.0,
+ 1855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1850.0,
+ 1404.0,
+ 1850.0,
+ 1404.0,
+ 1886.0,
+ 293.0,
+ 1886.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1876.0,
+ 1405.0,
+ 1876.0,
+ 1405.0,
+ 1919.0,
+ 292.0,
+ 1919.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1911.0,
+ 1407.0,
+ 1911.0,
+ 1407.0,
+ 1948.0,
+ 293.0,
+ 1948.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1942.0,
+ 1404.0,
+ 1942.0,
+ 1404.0,
+ 1976.0,
+ 294.0,
+ 1976.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1971.0,
+ 828.0,
+ 1971.0,
+ 828.0,
+ 2006.0,
+ 293.0,
+ 2006.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 906.0,
+ 1971.0,
+ 1405.0,
+ 1971.0,
+ 1405.0,
+ 2006.0,
+ 906.0,
+ 2006.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 2004.0,
+ 913.0,
+ 2004.0,
+ 913.0,
+ 2034.0,
+ 296.0,
+ 2034.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 176.0,
+ 1404.0,
+ 176.0,
+ 1404.0,
+ 210.0,
+ 295.0,
+ 210.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 205.0,
+ 1405.0,
+ 205.0,
+ 1405.0,
+ 241.0,
+ 295.0,
+ 241.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 238.0,
+ 1402.0,
+ 238.0,
+ 1402.0,
+ 271.0,
+ 295.0,
+ 271.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 268.0,
+ 1406.0,
+ 268.0,
+ 1406.0,
+ 304.0,
+ 291.0,
+ 304.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 299.0,
+ 1405.0,
+ 299.0,
+ 1405.0,
+ 333.0,
+ 295.0,
+ 333.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 328.0,
+ 1405.0,
+ 328.0,
+ 1405.0,
+ 363.0,
+ 292.0,
+ 363.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 361.0,
+ 1405.0,
+ 361.0,
+ 1405.0,
+ 395.0,
+ 295.0,
+ 395.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 391.0,
+ 730.0,
+ 391.0,
+ 730.0,
+ 425.0,
+ 295.0,
+ 425.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 6,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1362,
+ 1404,
+ 1362,
+ 1404,
+ 1668,
+ 298,
+ 1668
+ ],
+ "score": 0.982
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 460,
+ 1403,
+ 460,
+ 1403,
+ 766,
+ 297,
+ 766
+ ],
+ "score": 0.982
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1070,
+ 1403,
+ 1070,
+ 1403,
+ 1347,
+ 298,
+ 1347
+ ],
+ "score": 0.98
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 299,
+ 1682,
+ 1403,
+ 1682,
+ 1403,
+ 1897,
+ 299,
+ 1897
+ ],
+ "score": 0.979
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 781,
+ 1404,
+ 781,
+ 1404,
+ 1056,
+ 298,
+ 1056
+ ],
+ "score": 0.978
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 230,
+ 1403,
+ 230,
+ 1403,
+ 445,
+ 298,
+ 445
+ ],
+ "score": 0.978
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 301,
+ 1977,
+ 1403,
+ 1977,
+ 1403,
+ 2033,
+ 301,
+ 2033
+ ],
+ "score": 0.924
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 840,
+ 2089,
+ 858,
+ 2089,
+ 858,
+ 2112,
+ 840,
+ 2112
+ ],
+ "score": 0.798
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 299,
+ 75,
+ 857,
+ 75,
+ 857,
+ 104,
+ 299,
+ 104
+ ],
+ "score": 0.732
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 300,
+ 76,
+ 855,
+ 76,
+ 855,
+ 104,
+ 300,
+ 104
+ ],
+ "score": 0.422
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1116,
+ 734,
+ 1207,
+ 734,
+ 1207,
+ 765,
+ 1116,
+ 765
+ ],
+ "score": 0.92,
+ "latex": "< 0 . 1 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 598,
+ 872,
+ 675,
+ 872,
+ 675,
+ 903,
+ 598,
+ 903
+ ],
+ "score": 0.9,
+ "latex": "0 . 8 2 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 756,
+ 1224,
+ 831,
+ 1224,
+ 831,
+ 1254,
+ 756,
+ 1254
+ ],
+ "score": 0.89,
+ "latex": "3 . 5 5 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 583,
+ 1102,
+ 659,
+ 1102,
+ 659,
+ 1132,
+ 583,
+ 1132
+ ],
+ "score": 0.89,
+ "latex": "1 . 6 8 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 840,
+ 994,
+ 916,
+ 994,
+ 916,
+ 1025,
+ 840,
+ 1025
+ ],
+ "score": 0.88,
+ "latex": "0 . 2 5 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1253,
+ 703,
+ 1308,
+ 703,
+ 1308,
+ 733,
+ 1253,
+ 733
+ ],
+ "score": 0.88,
+ "latex": "2 5 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 619,
+ 734,
+ 674,
+ 734,
+ 674,
+ 764,
+ 619,
+ 764
+ ],
+ "score": 0.87,
+ "latex": "4 0 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1067,
+ 872,
+ 1145,
+ 872,
+ 1145,
+ 903,
+ 1067,
+ 903
+ ],
+ "score": 0.87,
+ "latex": "0 . 8 7 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1100,
+ 1393,
+ 1154,
+ 1393,
+ 1154,
+ 1422,
+ 1100,
+ 1422
+ ],
+ "score": 0.86,
+ "latex": "90 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 959,
+ 1606,
+ 1015,
+ 1606,
+ 1015,
+ 1635,
+ 959,
+ 1635
+ ],
+ "score": 0.86,
+ "latex": "20 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 551,
+ 1133,
+ 640,
+ 1133,
+ 640,
+ 1163,
+ 551,
+ 1163
+ ],
+ "score": 0.86,
+ "latex": "( 7 . 9 1 \\% )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 681,
+ 994,
+ 761,
+ 994,
+ 761,
+ 1025,
+ 681,
+ 1025
+ ],
+ "score": 0.86,
+ "latex": "( 0 . 2 9 \\%"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1231,
+ 1607,
+ 1269,
+ 1607,
+ 1269,
+ 1634,
+ 1231,
+ 1634
+ ],
+ "score": 0.61,
+ "latex": "\\mathbf { A } ^ { * }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1357,
+ 1715,
+ 1393,
+ 1715,
+ 1393,
+ 1743,
+ 1357,
+ 1743
+ ],
+ "score": 0.33,
+ "latex": "A ^ { * }"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 330.0,
+ 1971.0,
+ 1407.0,
+ 1971.0,
+ 1407.0,
+ 2012.0,
+ 330.0,
+ 2012.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 2004.0,
+ 419.0,
+ 2004.0,
+ 419.0,
+ 2035.0,
+ 295.0,
+ 2035.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 838.0,
+ 2085.0,
+ 862.0,
+ 2085.0,
+ 862.0,
+ 2117.0,
+ 838.0,
+ 2117.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 298.0,
+ 72.0,
+ 858.0,
+ 72.0,
+ 858.0,
+ 108.0,
+ 298.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 73.0,
+ 859.0,
+ 73.0,
+ 859.0,
+ 108.0,
+ 297.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1361.0,
+ 1405.0,
+ 1361.0,
+ 1405.0,
+ 1397.0,
+ 296.0,
+ 1397.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1393.0,
+ 1099.0,
+ 1393.0,
+ 1099.0,
+ 1425.0,
+ 296.0,
+ 1425.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1155.0,
+ 1393.0,
+ 1402.0,
+ 1393.0,
+ 1402.0,
+ 1425.0,
+ 1155.0,
+ 1425.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1424.0,
+ 1406.0,
+ 1424.0,
+ 1406.0,
+ 1459.0,
+ 294.0,
+ 1459.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1453.0,
+ 1406.0,
+ 1453.0,
+ 1406.0,
+ 1487.0,
+ 293.0,
+ 1487.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1486.0,
+ 1405.0,
+ 1486.0,
+ 1405.0,
+ 1518.0,
+ 296.0,
+ 1518.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1512.0,
+ 1405.0,
+ 1512.0,
+ 1405.0,
+ 1549.0,
+ 293.0,
+ 1549.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1544.0,
+ 1405.0,
+ 1544.0,
+ 1405.0,
+ 1582.0,
+ 293.0,
+ 1582.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1573.0,
+ 1404.0,
+ 1573.0,
+ 1404.0,
+ 1610.0,
+ 293.0,
+ 1610.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1605.0,
+ 958.0,
+ 1605.0,
+ 958.0,
+ 1641.0,
+ 294.0,
+ 1641.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1016.0,
+ 1605.0,
+ 1230.0,
+ 1605.0,
+ 1230.0,
+ 1641.0,
+ 1016.0,
+ 1641.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1270.0,
+ 1605.0,
+ 1405.0,
+ 1605.0,
+ 1405.0,
+ 1641.0,
+ 1270.0,
+ 1641.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1637.0,
+ 1158.0,
+ 1637.0,
+ 1158.0,
+ 1672.0,
+ 294.0,
+ 1672.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 459.0,
+ 1403.0,
+ 459.0,
+ 1403.0,
+ 491.0,
+ 295.0,
+ 491.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 487.0,
+ 1405.0,
+ 487.0,
+ 1405.0,
+ 527.0,
+ 292.0,
+ 527.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 519.0,
+ 1404.0,
+ 519.0,
+ 1404.0,
+ 555.0,
+ 292.0,
+ 555.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 550.0,
+ 1405.0,
+ 550.0,
+ 1405.0,
+ 586.0,
+ 294.0,
+ 586.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 584.0,
+ 1404.0,
+ 584.0,
+ 1404.0,
+ 616.0,
+ 295.0,
+ 616.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 613.0,
+ 1404.0,
+ 613.0,
+ 1404.0,
+ 645.0,
+ 295.0,
+ 645.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 641.0,
+ 1407.0,
+ 641.0,
+ 1407.0,
+ 678.0,
+ 292.0,
+ 678.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 673.0,
+ 1405.0,
+ 673.0,
+ 1405.0,
+ 708.0,
+ 293.0,
+ 708.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 703.0,
+ 1252.0,
+ 703.0,
+ 1252.0,
+ 739.0,
+ 293.0,
+ 739.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1309.0,
+ 703.0,
+ 1405.0,
+ 703.0,
+ 1405.0,
+ 739.0,
+ 1309.0,
+ 739.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 735.0,
+ 618.0,
+ 735.0,
+ 618.0,
+ 768.0,
+ 292.0,
+ 768.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 675.0,
+ 735.0,
+ 1115.0,
+ 735.0,
+ 1115.0,
+ 768.0,
+ 675.0,
+ 768.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1208.0,
+ 735.0,
+ 1217.0,
+ 735.0,
+ 1217.0,
+ 768.0,
+ 1208.0,
+ 768.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1067.0,
+ 1405.0,
+ 1067.0,
+ 1405.0,
+ 1106.0,
+ 294.0,
+ 1106.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1100.0,
+ 582.0,
+ 1100.0,
+ 582.0,
+ 1138.0,
+ 293.0,
+ 1138.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1100.0,
+ 1407.0,
+ 1100.0,
+ 1407.0,
+ 1138.0,
+ 660.0,
+ 1138.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1130.0,
+ 550.0,
+ 1130.0,
+ 550.0,
+ 1169.0,
+ 292.0,
+ 1169.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 641.0,
+ 1130.0,
+ 1407.0,
+ 1130.0,
+ 1407.0,
+ 1169.0,
+ 641.0,
+ 1169.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1160.0,
+ 1405.0,
+ 1160.0,
+ 1405.0,
+ 1199.0,
+ 293.0,
+ 1199.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1190.0,
+ 1407.0,
+ 1190.0,
+ 1407.0,
+ 1229.0,
+ 293.0,
+ 1229.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1223.0,
+ 755.0,
+ 1223.0,
+ 755.0,
+ 1260.0,
+ 294.0,
+ 1260.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 832.0,
+ 1223.0,
+ 1405.0,
+ 1223.0,
+ 1405.0,
+ 1260.0,
+ 832.0,
+ 1260.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1256.0,
+ 1404.0,
+ 1256.0,
+ 1404.0,
+ 1288.0,
+ 296.0,
+ 1288.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1282.0,
+ 1407.0,
+ 1282.0,
+ 1407.0,
+ 1322.0,
+ 293.0,
+ 1322.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1316.0,
+ 1206.0,
+ 1316.0,
+ 1206.0,
+ 1349.0,
+ 294.0,
+ 1349.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1680.0,
+ 1404.0,
+ 1680.0,
+ 1404.0,
+ 1721.0,
+ 294.0,
+ 1721.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1713.0,
+ 1356.0,
+ 1713.0,
+ 1356.0,
+ 1748.0,
+ 295.0,
+ 1748.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1394.0,
+ 1713.0,
+ 1404.0,
+ 1713.0,
+ 1404.0,
+ 1748.0,
+ 1394.0,
+ 1748.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1745.0,
+ 1404.0,
+ 1745.0,
+ 1404.0,
+ 1780.0,
+ 294.0,
+ 1780.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1775.0,
+ 1405.0,
+ 1775.0,
+ 1405.0,
+ 1808.0,
+ 293.0,
+ 1808.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1805.0,
+ 1404.0,
+ 1805.0,
+ 1404.0,
+ 1840.0,
+ 294.0,
+ 1840.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1834.0,
+ 1405.0,
+ 1834.0,
+ 1405.0,
+ 1872.0,
+ 294.0,
+ 1872.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1866.0,
+ 531.0,
+ 1866.0,
+ 531.0,
+ 1900.0,
+ 294.0,
+ 1900.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 779.0,
+ 1406.0,
+ 779.0,
+ 1406.0,
+ 817.0,
+ 295.0,
+ 817.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 813.0,
+ 1406.0,
+ 813.0,
+ 1406.0,
+ 846.0,
+ 296.0,
+ 846.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 842.0,
+ 1406.0,
+ 842.0,
+ 1406.0,
+ 878.0,
+ 294.0,
+ 878.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 872.0,
+ 597.0,
+ 872.0,
+ 597.0,
+ 908.0,
+ 294.0,
+ 908.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 676.0,
+ 872.0,
+ 1066.0,
+ 872.0,
+ 1066.0,
+ 908.0,
+ 676.0,
+ 908.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1146.0,
+ 872.0,
+ 1405.0,
+ 872.0,
+ 1405.0,
+ 908.0,
+ 1146.0,
+ 908.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 903.0,
+ 1405.0,
+ 903.0,
+ 1405.0,
+ 938.0,
+ 295.0,
+ 938.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 933.0,
+ 1405.0,
+ 933.0,
+ 1405.0,
+ 969.0,
+ 294.0,
+ 969.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 961.0,
+ 1402.0,
+ 961.0,
+ 1402.0,
+ 998.0,
+ 293.0,
+ 998.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 990.0,
+ 680.0,
+ 990.0,
+ 680.0,
+ 1033.0,
+ 292.0,
+ 1033.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 762.0,
+ 990.0,
+ 839.0,
+ 990.0,
+ 839.0,
+ 1033.0,
+ 762.0,
+ 1033.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 917.0,
+ 990.0,
+ 1405.0,
+ 990.0,
+ 1405.0,
+ 1033.0,
+ 917.0,
+ 1033.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1027.0,
+ 579.0,
+ 1027.0,
+ 579.0,
+ 1056.0,
+ 293.0,
+ 1056.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 228.0,
+ 1405.0,
+ 228.0,
+ 1405.0,
+ 265.0,
+ 293.0,
+ 265.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 262.0,
+ 1405.0,
+ 262.0,
+ 1405.0,
+ 297.0,
+ 294.0,
+ 297.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 289.0,
+ 1403.0,
+ 289.0,
+ 1403.0,
+ 328.0,
+ 294.0,
+ 328.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 318.0,
+ 1405.0,
+ 318.0,
+ 1405.0,
+ 361.0,
+ 292.0,
+ 361.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 351.0,
+ 1405.0,
+ 351.0,
+ 1405.0,
+ 388.0,
+ 293.0,
+ 388.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 381.0,
+ 1405.0,
+ 381.0,
+ 1405.0,
+ 417.0,
+ 293.0,
+ 417.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 414.0,
+ 989.0,
+ 414.0,
+ 989.0,
+ 448.0,
+ 294.0,
+ 448.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 7,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 1355,
+ 1405,
+ 1355,
+ 1405,
+ 1814,
+ 297,
+ 1814
+ ],
+ "score": 0.984
+ },
+ {
+ "category_id": 5,
+ "poly": [
+ 365,
+ 1049,
+ 1330,
+ 1049,
+ 1330,
+ 1256,
+ 365,
+ 1256
+ ],
+ "score": 0.98,
+ "html": "| Algorithm1ANT Optimisation | |
| Initialise topology T and parameters O | >T is set to a root node with one solver and one transformer |
| Optimise parameters in O via gradient descent on NLL Set the root node “suboptimal" | Learning root classifier |
| while true do Freeze all parameters O | Growth of T begins |
| Pick next“suboptimal"leaf node l ∈Nteaf in the breadth-first order | |
| Add(1) router to l and train new parameters | Split data |
| Add (2) transformer to the incoming edge of l and train new parameters | Deepen transform |
| Add (1)or (2) permanently to T if validation error decreases,otherwise leaf is set to “optimal" |
| Add any new modules to O | |
| if no “suboptimal’ leaves remain then | |
| Break Unfreeze and train all parameters in O | |
"
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 350,
+ 218,
+ 1348,
+ 218,
+ 1348,
+ 273,
+ 350,
+ 273
+ ],
+ "score": 0.941
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 298,
+ 75,
+ 858,
+ 75,
+ 858,
+ 105,
+ 298,
+ 105
+ ],
+ "score": 0.9
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 301,
+ 850,
+ 774,
+ 850,
+ 774,
+ 883,
+ 301,
+ 883
+ ],
+ "score": 0.894
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 302,
+ 313,
+ 689,
+ 313,
+ 689,
+ 348,
+ 302,
+ 348
+ ],
+ "score": 0.885
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 837,
+ 2088,
+ 864,
+ 2088,
+ 864,
+ 2112,
+ 837,
+ 2112
+ ],
+ "score": 0.846
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 298,
+ 396,
+ 662,
+ 396,
+ 662,
+ 429,
+ 298,
+ 429
+ ],
+ "score": 0.265
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 696,
+ 578,
+ 800,
+ 578,
+ 800,
+ 608,
+ 696,
+ 608
+ ],
+ "score": 0.92,
+ "latex": "l \\in \\mathcal { N } _ { l e a f }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 561,
+ 468,
+ 584,
+ 468,
+ 584,
+ 492,
+ 561,
+ 492
+ ],
+ "score": 0.77,
+ "latex": "\\mathbb { O }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 614,
+ 689,
+ 637,
+ 689,
+ 637,
+ 712,
+ 614,
+ 712
+ ],
+ "score": 0.75,
+ "latex": "\\mathbb { O }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 579,
+ 551,
+ 602,
+ 551,
+ 602,
+ 575,
+ 579,
+ 575
+ ],
+ "score": 0.73,
+ "latex": "\\mathbb { O }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 686,
+ 773,
+ 710,
+ 773,
+ 710,
+ 797,
+ 686,
+ 797
+ ],
+ "score": 0.7,
+ "latex": "\\mathbb { O }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 809,
+ 634,
+ 821,
+ 634,
+ 821,
+ 658,
+ 809,
+ 658
+ ],
+ "score": 0.67,
+ "latex": "l"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 691,
+ 440,
+ 714,
+ 440,
+ 714,
+ 464,
+ 691,
+ 464
+ ],
+ "score": 0.62,
+ "latex": "\\mathbb { O }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 535,
+ 606,
+ 547,
+ 606,
+ 547,
+ 629,
+ 535,
+ 629
+ ],
+ "score": 0.54,
+ "latex": "l"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 662,
+ 662,
+ 683,
+ 662,
+ 683,
+ 685,
+ 662,
+ 685
+ ],
+ "score": 0.51,
+ "latex": "\\mathbb { T }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 510,
+ 439,
+ 532,
+ 439,
+ 532,
+ 465,
+ 510,
+ 465
+ ],
+ "score": 0.37,
+ "latex": "\\mathbb { T }"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 345.0,
+ 216.0,
+ 1353.0,
+ 216.0,
+ 1353.0,
+ 278.0,
+ 345.0,
+ 278.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 70.0,
+ 859.0,
+ 70.0,
+ 859.0,
+ 109.0,
+ 296.0,
+ 109.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 847.0,
+ 780.0,
+ 847.0,
+ 780.0,
+ 888.0,
+ 293.0,
+ 888.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 833.0,
+ 2085.0,
+ 869.0,
+ 2085.0,
+ 869.0,
+ 2124.0,
+ 833.0,
+ 2124.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 394.0,
+ 663.0,
+ 394.0,
+ 663.0,
+ 433.0,
+ 297.0,
+ 433.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1024.0,
+ 1406.0,
+ 1024.0,
+ 1406.0,
+ 1063.0,
+ 295.0,
+ 1063.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1056.0,
+ 1406.0,
+ 1056.0,
+ 1406.0,
+ 1092.0,
+ 294.0,
+ 1092.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1084.0,
+ 1405.0,
+ 1084.0,
+ 1405.0,
+ 1121.0,
+ 294.0,
+ 1121.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1117.0,
+ 1404.0,
+ 1117.0,
+ 1404.0,
+ 1153.0,
+ 294.0,
+ 1153.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1148.0,
+ 1405.0,
+ 1148.0,
+ 1405.0,
+ 1183.0,
+ 292.0,
+ 1183.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1179.0,
+ 1406.0,
+ 1179.0,
+ 1406.0,
+ 1215.0,
+ 294.0,
+ 1215.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1206.0,
+ 1405.0,
+ 1206.0,
+ 1405.0,
+ 1245.0,
+ 294.0,
+ 1245.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1237.0,
+ 1405.0,
+ 1237.0,
+ 1405.0,
+ 1276.0,
+ 294.0,
+ 1276.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1269.0,
+ 1405.0,
+ 1269.0,
+ 1405.0,
+ 1305.0,
+ 294.0,
+ 1305.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1299.0,
+ 1405.0,
+ 1299.0,
+ 1405.0,
+ 1335.0,
+ 294.0,
+ 1335.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1329.0,
+ 1404.0,
+ 1329.0,
+ 1404.0,
+ 1365.0,
+ 294.0,
+ 1365.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1358.0,
+ 1404.0,
+ 1358.0,
+ 1404.0,
+ 1394.0,
+ 295.0,
+ 1394.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1391.0,
+ 778.0,
+ 1391.0,
+ 778.0,
+ 1427.0,
+ 295.0,
+ 1427.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1436.0,
+ 1406.0,
+ 1436.0,
+ 1406.0,
+ 1473.0,
+ 294.0,
+ 1473.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1466.0,
+ 1408.0,
+ 1466.0,
+ 1408.0,
+ 1503.0,
+ 292.0,
+ 1503.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1498.0,
+ 1406.0,
+ 1498.0,
+ 1406.0,
+ 1533.0,
+ 294.0,
+ 1533.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 1525.0,
+ 1405.0,
+ 1525.0,
+ 1405.0,
+ 1567.0,
+ 291.0,
+ 1567.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1559.0,
+ 1405.0,
+ 1559.0,
+ 1405.0,
+ 1597.0,
+ 292.0,
+ 1597.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1591.0,
+ 1404.0,
+ 1591.0,
+ 1404.0,
+ 1625.0,
+ 295.0,
+ 1625.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1619.0,
+ 1406.0,
+ 1619.0,
+ 1406.0,
+ 1657.0,
+ 294.0,
+ 1657.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1651.0,
+ 1405.0,
+ 1651.0,
+ 1405.0,
+ 1686.0,
+ 294.0,
+ 1686.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1683.0,
+ 1404.0,
+ 1683.0,
+ 1404.0,
+ 1714.0,
+ 295.0,
+ 1714.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1712.0,
+ 1406.0,
+ 1712.0,
+ 1406.0,
+ 1748.0,
+ 292.0,
+ 1748.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1740.0,
+ 1204.0,
+ 1740.0,
+ 1204.0,
+ 1777.0,
+ 292.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1787.0,
+ 1403.0,
+ 1787.0,
+ 1403.0,
+ 1823.0,
+ 294.0,
+ 1823.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1821.0,
+ 1402.0,
+ 1821.0,
+ 1402.0,
+ 1855.0,
+ 294.0,
+ 1855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1851.0,
+ 1404.0,
+ 1851.0,
+ 1404.0,
+ 1885.0,
+ 294.0,
+ 1885.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1882.0,
+ 1402.0,
+ 1882.0,
+ 1402.0,
+ 1916.0,
+ 294.0,
+ 1916.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1911.0,
+ 1403.0,
+ 1911.0,
+ 1403.0,
+ 1945.0,
+ 294.0,
+ 1945.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1941.0,
+ 1406.0,
+ 1941.0,
+ 1406.0,
+ 1978.0,
+ 293.0,
+ 1978.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1973.0,
+ 1406.0,
+ 1973.0,
+ 1406.0,
+ 2007.0,
+ 294.0,
+ 2007.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 2004.0,
+ 919.0,
+ 2004.0,
+ 919.0,
+ 2037.0,
+ 294.0,
+ 2037.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 919.0,
+ 1403.0,
+ 919.0,
+ 1403.0,
+ 952.0,
+ 296.0,
+ 952.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 947.0,
+ 1407.0,
+ 947.0,
+ 1407.0,
+ 983.0,
+ 293.0,
+ 983.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 979.0,
+ 741.0,
+ 979.0,
+ 741.0,
+ 1009.0,
+ 296.0,
+ 1009.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 313.0,
+ 692.0,
+ 313.0,
+ 692.0,
+ 353.0,
+ 296.0,
+ 353.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 14,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 294,
+ 1404,
+ 294,
+ 1404,
+ 571,
+ 298,
+ 571
+ ],
+ "score": 0.98
+ },
+ {
+ "category_id": 5,
+ "poly": [
+ 487,
+ 1352,
+ 1213,
+ 1352,
+ 1213,
+ 1546,
+ 487,
+ 1546
+ ],
+ "score": 0.979,
+ "html": "| Hyperparameter | Value | Description |
| 入 | 0.1 | Scale factor for computing regret surrogate |
| p² | 1.0 | Observation noise variance for DQN-IDS |
| ∈1,∈2 | 0.00001 | Information-ratio constants; prevent division by O |
| mini-batch size | 32 | Size of mini-batch samples for gradient descent step |
| replay buffer size | 1M | The number of most recent observations stored in the replay buffer |
| agent history length | 4 | The number of most recent frames concatenated as input to the network |
| action repeat | 4 | Repeat each action selected by the agent this many times |
| Y | 0.99 | Discount factor |
| training frequency | 4 | The number of times an action is selected by the agent be- tween successive gradient descent steps |
| K | 10 | Number of bootstrap heads |
| β1 | 0.9 | Adam optimizer parameter |
| β | 0.99 | Adam optimizer parameter |
| EADAM | 0.01/32 | Adam optimizer parameter |
| α | 0.00005 | learning rate |
| learning starts | 50000 | Agent step at which learning starts.Random policy before- hand |
| numberof bins | 51 | Number of bins for Categorical DQN (C51) |
| [VMIN, VmAx] | [-10,10] | C51 distribution range |
| number of quantiles | 200 | Number of quantiles for QR-DQN |
| target network update frequency | 40000 | Number of agent steps between consecutive target updates |
| evaluation length | 125K | Number of agent steps each evaluation window lasts for. |
| evaluation frequency | | Equivalent to 50OK frames |
| 250K | The number of steps the agent takes in training mode between two evaluation runs.Equivalent to 1M frames |
| eval episode length | 27K | Number of maximum agent steps during an evaluation episode.Equivalent to 108K frames |
| max no-ops | 30 | Maximum number no-op actions before the episode starts |
+
+# B SUPPLEMENTAL RESULTS
+
+Human-normalized scores are computed as (van Hasselt et al., 2016),
+
+$$
+s c o r e = \frac { a g e n t - r a n d o m } { h u m a n - r a n d o m } \times 1 0 0
+$$
+
+where agent, human and random represent the per-game raw scores.
+
+
+Figure 2: Training curves for DQN-IDS and C51-IDS averaged over 3 seeds. Shaded areas correspond to min and max returns.
+
+
+Figure 3: The return distributions learned by C51-IDS and C51. Plots obtained by sampling a random batch of 32 states from the replay buffer every 50000 steps and computing the estimates for $\rho ^ { 2 } ( \mathbf { s } , \mathbf { a } )$ based on eq. (9). A histogram over the resulting values is then computed and displayed as a distribution (by interpolation). From top to bottom, the lines on each plot correspond to standard deviation boundaries of a normal distribution [max, $\mu + 1 . 5 \sigma , \mu + \sigma , \mu + 0 . 5 \sigma , \mu , \mu - 0 . 5 \sigma , \mu -$ $\sigma , \mu - 1 . 5 \sigma , \mathrm { m i n } ]$ . The $x$ -axis indicates number of training frames.
+
+Table 3: Raw evaluation scores. Episodes start with up to 30 no-op actions. Reference values from Wang et al. (2016) and Osband et al. (2016a). DQN-IDS averaged over 3 seeds. Bootstrap DQN scores for Berzerk, Phoenix, Pitfall!, Skiing, Solaris and Yars’ Revenge obtained from our custom implementation.
+
+| Hyperparameter | Value | Description |
| 入 | 0.1 | Scale factor for computing regret surrogate |
| p² | 1.0 | Observation noise variance for DQN-IDS |
| ∈1,∈2 | 0.00001 | Information-ratio constants; prevent division by O |
| mini-batch size | 32 | Size of mini-batch samples for gradient descent step |
| replay buffer size | 1M | The number of most recent observations stored in the replay buffer |
| agent history length | 4 | The number of most recent frames concatenated as input to the network |
| action repeat | 4 | Repeat each action selected by the agent this many times |
| Y | 0.99 | Discount factor |
| training frequency | 4 | The number of times an action is selected by the agent be- tween successive gradient descent steps |
| K | 10 | Number of bootstrap heads |
| β1 | 0.9 | Adam optimizer parameter |
| β | 0.99 | Adam optimizer parameter |
| EADAM | 0.01/32 | Adam optimizer parameter |
| α | 0.00005 | learning rate |
| learning starts | 50000 | Agent step at which learning starts.Random policy before- hand |
| numberof bins | 51 | Number of bins for Categorical DQN (C51) |
| [VMIN, VmAx] | [-10,10] | C51 distribution range |
| number of quantiles | 200 | Number of quantiles for QR-DQN |
| target network update frequency | 40000 | Number of agent steps between consecutive target updates |
| evaluation length | 125K | Number of agent steps each evaluation window lasts for. |
| evaluation frequency | | Equivalent to 50OK frames |
| 250K | The number of steps the agent takes in training mode between two evaluation runs.Equivalent to 1M frames |
| eval episode length | 27K | Number of maximum agent steps during an evaluation episode.Equivalent to 108K frames |
| max no-ops | 30 | Maximum number no-op actions before the episode starts |
",
+ "bbox": [
+ 181,
+ 167,
+ 818,
+ 617
+ ],
+ "page_idx": 11
+ },
+ {
+ "type": "text",
+ "text": "B SUPPLEMENTAL RESULTS ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 102,
+ 424,
+ 118
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "Human-normalized scores are computed as (van Hasselt et al., 2016), ",
+ "bbox": [
+ 173,
+ 133,
+ 629,
+ 148
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "equation",
+ "img_path": "images/7436d9547ffd6ed74356af8304e96ebc039a87e96d8fbc8d98b424a934dfd70a.jpg",
+ "text": "$$\ns c o r e = \\frac { a g e n t - r a n d o m } { h u m a n - r a n d o m } \\times 1 0 0 \n$$",
+ "text_format": "latex",
+ "bbox": [
+ 377,
+ 155,
+ 620,
+ 186
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "where agent, human and random represent the per-game raw scores. ",
+ "bbox": [
+ 173,
+ 193,
+ 638,
+ 208
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "image",
+ "img_path": "images/6520836face41e055d558d39cb2cd5a95d86fea2e0ad93d90c9a6c44bb8731de.jpg",
+ "image_caption": [
+ "Figure 2: Training curves for DQN-IDS and C51-IDS averaged over 3 seeds. Shaded areas correspond to min and max returns. "
+ ],
+ "image_footnote": [],
+ "bbox": [
+ 197,
+ 226,
+ 800,
+ 775
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "image",
+ "img_path": "images/0372daad620b46e958f34f02945cf595e3e8e1bd097da2751f2ceb013467530b.jpg",
+ "image_caption": [
+ "Figure 3: The return distributions learned by C51-IDS and C51. Plots obtained by sampling a random batch of 32 states from the replay buffer every 50000 steps and computing the estimates for $\\rho ^ { 2 } ( \\mathbf { s } , \\mathbf { a } )$ based on eq. (9). A histogram over the resulting values is then computed and displayed as a distribution (by interpolation). From top to bottom, the lines on each plot correspond to standard deviation boundaries of a normal distribution [max, $\\mu + 1 . 5 \\sigma , \\mu + \\sigma , \\mu + 0 . 5 \\sigma , \\mu , \\mu - 0 . 5 \\sigma , \\mu -$ $\\sigma , \\mu - 1 . 5 \\sigma , \\mathrm { m i n } ]$ . The $x$ -axis indicates number of training frames. "
+ ],
+ "image_footnote": [],
+ "bbox": [
+ 187,
+ 199,
+ 807,
+ 733
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "table",
+ "img_path": "images/781adb217d8eba9d87a2cf978e721f444d1f484adfe964dd1311ad84b42200f4.jpg",
+ "table_caption": [
+ "Table 3: Raw evaluation scores. Episodes start with up to 30 no-op actions. Reference values from Wang et al. (2016) and Osband et al. (2016a). DQN-IDS averaged over 3 seeds. Bootstrap DQN scores for Berzerk, Phoenix, Pitfall!, Skiing, Solaris and Yars’ Revenge obtained from our custom implementation. "
+ ],
+ "table_footnote": [],
+ "table_body": "| Hyperparameter | Value | Description |
| 入 | 0.1 | Scale factor for computing regret surrogate |
| p² | 1.0 | Observation noise variance for DQN-IDS |
| ∈1,∈2 | 0.00001 | Information-ratio constants; prevent division by O |
| mini-batch size | 32 | Size of mini-batch samples for gradient descent step |
| replay buffer size | 1M | The number of most recent observations stored in the replay buffer |
| agent history length | 4 | The number of most recent frames concatenated as input to the network |
| action repeat | 4 | Repeat each action selected by the agent this many times |
| Y | 0.99 | Discount factor |
| training frequency | 4 | The number of times an action is selected by the agent be- tween successive gradient descent steps |
| K | 10 | Number of bootstrap heads |
| β1 | 0.9 | Adam optimizer parameter |
| β | 0.99 | Adam optimizer parameter |
| EADAM | 0.01/32 | Adam optimizer parameter |
| α | 0.00005 | learning rate |
| learning starts | 50000 | Agent step at which learning starts.Random policy before- hand |
| numberof bins | 51 | Number of bins for Categorical DQN (C51) |
| [VMIN, VmAx] | [-10,10] | C51 distribution range |
| number of quantiles | 200 | Number of quantiles for QR-DQN |
| target network update frequency | 40000 | Number of agent steps between consecutive target updates |
| evaluation length | 125K | Number of agent steps each evaluation window lasts for. |
| evaluation frequency | | Equivalent to 50OK frames |
| 250K | The number of steps the agent takes in training mode between two evaluation runs.Equivalent to 1M frames |
| eval episode length | 27K | Number of maximum agent steps during an evaluation episode.Equivalent to 108K frames |
| max no-ops | 30 | Maximum number no-op actions before the episode starts |
",
+ "type": "table",
+ "image_path": "a4e640413e243af1c4e57e4b396e5e62b76f48a39d3a6b765ebac012fb4b7044.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 3,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 111,
+ 133,
+ 501,
+ 251.66666666666669
+ ],
+ "spans": [],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 111,
+ 251.66666666666669,
+ 501,
+ 370.33333333333337
+ ],
+ "spans": [],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 111,
+ 370.33333333333337,
+ 501,
+ 489.00000000000006
+ ],
+ "spans": [],
+ "index": 4
+ }
+ ]
+ }
+ ],
+ "index": 2.0
+ }
+ ],
+ "page_idx": 11,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 293,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 294,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 294,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Published as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 300,
+ 751,
+ 311,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 764
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 764
+ ],
+ "score": 1.0,
+ "content": "12",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 82,
+ 234,
+ 93
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 80,
+ 235,
+ 96
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 80,
+ 235,
+ 96
+ ],
+ "score": 1.0,
+ "content": "A HYPERPARAMETERS",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ }
+ ],
+ "index": 0
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 111,
+ 133,
+ 501,
+ 489
+ ],
+ "blocks": [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 243,
+ 118,
+ 368,
+ 130
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 241,
+ 116,
+ 369,
+ 133
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 241,
+ 116,
+ 369,
+ 133
+ ],
+ "score": 1.0,
+ "content": "Table 2: ALE hyperparameters",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 1
+ },
+ {
+ "type": "table_body",
+ "bbox": [
+ 111,
+ 133,
+ 501,
+ 489
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 111,
+ 133,
+ 501,
+ 489
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 111,
+ 133,
+ 501,
+ 489
+ ],
+ "score": 0.956,
+ "html": "| Hyperparameter | Value | Description |
| 入 | 0.1 | Scale factor for computing regret surrogate |
| p² | 1.0 | Observation noise variance for DQN-IDS |
| ∈1,∈2 | 0.00001 | Information-ratio constants; prevent division by O |
| mini-batch size | 32 | Size of mini-batch samples for gradient descent step |
| replay buffer size | 1M | The number of most recent observations stored in the replay buffer |
| agent history length | 4 | The number of most recent frames concatenated as input to the network |
| action repeat | 4 | Repeat each action selected by the agent this many times |
| Y | 0.99 | Discount factor |
| training frequency | 4 | The number of times an action is selected by the agent be- tween successive gradient descent steps |
| K | 10 | Number of bootstrap heads |
| β1 | 0.9 | Adam optimizer parameter |
| β | 0.99 | Adam optimizer parameter |
| EADAM | 0.01/32 | Adam optimizer parameter |
| α | 0.00005 | learning rate |
| learning starts | 50000 | Agent step at which learning starts.Random policy before- hand |
| numberof bins | 51 | Number of bins for Categorical DQN (C51) |
| [VMIN, VmAx] | [-10,10] | C51 distribution range |
| number of quantiles | 200 | Number of quantiles for QR-DQN |
| target network update frequency | 40000 | Number of agent steps between consecutive target updates |
| evaluation length | 125K | Number of agent steps each evaluation window lasts for. |
| evaluation frequency | | Equivalent to 50OK frames |
| 250K | The number of steps the agent takes in training mode between two evaluation runs.Equivalent to 1M frames |
| eval episode length | 27K | Number of maximum agent steps during an evaluation episode.Equivalent to 108K frames |
| max no-ops | 30 | Maximum number no-op actions before the episode starts |
",
+ "type": "table",
+ "image_path": "a4e640413e243af1c4e57e4b396e5e62b76f48a39d3a6b765ebac012fb4b7044.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 3,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 111,
+ 133,
+ 501,
+ 251.66666666666669
+ ],
+ "spans": [],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 111,
+ 251.66666666666669,
+ 501,
+ 370.33333333333337
+ ],
+ "spans": [],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 111,
+ 370.33333333333337,
+ 501,
+ 489.00000000000006
+ ],
+ "spans": [],
+ "index": 4
+ }
+ ]
+ }
+ ],
+ "index": 2.0
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 81,
+ 260,
+ 94
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 80,
+ 261,
+ 95
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 80,
+ 261,
+ 95
+ ],
+ "score": 1.0,
+ "content": "B SUPPLEMENTAL RESULTS",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ }
+ ],
+ "index": 0
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 106,
+ 385,
+ 118
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 106,
+ 385,
+ 119
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 106,
+ 385,
+ 119
+ ],
+ "score": 1.0,
+ "content": "Human-normalized scores are computed as (van Hasselt et al., 2016),",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 1
+ },
+ {
+ "type": "interline_equation",
+ "bbox": [
+ 231,
+ 123,
+ 380,
+ 148
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 231,
+ 123,
+ 380,
+ 148
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 231,
+ 123,
+ 380,
+ 148
+ ],
+ "score": 0.94,
+ "content": "s c o r e = \\frac { a g e n t - r a n d o m } { h u m a n - r a n d o m } \\times 1 0 0 ",
+ "type": "interline_equation",
+ "image_path": "7436d9547ffd6ed74356af8304e96ebc039a87e96d8fbc8d98b424a934dfd70a.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 2,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 231,
+ 123,
+ 380,
+ 148
+ ],
+ "spans": [],
+ "index": 2
+ }
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 153,
+ 391,
+ 165
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 151,
+ 392,
+ 167
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 151,
+ 392,
+ 167
+ ],
+ "score": 1.0,
+ "content": "where agent, human and random represent the per-game raw scores.",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ }
+ ],
+ "index": 3
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 614
+ ],
+ "blocks": [
+ {
+ "type": "image_body",
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 614
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 614
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 614
+ ],
+ "score": 0.974,
+ "type": "image",
+ "image_path": "6520836face41e055d558d39cb2cd5a95d86fea2e0ad93d90c9a6c44bb8731de.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 5,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 324.0
+ ],
+ "spans": [],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 121,
+ 324.0,
+ 490,
+ 469.0
+ ],
+ "spans": [],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 121,
+ 469.0,
+ 490,
+ 614.0
+ ],
+ "spans": [],
+ "index": 6
+ }
+ ]
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 106,
+ 632,
+ 503,
+ 655
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 632,
+ 505,
+ 645
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 632,
+ 505,
+ 645
+ ],
+ "score": 1.0,
+ "content": "Figure 2: Training curves for DQN-IDS and C51-IDS averaged over 3 seeds. Shaded areas corre-",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 644,
+ 233,
+ 656
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 644,
+ 233,
+ 656
+ ],
+ "score": 1.0,
+ "content": "spond to min and max returns.",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ }
+ ],
+ "index": 7.5
+ }
+ ],
+ "index": 6.25
+ }
+ ],
+ "page_idx": 12,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 26,
+ 293,
+ 38
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 25,
+ 294,
+ 39
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 25,
+ 294,
+ 39
+ ],
+ "score": 1.0,
+ "content": "Published as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 300,
+ 751,
+ 311,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 764
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 764
+ ],
+ "score": 1.0,
+ "content": "13",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 81,
+ 260,
+ 94
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 80,
+ 261,
+ 95
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 80,
+ 261,
+ 95
+ ],
+ "score": 1.0,
+ "content": "B SUPPLEMENTAL RESULTS",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ }
+ ],
+ "index": 0
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 106,
+ 385,
+ 118
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 106,
+ 385,
+ 119
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 106,
+ 385,
+ 119
+ ],
+ "score": 1.0,
+ "content": "Human-normalized scores are computed as (van Hasselt et al., 2016),",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 1,
+ "bbox_fs": [
+ 106,
+ 106,
+ 385,
+ 119
+ ]
+ },
+ {
+ "type": "interline_equation",
+ "bbox": [
+ 231,
+ 123,
+ 380,
+ 148
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 231,
+ 123,
+ 380,
+ 148
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 231,
+ 123,
+ 380,
+ 148
+ ],
+ "score": 0.94,
+ "content": "s c o r e = \\frac { a g e n t - r a n d o m } { h u m a n - r a n d o m } \\times 1 0 0 ",
+ "type": "interline_equation",
+ "image_path": "7436d9547ffd6ed74356af8304e96ebc039a87e96d8fbc8d98b424a934dfd70a.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 2,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 231,
+ 123,
+ 380,
+ 148
+ ],
+ "spans": [],
+ "index": 2
+ }
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 153,
+ 391,
+ 165
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 151,
+ 392,
+ 167
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 151,
+ 392,
+ 167
+ ],
+ "score": 1.0,
+ "content": "where agent, human and random represent the per-game raw scores.",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ }
+ ],
+ "index": 3,
+ "bbox_fs": [
+ 106,
+ 151,
+ 392,
+ 167
+ ]
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 614
+ ],
+ "blocks": [
+ {
+ "type": "image_body",
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 614
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 614
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 614
+ ],
+ "score": 0.974,
+ "type": "image",
+ "image_path": "6520836face41e055d558d39cb2cd5a95d86fea2e0ad93d90c9a6c44bb8731de.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 5,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 121,
+ 179,
+ 490,
+ 324.0
+ ],
+ "spans": [],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 121,
+ 324.0,
+ 490,
+ 469.0
+ ],
+ "spans": [],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 121,
+ 469.0,
+ 490,
+ 614.0
+ ],
+ "spans": [],
+ "index": 6
+ }
+ ]
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 106,
+ 632,
+ 503,
+ 655
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 632,
+ 505,
+ 645
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 632,
+ 505,
+ 645
+ ],
+ "score": 1.0,
+ "content": "Figure 2: Training curves for DQN-IDS and C51-IDS averaged over 3 seeds. Shaded areas corre-",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 644,
+ 233,
+ 656
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 644,
+ 233,
+ 656
+ ],
+ "score": 1.0,
+ "content": "spond to min and max returns.",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ }
+ ],
+ "index": 7.5
+ }
+ ],
+ "index": 6.25
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "image",
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 581
+ ],
+ "blocks": [
+ {
+ "type": "image_body",
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 581
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 581
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 581
+ ],
+ "score": 0.969,
+ "type": "image",
+ "image_path": "0372daad620b46e958f34f02945cf595e3e8e1bd097da2751f2ceb013467530b.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 1,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 299.0
+ ],
+ "spans": [],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 115,
+ 299.0,
+ 494,
+ 440.0
+ ],
+ "spans": [],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 115,
+ 440.0,
+ 494,
+ 581.0
+ ],
+ "spans": [],
+ "index": 2
+ }
+ ]
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 106,
+ 597,
+ 505,
+ 664
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 595,
+ 506,
+ 610
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 595,
+ 506,
+ 610
+ ],
+ "score": 1.0,
+ "content": "Figure 3: The return distributions learned by C51-IDS and C51. Plots obtained by sampling a",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 609,
+ 506,
+ 620
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 609,
+ 506,
+ 620
+ ],
+ "score": 1.0,
+ "content": "random batch of 32 states from the replay buffer every 50000 steps and computing the estimates for",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 107,
+ 619,
+ 505,
+ 632
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 619,
+ 139,
+ 631
+ ],
+ "score": 0.92,
+ "content": "\\rho ^ { 2 } ( \\mathbf { s } , \\mathbf { a } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 140,
+ 619,
+ 505,
+ 632
+ ],
+ "score": 1.0,
+ "content": "based on eq. (9). A histogram over the resulting values is then computed and displayed as",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 630,
+ 505,
+ 643
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 630,
+ 505,
+ 643
+ ],
+ "score": 1.0,
+ "content": "a distribution (by interpolation). From top to bottom, the lines on each plot correspond to standard",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 641,
+ 505,
+ 654
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 641,
+ 318,
+ 654
+ ],
+ "score": 1.0,
+ "content": "deviation boundaries of a normal distribution [max,",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 318,
+ 641,
+ 505,
+ 653
+ ],
+ "score": 0.82,
+ "content": "\\mu + 1 . 5 \\sigma , \\mu + \\sigma , \\mu + 0 . 5 \\sigma , \\mu , \\mu - 0 . 5 \\sigma , \\mu -",
+ "type": "inline_equation"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 107,
+ 651,
+ 375,
+ 666
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 653,
+ 178,
+ 664
+ ],
+ "score": 0.9,
+ "content": "\\sigma , \\mu - 1 . 5 \\sigma , \\mathrm { m i n } ]",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 178,
+ 651,
+ 200,
+ 666
+ ],
+ "score": 1.0,
+ "content": ". The",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 200,
+ 654,
+ 207,
+ 662
+ ],
+ "score": 0.78,
+ "content": "x",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 208,
+ 651,
+ 375,
+ 666
+ ],
+ "score": 1.0,
+ "content": "-axis indicates number of training frames.",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ }
+ ],
+ "index": 5.5
+ }
+ ],
+ "index": 3.25
+ }
+ ],
+ "page_idx": 13,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 293,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 25,
+ 294,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 25,
+ 294,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Published as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 300,
+ 751,
+ 311,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 763
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 763
+ ],
+ "score": 1.0,
+ "content": "14",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 109,
+ 147,
+ 151,
+ 154
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 110,
+ 148,
+ 132,
+ 154
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 110,
+ 148,
+ 132,
+ 154
+ ],
+ "score": 0.961,
+ "content": "C51-IDS",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "image",
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 581
+ ],
+ "blocks": [
+ {
+ "type": "image_body",
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 581
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 581
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 581
+ ],
+ "score": 0.969,
+ "type": "image",
+ "image_path": "0372daad620b46e958f34f02945cf595e3e8e1bd097da2751f2ceb013467530b.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 1,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 115,
+ 158,
+ 494,
+ 299.0
+ ],
+ "spans": [],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 115,
+ 299.0,
+ 494,
+ 440.0
+ ],
+ "spans": [],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 115,
+ 440.0,
+ 494,
+ 581.0
+ ],
+ "spans": [],
+ "index": 2
+ }
+ ]
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 106,
+ 597,
+ 505,
+ 664
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 595,
+ 506,
+ 610
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 595,
+ 506,
+ 610
+ ],
+ "score": 1.0,
+ "content": "Figure 3: The return distributions learned by C51-IDS and C51. Plots obtained by sampling a",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 609,
+ 506,
+ 620
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 609,
+ 506,
+ 620
+ ],
+ "score": 1.0,
+ "content": "random batch of 32 states from the replay buffer every 50000 steps and computing the estimates for",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 107,
+ 619,
+ 505,
+ 632
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 619,
+ 139,
+ 631
+ ],
+ "score": 0.92,
+ "content": "\\rho ^ { 2 } ( \\mathbf { s } , \\mathbf { a } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 140,
+ 619,
+ 505,
+ 632
+ ],
+ "score": 1.0,
+ "content": "based on eq. (9). A histogram over the resulting values is then computed and displayed as",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 630,
+ 505,
+ 643
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 630,
+ 505,
+ 643
+ ],
+ "score": 1.0,
+ "content": "a distribution (by interpolation). From top to bottom, the lines on each plot correspond to standard",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 641,
+ 505,
+ 654
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 641,
+ 318,
+ 654
+ ],
+ "score": 1.0,
+ "content": "deviation boundaries of a normal distribution [max,",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 318,
+ 641,
+ 505,
+ 653
+ ],
+ "score": 0.82,
+ "content": "\\mu + 1 . 5 \\sigma , \\mu + \\sigma , \\mu + 0 . 5 \\sigma , \\mu , \\mu - 0 . 5 \\sigma , \\mu -",
+ "type": "inline_equation"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 107,
+ 651,
+ 375,
+ 666
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 653,
+ 178,
+ 664
+ ],
+ "score": 0.9,
+ "content": "\\sigma , \\mu - 1 . 5 \\sigma , \\mathrm { m i n } ]",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 178,
+ 651,
+ 200,
+ 666
+ ],
+ "score": 1.0,
+ "content": ". The",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 200,
+ 654,
+ 207,
+ 662
+ ],
+ "score": 0.78,
+ "content": "x",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 208,
+ 651,
+ 375,
+ 666
+ ],
+ "score": 1.0,
+ "content": "-axis indicates number of training frames.",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ }
+ ],
+ "index": 5.5
+ }
+ ],
+ "index": 3.25
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "table",
+ "bbox": [
+ 116,
+ 151,
+ 496,
+ 714
+ ],
+ "blocks": [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 106,
+ 102,
+ 505,
+ 147
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 101,
+ 506,
+ 115
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 101,
+ 506,
+ 115
+ ],
+ "score": 1.0,
+ "content": "Table 3: Raw evaluation scores. Episodes start with up to 30 no-op actions. Reference values from",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 106,
+ 114,
+ 505,
+ 126
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 114,
+ 505,
+ 126
+ ],
+ "score": 1.0,
+ "content": "Wang et al. (2016) and Osband et al. (2016a). DQN-IDS averaged over 3 seeds. Bootstrap DQN",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 106,
+ 125,
+ 505,
+ 137
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 125,
+ 505,
+ 137
+ ],
+ "score": 1.0,
+ "content": "scores for Berzerk, Phoenix, Pitfall!, Skiing, Solaris and Yars’ Revenge obtained from our custom",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 106,
+ 137,
+ 173,
+ 148
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 137,
+ 173,
+ 148
+ ],
+ "score": 1.0,
+ "content": "implementation.",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ }
+ ],
+ "index": 1.5
+ },
+ {
+ "type": "table_body",
+ "bbox": [
+ 116,
+ 151,
+ 496,
+ 714
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 116,
+ 151,
+ 496,
+ 714
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 151,
+ 496,
+ 714
+ ],
+ "score": 0.968,
+ "html": "| Input: X,action-value function Q with K outputs {Qk}k=1,action-value distribution Z forepisodei=1:Mdo Get initial state So |
| for step t=O :Tdo |
| g(st,a）²=k∑κ=1[Qk(st,a)-μ(st,a)]² 1K |
| △(st,a) = maxa'∈A[μ(st,a')+ λσ(st,a')] -[μ(st,a) - λσ(St,a)] |
| ρ(st,a)²= Var(Z(st,a)/ (∈1 +∑a'∈A Var(Z(st,a）)) |
| 1（st,a)=10g（1+） + |
| △(st,a）² Compute regret-information ratio: 亚(st, a) = |
| I(st,a) |
| Execute action at = arg mina∈.A 亚(st,a),observe rt and state St+1 end for end for |
"
+ },
+ {
+ "category_id": 14,
+ "poly": [
+ 603,
+ 1229,
+ 1095,
+ 1229,
+ 1095,
+ 1314,
+ 603,
+ 1314
+ ],
+ "score": 0.94,
+ "latex": "\\rho ( \\mathbf { s } , \\mathbf { a } ) ^ { 2 } = \\frac { \\operatorname { V a r } \\left( Z ( \\mathbf { s } , \\mathbf { a } ) \\right) } { \\epsilon _ { 1 } + \\frac { 1 } { | A | } \\sum _ { \\mathbf { a } ^ { \\prime } \\in \\mathcal { A } } \\operatorname { V a r } \\left( Z ( \\mathbf { s } , \\mathbf { a } ^ { \\prime } ) \\right) } ,"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 790,
+ 1157,
+ 1161,
+ 1157,
+ 1161,
+ 1214,
+ 790,
+ 1214
+ ],
+ "score": 0.93,
+ "latex": "\\begin{array} { r } { I ( \\mathbf { s } , \\mathbf { a } ) = \\log \\left( 1 + \\frac { \\sigma ( \\mathbf { s } , \\mathbf { a } ) ^ { 2 } } { \\rho ( \\mathbf { s } , \\mathbf { a } ) ^ { 2 } } \\right) + \\epsilon _ { 2 } } \\end{array}"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 431,
+ 1834,
+ 576,
+ 1834,
+ 576,
+ 1867,
+ 431,
+ 1867
+ ],
+ "score": 0.93,
+ "latex": "Q _ { k } ( \\mathbf { s } , \\mathbf { a } ; \\theta ^ { - } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1151,
+ 1600,
+ 1237,
+ 1600,
+ 1237,
+ 1633,
+ 1151,
+ 1633
+ ],
+ "score": 0.93,
+ "latex": "Q ( \\mathbf { s } , \\mathbf { a } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 575,
+ 1630,
+ 659,
+ 1630,
+ 659,
+ 1663,
+ 575,
+ 1663
+ ],
+ "score": 0.93,
+ "latex": "Z ( \\mathbf { s } , \\mathbf { a } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 551,
+ 662,
+ 849,
+ 662,
+ 849,
+ 699,
+ 551,
+ 699
+ ],
+ "score": 0.93,
+ "latex": "\\mathbf { a } _ { t } = \\arg \\operatorname* { m i n } _ { \\mathbf { a } \\in \\mathcal { A } } \\hat { \\Psi } ( \\mathbf { s } _ { t } , \\mathbf { a } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 355,
+ 1690,
+ 441,
+ 1690,
+ 441,
+ 1729,
+ 355,
+ 1729
+ ],
+ "score": 0.93,
+ "latex": "\\hat { \\Psi } ( \\mathbf { s } , \\mathbf { a } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 985,
+ 1804,
+ 1111,
+ 1804,
+ 1111,
+ 1837,
+ 985,
+ 1837
+ ],
+ "score": 0.93,
+ "latex": "Q _ { k } ( \\mathbf { s } , \\mathbf { a } ; \\theta )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 437,
+ 1911,
+ 521,
+ 1911,
+ 521,
+ 1945,
+ 437,
+ 1945
+ ],
+ "score": 0.93,
+ "latex": "Z ( \\mathbf { s } , \\mathbf { a } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 962,
+ 852,
+ 1328,
+ 852,
+ 1328,
+ 889,
+ 962,
+ 889
+ ],
+ "score": 0.92,
+ "latex": "I _ { t } ( \\mathbf { a } ) = \\log \\big ( 1 + \\sigma _ { t } ( \\mathbf { a } ) ^ { \\scriptscriptstyle \\bar { 2 } } / \\rho ( \\mathbf { a } ) ^ { 2 } \\big )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 409,
+ 1973,
+ 493,
+ 1973,
+ 493,
+ 2005,
+ 409,
+ 2005
+ ],
+ "score": 0.92,
+ "latex": "Z ( \\mathbf { s } , \\mathbf { a } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1181,
+ 1971,
+ 1272,
+ 1971,
+ 1272,
+ 2005,
+ 1181,
+ 2005
+ ],
+ "score": 0.92,
+ "latex": "\\rho ( \\mathbf { s } , \\mathbf { \\bar { a } } ) ^ { 2 }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1265,
+ 974,
+ 1332,
+ 974,
+ 1332,
+ 1008,
+ 1265,
+ 1008
+ ],
+ "score": 0.92,
+ "latex": "\\rho ( { \\mathbf { a } } ) ^ { 2 }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 768,
+ 612,
+ 989,
+ 612,
+ 989,
+ 664,
+ 768,
+ 664
+ ],
+ "score": 0.92,
+ "latex": "\\begin{array} { r } { \\hat { \\Psi } ( \\mathbf { s } _ { t } , \\mathbf { a } ) = \\frac { \\hat { \\Delta } ( \\mathbf { s } _ { t } , \\mathbf { a } ) ^ { 2 } } { I ( \\mathbf { s } _ { t } , \\mathbf { a } ) } } \\end{array}"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 886,
+ 268,
+ 993,
+ 268,
+ 993,
+ 306,
+ 886,
+ 306
+ ],
+ "score": 0.91,
+ "latex": "\\{ Q _ { k } \\} _ { k = 1 } ^ { K }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1014,
+ 1006,
+ 1168,
+ 1006,
+ 1168,
+ 1040,
+ 1014,
+ 1040
+ ],
+ "score": 0.91,
+ "latex": "\\mathrm { V a r } \\left( Z ( \\mathbf { s } , \\mathbf { a } ) \\right)"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 986,
+ 1943,
+ 1038,
+ 1943,
+ 1038,
+ 1975,
+ 986,
+ 1975
+ ],
+ "score": 0.91,
+ "latex": "\\phi ( \\mathbf { s } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 892,
+ 1439,
+ 1170,
+ 1439,
+ 1170,
+ 1475,
+ 892,
+ 1475
+ ],
+ "score": 0.91,
+ "latex": "\\rho ( \\mathbf { s } , \\mathbf { a } ) ^ { \\dot { 2 } } = \\mathrm { V a r } \\left( \\bar { Z ( \\mathbf { s } , \\mathbf { a } ) } \\right)"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 488,
+ 1036,
+ 640,
+ 1036,
+ 640,
+ 1070,
+ 488,
+ 1070
+ ],
+ "score": 0.9,
+ "latex": "\\mathrm { V a r } \\left( Z ( \\mathbf { s } , \\mathbf { a } ) \\right)"
+ },
+ {
+ "category_id": 14,
+ "poly": [
+ 377,
+ 389,
+ 1163,
+ 389,
+ 1163,
+ 617,
+ 377,
+ 617
+ ],
+ "score": 0.9,
+ "latex": "\\begin{array} { r l } & { \\quad _ { \\mu ( \\mathbf { s } _ { t } , \\mathbf { a } ) } ^ { \\star } = \\frac { 1 } { K } \\sum _ { k = 1 } ^ { K } Q _ { k } ( \\mathbf { s } _ { t } , \\mathbf { a } ) } \\\\ & { \\quad _ { \\sigma ( \\mathbf { s } _ { t } , \\mathbf { a } ) ^ { 2 } } = \\frac { 1 } { K } \\sum _ { k = 1 } ^ { K } \\left[ Q _ { k } ( \\mathbf { s } _ { t } , \\mathbf { a } ) - \\mu ( \\mathbf { s } _ { t } , \\mathbf { a } ) \\right] ^ { 2 } } \\\\ & { \\quad _ { \\Delta } ( \\mathbf { s } _ { t } , \\mathbf { a } ) = \\operatorname* { m a x } _ { \\mathbf { a } ^ { \\prime } \\in \\mathcal { A } } \\left[ \\mu ( \\mathbf { s } _ { t } , \\mathbf { a } ^ { \\prime } ) + \\lambda \\sigma ( \\mathbf { s } _ { t } , \\mathbf { a } ^ { \\prime } ) \\right] - \\left[ \\mu ( \\mathbf { s } _ { t } , \\mathbf { a } ) - \\lambda \\sigma ( \\mathbf { s } _ { t } , \\mathbf { a } ) \\right] } \\\\ & { \\quad _ { \\rho ( \\mathbf { s } _ { t } , \\mathbf { a } ) ^ { 2 } } = \\mathrm { V a r } \\left( Z ( \\mathbf { s } _ { t } , \\mathbf { a } ) \\right) / \\left( \\epsilon _ { 1 } + \\frac { 1 } { | \\mathcal { A } | } \\sum _ { \\mathbf { a } ^ { \\prime } \\in \\mathcal { A } } \\mathrm { V a r } \\left( Z ( \\mathbf { s } _ { t } , \\mathbf { a } ^ { \\prime } ) \\right) \\right) } \\\\ & { \\quad _ { I ( \\mathbf { s } _ { t } , \\mathbf { a } ) } = \\log \\left( 1 + \\frac { \\sigma ( \\mathbf { s } _ { t } , \\mathbf { a } ) ^ { 2 } } { \\rho ( \\mathbf { s } _ { t } , \\mathbf { a } ) ^ { 2 } } \\right) + \\epsilon _ { 2 } } \\end{array}"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 458,
+ 302,
+ 575,
+ 302,
+ 575,
+ 330,
+ 458,
+ 330
+ ],
+ "score": 0.9,
+ "latex": "i = 1 : M"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1249,
+ 1864,
+ 1305,
+ 1864,
+ 1305,
+ 1897,
+ 1249,
+ 1897
+ ],
+ "score": 0.9,
+ "latex": "1 / K"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 372,
+ 1327,
+ 434,
+ 1327,
+ 434,
+ 1352,
+ 372,
+ 1352
+ ],
+ "score": 0.88,
+ "latex": "\\epsilon _ { 1 } , \\epsilon _ { 2 }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1086,
+ 673,
+ 1139,
+ 673,
+ 1139,
+ 699,
+ 1086,
+ 699
+ ],
+ "score": 0.86,
+ "latex": "\\mathbf { s } _ { t + 1 }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 446,
+ 364,
+ 554,
+ 364,
+ 554,
+ 391,
+ 446,
+ 391
+ ],
+ "score": 0.85,
+ "latex": "t = 0 : T"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 687,
+ 855,
+ 712,
+ 855,
+ 712,
+ 885,
+ 687,
+ 885
+ ],
+ "score": 0.84,
+ "latex": "I _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 680,
+ 272,
+ 705,
+ 272,
+ 705,
+ 303,
+ 680,
+ 303
+ ],
+ "score": 0.84,
+ "latex": "Q"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 952,
+ 672,
+ 978,
+ 672,
+ 978,
+ 697,
+ 952,
+ 697
+ ],
+ "score": 0.84,
+ "latex": "r _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 298,
+ 1805,
+ 327,
+ 1805,
+ 327,
+ 1831,
+ 298,
+ 1831
+ ],
+ "score": 0.81,
+ "latex": "K"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 764,
+ 272,
+ 794,
+ 272,
+ 794,
+ 300,
+ 764,
+ 300
+ ],
+ "score": 0.8,
+ "latex": "K"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 528,
+ 338,
+ 557,
+ 338,
+ 557,
+ 363,
+ 528,
+ 363
+ ],
+ "score": 0.8,
+ "latex": "\\mathbf { s } _ { 0 }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1045,
+ 1913,
+ 1063,
+ 1913,
+ 1063,
+ 1939,
+ 1045,
+ 1939
+ ],
+ "score": 0.79,
+ "latex": "\\theta"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1376,
+ 921,
+ 1394,
+ 921,
+ 1394,
+ 947,
+ 1376,
+ 947
+ ],
+ "score": 0.73,
+ "latex": "\\rho"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 407,
+ 273,
+ 427,
+ 273,
+ 427,
+ 300,
+ 407,
+ 300
+ ],
+ "score": 0.68,
+ "latex": "\\lambda"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1281,
+ 272,
+ 1307,
+ 272,
+ 1307,
+ 300,
+ 1281,
+ 300
+ ],
+ "score": 0.45,
+ "latex": "Z"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 73.0,
+ 817.0,
+ 73.0,
+ 817.0,
+ 108.0,
+ 296.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1510.0,
+ 1024.0,
+ 1510.0,
+ 1024.0,
+ 1547.0,
+ 294.0,
+ 1547.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 840.0,
+ 2087.0,
+ 862.0,
+ 2087.0,
+ 862.0,
+ 2118.0,
+ 840.0,
+ 2118.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 221.0,
+ 979.0,
+ 221.0,
+ 979.0,
+ 271.0,
+ 294.0,
+ 271.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 1321.0,
+ 371.0,
+ 1321.0,
+ 371.0,
+ 1354.0,
+ 297.0,
+ 1354.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 435.0,
+ 1321.0,
+ 1404.0,
+ 1321.0,
+ 1404.0,
+ 1354.0,
+ 435.0,
+ 1354.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1349.0,
+ 1404.0,
+ 1349.0,
+ 1404.0,
+ 1385.0,
+ 295.0,
+ 1385.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1382.0,
+ 1405.0,
+ 1382.0,
+ 1405.0,
+ 1415.0,
+ 296.0,
+ 1415.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1408.0,
+ 1406.0,
+ 1408.0,
+ 1406.0,
+ 1448.0,
+ 293.0,
+ 1448.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1440.0,
+ 891.0,
+ 1440.0,
+ 891.0,
+ 1478.0,
+ 294.0,
+ 1478.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1171.0,
+ 1440.0,
+ 1181.0,
+ 1440.0,
+ 1181.0,
+ 1478.0,
+ 1171.0,
+ 1478.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 822.0,
+ 1405.0,
+ 822.0,
+ 1405.0,
+ 860.0,
+ 295.0,
+ 860.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 851.0,
+ 686.0,
+ 851.0,
+ 686.0,
+ 890.0,
+ 293.0,
+ 890.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 713.0,
+ 851.0,
+ 961.0,
+ 851.0,
+ 961.0,
+ 890.0,
+ 713.0,
+ 890.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1329.0,
+ 851.0,
+ 1406.0,
+ 851.0,
+ 1406.0,
+ 890.0,
+ 1329.0,
+ 890.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 885.0,
+ 1405.0,
+ 885.0,
+ 1405.0,
+ 919.0,
+ 294.0,
+ 919.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 912.0,
+ 1375.0,
+ 912.0,
+ 1375.0,
+ 953.0,
+ 291.0,
+ 953.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1395.0,
+ 912.0,
+ 1406.0,
+ 912.0,
+ 1406.0,
+ 953.0,
+ 1395.0,
+ 953.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 944.0,
+ 1405.0,
+ 944.0,
+ 1405.0,
+ 980.0,
+ 294.0,
+ 980.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 973.0,
+ 1264.0,
+ 973.0,
+ 1264.0,
+ 1012.0,
+ 293.0,
+ 1012.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1333.0,
+ 973.0,
+ 1406.0,
+ 973.0,
+ 1406.0,
+ 1012.0,
+ 1333.0,
+ 1012.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1007.0,
+ 1013.0,
+ 1007.0,
+ 1013.0,
+ 1041.0,
+ 294.0,
+ 1041.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1169.0,
+ 1007.0,
+ 1405.0,
+ 1007.0,
+ 1405.0,
+ 1041.0,
+ 1169.0,
+ 1041.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 1032.0,
+ 487.0,
+ 1032.0,
+ 487.0,
+ 1074.0,
+ 291.0,
+ 1074.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 641.0,
+ 1032.0,
+ 1405.0,
+ 1032.0,
+ 1405.0,
+ 1074.0,
+ 641.0,
+ 1074.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1067.0,
+ 1405.0,
+ 1067.0,
+ 1405.0,
+ 1101.0,
+ 295.0,
+ 1101.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1096.0,
+ 1406.0,
+ 1096.0,
+ 1406.0,
+ 1133.0,
+ 293.0,
+ 1133.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1125.0,
+ 1406.0,
+ 1125.0,
+ 1406.0,
+ 1165.0,
+ 294.0,
+ 1165.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 1161.0,
+ 789.0,
+ 1161.0,
+ 789.0,
+ 1211.0,
+ 291.0,
+ 1211.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1162.0,
+ 1169.0,
+ 1404.0,
+ 1169.0,
+ 1404.0,
+ 1202.0,
+ 1162.0,
+ 1202.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1211.0,
+ 396.0,
+ 1211.0,
+ 396.0,
+ 1239.0,
+ 295.0,
+ 1239.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1740.0,
+ 1407.0,
+ 1740.0,
+ 1407.0,
+ 1778.0,
+ 294.0,
+ 1778.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1772.0,
+ 1405.0,
+ 1772.0,
+ 1405.0,
+ 1809.0,
+ 294.0,
+ 1809.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 328.0,
+ 1802.0,
+ 984.0,
+ 1802.0,
+ 984.0,
+ 1839.0,
+ 328.0,
+ 1839.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1112.0,
+ 1802.0,
+ 1407.0,
+ 1802.0,
+ 1407.0,
+ 1839.0,
+ 1112.0,
+ 1839.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1833.0,
+ 430.0,
+ 1833.0,
+ 430.0,
+ 1869.0,
+ 293.0,
+ 1869.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 577.0,
+ 1833.0,
+ 1405.0,
+ 1833.0,
+ 1405.0,
+ 1869.0,
+ 577.0,
+ 1869.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1863.0,
+ 1248.0,
+ 1863.0,
+ 1248.0,
+ 1899.0,
+ 293.0,
+ 1899.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1306.0,
+ 1863.0,
+ 1316.0,
+ 1863.0,
+ 1316.0,
+ 1899.0,
+ 1306.0,
+ 1899.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1568.0,
+ 1405.0,
+ 1568.0,
+ 1405.0,
+ 1606.0,
+ 296.0,
+ 1606.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1596.0,
+ 1150.0,
+ 1596.0,
+ 1150.0,
+ 1635.0,
+ 293.0,
+ 1635.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1238.0,
+ 1596.0,
+ 1405.0,
+ 1596.0,
+ 1405.0,
+ 1635.0,
+ 1238.0,
+ 1635.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1626.0,
+ 574.0,
+ 1626.0,
+ 574.0,
+ 1666.0,
+ 293.0,
+ 1666.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1626.0,
+ 1405.0,
+ 1626.0,
+ 1405.0,
+ 1666.0,
+ 660.0,
+ 1666.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1657.0,
+ 1405.0,
+ 1657.0,
+ 1405.0,
+ 1696.0,
+ 293.0,
+ 1696.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 1686.0,
+ 354.0,
+ 1686.0,
+ 354.0,
+ 1734.0,
+ 291.0,
+ 1734.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 442.0,
+ 1686.0,
+ 455.0,
+ 1686.0,
+ 455.0,
+ 1734.0,
+ 442.0,
+ 1734.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1910.0,
+ 436.0,
+ 1910.0,
+ 436.0,
+ 1946.0,
+ 294.0,
+ 1946.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 522.0,
+ 1910.0,
+ 1044.0,
+ 1910.0,
+ 1044.0,
+ 1946.0,
+ 522.0,
+ 1946.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1064.0,
+ 1910.0,
+ 1404.0,
+ 1910.0,
+ 1404.0,
+ 1946.0,
+ 1064.0,
+ 1946.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1941.0,
+ 985.0,
+ 1941.0,
+ 985.0,
+ 1977.0,
+ 294.0,
+ 1977.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1039.0,
+ 1941.0,
+ 1407.0,
+ 1941.0,
+ 1407.0,
+ 1977.0,
+ 1039.0,
+ 1977.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1971.0,
+ 408.0,
+ 1971.0,
+ 408.0,
+ 2006.0,
+ 293.0,
+ 2006.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 494.0,
+ 1971.0,
+ 1180.0,
+ 1971.0,
+ 1180.0,
+ 2006.0,
+ 494.0,
+ 2006.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1273.0,
+ 1971.0,
+ 1407.0,
+ 1971.0,
+ 1407.0,
+ 2006.0,
+ 1273.0,
+ 2006.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 2002.0,
+ 1406.0,
+ 2002.0,
+ 1406.0,
+ 2038.0,
+ 293.0,
+ 2038.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 264.0,
+ 406.0,
+ 264.0,
+ 406.0,
+ 308.0,
+ 322.0,
+ 308.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 428.0,
+ 264.0,
+ 679.0,
+ 264.0,
+ 679.0,
+ 308.0,
+ 428.0,
+ 308.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 706.0,
+ 264.0,
+ 763.0,
+ 264.0,
+ 763.0,
+ 308.0,
+ 706.0,
+ 308.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 795.0,
+ 264.0,
+ 885.0,
+ 264.0,
+ 885.0,
+ 308.0,
+ 795.0,
+ 308.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 994.0,
+ 264.0,
+ 1280.0,
+ 264.0,
+ 1280.0,
+ 308.0,
+ 994.0,
+ 308.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1308.0,
+ 264.0,
+ 1311.0,
+ 264.0,
+ 1311.0,
+ 308.0,
+ 1308.0,
+ 308.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 299.0,
+ 457.0,
+ 299.0,
+ 457.0,
+ 332.0,
+ 323.0,
+ 332.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 576.0,
+ 299.0,
+ 614.0,
+ 299.0,
+ 614.0,
+ 332.0,
+ 576.0,
+ 332.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 349.0,
+ 328.0,
+ 527.0,
+ 328.0,
+ 527.0,
+ 367.0,
+ 349.0,
+ 367.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 558.0,
+ 328.0,
+ 562.0,
+ 328.0,
+ 562.0,
+ 367.0,
+ 558.0,
+ 367.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 361.0,
+ 445.0,
+ 361.0,
+ 445.0,
+ 450.0,
+ 350.0,
+ 450.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 555.0,
+ 361.0,
+ 739.0,
+ 361.0,
+ 739.0,
+ 450.0,
+ 555.0,
+ 450.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 368.0,
+ 414.0,
+ 376.0,
+ 414.0,
+ 376.0,
+ 487.0,
+ 368.0,
+ 487.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 373.0,
+ 508.0,
+ 376.0,
+ 508.0,
+ 376.0,
+ 563.0,
+ 373.0,
+ 563.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 380.0,
+ 606.0,
+ 767.0,
+ 606.0,
+ 767.0,
+ 669.0,
+ 380.0,
+ 669.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 990.0,
+ 606.0,
+ 994.0,
+ 606.0,
+ 994.0,
+ 669.0,
+ 990.0,
+ 669.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 376.0,
+ 661.0,
+ 550.0,
+ 661.0,
+ 550.0,
+ 705.0,
+ 376.0,
+ 705.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 850.0,
+ 661.0,
+ 951.0,
+ 661.0,
+ 951.0,
+ 705.0,
+ 850.0,
+ 705.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 979.0,
+ 661.0,
+ 1085.0,
+ 661.0,
+ 1085.0,
+ 705.0,
+ 979.0,
+ 705.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1140.0,
+ 661.0,
+ 1144.0,
+ 661.0,
+ 1144.0,
+ 705.0,
+ 1140.0,
+ 705.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 349.0,
+ 692.0,
+ 448.0,
+ 692.0,
+ 448.0,
+ 729.0,
+ 349.0,
+ 729.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 726.0,
+ 420.0,
+ 726.0,
+ 420.0,
+ 761.0,
+ 322.0,
+ 761.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 373.75,
+ 553.0,
+ 709.75,
+ 553.0,
+ 709.75,
+ 614.0,
+ 373.75,
+ 614.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 5,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 1498,
+ 1404,
+ 1498,
+ 1404,
+ 1743,
+ 297,
+ 1743
+ ],
+ "score": 0.982
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 1758,
+ 1404,
+ 1758,
+ 1404,
+ 2034,
+ 297,
+ 2034
+ ],
+ "score": 0.981
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 1117,
+ 1404,
+ 1117,
+ 1404,
+ 1332,
+ 297,
+ 1332
+ ],
+ "score": 0.981
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 915,
+ 1403,
+ 915,
+ 1403,
+ 1102,
+ 297,
+ 1102
+ ],
+ "score": 0.98
+ },
+ {
+ "category_id": 5,
+ "poly": [
+ 604,
+ 383,
+ 1094,
+ 383,
+ 1094,
+ 820,
+ 604,
+ 820
+ ],
+ "score": 0.978,
+ "html": "| Hyperparameter | Value | Description |
| 入 | 0.1 | Scale factor for computing regret surrogate |
| p² | 1.0 | Observation noise variance for DQN-IDS |
| ∈1,∈2 | 0.00001 | Information-ratio constants; prevent division by O |
| mini-batch size | 32 | Size of mini-batch samples for gradient descent step |
| replay buffer size | 1M | The number of most recent observations stored in the replay buffer |
| agent history length | 4 | The number of most recent frames concatenated as input to the network |
| action repeat | 4 | Repeat each action selected by the agent this many times |
| Y | 0.99 | Discount factor |
| training frequency | 4 | The number of times an action is selected by the agent be- tween successive gradient descent steps |
| K | 10 | Number of bootstrap heads |
| β1 | 0.9 | Adam optimizer parameter |
| β | 0.99 | Adam optimizer parameter |
| EADAM | 0.01/32 | Adam optimizer parameter |
| α | 0.00005 | learning rate |
| learning starts | 50000 | Agent step at which learning starts.Random policy before- hand |
| numberof bins | 51 | Number of bins for Categorical DQN (C51) |
| [VMIN, VmAx] | [-10,10] | C51 distribution range |
| number of quantiles | 200 | Number of quantiles for QR-DQN |
| target network update frequency | 40000 | Number of agent steps between consecutive target updates |
| evaluation length | 125K | Number of agent steps each evaluation window lasts for. |
| evaluation frequency | | Equivalent to 50OK frames |
| 250K | The number of steps the agent takes in training mode between two evaluation runs.Equivalent to 1M frames |
| eval episode length | 27K | Number of maximum agent steps during an evaluation episode.Equivalent to 108K frames |
| max no-ops | 30 | Maximum number no-op actions before the episode starts |
"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 672.0,
+ 323.0,
+ 1026.0,
+ 323.0,
+ 1026.0,
+ 371.0,
+ 672.0,
+ 371.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 73.0,
+ 817.0,
+ 73.0,
+ 817.0,
+ 108.0,
+ 295.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 832.0,
+ 2085.0,
+ 870.0,
+ 2085.0,
+ 870.0,
+ 2124.0,
+ 832.0,
+ 2124.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 224.0,
+ 654.0,
+ 224.0,
+ 654.0,
+ 268.0,
+ 293.0,
+ 268.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 11,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 3,
+ "poly": [
+ 338,
+ 498,
+ 1362,
+ 498,
+ 1362,
+ 1706,
+ 338,
+ 1706
+ ],
+ "score": 0.974
+ },
+ {
+ "category_id": 8,
+ "poly": [
+ 646,
+ 344,
+ 1054,
+ 344,
+ 1054,
+ 414,
+ 646,
+ 414
+ ],
+ "score": 0.948
+ },
+ {
+ "category_id": 4,
+ "poly": [
+ 297,
+ 1756,
+ 1399,
+ 1756,
+ 1399,
+ 1821,
+ 297,
+ 1821
+ ],
+ "score": 0.93
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 295,
+ 1071,
+ 295,
+ 1071,
+ 329,
+ 297,
+ 329
+ ],
+ "score": 0.92
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 295,
+ 426,
+ 1088,
+ 426,
+ 1088,
+ 459,
+ 295,
+ 459
+ ],
+ "score": 0.918
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 298,
+ 74,
+ 816,
+ 74,
+ 816,
+ 106,
+ 298,
+ 106
+ ],
+ "score": 0.903
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 301,
+ 226,
+ 724,
+ 226,
+ 724,
+ 263,
+ 301,
+ 263
+ ],
+ "score": 0.881
+ },
+ {
+ "category_id": 9,
+ "poly": [
+ 1351,
+ 363,
+ 1401,
+ 363,
+ 1401,
+ 394,
+ 1351,
+ 394
+ ],
+ "score": 0.876
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 836,
+ 2088,
+ 865,
+ 2088,
+ 865,
+ 2113,
+ 836,
+ 2113
+ ],
+ "score": 0.86
+ },
+ {
+ "category_id": 14,
+ "poly": [
+ 644,
+ 343,
+ 1057,
+ 343,
+ 1057,
+ 412,
+ 644,
+ 412
+ ],
+ "score": 0.94,
+ "latex": "s c o r e = \\frac { a g e n t - r a n d o m } { h u m a n - r a n d o m } \\times 1 0 0 "
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 399.0,
+ 507.0,
+ 453.0,
+ 507.0,
+ 453.0,
+ 534.0,
+ 399.0,
+ 534.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 561.0,
+ 509.0,
+ 630.0,
+ 509.0,
+ 630.0,
+ 532.0,
+ 561.0,
+ 532.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 728.0,
+ 508.0,
+ 800.0,
+ 508.0,
+ 800.0,
+ 532.0,
+ 728.0,
+ 532.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 901.0,
+ 505.0,
+ 969.0,
+ 505.0,
+ 969.0,
+ 536.0,
+ 901.0,
+ 536.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1062.0,
+ 508.0,
+ 1149.0,
+ 508.0,
+ 1149.0,
+ 534.0,
+ 1062.0,
+ 534.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1239.0,
+ 509.0,
+ 1309.0,
+ 509.0,
+ 1309.0,
+ 532.0,
+ 1239.0,
+ 532.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 601.0,
+ 366.0,
+ 601.0,
+ 366.0,
+ 620.0,
+ 350.0,
+ 620.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 407.0,
+ 598.0,
+ 445.0,
+ 598.0,
+ 445.0,
+ 622.0,
+ 407.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 598.0,
+ 514.0,
+ 598.0,
+ 514.0,
+ 622.0,
+ 474.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 516.0,
+ 599.0,
+ 538.0,
+ 599.0,
+ 538.0,
+ 621.0,
+ 516.0,
+ 621.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 577.0,
+ 598.0,
+ 614.0,
+ 598.0,
+ 614.0,
+ 622.0,
+ 577.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 598.0,
+ 682.0,
+ 598.0,
+ 682.0,
+ 622.0,
+ 645.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 689.0,
+ 602.0,
+ 705.0,
+ 602.0,
+ 705.0,
+ 620.0,
+ 689.0,
+ 620.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 749.0,
+ 601.0,
+ 782.0,
+ 601.0,
+ 782.0,
+ 621.0,
+ 749.0,
+ 621.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 814.0,
+ 598.0,
+ 851.0,
+ 598.0,
+ 851.0,
+ 622.0,
+ 814.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 858.0,
+ 601.0,
+ 876.0,
+ 601.0,
+ 876.0,
+ 620.0,
+ 858.0,
+ 620.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 916.0,
+ 598.0,
+ 954.0,
+ 598.0,
+ 954.0,
+ 622.0,
+ 916.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 598.0,
+ 1022.0,
+ 598.0,
+ 1022.0,
+ 622.0,
+ 984.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1028.0,
+ 602.0,
+ 1046.0,
+ 602.0,
+ 1046.0,
+ 620.0,
+ 1028.0,
+ 620.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1086.0,
+ 598.0,
+ 1123.0,
+ 598.0,
+ 1123.0,
+ 622.0,
+ 1086.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1153.0,
+ 598.0,
+ 1192.0,
+ 598.0,
+ 1192.0,
+ 622.0,
+ 1153.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1197.0,
+ 601.0,
+ 1215.0,
+ 601.0,
+ 1215.0,
+ 620.0,
+ 1197.0,
+ 620.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1257.0,
+ 598.0,
+ 1293.0,
+ 598.0,
+ 1293.0,
+ 622.0,
+ 1257.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1323.0,
+ 598.0,
+ 1359.0,
+ 598.0,
+ 1359.0,
+ 622.0,
+ 1323.0,
+ 622.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 380.0,
+ 624.0,
+ 474.0,
+ 624.0,
+ 474.0,
+ 650.0,
+ 380.0,
+ 650.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 544.0,
+ 622.0,
+ 648.0,
+ 622.0,
+ 648.0,
+ 651.0,
+ 544.0,
+ 651.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 715.0,
+ 624.0,
+ 815.0,
+ 624.0,
+ 815.0,
+ 650.0,
+ 715.0,
+ 650.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 900.0,
+ 625.0,
+ 970.0,
+ 625.0,
+ 970.0,
+ 648.0,
+ 900.0,
+ 648.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1068.0,
+ 622.0,
+ 1141.0,
+ 622.0,
+ 1141.0,
+ 651.0,
+ 1068.0,
+ 651.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1242.0,
+ 620.0,
+ 1309.0,
+ 620.0,
+ 1309.0,
+ 653.0,
+ 1242.0,
+ 653.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 528.0,
+ 703.0,
+ 542.0,
+ 703.0,
+ 542.0,
+ 715.0,
+ 528.0,
+ 715.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 718.0,
+ 366.0,
+ 718.0,
+ 366.0,
+ 735.0,
+ 350.0,
+ 735.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 408.0,
+ 715.0,
+ 445.0,
+ 715.0,
+ 445.0,
+ 740.0,
+ 408.0,
+ 740.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 715.0,
+ 512.0,
+ 715.0,
+ 512.0,
+ 738.0,
+ 474.0,
+ 738.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 519.0,
+ 718.0,
+ 537.0,
+ 718.0,
+ 537.0,
+ 735.0,
+ 519.0,
+ 735.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 580.0,
+ 716.0,
+ 612.0,
+ 716.0,
+ 612.0,
+ 737.0,
+ 580.0,
+ 737.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 715.0,
+ 682.0,
+ 715.0,
+ 682.0,
+ 738.0,
+ 645.0,
+ 738.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 689.0,
+ 718.0,
+ 705.0,
+ 718.0,
+ 705.0,
+ 735.0,
+ 689.0,
+ 735.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 747.0,
+ 715.0,
+ 784.0,
+ 715.0,
+ 784.0,
+ 740.0,
+ 747.0,
+ 740.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 815.0,
+ 715.0,
+ 851.0,
+ 715.0,
+ 851.0,
+ 740.0,
+ 815.0,
+ 740.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 858.0,
+ 718.0,
+ 876.0,
+ 718.0,
+ 876.0,
+ 735.0,
+ 858.0,
+ 735.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 919.0,
+ 716.0,
+ 953.0,
+ 716.0,
+ 953.0,
+ 737.0,
+ 919.0,
+ 737.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 715.0,
+ 1022.0,
+ 715.0,
+ 1022.0,
+ 738.0,
+ 984.0,
+ 738.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1030.0,
+ 718.0,
+ 1045.0,
+ 718.0,
+ 1045.0,
+ 735.0,
+ 1030.0,
+ 735.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1088.0,
+ 716.0,
+ 1122.0,
+ 716.0,
+ 1122.0,
+ 737.0,
+ 1088.0,
+ 737.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1155.0,
+ 716.0,
+ 1189.0,
+ 716.0,
+ 1189.0,
+ 737.0,
+ 1155.0,
+ 737.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1197.0,
+ 718.0,
+ 1215.0,
+ 718.0,
+ 1215.0,
+ 735.0,
+ 1197.0,
+ 735.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1258.0,
+ 716.0,
+ 1292.0,
+ 716.0,
+ 1292.0,
+ 737.0,
+ 1258.0,
+ 737.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1326.0,
+ 716.0,
+ 1358.0,
+ 716.0,
+ 1358.0,
+ 737.0,
+ 1326.0,
+ 737.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 382.0,
+ 739.0,
+ 469.0,
+ 739.0,
+ 469.0,
+ 770.0,
+ 382.0,
+ 770.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 550.0,
+ 744.0,
+ 642.0,
+ 744.0,
+ 642.0,
+ 765.0,
+ 550.0,
+ 765.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 685.0,
+ 742.0,
+ 847.0,
+ 742.0,
+ 847.0,
+ 768.0,
+ 685.0,
+ 768.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 876.0,
+ 744.0,
+ 995.0,
+ 744.0,
+ 995.0,
+ 765.0,
+ 876.0,
+ 765.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1045.0,
+ 741.0,
+ 1166.0,
+ 741.0,
+ 1166.0,
+ 767.0,
+ 1045.0,
+ 767.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1220.0,
+ 741.0,
+ 1331.0,
+ 741.0,
+ 1331.0,
+ 767.0,
+ 1220.0,
+ 767.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 422.0,
+ 763.0,
+ 495.0,
+ 763.0,
+ 495.0,
+ 785.0,
+ 422.0,
+ 785.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 930.0,
+ 764.0,
+ 1008.0,
+ 764.0,
+ 1008.0,
+ 782.0,
+ 930.0,
+ 782.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1226.0,
+ 771.0,
+ 1240.0,
+ 771.0,
+ 1240.0,
+ 780.0,
+ 1226.0,
+ 780.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1303.0,
+ 772.0,
+ 1317.0,
+ 772.0,
+ 1317.0,
+ 783.0,
+ 1303.0,
+ 783.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1201.0,
+ 819.0,
+ 1216.0,
+ 819.0,
+ 1216.0,
+ 836.0,
+ 1201.0,
+ 836.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 835.0,
+ 368.0,
+ 835.0,
+ 368.0,
+ 854.0,
+ 350.0,
+ 854.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 407.0,
+ 832.0,
+ 445.0,
+ 832.0,
+ 445.0,
+ 857.0,
+ 407.0,
+ 857.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 832.0,
+ 512.0,
+ 832.0,
+ 512.0,
+ 855.0,
+ 474.0,
+ 855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 519.0,
+ 835.0,
+ 537.0,
+ 835.0,
+ 537.0,
+ 853.0,
+ 519.0,
+ 853.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 577.0,
+ 832.0,
+ 615.0,
+ 832.0,
+ 615.0,
+ 857.0,
+ 577.0,
+ 857.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 832.0,
+ 682.0,
+ 832.0,
+ 682.0,
+ 857.0,
+ 645.0,
+ 857.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 689.0,
+ 836.0,
+ 707.0,
+ 836.0,
+ 707.0,
+ 853.0,
+ 689.0,
+ 853.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 749.0,
+ 834.0,
+ 782.0,
+ 834.0,
+ 782.0,
+ 854.0,
+ 749.0,
+ 854.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 814.0,
+ 832.0,
+ 851.0,
+ 832.0,
+ 851.0,
+ 855.0,
+ 814.0,
+ 855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 858.0,
+ 835.0,
+ 876.0,
+ 835.0,
+ 876.0,
+ 853.0,
+ 858.0,
+ 853.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 916.0,
+ 832.0,
+ 954.0,
+ 832.0,
+ 954.0,
+ 855.0,
+ 916.0,
+ 855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 832.0,
+ 1022.0,
+ 832.0,
+ 1022.0,
+ 855.0,
+ 984.0,
+ 855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1030.0,
+ 836.0,
+ 1046.0,
+ 836.0,
+ 1046.0,
+ 853.0,
+ 1030.0,
+ 853.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1086.0,
+ 832.0,
+ 1123.0,
+ 832.0,
+ 1123.0,
+ 857.0,
+ 1086.0,
+ 857.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1153.0,
+ 832.0,
+ 1190.0,
+ 832.0,
+ 1190.0,
+ 857.0,
+ 1153.0,
+ 857.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1197.0,
+ 835.0,
+ 1215.0,
+ 835.0,
+ 1215.0,
+ 854.0,
+ 1197.0,
+ 854.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1257.0,
+ 832.0,
+ 1293.0,
+ 832.0,
+ 1293.0,
+ 857.0,
+ 1257.0,
+ 857.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1323.0,
+ 832.0,
+ 1361.0,
+ 832.0,
+ 1361.0,
+ 855.0,
+ 1323.0,
+ 855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 392.0,
+ 855.0,
+ 461.0,
+ 855.0,
+ 461.0,
+ 886.0,
+ 392.0,
+ 886.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 537.0,
+ 858.0,
+ 655.0,
+ 858.0,
+ 655.0,
+ 884.0,
+ 537.0,
+ 884.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 726.0,
+ 858.0,
+ 804.0,
+ 858.0,
+ 804.0,
+ 884.0,
+ 726.0,
+ 884.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 893.0,
+ 858.0,
+ 977.0,
+ 858.0,
+ 977.0,
+ 884.0,
+ 893.0,
+ 884.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1068.0,
+ 855.0,
+ 1141.0,
+ 855.0,
+ 1141.0,
+ 886.0,
+ 1068.0,
+ 886.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1238.0,
+ 859.0,
+ 1312.0,
+ 859.0,
+ 1312.0,
+ 883.0,
+ 1238.0,
+ 883.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 537.0,
+ 887.0,
+ 557.0,
+ 887.0,
+ 557.0,
+ 902.0,
+ 537.0,
+ 902.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 952.0,
+ 366.0,
+ 952.0,
+ 366.0,
+ 970.0,
+ 350.0,
+ 970.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 407.0,
+ 949.0,
+ 445.0,
+ 949.0,
+ 445.0,
+ 973.0,
+ 407.0,
+ 973.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 949.0,
+ 512.0,
+ 949.0,
+ 512.0,
+ 973.0,
+ 474.0,
+ 973.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 519.0,
+ 952.0,
+ 537.0,
+ 952.0,
+ 537.0,
+ 970.0,
+ 519.0,
+ 970.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 578.0,
+ 951.0,
+ 612.0,
+ 951.0,
+ 612.0,
+ 971.0,
+ 578.0,
+ 971.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 949.0,
+ 682.0,
+ 949.0,
+ 682.0,
+ 973.0,
+ 645.0,
+ 973.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 689.0,
+ 952.0,
+ 705.0,
+ 952.0,
+ 705.0,
+ 970.0,
+ 689.0,
+ 970.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 747.0,
+ 949.0,
+ 785.0,
+ 949.0,
+ 785.0,
+ 973.0,
+ 747.0,
+ 973.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 814.0,
+ 949.0,
+ 851.0,
+ 949.0,
+ 851.0,
+ 973.0,
+ 814.0,
+ 973.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 952.0,
+ 876.0,
+ 952.0,
+ 876.0,
+ 970.0,
+ 859.0,
+ 970.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 916.0,
+ 949.0,
+ 954.0,
+ 949.0,
+ 954.0,
+ 973.0,
+ 916.0,
+ 973.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 949.0,
+ 1022.0,
+ 949.0,
+ 1022.0,
+ 973.0,
+ 984.0,
+ 973.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1030.0,
+ 952.0,
+ 1046.0,
+ 952.0,
+ 1046.0,
+ 970.0,
+ 1030.0,
+ 970.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1088.0,
+ 951.0,
+ 1122.0,
+ 951.0,
+ 1122.0,
+ 971.0,
+ 1088.0,
+ 971.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1153.0,
+ 949.0,
+ 1190.0,
+ 949.0,
+ 1190.0,
+ 973.0,
+ 1153.0,
+ 973.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1197.0,
+ 952.0,
+ 1215.0,
+ 952.0,
+ 1215.0,
+ 970.0,
+ 1197.0,
+ 970.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1258.0,
+ 951.0,
+ 1292.0,
+ 951.0,
+ 1292.0,
+ 971.0,
+ 1258.0,
+ 971.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1324.0,
+ 951.0,
+ 1358.0,
+ 951.0,
+ 1358.0,
+ 971.0,
+ 1324.0,
+ 971.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 403.0,
+ 975.0,
+ 450.0,
+ 975.0,
+ 450.0,
+ 1000.0,
+ 403.0,
+ 1000.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 548.0,
+ 975.0,
+ 642.0,
+ 975.0,
+ 642.0,
+ 1001.0,
+ 548.0,
+ 1001.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 716.0,
+ 977.0,
+ 815.0,
+ 977.0,
+ 815.0,
+ 998.0,
+ 716.0,
+ 998.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 891.0,
+ 974.0,
+ 979.0,
+ 974.0,
+ 979.0,
+ 1003.0,
+ 891.0,
+ 1003.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1081.0,
+ 975.0,
+ 1128.0,
+ 975.0,
+ 1128.0,
+ 1000.0,
+ 1081.0,
+ 1000.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1209.0,
+ 975.0,
+ 1339.0,
+ 975.0,
+ 1339.0,
+ 1001.0,
+ 1209.0,
+ 1001.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 950.0,
+ 1001.0,
+ 1005.0,
+ 1001.0,
+ 1005.0,
+ 1015.0,
+ 950.0,
+ 1015.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1161.0,
+ 1000.0,
+ 1173.0,
+ 1000.0,
+ 1173.0,
+ 1011.0,
+ 1161.0,
+ 1011.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 526.0,
+ 1043.0,
+ 535.0,
+ 1043.0,
+ 535.0,
+ 1060.0,
+ 526.0,
+ 1060.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 883.0,
+ 1019.0,
+ 903.0,
+ 1019.0,
+ 903.0,
+ 1068.0,
+ 883.0,
+ 1068.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 1068.0,
+ 366.0,
+ 1068.0,
+ 366.0,
+ 1087.0,
+ 350.0,
+ 1087.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 408.0,
+ 1065.0,
+ 445.0,
+ 1065.0,
+ 445.0,
+ 1090.0,
+ 408.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 1067.0,
+ 512.0,
+ 1067.0,
+ 512.0,
+ 1090.0,
+ 474.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 519.0,
+ 1068.0,
+ 537.0,
+ 1068.0,
+ 537.0,
+ 1087.0,
+ 519.0,
+ 1087.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 578.0,
+ 1068.0,
+ 612.0,
+ 1068.0,
+ 612.0,
+ 1088.0,
+ 578.0,
+ 1088.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 1067.0,
+ 682.0,
+ 1067.0,
+ 682.0,
+ 1090.0,
+ 645.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 689.0,
+ 1069.0,
+ 707.0,
+ 1069.0,
+ 707.0,
+ 1087.0,
+ 689.0,
+ 1087.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 747.0,
+ 1067.0,
+ 785.0,
+ 1067.0,
+ 785.0,
+ 1090.0,
+ 747.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 814.0,
+ 1067.0,
+ 851.0,
+ 1067.0,
+ 851.0,
+ 1090.0,
+ 814.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1068.0,
+ 876.0,
+ 1068.0,
+ 876.0,
+ 1087.0,
+ 859.0,
+ 1087.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 919.0,
+ 1068.0,
+ 953.0,
+ 1068.0,
+ 953.0,
+ 1088.0,
+ 919.0,
+ 1088.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 1067.0,
+ 1022.0,
+ 1067.0,
+ 1022.0,
+ 1090.0,
+ 984.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1030.0,
+ 1069.0,
+ 1046.0,
+ 1069.0,
+ 1046.0,
+ 1087.0,
+ 1030.0,
+ 1087.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1088.0,
+ 1068.0,
+ 1122.0,
+ 1068.0,
+ 1122.0,
+ 1088.0,
+ 1088.0,
+ 1088.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1153.0,
+ 1067.0,
+ 1190.0,
+ 1067.0,
+ 1190.0,
+ 1090.0,
+ 1153.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1199.0,
+ 1069.0,
+ 1215.0,
+ 1069.0,
+ 1215.0,
+ 1087.0,
+ 1199.0,
+ 1087.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1257.0,
+ 1067.0,
+ 1293.0,
+ 1067.0,
+ 1293.0,
+ 1091.0,
+ 1257.0,
+ 1091.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1323.0,
+ 1065.0,
+ 1359.0,
+ 1065.0,
+ 1359.0,
+ 1090.0,
+ 1323.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 337.0,
+ 1091.0,
+ 515.0,
+ 1091.0,
+ 515.0,
+ 1118.0,
+ 337.0,
+ 1118.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 549.0,
+ 1094.0,
+ 643.0,
+ 1094.0,
+ 643.0,
+ 1116.0,
+ 549.0,
+ 1116.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 696.0,
+ 1094.0,
+ 835.0,
+ 1094.0,
+ 835.0,
+ 1116.0,
+ 696.0,
+ 1116.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 899.0,
+ 1092.0,
+ 972.0,
+ 1092.0,
+ 972.0,
+ 1116.0,
+ 899.0,
+ 1116.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1076.0,
+ 1091.0,
+ 1134.0,
+ 1091.0,
+ 1134.0,
+ 1118.0,
+ 1076.0,
+ 1118.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1073.0,
+ 1117.0,
+ 1096.0,
+ 1117.0,
+ 1096.0,
+ 1131.0,
+ 1073.0,
+ 1131.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1104.0,
+ 1120.0,
+ 1117.0,
+ 1120.0,
+ 1117.0,
+ 1131.0,
+ 1104.0,
+ 1131.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1139.0,
+ 1118.0,
+ 1155.0,
+ 1118.0,
+ 1155.0,
+ 1129.0,
+ 1139.0,
+ 1129.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 349.0,
+ 1182.0,
+ 369.0,
+ 1182.0,
+ 369.0,
+ 1206.0,
+ 349.0,
+ 1206.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 407.0,
+ 1182.0,
+ 445.0,
+ 1182.0,
+ 445.0,
+ 1207.0,
+ 407.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 1182.0,
+ 514.0,
+ 1182.0,
+ 514.0,
+ 1207.0,
+ 474.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 519.0,
+ 1185.0,
+ 537.0,
+ 1185.0,
+ 537.0,
+ 1204.0,
+ 519.0,
+ 1204.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 577.0,
+ 1182.0,
+ 614.0,
+ 1182.0,
+ 614.0,
+ 1207.0,
+ 577.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 1182.0,
+ 684.0,
+ 1182.0,
+ 684.0,
+ 1207.0,
+ 645.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 687.0,
+ 1184.0,
+ 708.0,
+ 1184.0,
+ 708.0,
+ 1206.0,
+ 687.0,
+ 1206.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 747.0,
+ 1182.0,
+ 784.0,
+ 1182.0,
+ 784.0,
+ 1207.0,
+ 747.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 814.0,
+ 1182.0,
+ 853.0,
+ 1182.0,
+ 853.0,
+ 1207.0,
+ 814.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 858.0,
+ 1185.0,
+ 876.0,
+ 1185.0,
+ 876.0,
+ 1203.0,
+ 858.0,
+ 1203.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 916.0,
+ 1182.0,
+ 954.0,
+ 1182.0,
+ 954.0,
+ 1207.0,
+ 916.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 1182.0,
+ 1022.0,
+ 1182.0,
+ 1022.0,
+ 1207.0,
+ 984.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1026.0,
+ 1184.0,
+ 1047.0,
+ 1184.0,
+ 1047.0,
+ 1206.0,
+ 1026.0,
+ 1206.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1086.0,
+ 1182.0,
+ 1123.0,
+ 1182.0,
+ 1123.0,
+ 1207.0,
+ 1086.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1153.0,
+ 1182.0,
+ 1192.0,
+ 1182.0,
+ 1192.0,
+ 1207.0,
+ 1153.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1197.0,
+ 1185.0,
+ 1215.0,
+ 1185.0,
+ 1215.0,
+ 1204.0,
+ 1197.0,
+ 1204.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1257.0,
+ 1182.0,
+ 1293.0,
+ 1182.0,
+ 1293.0,
+ 1207.0,
+ 1257.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1323.0,
+ 1182.0,
+ 1361.0,
+ 1182.0,
+ 1361.0,
+ 1207.0,
+ 1323.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 376.0,
+ 1207.0,
+ 475.0,
+ 1207.0,
+ 475.0,
+ 1236.0,
+ 376.0,
+ 1236.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 566.0,
+ 1208.0,
+ 624.0,
+ 1208.0,
+ 624.0,
+ 1236.0,
+ 566.0,
+ 1236.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 723.0,
+ 1208.0,
+ 807.0,
+ 1208.0,
+ 807.0,
+ 1236.0,
+ 723.0,
+ 1236.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 880.0,
+ 1208.0,
+ 990.0,
+ 1208.0,
+ 990.0,
+ 1234.0,
+ 880.0,
+ 1234.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1061.0,
+ 1208.0,
+ 1150.0,
+ 1208.0,
+ 1150.0,
+ 1234.0,
+ 1061.0,
+ 1234.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1231.0,
+ 1208.0,
+ 1317.0,
+ 1208.0,
+ 1317.0,
+ 1236.0,
+ 1231.0,
+ 1236.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 528.0,
+ 1290.0,
+ 538.0,
+ 1290.0,
+ 538.0,
+ 1301.0,
+ 528.0,
+ 1301.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 1302.0,
+ 366.0,
+ 1302.0,
+ 366.0,
+ 1321.0,
+ 350.0,
+ 1321.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 408.0,
+ 1300.0,
+ 445.0,
+ 1300.0,
+ 445.0,
+ 1324.0,
+ 408.0,
+ 1324.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 1300.0,
+ 512.0,
+ 1300.0,
+ 512.0,
+ 1324.0,
+ 474.0,
+ 1324.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 519.0,
+ 1302.0,
+ 537.0,
+ 1302.0,
+ 537.0,
+ 1320.0,
+ 519.0,
+ 1320.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 577.0,
+ 1300.0,
+ 614.0,
+ 1300.0,
+ 614.0,
+ 1324.0,
+ 577.0,
+ 1324.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 1300.0,
+ 682.0,
+ 1300.0,
+ 682.0,
+ 1323.0,
+ 645.0,
+ 1323.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 689.0,
+ 1302.0,
+ 705.0,
+ 1302.0,
+ 705.0,
+ 1320.0,
+ 689.0,
+ 1320.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 749.0,
+ 1301.0,
+ 782.0,
+ 1301.0,
+ 782.0,
+ 1321.0,
+ 749.0,
+ 1321.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 815.0,
+ 1300.0,
+ 853.0,
+ 1300.0,
+ 853.0,
+ 1323.0,
+ 815.0,
+ 1323.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1302.0,
+ 876.0,
+ 1302.0,
+ 876.0,
+ 1320.0,
+ 859.0,
+ 1320.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 918.0,
+ 1300.0,
+ 954.0,
+ 1300.0,
+ 954.0,
+ 1324.0,
+ 918.0,
+ 1324.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 1300.0,
+ 1022.0,
+ 1300.0,
+ 1022.0,
+ 1324.0,
+ 984.0,
+ 1324.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1030.0,
+ 1302.0,
+ 1046.0,
+ 1302.0,
+ 1046.0,
+ 1320.0,
+ 1030.0,
+ 1320.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1086.0,
+ 1300.0,
+ 1123.0,
+ 1300.0,
+ 1123.0,
+ 1324.0,
+ 1086.0,
+ 1324.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1154.0,
+ 1300.0,
+ 1190.0,
+ 1300.0,
+ 1190.0,
+ 1324.0,
+ 1154.0,
+ 1324.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1199.0,
+ 1302.0,
+ 1215.0,
+ 1302.0,
+ 1215.0,
+ 1321.0,
+ 1199.0,
+ 1321.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1257.0,
+ 1300.0,
+ 1293.0,
+ 1300.0,
+ 1293.0,
+ 1324.0,
+ 1257.0,
+ 1324.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1326.0,
+ 1301.0,
+ 1358.0,
+ 1301.0,
+ 1358.0,
+ 1321.0,
+ 1326.0,
+ 1321.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 396.0,
+ 1322.0,
+ 456.0,
+ 1322.0,
+ 456.0,
+ 1353.0,
+ 396.0,
+ 1353.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 564.0,
+ 1324.0,
+ 630.0,
+ 1324.0,
+ 630.0,
+ 1351.0,
+ 564.0,
+ 1351.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 699.0,
+ 1324.0,
+ 831.0,
+ 1324.0,
+ 831.0,
+ 1353.0,
+ 699.0,
+ 1353.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 882.0,
+ 1322.0,
+ 988.0,
+ 1322.0,
+ 988.0,
+ 1354.0,
+ 882.0,
+ 1354.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1073.0,
+ 1322.0,
+ 1138.0,
+ 1322.0,
+ 1138.0,
+ 1353.0,
+ 1073.0,
+ 1353.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1231.0,
+ 1325.0,
+ 1319.0,
+ 1325.0,
+ 1319.0,
+ 1351.0,
+ 1231.0,
+ 1351.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 457.0,
+ 1350.0,
+ 485.0,
+ 1350.0,
+ 485.0,
+ 1364.0,
+ 457.0,
+ 1364.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1099.0,
+ 1368.0,
+ 1112.0,
+ 1368.0,
+ 1112.0,
+ 1379.0,
+ 1099.0,
+ 1379.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1030.0,
+ 1388.0,
+ 1084.0,
+ 1388.0,
+ 1084.0,
+ 1424.0,
+ 1030.0,
+ 1424.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1205.0,
+ 1404.0,
+ 1219.0,
+ 1404.0,
+ 1219.0,
+ 1415.0,
+ 1205.0,
+ 1415.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 1419.0,
+ 366.0,
+ 1419.0,
+ 366.0,
+ 1439.0,
+ 350.0,
+ 1439.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 407.0,
+ 1417.0,
+ 445.0,
+ 1417.0,
+ 445.0,
+ 1441.0,
+ 407.0,
+ 1441.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 1417.0,
+ 514.0,
+ 1417.0,
+ 514.0,
+ 1440.0,
+ 474.0,
+ 1440.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 519.0,
+ 1419.0,
+ 537.0,
+ 1419.0,
+ 537.0,
+ 1437.0,
+ 519.0,
+ 1437.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 577.0,
+ 1417.0,
+ 614.0,
+ 1417.0,
+ 614.0,
+ 1441.0,
+ 577.0,
+ 1441.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 1417.0,
+ 682.0,
+ 1417.0,
+ 682.0,
+ 1440.0,
+ 645.0,
+ 1440.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 689.0,
+ 1419.0,
+ 705.0,
+ 1419.0,
+ 705.0,
+ 1437.0,
+ 689.0,
+ 1437.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 749.0,
+ 1418.0,
+ 782.0,
+ 1418.0,
+ 782.0,
+ 1439.0,
+ 749.0,
+ 1439.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 814.0,
+ 1417.0,
+ 853.0,
+ 1417.0,
+ 853.0,
+ 1441.0,
+ 814.0,
+ 1441.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 858.0,
+ 1419.0,
+ 876.0,
+ 1419.0,
+ 876.0,
+ 1437.0,
+ 858.0,
+ 1437.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 916.0,
+ 1417.0,
+ 954.0,
+ 1417.0,
+ 954.0,
+ 1441.0,
+ 916.0,
+ 1441.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 1417.0,
+ 1022.0,
+ 1417.0,
+ 1022.0,
+ 1440.0,
+ 984.0,
+ 1440.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1028.0,
+ 1419.0,
+ 1046.0,
+ 1419.0,
+ 1046.0,
+ 1437.0,
+ 1028.0,
+ 1437.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1086.0,
+ 1417.0,
+ 1124.0,
+ 1417.0,
+ 1124.0,
+ 1441.0,
+ 1086.0,
+ 1441.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1153.0,
+ 1417.0,
+ 1192.0,
+ 1417.0,
+ 1192.0,
+ 1440.0,
+ 1153.0,
+ 1440.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1197.0,
+ 1418.0,
+ 1215.0,
+ 1418.0,
+ 1215.0,
+ 1437.0,
+ 1197.0,
+ 1437.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1255.0,
+ 1417.0,
+ 1293.0,
+ 1417.0,
+ 1293.0,
+ 1440.0,
+ 1255.0,
+ 1440.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1323.0,
+ 1417.0,
+ 1361.0,
+ 1417.0,
+ 1361.0,
+ 1441.0,
+ 1323.0,
+ 1441.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 376.0,
+ 1442.0,
+ 476.0,
+ 1442.0,
+ 476.0,
+ 1469.0,
+ 376.0,
+ 1469.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 550.0,
+ 1443.0,
+ 641.0,
+ 1443.0,
+ 641.0,
+ 1469.0,
+ 550.0,
+ 1469.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 727.0,
+ 1439.0,
+ 805.0,
+ 1439.0,
+ 805.0,
+ 1472.0,
+ 727.0,
+ 1472.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 881.0,
+ 1444.0,
+ 988.0,
+ 1444.0,
+ 988.0,
+ 1466.0,
+ 881.0,
+ 1466.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1047.0,
+ 1444.0,
+ 1162.0,
+ 1444.0,
+ 1162.0,
+ 1466.0,
+ 1047.0,
+ 1466.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1216.0,
+ 1443.0,
+ 1334.0,
+ 1443.0,
+ 1334.0,
+ 1469.0,
+ 1216.0,
+ 1469.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1073.0,
+ 1497.0,
+ 1096.0,
+ 1497.0,
+ 1096.0,
+ 1511.0,
+ 1073.0,
+ 1511.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 1535.0,
+ 366.0,
+ 1535.0,
+ 366.0,
+ 1554.0,
+ 350.0,
+ 1554.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 408.0,
+ 1533.0,
+ 445.0,
+ 1533.0,
+ 445.0,
+ 1557.0,
+ 408.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 1533.0,
+ 514.0,
+ 1533.0,
+ 514.0,
+ 1557.0,
+ 474.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 519.0,
+ 1535.0,
+ 537.0,
+ 1535.0,
+ 537.0,
+ 1554.0,
+ 519.0,
+ 1554.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 578.0,
+ 1533.0,
+ 614.0,
+ 1533.0,
+ 614.0,
+ 1557.0,
+ 578.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 645.0,
+ 1533.0,
+ 682.0,
+ 1533.0,
+ 682.0,
+ 1557.0,
+ 645.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 689.0,
+ 1535.0,
+ 705.0,
+ 1535.0,
+ 705.0,
+ 1553.0,
+ 689.0,
+ 1553.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 747.0,
+ 1533.0,
+ 784.0,
+ 1533.0,
+ 784.0,
+ 1557.0,
+ 747.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 815.0,
+ 1533.0,
+ 851.0,
+ 1533.0,
+ 851.0,
+ 1557.0,
+ 815.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1535.0,
+ 876.0,
+ 1535.0,
+ 876.0,
+ 1553.0,
+ 859.0,
+ 1553.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 916.0,
+ 1533.0,
+ 954.0,
+ 1533.0,
+ 954.0,
+ 1557.0,
+ 916.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 1533.0,
+ 1022.0,
+ 1533.0,
+ 1022.0,
+ 1557.0,
+ 984.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1028.0,
+ 1535.0,
+ 1046.0,
+ 1535.0,
+ 1046.0,
+ 1553.0,
+ 1028.0,
+ 1553.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1086.0,
+ 1533.0,
+ 1124.0,
+ 1533.0,
+ 1124.0,
+ 1557.0,
+ 1086.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1153.0,
+ 1533.0,
+ 1192.0,
+ 1533.0,
+ 1192.0,
+ 1557.0,
+ 1153.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1197.0,
+ 1535.0,
+ 1215.0,
+ 1535.0,
+ 1215.0,
+ 1553.0,
+ 1197.0,
+ 1553.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1255.0,
+ 1533.0,
+ 1293.0,
+ 1533.0,
+ 1293.0,
+ 1557.0,
+ 1255.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1323.0,
+ 1533.0,
+ 1361.0,
+ 1533.0,
+ 1361.0,
+ 1557.0,
+ 1323.0,
+ 1557.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 391.0,
+ 1556.0,
+ 463.0,
+ 1556.0,
+ 463.0,
+ 1589.0,
+ 391.0,
+ 1589.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 580.0,
+ 1594.0,
+ 649.0,
+ 1594.0,
+ 649.0,
+ 1617.0,
+ 580.0,
+ 1617.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 442.0,
+ 1609.0,
+ 465.0,
+ 1609.0,
+ 465.0,
+ 1624.0,
+ 442.0,
+ 1624.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 580.0,
+ 1614.0,
+ 646.0,
+ 1614.0,
+ 646.0,
+ 1637.0,
+ 580.0,
+ 1637.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 350.0,
+ 1654.0,
+ 366.0,
+ 1654.0,
+ 366.0,
+ 1672.0,
+ 350.0,
+ 1672.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 405.0,
+ 1651.0,
+ 443.0,
+ 1651.0,
+ 443.0,
+ 1671.0,
+ 405.0,
+ 1671.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 474.0,
+ 1650.0,
+ 512.0,
+ 1650.0,
+ 512.0,
+ 1674.0,
+ 474.0,
+ 1674.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 803.0,
+ 896.0,
+ 803.0,
+ 896.0,
+ 813.0,
+ 857.0,
+ 813.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1248.0,
+ 1090.0,
+ 1299.0,
+ 1090.0,
+ 1299.0,
+ 1119.0,
+ 1248.0,
+ 1119.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 712.75,
+ 1134.5,
+ 791.75,
+ 1134.5,
+ 791.75,
+ 1161.5,
+ 712.75,
+ 1161.5
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 445.25,
+ 1276.5,
+ 494.25,
+ 1276.5,
+ 494.25,
+ 1295.5,
+ 445.25,
+ 1295.5
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 539.0,
+ 1267.0,
+ 574.0,
+ 1267.0,
+ 574.0,
+ 1278.5,
+ 539.0,
+ 1278.5
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1758.0,
+ 1403.0,
+ 1758.0,
+ 1403.0,
+ 1794.0,
+ 295.0,
+ 1794.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1789.0,
+ 649.0,
+ 1789.0,
+ 649.0,
+ 1823.0,
+ 293.0,
+ 1823.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 72.0,
+ 817.0,
+ 72.0,
+ 817.0,
+ 109.0,
+ 296.0,
+ 109.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 223.0,
+ 726.0,
+ 223.0,
+ 726.0,
+ 266.0,
+ 292.0,
+ 266.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 832.0,
+ 2085.0,
+ 870.0,
+ 2085.0,
+ 870.0,
+ 2123.0,
+ 832.0,
+ 2123.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 295.0,
+ 1071.0,
+ 295.0,
+ 1071.0,
+ 332.0,
+ 296.0,
+ 332.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 421.0,
+ 1090.0,
+ 421.0,
+ 1090.0,
+ 464.0,
+ 295.0,
+ 464.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 12,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 3,
+ "poly": [
+ 320,
+ 441,
+ 1373,
+ 441,
+ 1373,
+ 1614,
+ 320,
+ 1614
+ ],
+ "score": 0.969
+ },
+ {
+ "category_id": 4,
+ "poly": [
+ 295,
+ 1659,
+ 1405,
+ 1659,
+ 1405,
+ 1846,
+ 295,
+ 1846
+ ],
+ "score": 0.943
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 299,
+ 76,
+ 815,
+ 76,
+ 815,
+ 105,
+ 299,
+ 105
+ ],
+ "score": 0.889
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 836,
+ 2088,
+ 865,
+ 2088,
+ 865,
+ 2112,
+ 836,
+ 2112
+ ],
+ "score": 0.848
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 304,
+ 411,
+ 420,
+ 411,
+ 420,
+ 429,
+ 304,
+ 429
+ ],
+ "score": 0.207
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 298,
+ 1720,
+ 388,
+ 1720,
+ 388,
+ 1755,
+ 298,
+ 1755
+ ],
+ "score": 0.92,
+ "latex": "\\rho ^ { 2 } ( \\mathbf { s } , \\mathbf { a } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 298,
+ 1814,
+ 495,
+ 1814,
+ 495,
+ 1846,
+ 298,
+ 1846
+ ],
+ "score": 0.9,
+ "latex": "\\sigma , \\mu - 1 . 5 \\sigma , \\mathrm { m i n } ]"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 886,
+ 1783,
+ 1405,
+ 1783,
+ 1405,
+ 1815,
+ 886,
+ 1815
+ ],
+ "score": 0.82,
+ "latex": "\\mu + 1 . 5 \\sigma , \\mu + \\sigma , \\mu + 0 . 5 \\sigma , \\mu , \\mu - 0 . 5 \\sigma , \\mu -"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 557,
+ 1818,
+ 577,
+ 1818,
+ 577,
+ 1841,
+ 557,
+ 1841
+ ],
+ "score": 0.78,
+ "latex": "x"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 434.0,
+ 455.0,
+ 469.0,
+ 455.0,
+ 469.0,
+ 473.0,
+ 434.0,
+ 473.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 702.0,
+ 455.0,
+ 737.0,
+ 455.0,
+ 737.0,
+ 473.0,
+ 702.0,
+ 473.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 465.0,
+ 884.0,
+ 465.0,
+ 884.0,
+ 484.0,
+ 857.0,
+ 484.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 967.0,
+ 455.0,
+ 1011.0,
+ 455.0,
+ 1011.0,
+ 473.0,
+ 967.0,
+ 473.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 461.0,
+ 1149.0,
+ 461.0,
+ 1149.0,
+ 481.0,
+ 1127.0,
+ 481.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1236.0,
+ 455.0,
+ 1280.0,
+ 455.0,
+ 1280.0,
+ 473.0,
+ 1236.0,
+ 473.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 582.0,
+ 473.0,
+ 610.0,
+ 473.0,
+ 610.0,
+ 492.0,
+ 582.0,
+ 492.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 484.0,
+ 341.0,
+ 484.0,
+ 341.0,
+ 500.0,
+ 319.0,
+ 500.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 582.0,
+ 490.0,
+ 610.0,
+ 490.0,
+ 610.0,
+ 509.0,
+ 582.0,
+ 509.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 496.0,
+ 880.0,
+ 496.0,
+ 880.0,
+ 512.0,
+ 859.0,
+ 512.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 488.0,
+ 1147.0,
+ 488.0,
+ 1147.0,
+ 504.0,
+ 1127.0,
+ 504.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 509.0,
+ 341.0,
+ 509.0,
+ 341.0,
+ 524.0,
+ 321.0,
+ 524.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 582.0,
+ 508.0,
+ 610.0,
+ 508.0,
+ 610.0,
+ 526.0,
+ 582.0,
+ 526.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 510.0,
+ 1148.0,
+ 510.0,
+ 1148.0,
+ 532.0,
+ 1127.0,
+ 532.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 533.0,
+ 341.0,
+ 533.0,
+ 341.0,
+ 573.0,
+ 321.0,
+ 573.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 582.0,
+ 525.0,
+ 610.0,
+ 525.0,
+ 610.0,
+ 579.0,
+ 582.0,
+ 579.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 524.0,
+ 881.0,
+ 524.0,
+ 881.0,
+ 570.0,
+ 857.0,
+ 570.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1125.0,
+ 536.0,
+ 1149.0,
+ 536.0,
+ 1149.0,
+ 582.0,
+ 1125.0,
+ 582.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 582.0,
+ 341.0,
+ 582.0,
+ 341.0,
+ 597.0,
+ 321.0,
+ 597.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 582.0,
+ 578.0,
+ 610.0,
+ 578.0,
+ 610.0,
+ 597.0,
+ 582.0,
+ 597.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 581.0,
+ 880.0,
+ 581.0,
+ 880.0,
+ 597.0,
+ 859.0,
+ 597.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 582.0,
+ 595.0,
+ 610.0,
+ 595.0,
+ 610.0,
+ 614.0,
+ 582.0,
+ 614.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 590.0,
+ 1148.0,
+ 590.0,
+ 1148.0,
+ 606.0,
+ 1127.0,
+ 606.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 606.0,
+ 566.0,
+ 606.0,
+ 566.0,
+ 639.0,
+ 319.0,
+ 639.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 584.0,
+ 615.0,
+ 836.0,
+ 615.0,
+ 836.0,
+ 638.0,
+ 584.0,
+ 638.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 610.0,
+ 1105.0,
+ 610.0,
+ 1105.0,
+ 640.0,
+ 859.0,
+ 640.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1128.0,
+ 615.0,
+ 1374.0,
+ 615.0,
+ 1374.0,
+ 639.0,
+ 1128.0,
+ 639.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 544.0,
+ 632.0,
+ 566.0,
+ 632.0,
+ 566.0,
+ 647.0,
+ 544.0,
+ 647.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 813.0,
+ 632.0,
+ 834.0,
+ 632.0,
+ 834.0,
+ 647.0,
+ 813.0,
+ 647.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1081.0,
+ 632.0,
+ 1104.0,
+ 632.0,
+ 1104.0,
+ 647.0,
+ 1081.0,
+ 647.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1351.0,
+ 632.0,
+ 1374.0,
+ 632.0,
+ 1374.0,
+ 647.0,
+ 1351.0,
+ 647.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 430.0,
+ 646.0,
+ 473.0,
+ 646.0,
+ 473.0,
+ 664.0,
+ 430.0,
+ 664.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 698.0,
+ 646.0,
+ 741.0,
+ 646.0,
+ 741.0,
+ 664.0,
+ 698.0,
+ 664.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 958.0,
+ 643.0,
+ 1020.0,
+ 643.0,
+ 1020.0,
+ 667.0,
+ 958.0,
+ 667.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1226.0,
+ 643.0,
+ 1290.0,
+ 643.0,
+ 1290.0,
+ 667.0,
+ 1226.0,
+ 667.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 663.0,
+ 610.0,
+ 663.0,
+ 610.0,
+ 677.0,
+ 589.0,
+ 677.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 673.0,
+ 341.0,
+ 673.0,
+ 341.0,
+ 689.0,
+ 321.0,
+ 689.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 680.0,
+ 609.0,
+ 680.0,
+ 609.0,
+ 695.0,
+ 589.0,
+ 695.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1125.0,
+ 673.0,
+ 1148.0,
+ 673.0,
+ 1148.0,
+ 693.0,
+ 1125.0,
+ 693.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 697.0,
+ 341.0,
+ 697.0,
+ 341.0,
+ 712.0,
+ 321.0,
+ 712.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 590.0,
+ 697.0,
+ 609.0,
+ 697.0,
+ 609.0,
+ 713.0,
+ 590.0,
+ 713.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 695.0,
+ 881.0,
+ 695.0,
+ 881.0,
+ 711.0,
+ 859.0,
+ 711.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 700.0,
+ 1148.0,
+ 700.0,
+ 1148.0,
+ 716.0,
+ 1127.0,
+ 716.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 720.0,
+ 341.0,
+ 720.0,
+ 341.0,
+ 734.0,
+ 321.0,
+ 734.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 716.0,
+ 609.0,
+ 716.0,
+ 609.0,
+ 748.0,
+ 589.0,
+ 748.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 728.0,
+ 880.0,
+ 728.0,
+ 880.0,
+ 744.0,
+ 859.0,
+ 744.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1125.0,
+ 724.0,
+ 1149.0,
+ 724.0,
+ 1149.0,
+ 744.0,
+ 1125.0,
+ 744.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 742.0,
+ 341.0,
+ 742.0,
+ 341.0,
+ 758.0,
+ 321.0,
+ 758.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 750.0,
+ 609.0,
+ 750.0,
+ 609.0,
+ 765.0,
+ 589.0,
+ 765.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 750.0,
+ 1148.0,
+ 750.0,
+ 1148.0,
+ 766.0,
+ 1127.0,
+ 766.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 766.0,
+ 341.0,
+ 766.0,
+ 341.0,
+ 781.0,
+ 321.0,
+ 781.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 768.0,
+ 610.0,
+ 768.0,
+ 610.0,
+ 782.0,
+ 589.0,
+ 782.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 760.0,
+ 881.0,
+ 760.0,
+ 881.0,
+ 776.0,
+ 859.0,
+ 776.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 777.0,
+ 1148.0,
+ 777.0,
+ 1148.0,
+ 793.0,
+ 1127.0,
+ 793.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 789.0,
+ 341.0,
+ 789.0,
+ 341.0,
+ 805.0,
+ 319.0,
+ 805.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 785.0,
+ 609.0,
+ 785.0,
+ 609.0,
+ 801.0,
+ 589.0,
+ 801.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 793.0,
+ 881.0,
+ 793.0,
+ 881.0,
+ 807.0,
+ 857.0,
+ 807.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 802.0,
+ 610.0,
+ 802.0,
+ 610.0,
+ 817.0,
+ 589.0,
+ 817.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1128.0,
+ 802.0,
+ 1151.0,
+ 802.0,
+ 1151.0,
+ 817.0,
+ 1128.0,
+ 817.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 335.0,
+ 813.0,
+ 566.0,
+ 813.0,
+ 566.0,
+ 830.0,
+ 335.0,
+ 830.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 605.0,
+ 813.0,
+ 836.0,
+ 813.0,
+ 836.0,
+ 830.0,
+ 605.0,
+ 830.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 871.0,
+ 809.0,
+ 1105.0,
+ 809.0,
+ 1105.0,
+ 831.0,
+ 871.0,
+ 831.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1144.0,
+ 813.0,
+ 1374.0,
+ 813.0,
+ 1374.0,
+ 830.0,
+ 1144.0,
+ 830.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 544.0,
+ 823.0,
+ 566.0,
+ 823.0,
+ 566.0,
+ 838.0,
+ 544.0,
+ 838.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 812.0,
+ 823.0,
+ 836.0,
+ 823.0,
+ 836.0,
+ 838.0,
+ 812.0,
+ 838.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1081.0,
+ 823.0,
+ 1104.0,
+ 823.0,
+ 1104.0,
+ 838.0,
+ 1081.0,
+ 838.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1351.0,
+ 825.0,
+ 1374.0,
+ 825.0,
+ 1374.0,
+ 838.0,
+ 1351.0,
+ 838.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 429.0,
+ 837.0,
+ 474.0,
+ 837.0,
+ 474.0,
+ 855.0,
+ 429.0,
+ 855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 697.0,
+ 837.0,
+ 742.0,
+ 837.0,
+ 742.0,
+ 855.0,
+ 697.0,
+ 855.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 962.0,
+ 835.0,
+ 1016.0,
+ 835.0,
+ 1016.0,
+ 857.0,
+ 962.0,
+ 857.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1232.0,
+ 835.0,
+ 1285.0,
+ 835.0,
+ 1285.0,
+ 857.0,
+ 1232.0,
+ 857.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 847.0,
+ 885.0,
+ 847.0,
+ 885.0,
+ 866.0,
+ 852.0,
+ 866.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 330.0,
+ 866.0,
+ 339.0,
+ 866.0,
+ 339.0,
+ 876.0,
+ 330.0,
+ 876.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 862.0,
+ 609.0,
+ 862.0,
+ 609.0,
+ 878.0,
+ 589.0,
+ 878.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 867.0,
+ 881.0,
+ 867.0,
+ 881.0,
+ 886.0,
+ 852.0,
+ 886.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 862.0,
+ 1147.0,
+ 862.0,
+ 1147.0,
+ 878.0,
+ 1127.0,
+ 878.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 886.0,
+ 609.0,
+ 886.0,
+ 609.0,
+ 900.0,
+ 589.0,
+ 900.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 887.0,
+ 881.0,
+ 887.0,
+ 881.0,
+ 906.0,
+ 852.0,
+ 906.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 891.0,
+ 1148.0,
+ 891.0,
+ 1148.0,
+ 907.0,
+ 1127.0,
+ 907.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 908.0,
+ 609.0,
+ 908.0,
+ 609.0,
+ 923.0,
+ 589.0,
+ 923.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 908.0,
+ 881.0,
+ 908.0,
+ 881.0,
+ 927.0,
+ 852.0,
+ 927.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 920.0,
+ 1147.0,
+ 920.0,
+ 1147.0,
+ 936.0,
+ 1127.0,
+ 936.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 931.0,
+ 608.0,
+ 931.0,
+ 608.0,
+ 947.0,
+ 589.0,
+ 947.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 929.0,
+ 883.0,
+ 929.0,
+ 883.0,
+ 948.0,
+ 852.0,
+ 948.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 443.0,
+ 960.0,
+ 472.0,
+ 960.0,
+ 472.0,
+ 969.0,
+ 443.0,
+ 969.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 953.0,
+ 609.0,
+ 953.0,
+ 609.0,
+ 968.0,
+ 589.0,
+ 968.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 949.0,
+ 883.0,
+ 949.0,
+ 883.0,
+ 968.0,
+ 852.0,
+ 968.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1125.0,
+ 947.0,
+ 1149.0,
+ 947.0,
+ 1149.0,
+ 967.0,
+ 1125.0,
+ 967.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 330.0,
+ 968.0,
+ 339.0,
+ 968.0,
+ 339.0,
+ 978.0,
+ 330.0,
+ 978.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 399.0,
+ 973.0,
+ 435.0,
+ 973.0,
+ 435.0,
+ 990.0,
+ 399.0,
+ 990.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 976.0,
+ 609.0,
+ 976.0,
+ 609.0,
+ 990.0,
+ 589.0,
+ 990.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 969.0,
+ 883.0,
+ 969.0,
+ 883.0,
+ 988.0,
+ 852.0,
+ 988.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 977.0,
+ 1147.0,
+ 977.0,
+ 1147.0,
+ 992.0,
+ 1127.0,
+ 992.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 853.0,
+ 992.0,
+ 884.0,
+ 992.0,
+ 884.0,
+ 1006.0,
+ 853.0,
+ 1006.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 335.0,
+ 1004.0,
+ 566.0,
+ 1004.0,
+ 566.0,
+ 1021.0,
+ 335.0,
+ 1021.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 875.0,
+ 1004.0,
+ 1105.0,
+ 1004.0,
+ 1105.0,
+ 1021.0,
+ 875.0,
+ 1021.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1143.0,
+ 1004.0,
+ 1374.0,
+ 1004.0,
+ 1374.0,
+ 1021.0,
+ 1143.0,
+ 1021.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 544.0,
+ 1014.0,
+ 566.0,
+ 1014.0,
+ 566.0,
+ 1029.0,
+ 544.0,
+ 1029.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 812.0,
+ 1016.0,
+ 836.0,
+ 1016.0,
+ 836.0,
+ 1029.0,
+ 812.0,
+ 1029.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1081.0,
+ 1014.0,
+ 1104.0,
+ 1014.0,
+ 1104.0,
+ 1029.0,
+ 1081.0,
+ 1029.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1351.0,
+ 1016.0,
+ 1374.0,
+ 1016.0,
+ 1374.0,
+ 1029.0,
+ 1351.0,
+ 1029.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 421.0,
+ 1026.0,
+ 483.0,
+ 1026.0,
+ 483.0,
+ 1048.0,
+ 421.0,
+ 1048.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 688.0,
+ 1026.0,
+ 752.0,
+ 1026.0,
+ 752.0,
+ 1048.0,
+ 688.0,
+ 1048.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 972.0,
+ 1027.0,
+ 1009.0,
+ 1027.0,
+ 1009.0,
+ 1046.0,
+ 972.0,
+ 1046.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1239.0,
+ 1027.0,
+ 1278.0,
+ 1027.0,
+ 1278.0,
+ 1046.0,
+ 1239.0,
+ 1046.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1051.0,
+ 341.0,
+ 1051.0,
+ 341.0,
+ 1067.0,
+ 321.0,
+ 1067.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 590.0,
+ 1046.0,
+ 609.0,
+ 1046.0,
+ 609.0,
+ 1061.0,
+ 590.0,
+ 1061.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1049.0,
+ 880.0,
+ 1049.0,
+ 880.0,
+ 1065.0,
+ 859.0,
+ 1065.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1050.0,
+ 1148.0,
+ 1050.0,
+ 1148.0,
+ 1065.0,
+ 1127.0,
+ 1065.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1070.0,
+ 341.0,
+ 1070.0,
+ 341.0,
+ 1086.0,
+ 321.0,
+ 1086.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 590.0,
+ 1071.0,
+ 609.0,
+ 1071.0,
+ 609.0,
+ 1086.0,
+ 590.0,
+ 1086.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 1070.0,
+ 881.0,
+ 1070.0,
+ 881.0,
+ 1085.0,
+ 857.0,
+ 1085.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1074.0,
+ 1148.0,
+ 1074.0,
+ 1148.0,
+ 1090.0,
+ 1127.0,
+ 1090.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1090.0,
+ 341.0,
+ 1090.0,
+ 341.0,
+ 1106.0,
+ 321.0,
+ 1106.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1095.0,
+ 609.0,
+ 1095.0,
+ 609.0,
+ 1111.0,
+ 589.0,
+ 1111.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 1091.0,
+ 880.0,
+ 1091.0,
+ 880.0,
+ 1106.0,
+ 857.0,
+ 1106.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1098.0,
+ 1148.0,
+ 1098.0,
+ 1148.0,
+ 1112.0,
+ 1127.0,
+ 1112.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1108.0,
+ 341.0,
+ 1108.0,
+ 341.0,
+ 1124.0,
+ 321.0,
+ 1124.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1111.0,
+ 880.0,
+ 1111.0,
+ 880.0,
+ 1127.0,
+ 859.0,
+ 1127.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1127.0,
+ 341.0,
+ 1127.0,
+ 341.0,
+ 1143.0,
+ 321.0,
+ 1143.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1122.0,
+ 609.0,
+ 1122.0,
+ 609.0,
+ 1136.0,
+ 589.0,
+ 1136.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1132.0,
+ 880.0,
+ 1132.0,
+ 880.0,
+ 1148.0,
+ 859.0,
+ 1148.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1125.0,
+ 1119.0,
+ 1148.0,
+ 1119.0,
+ 1148.0,
+ 1139.0,
+ 1125.0,
+ 1139.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 1147.0,
+ 341.0,
+ 1147.0,
+ 341.0,
+ 1163.0,
+ 319.0,
+ 1163.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1146.0,
+ 609.0,
+ 1146.0,
+ 609.0,
+ 1160.0,
+ 589.0,
+ 1160.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1153.0,
+ 880.0,
+ 1153.0,
+ 880.0,
+ 1169.0,
+ 859.0,
+ 1169.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1125.0,
+ 1143.0,
+ 1149.0,
+ 1143.0,
+ 1149.0,
+ 1163.0,
+ 1125.0,
+ 1163.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1167.0,
+ 341.0,
+ 1167.0,
+ 341.0,
+ 1181.0,
+ 321.0,
+ 1181.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1171.0,
+ 609.0,
+ 1171.0,
+ 609.0,
+ 1185.0,
+ 589.0,
+ 1185.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1173.0,
+ 880.0,
+ 1173.0,
+ 880.0,
+ 1189.0,
+ 859.0,
+ 1189.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1168.0,
+ 1147.0,
+ 1168.0,
+ 1147.0,
+ 1184.0,
+ 1127.0,
+ 1184.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1185.0,
+ 342.0,
+ 1185.0,
+ 342.0,
+ 1200.0,
+ 321.0,
+ 1200.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 333.0,
+ 1192.0,
+ 568.0,
+ 1192.0,
+ 568.0,
+ 1212.0,
+ 333.0,
+ 1212.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 605.0,
+ 1195.0,
+ 836.0,
+ 1195.0,
+ 836.0,
+ 1212.0,
+ 605.0,
+ 1212.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 873.0,
+ 1195.0,
+ 1104.0,
+ 1195.0,
+ 1104.0,
+ 1212.0,
+ 873.0,
+ 1212.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1144.0,
+ 1195.0,
+ 1374.0,
+ 1195.0,
+ 1374.0,
+ 1212.0,
+ 1144.0,
+ 1212.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 544.0,
+ 1205.0,
+ 566.0,
+ 1205.0,
+ 566.0,
+ 1220.0,
+ 544.0,
+ 1220.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 812.0,
+ 1207.0,
+ 834.0,
+ 1207.0,
+ 834.0,
+ 1220.0,
+ 812.0,
+ 1220.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1081.0,
+ 1205.0,
+ 1104.0,
+ 1205.0,
+ 1104.0,
+ 1220.0,
+ 1081.0,
+ 1220.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1351.0,
+ 1207.0,
+ 1374.0,
+ 1207.0,
+ 1374.0,
+ 1220.0,
+ 1351.0,
+ 1220.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 415.0,
+ 1217.0,
+ 486.0,
+ 1217.0,
+ 486.0,
+ 1238.0,
+ 415.0,
+ 1238.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 683.0,
+ 1215.0,
+ 755.0,
+ 1215.0,
+ 755.0,
+ 1240.0,
+ 683.0,
+ 1240.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 962.0,
+ 1215.0,
+ 1016.0,
+ 1215.0,
+ 1016.0,
+ 1240.0,
+ 962.0,
+ 1240.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1231.0,
+ 1217.0,
+ 1287.0,
+ 1217.0,
+ 1287.0,
+ 1238.0,
+ 1231.0,
+ 1238.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1233.0,
+ 343.0,
+ 1233.0,
+ 343.0,
+ 1248.0,
+ 321.0,
+ 1248.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1232.0,
+ 887.0,
+ 1232.0,
+ 887.0,
+ 1250.0,
+ 852.0,
+ 1250.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1236.0,
+ 1149.0,
+ 1236.0,
+ 1149.0,
+ 1252.0,
+ 1127.0,
+ 1252.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1252.0,
+ 341.0,
+ 1252.0,
+ 341.0,
+ 1266.0,
+ 321.0,
+ 1266.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1256.0,
+ 609.0,
+ 1256.0,
+ 609.0,
+ 1270.0,
+ 589.0,
+ 1270.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1249.0,
+ 881.0,
+ 1249.0,
+ 881.0,
+ 1269.0,
+ 852.0,
+ 1269.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1260.0,
+ 1147.0,
+ 1260.0,
+ 1147.0,
+ 1275.0,
+ 1127.0,
+ 1275.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1270.0,
+ 341.0,
+ 1270.0,
+ 341.0,
+ 1285.0,
+ 321.0,
+ 1285.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1268.0,
+ 881.0,
+ 1268.0,
+ 881.0,
+ 1286.0,
+ 852.0,
+ 1286.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1287.0,
+ 341.0,
+ 1287.0,
+ 341.0,
+ 1302.0,
+ 321.0,
+ 1302.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 590.0,
+ 1289.0,
+ 609.0,
+ 1289.0,
+ 609.0,
+ 1305.0,
+ 590.0,
+ 1305.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1285.0,
+ 881.0,
+ 1285.0,
+ 881.0,
+ 1303.0,
+ 852.0,
+ 1303.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1283.0,
+ 1148.0,
+ 1283.0,
+ 1148.0,
+ 1299.0,
+ 1127.0,
+ 1299.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1306.0,
+ 341.0,
+ 1306.0,
+ 341.0,
+ 1321.0,
+ 321.0,
+ 1321.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1302.0,
+ 881.0,
+ 1302.0,
+ 881.0,
+ 1321.0,
+ 852.0,
+ 1321.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1307.0,
+ 1147.0,
+ 1307.0,
+ 1147.0,
+ 1323.0,
+ 1127.0,
+ 1323.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1323.0,
+ 341.0,
+ 1323.0,
+ 341.0,
+ 1339.0,
+ 321.0,
+ 1339.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 590.0,
+ 1323.0,
+ 608.0,
+ 1323.0,
+ 608.0,
+ 1338.0,
+ 590.0,
+ 1338.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1321.0,
+ 881.0,
+ 1321.0,
+ 881.0,
+ 1339.0,
+ 852.0,
+ 1339.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1342.0,
+ 341.0,
+ 1342.0,
+ 341.0,
+ 1356.0,
+ 321.0,
+ 1356.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1336.0,
+ 881.0,
+ 1336.0,
+ 881.0,
+ 1356.0,
+ 852.0,
+ 1356.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1331.0,
+ 1148.0,
+ 1331.0,
+ 1148.0,
+ 1347.0,
+ 1127.0,
+ 1347.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 1360.0,
+ 341.0,
+ 1360.0,
+ 341.0,
+ 1375.0,
+ 319.0,
+ 1375.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1356.0,
+ 608.0,
+ 1356.0,
+ 608.0,
+ 1371.0,
+ 589.0,
+ 1371.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1355.0,
+ 881.0,
+ 1355.0,
+ 881.0,
+ 1374.0,
+ 852.0,
+ 1374.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1355.0,
+ 1147.0,
+ 1355.0,
+ 1147.0,
+ 1371.0,
+ 1127.0,
+ 1371.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1379.0,
+ 566.0,
+ 1379.0,
+ 566.0,
+ 1403.0,
+ 321.0,
+ 1403.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 605.0,
+ 1386.0,
+ 836.0,
+ 1386.0,
+ 836.0,
+ 1403.0,
+ 605.0,
+ 1403.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1372.0,
+ 1105.0,
+ 1372.0,
+ 1105.0,
+ 1403.0,
+ 852.0,
+ 1403.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 544.0,
+ 1396.0,
+ 566.0,
+ 1396.0,
+ 566.0,
+ 1411.0,
+ 544.0,
+ 1411.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 813.0,
+ 1397.0,
+ 836.0,
+ 1397.0,
+ 836.0,
+ 1411.0,
+ 813.0,
+ 1411.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1081.0,
+ 1396.0,
+ 1104.0,
+ 1396.0,
+ 1104.0,
+ 1411.0,
+ 1081.0,
+ 1411.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1351.0,
+ 1397.0,
+ 1374.0,
+ 1397.0,
+ 1374.0,
+ 1411.0,
+ 1351.0,
+ 1411.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 411.0,
+ 1411.0,
+ 492.0,
+ 1411.0,
+ 492.0,
+ 1428.0,
+ 411.0,
+ 1428.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 681.0,
+ 1411.0,
+ 760.0,
+ 1411.0,
+ 760.0,
+ 1428.0,
+ 681.0,
+ 1428.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 961.0,
+ 1411.0,
+ 1019.0,
+ 1411.0,
+ 1019.0,
+ 1428.0,
+ 961.0,
+ 1428.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1229.0,
+ 1411.0,
+ 1287.0,
+ 1411.0,
+ 1287.0,
+ 1428.0,
+ 1229.0,
+ 1428.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 1423.0,
+ 887.0,
+ 1423.0,
+ 887.0,
+ 1441.0,
+ 857.0,
+ 1441.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1420.0,
+ 1148.0,
+ 1420.0,
+ 1148.0,
+ 1435.0,
+ 1127.0,
+ 1435.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1435.0,
+ 341.0,
+ 1435.0,
+ 341.0,
+ 1449.0,
+ 321.0,
+ 1449.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1433.0,
+ 609.0,
+ 1433.0,
+ 609.0,
+ 1449.0,
+ 589.0,
+ 1449.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1441.0,
+ 881.0,
+ 1441.0,
+ 881.0,
+ 1457.0,
+ 859.0,
+ 1457.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1454.0,
+ 341.0,
+ 1454.0,
+ 341.0,
+ 1470.0,
+ 321.0,
+ 1470.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1462.0,
+ 609.0,
+ 1462.0,
+ 609.0,
+ 1477.0,
+ 589.0,
+ 1477.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1460.0,
+ 881.0,
+ 1460.0,
+ 881.0,
+ 1476.0,
+ 859.0,
+ 1476.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1451.0,
+ 1148.0,
+ 1451.0,
+ 1148.0,
+ 1466.0,
+ 1127.0,
+ 1466.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1474.0,
+ 341.0,
+ 1474.0,
+ 341.0,
+ 1490.0,
+ 321.0,
+ 1490.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1478.0,
+ 880.0,
+ 1478.0,
+ 880.0,
+ 1494.0,
+ 859.0,
+ 1494.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1128.0,
+ 1482.0,
+ 1147.0,
+ 1482.0,
+ 1147.0,
+ 1498.0,
+ 1128.0,
+ 1498.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1496.0,
+ 341.0,
+ 1496.0,
+ 341.0,
+ 1510.0,
+ 321.0,
+ 1510.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 590.0,
+ 1490.0,
+ 609.0,
+ 1490.0,
+ 609.0,
+ 1506.0,
+ 590.0,
+ 1506.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 1494.0,
+ 881.0,
+ 1494.0,
+ 881.0,
+ 1514.0,
+ 857.0,
+ 1514.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1517.0,
+ 341.0,
+ 1517.0,
+ 341.0,
+ 1531.0,
+ 321.0,
+ 1531.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1519.0,
+ 609.0,
+ 1519.0,
+ 609.0,
+ 1535.0,
+ 589.0,
+ 1535.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1514.0,
+ 880.0,
+ 1514.0,
+ 880.0,
+ 1530.0,
+ 859.0,
+ 1530.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1513.0,
+ 1148.0,
+ 1513.0,
+ 1148.0,
+ 1529.0,
+ 1127.0,
+ 1529.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1537.0,
+ 341.0,
+ 1537.0,
+ 341.0,
+ 1553.0,
+ 321.0,
+ 1553.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1533.0,
+ 880.0,
+ 1533.0,
+ 880.0,
+ 1549.0,
+ 859.0,
+ 1549.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 589.0,
+ 1549.0,
+ 609.0,
+ 1549.0,
+ 609.0,
+ 1563.0,
+ 589.0,
+ 1563.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1551.0,
+ 880.0,
+ 1551.0,
+ 880.0,
+ 1567.0,
+ 859.0,
+ 1567.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1127.0,
+ 1545.0,
+ 1147.0,
+ 1545.0,
+ 1147.0,
+ 1561.0,
+ 1127.0,
+ 1561.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 1558.0,
+ 341.0,
+ 1558.0,
+ 341.0,
+ 1573.0,
+ 319.0,
+ 1573.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 859.0,
+ 1570.0,
+ 881.0,
+ 1570.0,
+ 881.0,
+ 1584.0,
+ 859.0,
+ 1584.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 335.0,
+ 1576.0,
+ 566.0,
+ 1576.0,
+ 566.0,
+ 1594.0,
+ 335.0,
+ 1594.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 606.0,
+ 1576.0,
+ 836.0,
+ 1576.0,
+ 836.0,
+ 1594.0,
+ 606.0,
+ 1594.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 875.0,
+ 1576.0,
+ 1104.0,
+ 1576.0,
+ 1104.0,
+ 1594.0,
+ 875.0,
+ 1594.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1144.0,
+ 1576.0,
+ 1374.0,
+ 1576.0,
+ 1374.0,
+ 1594.0,
+ 1144.0,
+ 1594.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 544.0,
+ 1587.0,
+ 566.0,
+ 1587.0,
+ 566.0,
+ 1602.0,
+ 544.0,
+ 1602.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 813.0,
+ 1588.0,
+ 834.0,
+ 1588.0,
+ 834.0,
+ 1602.0,
+ 813.0,
+ 1602.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1083.0,
+ 1587.0,
+ 1104.0,
+ 1587.0,
+ 1104.0,
+ 1602.0,
+ 1083.0,
+ 1602.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1351.0,
+ 1587.0,
+ 1374.0,
+ 1587.0,
+ 1374.0,
+ 1602.0,
+ 1351.0,
+ 1602.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 855.0,
+ 660.0,
+ 885.0,
+ 660.0,
+ 885.0,
+ 679.0,
+ 855.0,
+ 679.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 582.25,
+ 994.5,
+ 840.25,
+ 994.5,
+ 840.25,
+ 1028.5,
+ 582.25,
+ 1028.5
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1121.0,
+ 1376.0,
+ 1378.0,
+ 1376.0,
+ 1378.0,
+ 1410.0,
+ 1121.0,
+ 1410.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1655.0,
+ 1407.0,
+ 1655.0,
+ 1407.0,
+ 1697.0,
+ 293.0,
+ 1697.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1692.0,
+ 1406.0,
+ 1692.0,
+ 1406.0,
+ 1724.0,
+ 294.0,
+ 1724.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 389.0,
+ 1720.0,
+ 1405.0,
+ 1720.0,
+ 1405.0,
+ 1756.0,
+ 389.0,
+ 1756.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1751.0,
+ 1405.0,
+ 1751.0,
+ 1405.0,
+ 1787.0,
+ 293.0,
+ 1787.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1781.0,
+ 885.0,
+ 1781.0,
+ 885.0,
+ 1819.0,
+ 293.0,
+ 1819.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1811.0,
+ 297.0,
+ 1811.0,
+ 297.0,
+ 1850.0,
+ 293.0,
+ 1850.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 496.0,
+ 1811.0,
+ 556.0,
+ 1811.0,
+ 556.0,
+ 1850.0,
+ 496.0,
+ 1850.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 578.0,
+ 1811.0,
+ 1044.0,
+ 1811.0,
+ 1044.0,
+ 1850.0,
+ 578.0,
+ 1850.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 72.0,
+ 817.0,
+ 72.0,
+ 817.0,
+ 108.0,
+ 296.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 832.0,
+ 2084.0,
+ 871.0,
+ 2084.0,
+ 871.0,
+ 2122.0,
+ 832.0,
+ 2122.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 306.0,
+ 412.0,
+ 369.0,
+ 412.0,
+ 369.0,
+ 429.0,
+ 306.0,
+ 429.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 390.0,
+ 411.0,
+ 422.0,
+ 411.0,
+ 422.0,
+ 430.0,
+ 390.0,
+ 430.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 13,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 5,
+ "poly": [
+ 324,
+ 420,
+ 1380,
+ 420,
+ 1380,
+ 1985,
+ 324,
+ 1985
+ ],
+ "score": 0.968,
+ "html": " | The rate of correct answering on the test set,10 runs |
| n = 2, neighbor2(a,b,c):-neighborOf(a,b), neighborOf(b,c) Dataset: 2858 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Target ordering | Fixed | Random |
| Best 0.32 | Worst 0.23 | Median 0.29 | Mean 0.28 | Best 0.36 | Worst 0.25 | Median 0.31 | Mean 0.31 |
| H SH | 0.96 | 0.90 | 0.91 | 0.92 | 0.94 | 0.88 | 0.91 | 0.91 |
| A1H | 0.91 | 0.79 | 0.86 | 0.86 | 0.94 | 0.72 | 0.88 | 0.87 |
| H1H | 0.87 | 0.66 | 0.82 | 0.80 | 0.85 | 0.66 | 0.83 | 0.81 |
| n = 3, neighbor3(a,b,c,d):-.. |
| Target ordering | Dataset: 11000 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst 0.06 | Median | Mean |
| H | 0.10 | 0.04 | 0.06 | 0.06 | 0.10 | 0.07 | 0.07 |
| SH | 0.72 | 0.55 | 0.61 | 0.62 | 0.70 | 0.53 | 0.66 | 0.64 |
| A1H | 0.61 0.55 | 0.52 0.31 | 0.55 | 0.56 | 0.60 | 0.53 | 0.57 | 0.57 |
| H1H | | | 0.44 | 0.44 | 0.57 | 0.37 | 0.43 | 0.45 |
| Target ordering | n =4,neighbor4(a,b,c,d,e):-.. |
| Dataset: 39878 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Best | Worst | Fixed Median | Mean | Best | Random Worst | Median | Mean |
| H | 0.02 | 0.00 | 0.01 | 0.01 | 0.03 0.00 | 0.02 | 0.02 |
| SH | 0.38 | 0.24 | 0.33 | 0.32 | 0.36 | 0.28 0.32 | 0.32 |
| A1H | 0.33 | 0.22 | 0.27 | 0.26 | 0.34 | 0.22 0.26 | 0.26 |
| H1H | 0.22 | 0.12 | 0.18 | 0.18 | 0.24 | 0.13 0.18 | 0.18 |
| n = 4, neighbor4(a,b,c,d,e):-... Dataset: 39878 ground clauses; Training: 90o0 clauses; Test: 1000 clauses. |
| Target ordering H | | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst Median | Mean |
| 0.04 | 0.03 | 0.04 | 0.03 | 0.04 | 0.02 0.03 | 0.03 |
| 0.87 | 0.81 | 0.82 | 0.83 | 0.86 | 0.77 0.82 | 0.82 |
| SH | | 0.77 | 0.76 | 0.79 | 0.59 | 0.73 | 0.72 |
| A1H | 0.81 0.50 | 0.71 | | | | 0.42 | 0.41 |
| H1H | 0.12 | 0.40 | 0.37 n = 5, neighbor5(a,b,c,d,e,f):-... | 0.53 | 0.24 | | |
|
| Target ordering H | Dataset: 137738 ground clauses; Training: 2250 clauses; Test: 250 clauses. | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst | Median Mean |
| 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 0.00 | 0.00 |
| SH | 0.17 | 0.10 0.11 | 0.12 | 0.15 | 0.06 | 0.11 | 0.11 |
| A1H | 0.13 | 0.06 0.10 | 0.10 | 0.13 | 0.06 | 0.11 | 0.10 |
| H1H | 0.06 | 0.01 0.04 | 0.04 | 0.06 | 0.04 | 0.05 | 0.05 |
| | | n = 5, neighbor5(a,b,c,d,e,f):-... | | | | |
| Target ordering | Dataset: 137738 ground clauses; Training: 9000 clauses; Test: 1000 clauses. | |
| Fixed | | | | Random | |
| H | Best Worst | Median 0.00 | Mean 0.00 | Best 0.01 | Worst | Median 0.01 | Mean 0.01 |
| SH | 0.01 | 0.00 | | | 0.00 0.50 | | 0.55 |
| A1H | 0.65 0.53 | 0.52 0.46 | 0.55 0.48 | 0.56 0.48 | 0.60 | 0.56 0.50 | 0.50 |
| | | | 0.56 | 0.46 | | |
| H1H | 0.20 | 0.04 | 0.11 | 0.11 | 0.18 0.07 | 0.13 | 0.13 |
| | | | | | | |
+
+Table 6: The summary of the rule learning task, 10 runs.
+
+# REFERENCES
+
+Ryan Prescott Adams and Richard S Zemel. Ranking via Sinkhorn Propagation. arXiv preprint arXiv:1106.1925, 2011.
+Masataro Asai and Alex Fukunaga. Classical Planning in Deep Latent Space: Bridging the SubsymbolicSymbolic Boundary. In Proc. of AAAI Conference on Artificial Intelligence, 2018. URL https: //www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16302.
+Guillaume Bouchard, Sameer Singh, and Theo Trouillon. On Approximate Reasoning Capabilities of Low-Rank Vector Spaces. AAAI Spring Syposium on Knowledge Representation and Reasoning (KRR): Integrating Symbolic and Neural Approaches, 2015.
+Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford University — Princeton University — Toyota Technological Institute at Chicago, 2015.
+M-P Dubuisson and Anil K Jain. A Modified Hausdorff Distance for Object Matching. In Proceedings of 12th International Conference on Pattern Recognition, pp. 566–568. IEEE, 1994.
+Dominik Maria Endres and Johannes E Schindelin. A New Metric for Probability Distributions. IEEE Transactions on Information theory, 2003.
+Nicholas Guttenberg, Nathaniel Virgo, Olaf Witkowski, Hidetoshi Aoki, and Ryota Kanai. PermutationEquivariant Neural Networks Applied to Dynamics Prediction. arXiv preprint arXiv:1612.04530, 2016.
+Malte Helmert. A Planning Heuristic Based on Causal Graph Analysis. In Proc. of the International Conference on Automated Planning and Scheduling(ICAPS), pp. 161–170, 2004. URL http:// www.aaai.org/Library/ICAPS/2004/icaps04-021.php.
+Sepp Hochreiter and Jurgen Schmidhuber. Long Short-Term Memory. ¨ Neural Computation, 9(8):1735– 1780, 1997.
+Daniel P. Huttenlocher, Gregory A. Klanderman, and William J Rucklidge. Comparing Images using the Hausdorff Distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9):850–863, 1993.
+Piotr Indyk and Rajeev Motwani. Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality. In Proceedings of the thirtieth annual ACM symposium on Theory of computing, pp. 604–613. ACM, 1998.
+Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with Gumbel-Softmax. In Proc. of the International Conference on Learning Representations, 2017.
+Thanard Kurutach, Aviv Tamar, Ge Yang, Stuart Russell, and Pieter Abbeel. Learning Plannable Representations with Causal InfoGAN. In In Proceedings of ICML / IJCAI / AAMAS 2018 Workshop on Planning and Learning (PAL-18), 2018.
+Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables. In Proc. of the International Conference on Learning Representations, 2017.
+Xianling Mao, Bo-Si Feng, Yi-Jing Hao, Liqiang Nie, Heyan Huang, and Guihua Wen. S2JSD-LSH: A Locality-Sensitive Hashing Schema for Probability Distributions. In AAAI, pp. 3244–3251, 2017.
+Drew V. McDermott. The 1998 AI Planning Systems Competition. AI Magazine, 21(2):35–55, 2000. URL http://www.aaai.org/ojs/index.php/aimagazine/article/view/1506.
+Gonzalo Mena, David Belanger, Scott Linderman, and Jasper Snoek. Learning Latent Permutations with Gumbel-Sinkhorn Networks. In Proc. of the International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id $\underline { { \underline { { \mathbf { \Pi } } } } } =$ Byt3oJ-0W.
+Selwyn Piramuthu. The Hausdorff Distance Measure for Feature Selection in Learning Applications. In Systems Sciences, 1999. HICSS-32. Proceedings of the 32nd Annual Hawaii International Conference on, pp. 6–pp. IEEE, 1999.
+Malte Probst. The Set Autoencoder: Unsupervised Representation Learning for Sets. 2018. A rejected submission to ICLR2018.
+Siamak Ravanbakhsh, Jeff Schneider, and Barnabas Poczos. Deep Learning with Sets and Point Clouds. arXiv preprint arXiv:1611.04500, 2016.
+Joseph Redmon, Santosh Divvala, Ross Girshick, and Ali Farhadi. You Only Look Once: Unified, RealTime Object Detection. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp. 779–788, 2016.
+Tim Rocktaschel and Sebastian Riedel. End-to-End Differentiable Proving. In ¨ Advances in Neural Information Processing Systems, pp. 3788–3800, 2017.
+Rodrigo Santa Cruz, Basura Fernando, Anoop Cherian, and Stephen Gould. DeepPermNet: Visual Permutation Learning. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp. 6044–6052. IEEE, 2017.
+Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Advances in Neural Information Processing Systems, pp. 2692–2700, 2015. URL http://papers.nips.cc/paper/ 5866-pointer-networks.
+Oriol Vinyals, Samy Bengio, and Manjunath Kudlur. Order Matters: Sequence to Sequence for Sets. Proc. of the International Conference on Learning Representations, 2016.
+Jun Wang, Wei Liu, Sanjiv Kumar, and Shih-Fu Chang. Learning to Hash for Indexing Big DataA Survey. Proceedings of the IEEE, 104(1):34–57, 2016.
+Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Ruslan R Salakhutdinov, and Alexander J Smola. Deep Sets. In Advances in Neural Information Processing Systems, pp. 3391– 3401, 2017.
+Zhuotun Zhu, Xinggang Wang, Song Bai, Cong Yao, and Xiang Bai. Deep Learning Representation using Autoencoder for 3D Shape Retrieval. Neurocomputing, 204:41–50, 2016.
+
+# APPENDIX
+
+# 6.1 NETWORK MODEL FOR 8 PUZZLE
+
+As mentioned in the earlier sections, the network has a permutation invariant encoder and the fullyconnected decoder.
+
+The input to the network is a $9 \times 1 5$ matrix, where the first dimension represents the objects and the second dimension represents the features of each object. The encoder has two 1D convolution layers of 1000 neurons with filter size 1, modeling the element-wise network $\rho$ . The output of these layers is then aggregated by taking the sum of the first dimension. The result is then fed to two another fully-connected layers of width 1000, which maps to the latent layer of 100 neurons. All encoder layers are activated by ReLU. The latent representation is regularized and activated by Gumbel-Softmax Maddison et al. (2017); Jang et al. (2017) as the input is a categorical model.
+
+The decoder consists of three fully-connected layers with dropout and batch normalization as shown below:
+
+fc(1000), relu, batchnorm, dropout(0.5), fc(1000), relu, batchnorm, dropout(0.5), dense(135), reshape $( 9 \times 1 5 )$
+
+The last layer is then split into $9 \times 9 , 9 \times 3 , 9 \times 3$ matrices and separately activated by softmax, reflecting the input dataset (Fig. 1).
+
+# 6.2 NETWORK MODEL FOR BLOCKSWOLRD
+
+The same network as the 8-puzzle was used, except that the input and the output is a $5 \times 1 2 2 4$ matrix. The activations of the last layer is different: The first 1024 features are activated by a sigmoid function, while the 200 features are divided into 40, 60, 40, 60 dimensions (for the one-hot bounding box information) and are separately activated by softmax.
+
+# 6.3 FEATURE EXTRACTION FOR BLOCKSWORLD
+
+The 32x32 RGB image patches in the Blocksworld states are compressed into the feature vectors that are later used as the input. The image features are learned by a convolutional autoencoder depicted in Fig. 4 and Fig. 5.
+
+Input $3 2 \times 3 2 \times 3 )$ ,
+GaussianNoise(0.1),
+conv2d(filte ${ = } 1 6$ , kerne $\mathsf { 1 { = } 3 \times 3 , }$ ),
+relu,
+MaxPooling ${ \mathfrak { Q } } ( 2 \times 2 )$ ,
+conv2d(filte ${ = } 1 6$ , kerne $\mathrm { { \Omega } | = 3 \times 3 . }$ ,),
+relu,
+MaxPooling $2 { \mathrm { d } } ( 2 \times 2 )$ ,
+conv2d(filte ${ = } 1 6$ , kernel $\mathrm { = 3 \times 3 }$ ,),
+sigmoid
+
+Figure 4: The implementation of the encoder for feature selection, which outputs a $8 \times 8 \times 1 6$ tensor.
+
+Input(8 × 8 × 16),
+conv2d(filte ${ = } 1 6$ , kernel=3 × 3,),
+relu,
+UpSampling2d $( 2 \times 2 )$ ,
+conv2d(filte ${ = } 1 6$ , kerne $\mathrm { = } 3 \times 3 ,$ ,),
+relu,
+UpSampling $2 { \mathrm { d } } ( 2 \times 2 )$ ,
+conv2d(filte ${ = } 1 6$ , kernel $= 3 \times 3 .$ ,),
+relu,
+fc(3072),
+sigmoid,
+reshape $( 3 2 \times 3 2 \times 3 )$
+
+# 6.4 NETWORK MODEL FOR RULE LEARNING
+
+We removed the encoder and the latent layer from the above models, and connected the input directly to the decoder. While the decoder has the same types of layers, the width is shrinked to 400. In the $_ n$ - neighbor scenario, the input is a $2 + 1 6 3 ( n + 1 )$ vector, which consists of a one-hot label of 2 categories for the predicate of the head, and $n + 1$ one-hot labels of 163 categories for the arguments of the head. 163 categories corresponds to the number of countries in the Countries dataset (Bouchard et al., 2015). The output is a $[ n , 3 2 8 ]$ matrix, where each row represents a binary predicate $3 2 8 = 2 + 2 \cdot 1 6 3$ ).
+
+# 6.5 EXAMPLE APPLICATION OF THE PERMUTATION-INVARIANT REPRESENTATION & RECONSTRUCTION
+
+To address the practical utility of “set reconstruction” or “set autoencoding”, we added a new experiment. We modified Latplan (Asai & Fukunaga, 2018) neural-symbolic classical planning system, a system that operates on a discrete symbolic latent space of the real-valued inputs and runs Dijkstra $\mathrm { \Phi _ { s / A ^ { * } } }$ search using a state-of-the-art symbolic classical planning solver. We modified Latplan to take the set-of-object-featurevector input rather than images. It is a high-level task planner (unlike motion planning / actuator control) that has implications on robotic systems, which perceives a set of inputs already preprocessed by the external system. For example, the image input is first fed into Object Recognition system (e.g. YOLO, (Redmon et al., 2016)) and the planner receives a set of feature vectors extracted from the image patches segmented from the raw image, rather than feeding the image input directly to the planning system.
+
+Latplan system learns the binary latent space of an arbitrary raw input (e.g. images) with a GumbelSoftmax variational autoencoder, learns a discrete state space from the transition examples, and runs a symbolic, systematic search algorithm such as Dijkstra or $\mathbf { A } ^ { * }$ search which guarantee the optimality of the solution. Unlike RL-based planning systems, the search agent does not contain the learning aspects. The discrete plan in the latent space is mapped back to the raw image visualization of the plan execution, which requires the reconstruction capability of (V)AE. A similar system replacing Gumbel Softmax VAE with Causal InfoGAN was later proposed (Kurutach et al., 2018).
+
+We replaced Latplan’s Gumbel-Softmax VAE with our autoencoder used in the 8-Puzzle and the Blocksworld experiments (Appendix, Sec. 6.1,Sec. 6.2). Our autoencoder also uses Gumbel Softmax in the latent layer, but it uses (Zaheer et al., 2017) encoder and is trained with Set Cross Entropy.
+
+When the network learned the representation, it guarantees that the planner finds a solution because the search algorithm being used (e.g. Dijkstra) is a complete, systematic, symbolic search algorithm, which guarantees to find a solution whenever it is reachable in the state space. If the network cannot learn the permutation-invariant representation, the system cannot solve the problem and/or return the humancomprehensive visualization. This makes the specific permutation-invariant representation using (Zaheer et al., 2017) and the proposed Set Cross Entropy necessary when the input is given as a set of future vectors.
+
+# 8 PUZZLE
+
+First, the training was performed on a dataset in which the object vector ordering is randomized. The autoencoder compresses the $1 5 \times 9 = 1 3 5$ -bit binary representation (object vectors) into a permutationinvariant 100-bit discrete latent binary representation. We provided 5000 states for training the autoencoder, while the search space consists of $3 6 2 8 8 0 ( = 9 ! )$ states and 967680 transitions.
+
+Note that each state have 9! variations due to the permutations in the order the tiles and the locations are reported. This also increases the number of transition quadratically $( ( 9 ! ) ^ { 2 } ,$ ).
+
+We generated 40 problem instances of 8-puzzle each generated by a random walk from the goal state. 40 instances consist of 20 instances each generated by a 7-steps random walk and another 20 by 14 steps. We solved 40 instances using Fast Downward classical planner Helmert (2004) with blind heuristics in order to remove the effect of heuristics.
+
+We compared the number of problems successfully solved by two variations of Latplan where each uses the autoencoder trained with Set Average and Set Cross Entropy, respectively, for encoding the input into binary latent space. Both version managed to solve all instances because both Set Average and Set Cross Entropy managed to train the AE from 5000 examples with a sufficient accuracy. All solutions were correct (checked manually). Since the search algorithm being used is optimal, the quality of the solution was also identical.
+
+# BLOCKSWORLD
+
+We solved 30 planning instances in a 4-blocks, 3-stacks environment. The instances are generated by taking a random initial state and choosing a goal state by the 3, 7, or 14 steps random walks (10 instances each). The correctness of the plans are again checked manually. The same planner configuration was used for all instances.
+
+The search space consists of 5760 states and 34560 transitions, and each state have 4! variations due to permutations of 4 blocks. We provided 1000 randomly selected states for training the autoencoder.
+
+
+
+
+Figure 6: (Left) An example plan in a set-of-object-vector form, decoded from its binary latent representation using the permutation-invariant autoencoder (the plan is executed from top to bottom). (Right) Its visualization using the tile images (taken from MNIST) pasted onto a black canvas (The plan is executed from left to right, top to bottom).
+
+We compared the number of problems successfully solved by Latplan between two variations of Latplan using the autoencoder trained with Set Average and Set Cross Entropy, respectively. For the total of 30 instances, both Latplan $\mathbf { \Gamma } _ { \mathrm { + } \mathrm { S e t } }$ Avg and Latplan $\mathrm { \mathbf { \Omega } _ { 1 + } S C E }$ returned plans, however the plans returned by Latplan $+ \mathrm { S e t }$ Avg were correct in 11 instnaces, while Latplan $+ \mathrm { S C E }$ returned 14 correct instances (Details in Table 7).
+
+As the autoencoder trained by Set Average had larger reconstruction error, it sometimes fails to capture the essential feature of the input, causing the system to return an invalid plan. The common error was changing the surface of the blocks or swapping the blocks without a proper action needed, e.g., moving more than two blocks, move a block and polish another block in a single time step, etc.
+
+ | The rate of correct answering on the test set,10 runs |
| n = 2, neighbor2(a,b,c):-neighborOf(a,b), neighborOf(b,c) Dataset: 2858 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Target ordering | Fixed | Random |
| Best 0.32 | Worst 0.23 | Median 0.29 | Mean 0.28 | Best 0.36 | Worst 0.25 | Median 0.31 | Mean 0.31 |
| H SH | 0.96 | 0.90 | 0.91 | 0.92 | 0.94 | 0.88 | 0.91 | 0.91 |
| A1H | 0.91 | 0.79 | 0.86 | 0.86 | 0.94 | 0.72 | 0.88 | 0.87 |
| H1H | 0.87 | 0.66 | 0.82 | 0.80 | 0.85 | 0.66 | 0.83 | 0.81 |
| n = 3, neighbor3(a,b,c,d):-.. |
| Target ordering | Dataset: 11000 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst 0.06 | Median | Mean |
| H | 0.10 | 0.04 | 0.06 | 0.06 | 0.10 | 0.07 | 0.07 |
| SH | 0.72 | 0.55 | 0.61 | 0.62 | 0.70 | 0.53 | 0.66 | 0.64 |
| A1H | 0.61 0.55 | 0.52 0.31 | 0.55 | 0.56 | 0.60 | 0.53 | 0.57 | 0.57 |
| H1H | | | 0.44 | 0.44 | 0.57 | 0.37 | 0.43 | 0.45 |
| Target ordering | n =4,neighbor4(a,b,c,d,e):-.. |
| Dataset: 39878 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Best | Worst | Fixed Median | Mean | Best | Random Worst | Median | Mean |
| H | 0.02 | 0.00 | 0.01 | 0.01 | 0.03 0.00 | 0.02 | 0.02 |
| SH | 0.38 | 0.24 | 0.33 | 0.32 | 0.36 | 0.28 0.32 | 0.32 |
| A1H | 0.33 | 0.22 | 0.27 | 0.26 | 0.34 | 0.22 0.26 | 0.26 |
| H1H | 0.22 | 0.12 | 0.18 | 0.18 | 0.24 | 0.13 0.18 | 0.18 |
| n = 4, neighbor4(a,b,c,d,e):-... Dataset: 39878 ground clauses; Training: 90o0 clauses; Test: 1000 clauses. |
| Target ordering H | | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst Median | Mean |
| 0.04 | 0.03 | 0.04 | 0.03 | 0.04 | 0.02 0.03 | 0.03 |
| 0.87 | 0.81 | 0.82 | 0.83 | 0.86 | 0.77 0.82 | 0.82 |
| SH | | 0.77 | 0.76 | 0.79 | 0.59 | 0.73 | 0.72 |
| A1H | 0.81 0.50 | 0.71 | | | | 0.42 | 0.41 |
| H1H | 0.12 | 0.40 | 0.37 n = 5, neighbor5(a,b,c,d,e,f):-... | 0.53 | 0.24 | | |
|
| Target ordering H | Dataset: 137738 ground clauses; Training: 2250 clauses; Test: 250 clauses. | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst | Median Mean |
| 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 0.00 | 0.00 |
| SH | 0.17 | 0.10 0.11 | 0.12 | 0.15 | 0.06 | 0.11 | 0.11 |
| A1H | 0.13 | 0.06 0.10 | 0.10 | 0.13 | 0.06 | 0.11 | 0.10 |
| H1H | 0.06 | 0.01 0.04 | 0.04 | 0.06 | 0.04 | 0.05 | 0.05 |
| | | n = 5, neighbor5(a,b,c,d,e,f):-... | | | | |
| Target ordering | Dataset: 137738 ground clauses; Training: 9000 clauses; Test: 1000 clauses. | |
| Fixed | | | | Random | |
| H | Best Worst | Median 0.00 | Mean 0.00 | Best 0.01 | Worst | Median 0.01 | Mean 0.01 |
| SH | 0.01 | 0.00 | | | 0.00 0.50 | | 0.55 |
| A1H | 0.65 0.53 | 0.52 0.46 | 0.55 0.48 | 0.56 0.48 | 0.60 | 0.56 0.50 | 0.50 |
| | | | 0.56 | 0.46 | | |
| H1H | 0.20 | 0.04 | 0.11 | 0.11 | 0.18 0.07 | 0.13 | 0.13 |
| | | | | | | |
",
+ "bbox": [
+ 173,
+ 155,
+ 825,
+ 847
+ ],
+ "page_idx": 10
+ },
+ {
+ "type": "text",
+ "text": "",
+ "bbox": [
+ 174,
+ 104,
+ 825,
+ 242
+ ],
+ "page_idx": 11
+ },
+ {
+ "type": "text",
+ "text": "REFERENCES ",
+ "text_level": 1,
+ "bbox": [
+ 174,
+ 263,
+ 285,
+ 279
+ ],
+ "page_idx": 11
+ },
+ {
+ "type": "text",
+ "text": "Ryan Prescott Adams and Richard S Zemel. Ranking via Sinkhorn Propagation. arXiv preprint arXiv:1106.1925, 2011. \nMasataro Asai and Alex Fukunaga. Classical Planning in Deep Latent Space: Bridging the SubsymbolicSymbolic Boundary. In Proc. of AAAI Conference on Artificial Intelligence, 2018. URL https: //www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16302. \nGuillaume Bouchard, Sameer Singh, and Theo Trouillon. On Approximate Reasoning Capabilities of Low-Rank Vector Spaces. AAAI Spring Syposium on Knowledge Representation and Reasoning (KRR): Integrating Symbolic and Neural Approaches, 2015. \nAngel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford University — Princeton University — Toyota Technological Institute at Chicago, 2015. \nM-P Dubuisson and Anil K Jain. A Modified Hausdorff Distance for Object Matching. In Proceedings of 12th International Conference on Pattern Recognition, pp. 566–568. IEEE, 1994. \nDominik Maria Endres and Johannes E Schindelin. A New Metric for Probability Distributions. IEEE Transactions on Information theory, 2003. \nNicholas Guttenberg, Nathaniel Virgo, Olaf Witkowski, Hidetoshi Aoki, and Ryota Kanai. PermutationEquivariant Neural Networks Applied to Dynamics Prediction. arXiv preprint arXiv:1612.04530, 2016. \nMalte Helmert. A Planning Heuristic Based on Causal Graph Analysis. In Proc. of the International Conference on Automated Planning and Scheduling(ICAPS), pp. 161–170, 2004. URL http:// www.aaai.org/Library/ICAPS/2004/icaps04-021.php. \nSepp Hochreiter and Jurgen Schmidhuber. Long Short-Term Memory. ¨ Neural Computation, 9(8):1735– 1780, 1997. \nDaniel P. Huttenlocher, Gregory A. Klanderman, and William J Rucklidge. Comparing Images using the Hausdorff Distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9):850–863, 1993. \nPiotr Indyk and Rajeev Motwani. Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality. In Proceedings of the thirtieth annual ACM symposium on Theory of computing, pp. 604–613. ACM, 1998. \nEric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with Gumbel-Softmax. In Proc. of the International Conference on Learning Representations, 2017. \nThanard Kurutach, Aviv Tamar, Ge Yang, Stuart Russell, and Pieter Abbeel. Learning Plannable Representations with Causal InfoGAN. In In Proceedings of ICML / IJCAI / AAMAS 2018 Workshop on Planning and Learning (PAL-18), 2018. \nChris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables. In Proc. of the International Conference on Learning Representations, 2017. \nXianling Mao, Bo-Si Feng, Yi-Jing Hao, Liqiang Nie, Heyan Huang, and Guihua Wen. S2JSD-LSH: A Locality-Sensitive Hashing Schema for Probability Distributions. In AAAI, pp. 3244–3251, 2017. \nDrew V. McDermott. The 1998 AI Planning Systems Competition. AI Magazine, 21(2):35–55, 2000. URL http://www.aaai.org/ojs/index.php/aimagazine/article/view/1506. \nGonzalo Mena, David Belanger, Scott Linderman, and Jasper Snoek. Learning Latent Permutations with Gumbel-Sinkhorn Networks. In Proc. of the International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id $\\underline { { \\underline { { \\mathbf { \\Pi } } } } } =$ Byt3oJ-0W. \nSelwyn Piramuthu. The Hausdorff Distance Measure for Feature Selection in Learning Applications. In Systems Sciences, 1999. HICSS-32. Proceedings of the 32nd Annual Hawaii International Conference on, pp. 6–pp. IEEE, 1999. \nMalte Probst. The Set Autoencoder: Unsupervised Representation Learning for Sets. 2018. A rejected submission to ICLR2018. \nSiamak Ravanbakhsh, Jeff Schneider, and Barnabas Poczos. Deep Learning with Sets and Point Clouds. arXiv preprint arXiv:1611.04500, 2016. \nJoseph Redmon, Santosh Divvala, Ross Girshick, and Ali Farhadi. You Only Look Once: Unified, RealTime Object Detection. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp. 779–788, 2016. \nTim Rocktaschel and Sebastian Riedel. End-to-End Differentiable Proving. In ¨ Advances in Neural Information Processing Systems, pp. 3788–3800, 2017. \nRodrigo Santa Cruz, Basura Fernando, Anoop Cherian, and Stephen Gould. DeepPermNet: Visual Permutation Learning. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp. 6044–6052. IEEE, 2017. \nOriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Advances in Neural Information Processing Systems, pp. 2692–2700, 2015. URL http://papers.nips.cc/paper/ 5866-pointer-networks. \nOriol Vinyals, Samy Bengio, and Manjunath Kudlur. Order Matters: Sequence to Sequence for Sets. Proc. of the International Conference on Learning Representations, 2016. \nJun Wang, Wei Liu, Sanjiv Kumar, and Shih-Fu Chang. Learning to Hash for Indexing Big DataA Survey. Proceedings of the IEEE, 104(1):34–57, 2016. \nManzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Ruslan R Salakhutdinov, and Alexander J Smola. Deep Sets. In Advances in Neural Information Processing Systems, pp. 3391– 3401, 2017. \nZhuotun Zhu, Xinggang Wang, Song Bai, Cong Yao, and Xiang Bai. Deep Learning Representation using Autoencoder for 3D Shape Retrieval. Neurocomputing, 204:41–50, 2016. ",
+ "bbox": [
+ 169,
+ 275,
+ 826,
+ 926
+ ],
+ "page_idx": 11
+ },
+ {
+ "type": "text",
+ "text": "",
+ "bbox": [
+ 171,
+ 98,
+ 826,
+ 688
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "APPENDIX ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 707,
+ 263,
+ 722
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "6.1 NETWORK MODEL FOR 8 PUZZLE ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 736,
+ 449,
+ 751
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "As mentioned in the earlier sections, the network has a permutation invariant encoder and the fullyconnected decoder. ",
+ "bbox": [
+ 176,
+ 762,
+ 823,
+ 790
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "The input to the network is a $9 \\times 1 5$ matrix, where the first dimension represents the objects and the second dimension represents the features of each object. The encoder has two 1D convolution layers of 1000 neurons with filter size 1, modeling the element-wise network $\\rho$ . The output of these layers is then aggregated by taking the sum of the first dimension. The result is then fed to two another fully-connected layers of width 1000, which maps to the latent layer of 100 neurons. All encoder layers are activated by ReLU. The latent representation is regularized and activated by Gumbel-Softmax Maddison et al. (2017); Jang et al. (2017) as the input is a categorical model. ",
+ "bbox": [
+ 174,
+ 796,
+ 825,
+ 890
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "The decoder consists of three fully-connected layers with dropout and batch normalization as shown below: ",
+ "bbox": [
+ 176,
+ 896,
+ 823,
+ 922
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "fc(1000), relu, batchnorm, dropout(0.5), fc(1000), relu, batchnorm, dropout(0.5), dense(135), reshape $( 9 \\times 1 5 )$ ",
+ "bbox": [
+ 362,
+ 101,
+ 635,
+ 142
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "The last layer is then split into $9 \\times 9 , 9 \\times 3 , 9 \\times 3$ matrices and separately activated by softmax, reflecting the input dataset (Fig. 1). ",
+ "bbox": [
+ 173,
+ 155,
+ 823,
+ 183
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "6.2 NETWORK MODEL FOR BLOCKSWOLRD ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 204,
+ 491,
+ 219
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "The same network as the 8-puzzle was used, except that the input and the output is a $5 \\times 1 2 2 4$ matrix. The activations of the last layer is different: The first 1024 features are activated by a sigmoid function, while the 200 features are divided into 40, 60, 40, 60 dimensions (for the one-hot bounding box information) and are separately activated by softmax. ",
+ "bbox": [
+ 174,
+ 231,
+ 825,
+ 286
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "6.3 FEATURE EXTRACTION FOR BLOCKSWORLD ",
+ "text_level": 1,
+ "bbox": [
+ 174,
+ 308,
+ 522,
+ 321
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "The 32x32 RGB image patches in the Blocksworld states are compressed into the feature vectors that are later used as the input. The image features are learned by a convolutional autoencoder depicted in Fig. 4 and Fig. 5. ",
+ "bbox": [
+ 174,
+ 334,
+ 825,
+ 376
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "Input $3 2 \\times 3 2 \\times 3 )$ , \nGaussianNoise(0.1), \nconv2d(filte ${ = } 1 6$ , kerne $\\mathsf { 1 { = } 3 \\times 3 , }$ ), \nrelu, \nMaxPooling ${ \\mathfrak { Q } } ( 2 \\times 2 )$ , \nconv2d(filte ${ = } 1 6$ , kerne $\\mathrm { { \\Omega } | = 3 \\times 3 . }$ ,), \nrelu, \nMaxPooling $2 { \\mathrm { d } } ( 2 \\times 2 )$ , \nconv2d(filte ${ = } 1 6$ , kernel $\\mathrm { = 3 \\times 3 }$ ,), \nsigmoid ",
+ "bbox": [
+ 385,
+ 392,
+ 616,
+ 532
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "Figure 4: The implementation of the encoder for feature selection, which outputs a $8 \\times 8 \\times 1 6$ tensor. ",
+ "bbox": [
+ 171,
+ 544,
+ 823,
+ 559
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "Input(8 × 8 × 16), \nconv2d(filte ${ = } 1 6$ , kernel=3 × 3,), \nrelu, \nUpSampling2d $( 2 \\times 2 )$ , \nconv2d(filte ${ = } 1 6$ , kerne $\\mathrm { = } 3 \\times 3 ,$ ,), \nrelu, \nUpSampling $2 { \\mathrm { d } } ( 2 \\times 2 )$ , \nconv2d(filte ${ = } 1 6$ , kernel $= 3 \\times 3 .$ ,), \nrelu, \nfc(3072), \nsigmoid, \nreshape $( 3 2 \\times 3 2 \\times 3 )$ ",
+ "bbox": [
+ 382,
+ 588,
+ 617,
+ 757
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "6.4 NETWORK MODEL FOR RULE LEARNING ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 815,
+ 498,
+ 830
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "We removed the encoder and the latent layer from the above models, and connected the input directly to the decoder. While the decoder has the same types of layers, the width is shrinked to 400. In the $_ n$ - neighbor scenario, the input is a $2 + 1 6 3 ( n + 1 )$ vector, which consists of a one-hot label of 2 categories for the predicate of the head, and $n + 1$ one-hot labels of 163 categories for the arguments of the head. 163 categories corresponds to the number of countries in the Countries dataset (Bouchard et al., 2015). The output is a $[ n , 3 2 8 ]$ matrix, where each row represents a binary predicate $3 2 8 = 2 + 2 \\cdot 1 6 3$ ). ",
+ "bbox": [
+ 173,
+ 843,
+ 825,
+ 924
+ ],
+ "page_idx": 13
+ },
+ {
+ "type": "text",
+ "text": "6.5 EXAMPLE APPLICATION OF THE PERMUTATION-INVARIANT REPRESENTATION & RECONSTRUCTION ",
+ "text_level": 1,
+ "bbox": [
+ 173,
+ 103,
+ 772,
+ 131
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "To address the practical utility of “set reconstruction” or “set autoencoding”, we added a new experiment. We modified Latplan (Asai & Fukunaga, 2018) neural-symbolic classical planning system, a system that operates on a discrete symbolic latent space of the real-valued inputs and runs Dijkstra $\\mathrm { \\Phi _ { s / A ^ { * } } }$ search using a state-of-the-art symbolic classical planning solver. We modified Latplan to take the set-of-object-featurevector input rather than images. It is a high-level task planner (unlike motion planning / actuator control) that has implications on robotic systems, which perceives a set of inputs already preprocessed by the external system. For example, the image input is first fed into Object Recognition system (e.g. YOLO, (Redmon et al., 2016)) and the planner receives a set of feature vectors extracted from the image patches segmented from the raw image, rather than feeding the image input directly to the planning system. ",
+ "bbox": [
+ 174,
+ 143,
+ 825,
+ 265
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "Latplan system learns the binary latent space of an arbitrary raw input (e.g. images) with a GumbelSoftmax variational autoencoder, learns a discrete state space from the transition examples, and runs a symbolic, systematic search algorithm such as Dijkstra or $\\mathbf { A } ^ { * }$ search which guarantee the optimality of the solution. Unlike RL-based planning systems, the search agent does not contain the learning aspects. The discrete plan in the latent space is mapped back to the raw image visualization of the plan execution, which requires the reconstruction capability of (V)AE. A similar system replacing Gumbel Softmax VAE with Causal InfoGAN was later proposed (Kurutach et al., 2018). ",
+ "bbox": [
+ 174,
+ 271,
+ 825,
+ 364
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "We replaced Latplan’s Gumbel-Softmax VAE with our autoencoder used in the 8-Puzzle and the Blocksworld experiments (Appendix, Sec. 6.1,Sec. 6.2). Our autoencoder also uses Gumbel Softmax in the latent layer, but it uses (Zaheer et al., 2017) encoder and is trained with Set Cross Entropy. ",
+ "bbox": [
+ 176,
+ 371,
+ 825,
+ 411
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "When the network learned the representation, it guarantees that the planner finds a solution because the search algorithm being used (e.g. Dijkstra) is a complete, systematic, symbolic search algorithm, which guarantees to find a solution whenever it is reachable in the state space. If the network cannot learn the permutation-invariant representation, the system cannot solve the problem and/or return the humancomprehensive visualization. This makes the specific permutation-invariant representation using (Zaheer et al., 2017) and the proposed Set Cross Entropy necessary when the input is given as a set of future vectors. ",
+ "bbox": [
+ 174,
+ 417,
+ 825,
+ 511
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "8 PUZZLE ",
+ "text_level": 1,
+ "bbox": [
+ 174,
+ 530,
+ 243,
+ 545
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "First, the training was performed on a dataset in which the object vector ordering is randomized. The autoencoder compresses the $1 5 \\times 9 = 1 3 5$ -bit binary representation (object vectors) into a permutationinvariant 100-bit discrete latent binary representation. We provided 5000 states for training the autoencoder, while the search space consists of $3 6 2 8 8 0 ( = 9 ! )$ states and 967680 transitions. ",
+ "bbox": [
+ 174,
+ 556,
+ 823,
+ 609
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "Note that each state have 9! variations due to the permutations in the order the tiles and the locations are reported. This also increases the number of transition quadratically $( ( 9 ! ) ^ { 2 } ,$ ). ",
+ "bbox": [
+ 171,
+ 617,
+ 821,
+ 643
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "We generated 40 problem instances of 8-puzzle each generated by a random walk from the goal state. 40 instances consist of 20 instances each generated by a 7-steps random walk and another 20 by 14 steps. We solved 40 instances using Fast Downward classical planner Helmert (2004) with blind heuristics in order to remove the effect of heuristics. ",
+ "bbox": [
+ 174,
+ 651,
+ 825,
+ 704
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "We compared the number of problems successfully solved by two variations of Latplan where each uses the autoencoder trained with Set Average and Set Cross Entropy, respectively, for encoding the input into binary latent space. Both version managed to solve all instances because both Set Average and Set Cross Entropy managed to train the AE from 5000 examples with a sufficient accuracy. All solutions were correct (checked manually). Since the search algorithm being used is optimal, the quality of the solution was also identical. ",
+ "bbox": [
+ 174,
+ 710,
+ 825,
+ 790
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "BLOCKSWORLD ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 811,
+ 285,
+ 824
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "We solved 30 planning instances in a 4-blocks, 3-stacks environment. The instances are generated by taking a random initial state and choosing a goal state by the 3, 7, or 14 steps random walks (10 instances each). The correctness of the plans are again checked manually. The same planner configuration was used for all instances. ",
+ "bbox": [
+ 176,
+ 837,
+ 823,
+ 888
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "text",
+ "text": "The search space consists of 5760 states and 34560 transitions, and each state have 4! variations due to permutations of 4 blocks. We provided 1000 randomly selected states for training the autoencoder. ",
+ "bbox": [
+ 176,
+ 896,
+ 823,
+ 922
+ ],
+ "page_idx": 14
+ },
+ {
+ "type": "image",
+ "img_path": "images/621af72adc23d14c4b28f2afa847ccd90aaba22caeaa51c7890c8dc90150fe21.jpg",
+ "image_caption": [],
+ "image_footnote": [],
+ "bbox": [
+ 504,
+ 132,
+ 808,
+ 210
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "image",
+ "img_path": "images/75a2ab5601ad767c6e9f8540ba5250aa4daa56431c7aa98b701962e33e106c96.jpg",
+ "image_caption": [
+ "Figure 6: (Left) An example plan in a set-of-object-vector form, decoded from its binary latent representation using the permutation-invariant autoencoder (the plan is executed from top to bottom). (Right) Its visualization using the tile images (taken from MNIST) pasted onto a black canvas (The plan is executed from left to right, top to bottom). "
+ ],
+ "image_footnote": [],
+ "bbox": [
+ 321,
+ 99,
+ 361,
+ 239
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "text",
+ "text": "We compared the number of problems successfully solved by Latplan between two variations of Latplan using the autoencoder trained with Set Average and Set Cross Entropy, respectively. For the total of 30 instances, both Latplan $\\mathbf { \\Gamma } _ { \\mathrm { + } \\mathrm { S e t } }$ Avg and Latplan $\\mathrm { \\mathbf { \\Omega } _ { 1 + } S C E }$ returned plans, however the plans returned by Latplan $+ \\mathrm { S e t }$ Avg were correct in 11 instnaces, while Latplan $+ \\mathrm { S C E }$ returned 14 correct instances (Details in Table 7). ",
+ "bbox": [
+ 173,
+ 332,
+ 825,
+ 400
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "text",
+ "text": "As the autoencoder trained by Set Average had larger reconstruction error, it sometimes fails to capture the essential feature of the input, causing the system to return an invalid plan. The common error was changing the surface of the blocks or swapping the blocks without a proper action needed, e.g., moving more than two blocks, move a block and polish another block in a single time step, etc. ",
+ "bbox": [
+ 174,
+ 406,
+ 825,
+ 460
+ ],
+ "page_idx": 15
+ },
+ {
+ "type": "table",
+ "img_path": "images/af8f0e4e5850775429ddb36165efef05815ff31ea8c7d4268abd7f98aa37333f.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": " | The rate of correct answering on the test set,10 runs |
| n = 2, neighbor2(a,b,c):-neighborOf(a,b), neighborOf(b,c) Dataset: 2858 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Target ordering | Fixed | Random |
| Best 0.32 | Worst 0.23 | Median 0.29 | Mean 0.28 | Best 0.36 | Worst 0.25 | Median 0.31 | Mean 0.31 |
| H SH | 0.96 | 0.90 | 0.91 | 0.92 | 0.94 | 0.88 | 0.91 | 0.91 |
| A1H | 0.91 | 0.79 | 0.86 | 0.86 | 0.94 | 0.72 | 0.88 | 0.87 |
| H1H | 0.87 | 0.66 | 0.82 | 0.80 | 0.85 | 0.66 | 0.83 | 0.81 |
| n = 3, neighbor3(a,b,c,d):-.. |
| Target ordering | Dataset: 11000 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst 0.06 | Median | Mean |
| H | 0.10 | 0.04 | 0.06 | 0.06 | 0.10 | 0.07 | 0.07 |
| SH | 0.72 | 0.55 | 0.61 | 0.62 | 0.70 | 0.53 | 0.66 | 0.64 |
| A1H | 0.61 0.55 | 0.52 0.31 | 0.55 | 0.56 | 0.60 | 0.53 | 0.57 | 0.57 |
| H1H | | | 0.44 | 0.44 | 0.57 | 0.37 | 0.43 | 0.45 |
| Target ordering | n =4,neighbor4(a,b,c,d,e):-.. |
| Dataset: 39878 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Best | Worst | Fixed Median | Mean | Best | Random Worst | Median | Mean |
| H | 0.02 | 0.00 | 0.01 | 0.01 | 0.03 0.00 | 0.02 | 0.02 |
| SH | 0.38 | 0.24 | 0.33 | 0.32 | 0.36 | 0.28 0.32 | 0.32 |
| A1H | 0.33 | 0.22 | 0.27 | 0.26 | 0.34 | 0.22 0.26 | 0.26 |
| H1H | 0.22 | 0.12 | 0.18 | 0.18 | 0.24 | 0.13 0.18 | 0.18 |
| n = 4, neighbor4(a,b,c,d,e):-... Dataset: 39878 ground clauses; Training: 90o0 clauses; Test: 1000 clauses. |
| Target ordering H | | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst Median | Mean |
| 0.04 | 0.03 | 0.04 | 0.03 | 0.04 | 0.02 0.03 | 0.03 |
| 0.87 | 0.81 | 0.82 | 0.83 | 0.86 | 0.77 0.82 | 0.82 |
| SH | | 0.77 | 0.76 | 0.79 | 0.59 | 0.73 | 0.72 |
| A1H | 0.81 0.50 | 0.71 | | | | 0.42 | 0.41 |
| H1H | 0.12 | 0.40 | 0.37 n = 5, neighbor5(a,b,c,d,e,f):-... | 0.53 | 0.24 | | |
|
| Target ordering H | Dataset: 137738 ground clauses; Training: 2250 clauses; Test: 250 clauses. | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst | Median Mean |
| 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 0.00 | 0.00 |
| SH | 0.17 | 0.10 0.11 | 0.12 | 0.15 | 0.06 | 0.11 | 0.11 |
| A1H | 0.13 | 0.06 0.10 | 0.10 | 0.13 | 0.06 | 0.11 | 0.10 |
| H1H | 0.06 | 0.01 0.04 | 0.04 | 0.06 | 0.04 | 0.05 | 0.05 |
| | | n = 5, neighbor5(a,b,c,d,e,f):-... | | | | |
| Target ordering | Dataset: 137738 ground clauses; Training: 9000 clauses; Test: 1000 clauses. | |
| Fixed | | | | Random | |
| H | Best Worst | Median 0.00 | Mean 0.00 | Best 0.01 | Worst | Median 0.01 | Mean 0.01 |
| SH | 0.01 | 0.00 | | | 0.00 0.50 | | 0.55 |
| A1H | 0.65 0.53 | 0.52 0.46 | 0.55 0.48 | 0.56 0.48 | 0.60 | 0.56 0.50 | 0.50 |
| | | | 0.56 | 0.46 | | |
| H1H | 0.20 | 0.04 | 0.11 | 0.11 | 0.18 0.07 | 0.13 | 0.13 |
| | | | | | | |
",
+ "type": "table",
+ "image_path": "dd34965d221808a5a04e447a72e7c0558510c7fc80f59ab6b3c914768c11efd7.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 1,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 106,
+ 123,
+ 505,
+ 305.66666666666663
+ ],
+ "spans": [],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 106,
+ 305.66666666666663,
+ 505,
+ 488.33333333333326
+ ],
+ "spans": [],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 106,
+ 488.33333333333326,
+ 505,
+ 670.9999999999999
+ ],
+ "spans": [],
+ "index": 2
+ }
+ ]
+ },
+ {
+ "type": "table_footnote",
+ "bbox": [
+ 192,
+ 674,
+ 418,
+ 686
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 191,
+ 673,
+ 419,
+ 687
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 191,
+ 673,
+ 419,
+ 687
+ ],
+ "score": 1.0,
+ "content": "Table 6: The summary of the rule learning task, 10 runs.",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ }
+ ],
+ "index": 3
+ }
+ ],
+ "index": 2.0
+ }
+ ],
+ "page_idx": 10,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 106,
+ 27,
+ 308,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 300,
+ 751,
+ 310,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 312,
+ 765
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 312,
+ 765
+ ],
+ "score": 1.0,
+ "content": "",
+ "type": "text",
+ "height": 15,
+ "width": 13
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "table",
+ "bbox": [
+ 106,
+ 123,
+ 505,
+ 671
+ ],
+ "blocks": [
+ {
+ "type": "table_body",
+ "bbox": [
+ 106,
+ 123,
+ 505,
+ 671
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 123,
+ 505,
+ 671
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 123,
+ 505,
+ 671
+ ],
+ "score": 0.966,
+ "html": " | The rate of correct answering on the test set,10 runs |
| n = 2, neighbor2(a,b,c):-neighborOf(a,b), neighborOf(b,c) Dataset: 2858 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Target ordering | Fixed | Random |
| Best 0.32 | Worst 0.23 | Median 0.29 | Mean 0.28 | Best 0.36 | Worst 0.25 | Median 0.31 | Mean 0.31 |
| H SH | 0.96 | 0.90 | 0.91 | 0.92 | 0.94 | 0.88 | 0.91 | 0.91 |
| A1H | 0.91 | 0.79 | 0.86 | 0.86 | 0.94 | 0.72 | 0.88 | 0.87 |
| H1H | 0.87 | 0.66 | 0.82 | 0.80 | 0.85 | 0.66 | 0.83 | 0.81 |
| n = 3, neighbor3(a,b,c,d):-.. |
| Target ordering | Dataset: 11000 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst 0.06 | Median | Mean |
| H | 0.10 | 0.04 | 0.06 | 0.06 | 0.10 | 0.07 | 0.07 |
| SH | 0.72 | 0.55 | 0.61 | 0.62 | 0.70 | 0.53 | 0.66 | 0.64 |
| A1H | 0.61 0.55 | 0.52 0.31 | 0.55 | 0.56 | 0.60 | 0.53 | 0.57 | 0.57 |
| H1H | | | 0.44 | 0.44 | 0.57 | 0.37 | 0.43 | 0.45 |
| Target ordering | n =4,neighbor4(a,b,c,d,e):-.. |
| Dataset: 39878 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Best | Worst | Fixed Median | Mean | Best | Random Worst | Median | Mean |
| H | 0.02 | 0.00 | 0.01 | 0.01 | 0.03 0.00 | 0.02 | 0.02 |
| SH | 0.38 | 0.24 | 0.33 | 0.32 | 0.36 | 0.28 0.32 | 0.32 |
| A1H | 0.33 | 0.22 | 0.27 | 0.26 | 0.34 | 0.22 0.26 | 0.26 |
| H1H | 0.22 | 0.12 | 0.18 | 0.18 | 0.24 | 0.13 0.18 | 0.18 |
| n = 4, neighbor4(a,b,c,d,e):-... Dataset: 39878 ground clauses; Training: 90o0 clauses; Test: 1000 clauses. |
| Target ordering H | | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst Median | Mean |
| 0.04 | 0.03 | 0.04 | 0.03 | 0.04 | 0.02 0.03 | 0.03 |
| 0.87 | 0.81 | 0.82 | 0.83 | 0.86 | 0.77 0.82 | 0.82 |
| SH | | 0.77 | 0.76 | 0.79 | 0.59 | 0.73 | 0.72 |
| A1H | 0.81 0.50 | 0.71 | | | | 0.42 | 0.41 |
| H1H | 0.12 | 0.40 | 0.37 n = 5, neighbor5(a,b,c,d,e,f):-... | 0.53 | 0.24 | | |
|
| Target ordering H | Dataset: 137738 ground clauses; Training: 2250 clauses; Test: 250 clauses. | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst | Median Mean |
| 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 0.00 | 0.00 |
| SH | 0.17 | 0.10 0.11 | 0.12 | 0.15 | 0.06 | 0.11 | 0.11 |
| A1H | 0.13 | 0.06 0.10 | 0.10 | 0.13 | 0.06 | 0.11 | 0.10 |
| H1H | 0.06 | 0.01 0.04 | 0.04 | 0.06 | 0.04 | 0.05 | 0.05 |
| | | n = 5, neighbor5(a,b,c,d,e,f):-... | | | | |
| Target ordering | Dataset: 137738 ground clauses; Training: 9000 clauses; Test: 1000 clauses. | |
| Fixed | | | | Random | |
| H | Best Worst | Median 0.00 | Mean 0.00 | Best 0.01 | Worst | Median 0.01 | Mean 0.01 |
| SH | 0.01 | 0.00 | | | 0.00 0.50 | | 0.55 |
| A1H | 0.65 0.53 | 0.52 0.46 | 0.55 0.48 | 0.56 0.48 | 0.60 | 0.56 0.50 | 0.50 |
| | | | 0.56 | 0.46 | | |
| H1H | 0.20 | 0.04 | 0.11 | 0.11 | 0.18 0.07 | 0.13 | 0.13 |
| | | | | | | |
",
+ "type": "table",
+ "image_path": "dd34965d221808a5a04e447a72e7c0558510c7fc80f59ab6b3c914768c11efd7.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 1,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 106,
+ 123,
+ 505,
+ 305.66666666666663
+ ],
+ "spans": [],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 106,
+ 305.66666666666663,
+ 505,
+ 488.33333333333326
+ ],
+ "spans": [],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 106,
+ 488.33333333333326,
+ 505,
+ 670.9999999999999
+ ],
+ "spans": [],
+ "index": 2
+ }
+ ]
+ },
+ {
+ "type": "table_footnote",
+ "bbox": [
+ 192,
+ 674,
+ 418,
+ 686
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 191,
+ 673,
+ 419,
+ 687
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 191,
+ 673,
+ 419,
+ 687
+ ],
+ "score": 1.0,
+ "content": "Table 6: The summary of the rule learning task, 10 runs.",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ }
+ ],
+ "index": 3
+ }
+ ],
+ "index": 2.0
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 83,
+ 505,
+ 192
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 83,
+ 505,
+ 94
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 83,
+ 505,
+ 94
+ ],
+ "score": 1.0,
+ "content": "ad-hoc methods that reorder the dataset using the domain-specific expert knowledge. Training based",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 105,
+ 94,
+ 505,
+ 105
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 94,
+ 505,
+ 105
+ ],
+ "score": 1.0,
+ "content": "on the Set Cross Entropy is also robust against the dataset which contains vectors whose internal",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 105,
+ 104,
+ 505,
+ 117
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 104,
+ 505,
+ 117
+ ],
+ "score": 1.0,
+ "content": "ordering may change time to time in an arbitrary manner. We demonstrated the effectiveness of the",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 105,
+ 116,
+ 505,
+ 128
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 116,
+ 505,
+ 128
+ ],
+ "score": 1.0,
+ "content": "approach by comparing Set Cross Entropy against the normal cross entropy, as well as the other",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 106,
+ 127,
+ 505,
+ 138
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 127,
+ 505,
+ 138
+ ],
+ "score": 1.0,
+ "content": "set-based metrics such as Hausdorff distance or set average (Chamfer) distance. set average distance",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 106,
+ 138,
+ 505,
+ 149
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 138,
+ 505,
+ 149
+ ],
+ "score": 1.0,
+ "content": "was shown to upper-bound Set Cross Entropy, and while it performed comparably well in the object",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 104,
+ 147,
+ 506,
+ 162
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 147,
+ 506,
+ 162
+ ],
+ "score": 1.0,
+ "content": "reconstruction task, it was outperformed by Set Cross Entropy in the rule learning task. Training",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 104,
+ 159,
+ 505,
+ 172
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 159,
+ 505,
+ 172
+ ],
+ "score": 1.0,
+ "content": "a neural network with Hausdorff distance turned out to be particularly hard, and it failed in many",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 171,
+ 506,
+ 183
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 171,
+ 506,
+ 183
+ ],
+ "score": 1.0,
+ "content": "scenarios, showing that it is not suitable as a loss function for the set reconstruction tasks considered",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 180,
+ 160,
+ 195
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 180,
+ 160,
+ 195
+ ],
+ "score": 1.0,
+ "content": "in this paper.",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ }
+ ],
+ "index": 4.5
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 107,
+ 209,
+ 175,
+ 221
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 209,
+ 176,
+ 222
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 209,
+ 176,
+ 222
+ ],
+ "score": 1.0,
+ "content": "REFERENCES",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ }
+ ],
+ "index": 10
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 104,
+ 218,
+ 506,
+ 734
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 226,
+ 506,
+ 240
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 226,
+ 506,
+ 240
+ ],
+ "score": 1.0,
+ "content": "Ryan Prescott Adams and Richard S Zemel. Ranking via Sinkhorn Propagation. arXiv preprint",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 115,
+ 237,
+ 210,
+ 250
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 237,
+ 210,
+ 250
+ ],
+ "score": 1.0,
+ "content": "arXiv:1106.1925, 2011.",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 255,
+ 504,
+ 270
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 255,
+ 504,
+ 270
+ ],
+ "score": 1.0,
+ "content": "Masataro Asai and Alex Fukunaga. Classical Planning in Deep Latent Space: Bridging the Subsymbolic-",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 114,
+ 266,
+ 505,
+ 280
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 266,
+ 505,
+ 280
+ ],
+ "score": 1.0,
+ "content": "Symbolic Boundary. In Proc. of AAAI Conference on Artificial Intelligence, 2018. URL https:",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 116,
+ 277,
+ 445,
+ 290
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 277,
+ 445,
+ 290
+ ],
+ "score": 1.0,
+ "content": "//www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16302.",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 295,
+ 506,
+ 309
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 295,
+ 506,
+ 309
+ ],
+ "score": 1.0,
+ "content": "Guillaume Bouchard, Sameer Singh, and Theo Trouillon. On Approximate Reasoning Capabilities",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 114,
+ 304,
+ 506,
+ 321
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 304,
+ 506,
+ 321
+ ],
+ "score": 1.0,
+ "content": "of Low-Rank Vector Spaces. AAAI Spring Syposium on Knowledge Representation and Reasoning",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 116,
+ 317,
+ 346,
+ 330
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 317,
+ 346,
+ 330
+ ],
+ "score": 1.0,
+ "content": "(KRR): Integrating Symbolic and Neural Approaches, 2015.",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 104,
+ 334,
+ 506,
+ 348
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 334,
+ 506,
+ 348
+ ],
+ "score": 1.0,
+ "content": "Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 115,
+ 346,
+ 506,
+ 358
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 346,
+ 506,
+ 358
+ ],
+ "score": 1.0,
+ "content": "Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet:",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 115,
+ 356,
+ 505,
+ 369
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 356,
+ 505,
+ 369
+ ],
+ "score": 1.0,
+ "content": "An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 115,
+ 367,
+ 450,
+ 380
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 367,
+ 450,
+ 380
+ ],
+ "score": 1.0,
+ "content": "University — Princeton University — Toyota Technological Institute at Chicago, 2015.",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 104,
+ 383,
+ 506,
+ 399
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 383,
+ 506,
+ 399
+ ],
+ "score": 1.0,
+ "content": "M-P Dubuisson and Anil K Jain. A Modified Hausdorff Distance for Object Matching. In Proceedings",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 114,
+ 396,
+ 437,
+ 409
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 396,
+ 437,
+ 409
+ ],
+ "score": 1.0,
+ "content": "of 12th International Conference on Pattern Recognition, pp. 566–568. IEEE, 1994.",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 414,
+ 505,
+ 427
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 414,
+ 505,
+ 427
+ ],
+ "score": 1.0,
+ "content": "Dominik Maria Endres and Johannes E Schindelin. A New Metric for Probability Distributions. IEEE",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 117,
+ 426,
+ 280,
+ 437
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 117,
+ 426,
+ 280,
+ 437
+ ],
+ "score": 1.0,
+ "content": "Transactions on Information theory, 2003.",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 444,
+ 505,
+ 456
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 444,
+ 505,
+ 456
+ ],
+ "score": 1.0,
+ "content": "Nicholas Guttenberg, Nathaniel Virgo, Olaf Witkowski, Hidetoshi Aoki, and Ryota Kanai. Permutation-",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 115,
+ 455,
+ 505,
+ 467
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 455,
+ 505,
+ 467
+ ],
+ "score": 1.0,
+ "content": "Equivariant Neural Networks Applied to Dynamics Prediction. arXiv preprint arXiv:1612.04530,",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 115,
+ 464,
+ 140,
+ 477
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 464,
+ 140,
+ 477
+ ],
+ "score": 1.0,
+ "content": "2016.",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 105,
+ 483,
+ 506,
+ 496
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 483,
+ 506,
+ 496
+ ],
+ "score": 1.0,
+ "content": "Malte Helmert. A Planning Heuristic Based on Causal Graph Analysis. In Proc. of the International",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 116,
+ 493,
+ 505,
+ 506
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 493,
+ 505,
+ 506
+ ],
+ "score": 1.0,
+ "content": "Conference on Automated Planning and Scheduling(ICAPS), pp. 161–170, 2004. URL http://",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 115,
+ 504,
+ 389,
+ 517
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 504,
+ 389,
+ 517
+ ],
+ "score": 1.0,
+ "content": "www.aaai.org/Library/ICAPS/2004/icaps04-021.php.",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 106,
+ 523,
+ 504,
+ 536
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 523,
+ 504,
+ 536
+ ],
+ "score": 1.0,
+ "content": "Sepp Hochreiter and Jurgen Schmidhuber. Long Short-Term Memory. ¨ Neural Computation, 9(8):1735–",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 115,
+ 533,
+ 165,
+ 545
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 533,
+ 165,
+ 545
+ ],
+ "score": 1.0,
+ "content": "1780, 1997.",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 552,
+ 506,
+ 565
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 552,
+ 506,
+ 565
+ ],
+ "score": 1.0,
+ "content": "Daniel P. Huttenlocher, Gregory A. Klanderman, and William J Rucklidge. Comparing Images using the",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 115,
+ 562,
+ 505,
+ 575
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 562,
+ 505,
+ 575
+ ],
+ "score": 1.0,
+ "content": "Hausdorff Distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9):850–863,",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 117,
+ 573,
+ 140,
+ 585
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 117,
+ 573,
+ 140,
+ 585
+ ],
+ "score": 1.0,
+ "content": "1993.",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 590,
+ 506,
+ 605
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 590,
+ 506,
+ 605
+ ],
+ "score": 1.0,
+ "content": "Piotr Indyk and Rajeev Motwani. Approximate Nearest Neighbors: Towards Removing the Curse of",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 114,
+ 600,
+ 505,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 600,
+ 505,
+ 617
+ ],
+ "score": 1.0,
+ "content": "Dimensionality. In Proceedings of the thirtieth annual ACM symposium on Theory of computing, pp.",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 116,
+ 612,
+ 204,
+ 624
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 612,
+ 204,
+ 624
+ ],
+ "score": 1.0,
+ "content": "604–613. ACM, 1998.",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 630,
+ 505,
+ 644
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 630,
+ 505,
+ 644
+ ],
+ "score": 1.0,
+ "content": "Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with Gumbel-Softmax. In Proc.",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 115,
+ 641,
+ 378,
+ 654
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 641,
+ 378,
+ 654
+ ],
+ "score": 1.0,
+ "content": "of the International Conference on Learning Representations, 2017.",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 658,
+ 505,
+ 674
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 658,
+ 505,
+ 674
+ ],
+ "score": 1.0,
+ "content": "Thanard Kurutach, Aviv Tamar, Ge Yang, Stuart Russell, and Pieter Abbeel. Learning Plannable Rep-",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 115,
+ 671,
+ 505,
+ 684
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 671,
+ 505,
+ 684
+ ],
+ "score": 1.0,
+ "content": "resentations with Causal InfoGAN. In In Proceedings of ICML / IJCAI / AAMAS 2018 Workshop on",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ },
+ {
+ "bbox": [
+ 116,
+ 681,
+ 270,
+ 694
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 681,
+ 270,
+ 694
+ ],
+ "score": 1.0,
+ "content": "Planning and Learning (PAL-18), 2018.",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ },
+ {
+ "bbox": [
+ 106,
+ 700,
+ 505,
+ 712
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 700,
+ 505,
+ 712
+ ],
+ "score": 1.0,
+ "content": "Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution: A Continuous Relax-",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 115,
+ 711,
+ 504,
+ 723
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 711,
+ 504,
+ 723
+ ],
+ "score": 1.0,
+ "content": "ation of Discrete Random Variables. In Proc. of the International Conference on Learning Represen-",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 115,
+ 722,
+ 171,
+ 732
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 722,
+ 171,
+ 732
+ ],
+ "score": 1.0,
+ "content": "tations, 2017.",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ }
+ ],
+ "index": 29.5
+ }
+ ],
+ "page_idx": 11,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 308,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 107,
+ 26,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 26,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 300,
+ 751,
+ 311,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 764
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 764
+ ],
+ "score": 1.0,
+ "content": "12",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 83,
+ 505,
+ 192
+ ],
+ "lines": [],
+ "index": 4.5,
+ "bbox_fs": [
+ 104,
+ 83,
+ 506,
+ 195
+ ],
+ "lines_deleted": true
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 107,
+ 209,
+ 175,
+ 221
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 209,
+ 176,
+ 222
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 209,
+ 176,
+ 222
+ ],
+ "score": 1.0,
+ "content": "REFERENCES",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ }
+ ],
+ "index": 10
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 104,
+ 218,
+ 506,
+ 734
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 226,
+ 506,
+ 240
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 226,
+ 506,
+ 240
+ ],
+ "score": 1.0,
+ "content": "Ryan Prescott Adams and Richard S Zemel. Ranking via Sinkhorn Propagation. arXiv preprint",
+ "type": "text"
+ }
+ ],
+ "index": 11,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 237,
+ 210,
+ 250
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 237,
+ 210,
+ 250
+ ],
+ "score": 1.0,
+ "content": "arXiv:1106.1925, 2011.",
+ "type": "text"
+ }
+ ],
+ "index": 12,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 255,
+ 504,
+ 270
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 255,
+ 504,
+ 270
+ ],
+ "score": 1.0,
+ "content": "Masataro Asai and Alex Fukunaga. Classical Planning in Deep Latent Space: Bridging the Subsymbolic-",
+ "type": "text"
+ }
+ ],
+ "index": 13,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 114,
+ 266,
+ 505,
+ 280
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 266,
+ 505,
+ 280
+ ],
+ "score": 1.0,
+ "content": "Symbolic Boundary. In Proc. of AAAI Conference on Artificial Intelligence, 2018. URL https:",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 116,
+ 277,
+ 445,
+ 290
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 277,
+ 445,
+ 290
+ ],
+ "score": 1.0,
+ "content": "//www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16302.",
+ "type": "text"
+ }
+ ],
+ "index": 15,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 295,
+ 506,
+ 309
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 295,
+ 506,
+ 309
+ ],
+ "score": 1.0,
+ "content": "Guillaume Bouchard, Sameer Singh, and Theo Trouillon. On Approximate Reasoning Capabilities",
+ "type": "text"
+ }
+ ],
+ "index": 16,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 114,
+ 304,
+ 506,
+ 321
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 304,
+ 506,
+ 321
+ ],
+ "score": 1.0,
+ "content": "of Low-Rank Vector Spaces. AAAI Spring Syposium on Knowledge Representation and Reasoning",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 116,
+ 317,
+ 346,
+ 330
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 317,
+ 346,
+ 330
+ ],
+ "score": 1.0,
+ "content": "(KRR): Integrating Symbolic and Neural Approaches, 2015.",
+ "type": "text"
+ }
+ ],
+ "index": 18,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 104,
+ 334,
+ 506,
+ 348
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 334,
+ 506,
+ 348
+ ],
+ "score": 1.0,
+ "content": "Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio",
+ "type": "text"
+ }
+ ],
+ "index": 19,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 346,
+ 506,
+ 358
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 346,
+ 506,
+ 358
+ ],
+ "score": 1.0,
+ "content": "Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet:",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 115,
+ 356,
+ 505,
+ 369
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 356,
+ 505,
+ 369
+ ],
+ "score": 1.0,
+ "content": "An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 115,
+ 367,
+ 450,
+ 380
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 367,
+ 450,
+ 380
+ ],
+ "score": 1.0,
+ "content": "University — Princeton University — Toyota Technological Institute at Chicago, 2015.",
+ "type": "text"
+ }
+ ],
+ "index": 22,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 104,
+ 383,
+ 506,
+ 399
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 383,
+ 506,
+ 399
+ ],
+ "score": 1.0,
+ "content": "M-P Dubuisson and Anil K Jain. A Modified Hausdorff Distance for Object Matching. In Proceedings",
+ "type": "text"
+ }
+ ],
+ "index": 23,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 114,
+ 396,
+ 437,
+ 409
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 396,
+ 437,
+ 409
+ ],
+ "score": 1.0,
+ "content": "of 12th International Conference on Pattern Recognition, pp. 566–568. IEEE, 1994.",
+ "type": "text"
+ }
+ ],
+ "index": 24,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 414,
+ 505,
+ 427
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 414,
+ 505,
+ 427
+ ],
+ "score": 1.0,
+ "content": "Dominik Maria Endres and Johannes E Schindelin. A New Metric for Probability Distributions. IEEE",
+ "type": "text"
+ }
+ ],
+ "index": 25,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 117,
+ 426,
+ 280,
+ 437
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 117,
+ 426,
+ 280,
+ 437
+ ],
+ "score": 1.0,
+ "content": "Transactions on Information theory, 2003.",
+ "type": "text"
+ }
+ ],
+ "index": 26,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 444,
+ 505,
+ 456
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 444,
+ 505,
+ 456
+ ],
+ "score": 1.0,
+ "content": "Nicholas Guttenberg, Nathaniel Virgo, Olaf Witkowski, Hidetoshi Aoki, and Ryota Kanai. Permutation-",
+ "type": "text"
+ }
+ ],
+ "index": 27,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 455,
+ 505,
+ 467
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 455,
+ 505,
+ 467
+ ],
+ "score": 1.0,
+ "content": "Equivariant Neural Networks Applied to Dynamics Prediction. arXiv preprint arXiv:1612.04530,",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 115,
+ 464,
+ 140,
+ 477
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 464,
+ 140,
+ 477
+ ],
+ "score": 1.0,
+ "content": "2016.",
+ "type": "text"
+ }
+ ],
+ "index": 29,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 483,
+ 506,
+ 496
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 483,
+ 506,
+ 496
+ ],
+ "score": 1.0,
+ "content": "Malte Helmert. A Planning Heuristic Based on Causal Graph Analysis. In Proc. of the International",
+ "type": "text"
+ }
+ ],
+ "index": 30,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 116,
+ 493,
+ 505,
+ 506
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 493,
+ 505,
+ 506
+ ],
+ "score": 1.0,
+ "content": "Conference on Automated Planning and Scheduling(ICAPS), pp. 161–170, 2004. URL http://",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 115,
+ 504,
+ 389,
+ 517
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 504,
+ 389,
+ 517
+ ],
+ "score": 1.0,
+ "content": "www.aaai.org/Library/ICAPS/2004/icaps04-021.php.",
+ "type": "text"
+ }
+ ],
+ "index": 32,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 106,
+ 523,
+ 504,
+ 536
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 523,
+ 504,
+ 536
+ ],
+ "score": 1.0,
+ "content": "Sepp Hochreiter and Jurgen Schmidhuber. Long Short-Term Memory. ¨ Neural Computation, 9(8):1735–",
+ "type": "text"
+ }
+ ],
+ "index": 33,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 533,
+ 165,
+ 545
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 533,
+ 165,
+ 545
+ ],
+ "score": 1.0,
+ "content": "1780, 1997.",
+ "type": "text"
+ }
+ ],
+ "index": 34,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 552,
+ 506,
+ 565
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 552,
+ 506,
+ 565
+ ],
+ "score": 1.0,
+ "content": "Daniel P. Huttenlocher, Gregory A. Klanderman, and William J Rucklidge. Comparing Images using the",
+ "type": "text"
+ }
+ ],
+ "index": 35,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 562,
+ 505,
+ 575
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 562,
+ 505,
+ 575
+ ],
+ "score": 1.0,
+ "content": "Hausdorff Distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9):850–863,",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 117,
+ 573,
+ 140,
+ 585
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 117,
+ 573,
+ 140,
+ 585
+ ],
+ "score": 1.0,
+ "content": "1993.",
+ "type": "text"
+ }
+ ],
+ "index": 37,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 590,
+ 506,
+ 605
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 590,
+ 506,
+ 605
+ ],
+ "score": 1.0,
+ "content": "Piotr Indyk and Rajeev Motwani. Approximate Nearest Neighbors: Towards Removing the Curse of",
+ "type": "text"
+ }
+ ],
+ "index": 38,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 114,
+ 600,
+ 505,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 600,
+ 505,
+ 617
+ ],
+ "score": 1.0,
+ "content": "Dimensionality. In Proceedings of the thirtieth annual ACM symposium on Theory of computing, pp.",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 116,
+ 612,
+ 204,
+ 624
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 612,
+ 204,
+ 624
+ ],
+ "score": 1.0,
+ "content": "604–613. ACM, 1998.",
+ "type": "text"
+ }
+ ],
+ "index": 40,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 630,
+ 505,
+ 644
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 630,
+ 505,
+ 644
+ ],
+ "score": 1.0,
+ "content": "Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with Gumbel-Softmax. In Proc.",
+ "type": "text"
+ }
+ ],
+ "index": 41,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 641,
+ 378,
+ 654
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 641,
+ 378,
+ 654
+ ],
+ "score": 1.0,
+ "content": "of the International Conference on Learning Representations, 2017.",
+ "type": "text"
+ }
+ ],
+ "index": 42,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 658,
+ 505,
+ 674
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 658,
+ 505,
+ 674
+ ],
+ "score": 1.0,
+ "content": "Thanard Kurutach, Aviv Tamar, Ge Yang, Stuart Russell, and Pieter Abbeel. Learning Plannable Rep-",
+ "type": "text"
+ }
+ ],
+ "index": 43,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 671,
+ 505,
+ 684
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 671,
+ 505,
+ 684
+ ],
+ "score": 1.0,
+ "content": "resentations with Causal InfoGAN. In In Proceedings of ICML / IJCAI / AAMAS 2018 Workshop on",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ },
+ {
+ "bbox": [
+ 116,
+ 681,
+ 270,
+ 694
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 681,
+ 270,
+ 694
+ ],
+ "score": 1.0,
+ "content": "Planning and Learning (PAL-18), 2018.",
+ "type": "text"
+ }
+ ],
+ "index": 45,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 106,
+ 700,
+ 505,
+ 712
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 700,
+ 505,
+ 712
+ ],
+ "score": 1.0,
+ "content": "Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution: A Continuous Relax-",
+ "type": "text"
+ }
+ ],
+ "index": 46,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 711,
+ 504,
+ 723
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 711,
+ 504,
+ 723
+ ],
+ "score": 1.0,
+ "content": "ation of Discrete Random Variables. In Proc. of the International Conference on Learning Represen-",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 115,
+ 722,
+ 171,
+ 732
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 722,
+ 171,
+ 732
+ ],
+ "score": 1.0,
+ "content": "tations, 2017.",
+ "type": "text"
+ }
+ ],
+ "index": 48,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 83,
+ 506,
+ 96
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 83,
+ 506,
+ 96
+ ],
+ "score": 1.0,
+ "content": "Xianling Mao, Bo-Si Feng, Yi-Jing Hao, Liqiang Nie, Heyan Huang, and Guihua Wen. S2JSD-LSH: A",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 0,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 93,
+ 487,
+ 107
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 93,
+ 487,
+ 107
+ ],
+ "score": 1.0,
+ "content": "Locality-Sensitive Hashing Schema for Probability Distributions. In AAAI, pp. 3244–3251, 2017.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 1,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 112,
+ 505,
+ 125
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 112,
+ 505,
+ 125
+ ],
+ "score": 1.0,
+ "content": "Drew V. McDermott. The 1998 AI Planning Systems Competition. AI Magazine, 21(2):35–55, 2000.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 2,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 116,
+ 122,
+ 495,
+ 136
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 122,
+ 495,
+ 136
+ ],
+ "score": 1.0,
+ "content": "URL http://www.aaai.org/ojs/index.php/aimagazine/article/view/1506.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 106,
+ 140,
+ 505,
+ 153
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 140,
+ 505,
+ 153
+ ],
+ "score": 1.0,
+ "content": "Gonzalo Mena, David Belanger, Scott Linderman, and Jasper Snoek. Learning Latent Permutations with",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 4,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 150,
+ 506,
+ 164
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 150,
+ 506,
+ 164
+ ],
+ "score": 1.0,
+ "content": "Gumbel-Sinkhorn Networks. In Proc. of the International Conference on Learning Representations,",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 115,
+ 160,
+ 401,
+ 175
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 160,
+ 339,
+ 175
+ ],
+ "score": 1.0,
+ "content": "2018. URL https://openreview.net/forum?id",
+ "type": "text",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 339,
+ 162,
+ 345,
+ 170
+ ],
+ "score": 0.6,
+ "content": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } } =",
+ "type": "inline_equation",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 345,
+ 160,
+ 401,
+ 175
+ ],
+ "score": 1.0,
+ "content": "Byt3oJ-0W.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 6,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 179,
+ 505,
+ 192
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 179,
+ 505,
+ 192
+ ],
+ "score": 1.0,
+ "content": "Selwyn Piramuthu. The Hausdorff Distance Measure for Feature Selection in Learning Applications. In",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 7,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 114,
+ 189,
+ 506,
+ 204
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 189,
+ 506,
+ 204
+ ],
+ "score": 1.0,
+ "content": "Systems Sciences, 1999. HICSS-32. Proceedings of the 32nd Annual Hawaii International Conference",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 115,
+ 200,
+ 218,
+ 213
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 200,
+ 218,
+ 213
+ ],
+ "score": 1.0,
+ "content": "on, pp. 6–pp. IEEE, 1999.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 9,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 104,
+ 217,
+ 506,
+ 232
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 217,
+ 506,
+ 232
+ ],
+ "score": 1.0,
+ "content": "Malte Probst. The Set Autoencoder: Unsupervised Representation Learning for Sets. 2018. A rejected",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 10,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 229,
+ 217,
+ 241
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 229,
+ 217,
+ 241
+ ],
+ "score": 1.0,
+ "content": "submission to ICLR2018.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 11,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 246,
+ 505,
+ 261
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 246,
+ 505,
+ 261
+ ],
+ "score": 1.0,
+ "content": "Siamak Ravanbakhsh, Jeff Schneider, and Barnabas Poczos. Deep Learning with Sets and Point Clouds.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 12,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 258,
+ 271,
+ 271
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 258,
+ 271,
+ 271
+ ],
+ "score": 1.0,
+ "content": "arXiv preprint arXiv:1611.04500, 2016.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 13,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 275,
+ 505,
+ 288
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 275,
+ 505,
+ 288
+ ],
+ "score": 1.0,
+ "content": "Joseph Redmon, Santosh Divvala, Ross Girshick, and Ali Farhadi. You Only Look Once: Unified, Real-",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 14,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 285,
+ 506,
+ 301
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 285,
+ 506,
+ 301
+ ],
+ "score": 1.0,
+ "content": "Time Object Detection. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 116,
+ 296,
+ 178,
+ 309
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 296,
+ 178,
+ 309
+ ],
+ "score": 1.0,
+ "content": "779–788, 2016.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 16,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 104,
+ 313,
+ 505,
+ 329
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 313,
+ 505,
+ 329
+ ],
+ "score": 1.0,
+ "content": "Tim Rocktaschel and Sebastian Riedel. End-to-End Differentiable Proving. In ¨ Advances in Neural Infor-",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 17,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 325,
+ 309,
+ 338
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 325,
+ 309,
+ 338
+ ],
+ "score": 1.0,
+ "content": "mation Processing Systems, pp. 3788–3800, 2017.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 18,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 106,
+ 344,
+ 504,
+ 356
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 344,
+ 504,
+ 356
+ ],
+ "score": 1.0,
+ "content": "Rodrigo Santa Cruz, Basura Fernando, Anoop Cherian, and Stephen Gould. DeepPermNet: Visual Per-",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 19,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 114,
+ 353,
+ 506,
+ 369
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 353,
+ 506,
+ 369
+ ],
+ "score": 1.0,
+ "content": "mutation Learning. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 116,
+ 364,
+ 213,
+ 378
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 364,
+ 213,
+ 378
+ ],
+ "score": 1.0,
+ "content": "6044–6052. IEEE, 2017.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 21,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 381,
+ 505,
+ 396
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 381,
+ 505,
+ 396
+ ],
+ "score": 1.0,
+ "content": "Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Advances in Neural Infor-",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 22,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 114,
+ 392,
+ 505,
+ 406
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 392,
+ 505,
+ 406
+ ],
+ "score": 1.0,
+ "content": "mation Processing Systems, pp. 2692–2700, 2015. URL http://papers.nips.cc/paper/",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 115,
+ 403,
+ 243,
+ 417
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 403,
+ 243,
+ 417
+ ],
+ "score": 1.0,
+ "content": "5866-pointer-networks.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 24,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 106,
+ 422,
+ 504,
+ 434
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 422,
+ 504,
+ 434
+ ],
+ "score": 1.0,
+ "content": "Oriol Vinyals, Samy Bengio, and Manjunath Kudlur. Order Matters: Sequence to Sequence for Sets.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 25,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 433,
+ 399,
+ 446
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 433,
+ 399,
+ 446
+ ],
+ "score": 1.0,
+ "content": "Proc. of the International Conference on Learning Representations, 2016.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 26,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 104,
+ 449,
+ 506,
+ 464
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 449,
+ 506,
+ 464
+ ],
+ "score": 1.0,
+ "content": "Jun Wang, Wei Liu, Sanjiv Kumar, and Shih-Fu Chang. Learning to Hash for Indexing Big DataA Survey.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 27,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 117,
+ 461,
+ 294,
+ 473
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 117,
+ 461,
+ 294,
+ 473
+ ],
+ "score": 1.0,
+ "content": "Proceedings of the IEEE, 104(1):34–57, 2016.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 28,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 105,
+ 480,
+ 504,
+ 491
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 480,
+ 504,
+ 491
+ ],
+ "score": 1.0,
+ "content": "Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Ruslan R Salakhutdinov, and",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 29,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 115,
+ 489,
+ 505,
+ 503
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 489,
+ 505,
+ 503
+ ],
+ "score": 1.0,
+ "content": "Alexander J Smola. Deep Sets. In Advances in Neural Information Processing Systems, pp. 3391–",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 116,
+ 500,
+ 164,
+ 512
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 500,
+ 164,
+ 512
+ ],
+ "score": 1.0,
+ "content": "3401, 2017.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 31,
+ "is_list_end_line": true
+ },
+ {
+ "bbox": [
+ 104,
+ 516,
+ 506,
+ 533
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 516,
+ 506,
+ 533
+ ],
+ "score": 1.0,
+ "content": "Zhuotun Zhu, Xinggang Wang, Song Bai, Cong Yao, and Xiang Bai. Deep Learning Representation using",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 32,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 114,
+ 528,
+ 398,
+ 541
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 528,
+ 398,
+ 541
+ ],
+ "score": 1.0,
+ "content": "Autoencoder for 3D Shape Retrieval. Neurocomputing, 204:41–50, 2016.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 33,
+ "is_list_end_line": true
+ }
+ ],
+ "index": 29.5,
+ "bbox_fs": [
+ 104,
+ 226,
+ 506,
+ 732
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 105,
+ 78,
+ 506,
+ 545
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 83,
+ 506,
+ 96
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 83,
+ 506,
+ 96
+ ],
+ "score": 1.0,
+ "content": "Xianling Mao, Bo-Si Feng, Yi-Jing Hao, Liqiang Nie, Heyan Huang, and Guihua Wen. S2JSD-LSH: A",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 115,
+ 93,
+ 487,
+ 107
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 93,
+ 487,
+ 107
+ ],
+ "score": 1.0,
+ "content": "Locality-Sensitive Hashing Schema for Probability Distributions. In AAAI, pp. 3244–3251, 2017.",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 105,
+ 112,
+ 505,
+ 125
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 112,
+ 505,
+ 125
+ ],
+ "score": 1.0,
+ "content": "Drew V. McDermott. The 1998 AI Planning Systems Competition. AI Magazine, 21(2):35–55, 2000.",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 116,
+ 122,
+ 495,
+ 136
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 122,
+ 495,
+ 136
+ ],
+ "score": 1.0,
+ "content": "URL http://www.aaai.org/ojs/index.php/aimagazine/article/view/1506.",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 106,
+ 140,
+ 505,
+ 153
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 140,
+ 505,
+ 153
+ ],
+ "score": 1.0,
+ "content": "Gonzalo Mena, David Belanger, Scott Linderman, and Jasper Snoek. Learning Latent Permutations with",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 115,
+ 150,
+ 506,
+ 164
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 150,
+ 506,
+ 164
+ ],
+ "score": 1.0,
+ "content": "Gumbel-Sinkhorn Networks. In Proc. of the International Conference on Learning Representations,",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 115,
+ 160,
+ 401,
+ 175
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 160,
+ 339,
+ 175
+ ],
+ "score": 1.0,
+ "content": "2018. URL https://openreview.net/forum?id",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 339,
+ 162,
+ 345,
+ 170
+ ],
+ "score": 0.6,
+ "content": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } } =",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 345,
+ 160,
+ 401,
+ 175
+ ],
+ "score": 1.0,
+ "content": "Byt3oJ-0W.",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 179,
+ 505,
+ 192
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 179,
+ 505,
+ 192
+ ],
+ "score": 1.0,
+ "content": "Selwyn Piramuthu. The Hausdorff Distance Measure for Feature Selection in Learning Applications. In",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 114,
+ 189,
+ 506,
+ 204
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 189,
+ 506,
+ 204
+ ],
+ "score": 1.0,
+ "content": "Systems Sciences, 1999. HICSS-32. Proceedings of the 32nd Annual Hawaii International Conference",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 115,
+ 200,
+ 218,
+ 213
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 200,
+ 218,
+ 213
+ ],
+ "score": 1.0,
+ "content": "on, pp. 6–pp. IEEE, 1999.",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 104,
+ 217,
+ 506,
+ 232
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 217,
+ 506,
+ 232
+ ],
+ "score": 1.0,
+ "content": "Malte Probst. The Set Autoencoder: Unsupervised Representation Learning for Sets. 2018. A rejected",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 115,
+ 229,
+ 217,
+ 241
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 229,
+ 217,
+ 241
+ ],
+ "score": 1.0,
+ "content": "submission to ICLR2018.",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 105,
+ 246,
+ 505,
+ 261
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 246,
+ 505,
+ 261
+ ],
+ "score": 1.0,
+ "content": "Siamak Ravanbakhsh, Jeff Schneider, and Barnabas Poczos. Deep Learning with Sets and Point Clouds.",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 115,
+ 258,
+ 271,
+ 271
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 258,
+ 271,
+ 271
+ ],
+ "score": 1.0,
+ "content": "arXiv preprint arXiv:1611.04500, 2016.",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 275,
+ 505,
+ 288
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 275,
+ 505,
+ 288
+ ],
+ "score": 1.0,
+ "content": "Joseph Redmon, Santosh Divvala, Ross Girshick, and Ali Farhadi. You Only Look Once: Unified, Real-",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 115,
+ 285,
+ 506,
+ 301
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 285,
+ 506,
+ 301
+ ],
+ "score": 1.0,
+ "content": "Time Object Detection. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp.",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 116,
+ 296,
+ 178,
+ 309
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 296,
+ 178,
+ 309
+ ],
+ "score": 1.0,
+ "content": "779–788, 2016.",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 104,
+ 313,
+ 505,
+ 329
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 313,
+ 505,
+ 329
+ ],
+ "score": 1.0,
+ "content": "Tim Rocktaschel and Sebastian Riedel. End-to-End Differentiable Proving. In ¨ Advances in Neural Infor-",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 115,
+ 325,
+ 309,
+ 338
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 325,
+ 309,
+ 338
+ ],
+ "score": 1.0,
+ "content": "mation Processing Systems, pp. 3788–3800, 2017.",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 106,
+ 344,
+ 504,
+ 356
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 344,
+ 504,
+ 356
+ ],
+ "score": 1.0,
+ "content": "Rodrigo Santa Cruz, Basura Fernando, Anoop Cherian, and Stephen Gould. DeepPermNet: Visual Per-",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 114,
+ 353,
+ 506,
+ 369
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 353,
+ 506,
+ 369
+ ],
+ "score": 1.0,
+ "content": "mutation Learning. In Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp.",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 116,
+ 364,
+ 213,
+ 378
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 364,
+ 213,
+ 378
+ ],
+ "score": 1.0,
+ "content": "6044–6052. IEEE, 2017.",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 381,
+ 505,
+ 396
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 381,
+ 505,
+ 396
+ ],
+ "score": 1.0,
+ "content": "Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. In Advances in Neural Infor-",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 114,
+ 392,
+ 505,
+ 406
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 392,
+ 505,
+ 406
+ ],
+ "score": 1.0,
+ "content": "mation Processing Systems, pp. 2692–2700, 2015. URL http://papers.nips.cc/paper/",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 115,
+ 403,
+ 243,
+ 417
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 403,
+ 243,
+ 417
+ ],
+ "score": 1.0,
+ "content": "5866-pointer-networks.",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 106,
+ 422,
+ 504,
+ 434
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 422,
+ 504,
+ 434
+ ],
+ "score": 1.0,
+ "content": "Oriol Vinyals, Samy Bengio, and Manjunath Kudlur. Order Matters: Sequence to Sequence for Sets.",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 115,
+ 433,
+ 399,
+ 446
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 433,
+ 399,
+ 446
+ ],
+ "score": 1.0,
+ "content": "Proc. of the International Conference on Learning Representations, 2016.",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 104,
+ 449,
+ 506,
+ 464
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 449,
+ 506,
+ 464
+ ],
+ "score": 1.0,
+ "content": "Jun Wang, Wei Liu, Sanjiv Kumar, and Shih-Fu Chang. Learning to Hash for Indexing Big DataA Survey.",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 117,
+ 461,
+ 294,
+ 473
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 117,
+ 461,
+ 294,
+ 473
+ ],
+ "score": 1.0,
+ "content": "Proceedings of the IEEE, 104(1):34–57, 2016.",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 480,
+ 504,
+ 491
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 480,
+ 504,
+ 491
+ ],
+ "score": 1.0,
+ "content": "Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Ruslan R Salakhutdinov, and",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 115,
+ 489,
+ 505,
+ 503
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 115,
+ 489,
+ 505,
+ 503
+ ],
+ "score": 1.0,
+ "content": "Alexander J Smola. Deep Sets. In Advances in Neural Information Processing Systems, pp. 3391–",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 116,
+ 500,
+ 164,
+ 512
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 116,
+ 500,
+ 164,
+ 512
+ ],
+ "score": 1.0,
+ "content": "3401, 2017.",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 104,
+ 516,
+ 506,
+ 533
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 516,
+ 506,
+ 533
+ ],
+ "score": 1.0,
+ "content": "Zhuotun Zhu, Xinggang Wang, Song Bai, Cong Yao, and Xiang Bai. Deep Learning Representation using",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 114,
+ 528,
+ 398,
+ 541
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 114,
+ 528,
+ 398,
+ 541
+ ],
+ "score": 1.0,
+ "content": "Autoencoder for 3D Shape Retrieval. Neurocomputing, 204:41–50, 2016.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ }
+ ],
+ "index": 16.5
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 560,
+ 161,
+ 572
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 559,
+ 163,
+ 574
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 559,
+ 163,
+ 574
+ ],
+ "score": 1.0,
+ "content": "APPENDIX",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ }
+ ],
+ "index": 34
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 583,
+ 275,
+ 595
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 583,
+ 276,
+ 596
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 583,
+ 276,
+ 596
+ ],
+ "score": 1.0,
+ "content": "6.1 NETWORK MODEL FOR 8 PUZZLE",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ }
+ ],
+ "index": 35
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 604,
+ 504,
+ 626
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 603,
+ 505,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 603,
+ 505,
+ 617
+ ],
+ "score": 1.0,
+ "content": "As mentioned in the earlier sections, the network has a permutation invariant encoder and the fully-",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 614,
+ 182,
+ 626
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 614,
+ 182,
+ 626
+ ],
+ "score": 1.0,
+ "content": "connected decoder.",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ }
+ ],
+ "index": 36.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 631,
+ 505,
+ 705
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 631,
+ 505,
+ 642
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 631,
+ 224,
+ 642
+ ],
+ "score": 1.0,
+ "content": "The input to the network is a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 225,
+ 632,
+ 253,
+ 641
+ ],
+ "score": 0.87,
+ "content": "9 \\times 1 5",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 253,
+ 631,
+ 505,
+ 642
+ ],
+ "score": 1.0,
+ "content": "matrix, where the first dimension represents the objects and the",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 106,
+ 642,
+ 505,
+ 653
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 642,
+ 505,
+ 653
+ ],
+ "score": 1.0,
+ "content": "second dimension represents the features of each object. The encoder has two 1D convolution layers of",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 651,
+ 505,
+ 664
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 651,
+ 366,
+ 664
+ ],
+ "score": 1.0,
+ "content": "1000 neurons with filter size 1, modeling the element-wise network",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 366,
+ 654,
+ 372,
+ 663
+ ],
+ "score": 0.8,
+ "content": "\\rho",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 372,
+ 651,
+ 505,
+ 664
+ ],
+ "score": 1.0,
+ "content": ". The output of these layers is then",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 662,
+ 506,
+ 675
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 662,
+ 506,
+ 675
+ ],
+ "score": 1.0,
+ "content": "aggregated by taking the sum of the first dimension. The result is then fed to two another fully-connected",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 105,
+ 672,
+ 505,
+ 686
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 672,
+ 505,
+ 686
+ ],
+ "score": 1.0,
+ "content": "layers of width 1000, which maps to the latent layer of 100 neurons. All encoder layers are activated by",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 683,
+ 505,
+ 696
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 683,
+ 505,
+ 696
+ ],
+ "score": 1.0,
+ "content": "ReLU. The latent representation is regularized and activated by Gumbel-Softmax Maddison et al. (2017);",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 106,
+ 694,
+ 308,
+ 706
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 694,
+ 308,
+ 706
+ ],
+ "score": 1.0,
+ "content": "Jang et al. (2017) as the input is a categorical model.",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ }
+ ],
+ "index": 41
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 710,
+ 504,
+ 731
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 708,
+ 506,
+ 723
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 708,
+ 506,
+ 723
+ ],
+ "score": 1.0,
+ "content": "The decoder consists of three fully-connected layers with dropout and batch normalization as shown",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ },
+ {
+ "bbox": [
+ 105,
+ 719,
+ 136,
+ 734
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 719,
+ 136,
+ 734
+ ],
+ "score": 1.0,
+ "content": "below:",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ }
+ ],
+ "index": 45.5
+ }
+ ],
+ "page_idx": 12,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 308,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 107,
+ 26,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 26,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 301,
+ 751,
+ 311,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 298,
+ 750,
+ 312,
+ 763
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 298,
+ 750,
+ 312,
+ 763
+ ],
+ "score": 1.0,
+ "content": "",
+ "type": "text",
+ "height": 13,
+ "width": 14
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "list",
+ "bbox": [
+ 105,
+ 78,
+ 506,
+ 545
+ ],
+ "lines": [],
+ "index": 16.5,
+ "bbox_fs": [
+ 104,
+ 83,
+ 506,
+ 541
+ ],
+ "lines_deleted": true
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 560,
+ 161,
+ 572
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 559,
+ 163,
+ 574
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 559,
+ 163,
+ 574
+ ],
+ "score": 1.0,
+ "content": "APPENDIX",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ }
+ ],
+ "index": 34
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 583,
+ 275,
+ 595
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 583,
+ 276,
+ 596
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 583,
+ 276,
+ 596
+ ],
+ "score": 1.0,
+ "content": "6.1 NETWORK MODEL FOR 8 PUZZLE",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ }
+ ],
+ "index": 35
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 604,
+ 504,
+ 626
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 603,
+ 505,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 603,
+ 505,
+ 617
+ ],
+ "score": 1.0,
+ "content": "As mentioned in the earlier sections, the network has a permutation invariant encoder and the fully-",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 614,
+ 182,
+ 626
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 614,
+ 182,
+ 626
+ ],
+ "score": 1.0,
+ "content": "connected decoder.",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ }
+ ],
+ "index": 36.5,
+ "bbox_fs": [
+ 105,
+ 603,
+ 505,
+ 626
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 631,
+ 505,
+ 705
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 631,
+ 505,
+ 642
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 631,
+ 224,
+ 642
+ ],
+ "score": 1.0,
+ "content": "The input to the network is a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 225,
+ 632,
+ 253,
+ 641
+ ],
+ "score": 0.87,
+ "content": "9 \\times 1 5",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 253,
+ 631,
+ 505,
+ 642
+ ],
+ "score": 1.0,
+ "content": "matrix, where the first dimension represents the objects and the",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 106,
+ 642,
+ 505,
+ 653
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 642,
+ 505,
+ 653
+ ],
+ "score": 1.0,
+ "content": "second dimension represents the features of each object. The encoder has two 1D convolution layers of",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 651,
+ 505,
+ 664
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 651,
+ 366,
+ 664
+ ],
+ "score": 1.0,
+ "content": "1000 neurons with filter size 1, modeling the element-wise network",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 366,
+ 654,
+ 372,
+ 663
+ ],
+ "score": 0.8,
+ "content": "\\rho",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 372,
+ 651,
+ 505,
+ 664
+ ],
+ "score": 1.0,
+ "content": ". The output of these layers is then",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 662,
+ 506,
+ 675
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 662,
+ 506,
+ 675
+ ],
+ "score": 1.0,
+ "content": "aggregated by taking the sum of the first dimension. The result is then fed to two another fully-connected",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 105,
+ 672,
+ 505,
+ 686
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 672,
+ 505,
+ 686
+ ],
+ "score": 1.0,
+ "content": "layers of width 1000, which maps to the latent layer of 100 neurons. All encoder layers are activated by",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 683,
+ 505,
+ 696
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 683,
+ 505,
+ 696
+ ],
+ "score": 1.0,
+ "content": "ReLU. The latent representation is regularized and activated by Gumbel-Softmax Maddison et al. (2017);",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 106,
+ 694,
+ 308,
+ 706
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 694,
+ 308,
+ 706
+ ],
+ "score": 1.0,
+ "content": "Jang et al. (2017) as the input is a categorical model.",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ }
+ ],
+ "index": 41,
+ "bbox_fs": [
+ 105,
+ 631,
+ 506,
+ 706
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 710,
+ 504,
+ 731
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 708,
+ 506,
+ 723
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 708,
+ 506,
+ 723
+ ],
+ "score": 1.0,
+ "content": "The decoder consists of three fully-connected layers with dropout and batch normalization as shown",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ },
+ {
+ "bbox": [
+ 105,
+ 719,
+ 136,
+ 734
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 719,
+ 136,
+ 734
+ ],
+ "score": 1.0,
+ "content": "below:",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ }
+ ],
+ "index": 45.5,
+ "bbox_fs": [
+ 105,
+ 708,
+ 506,
+ 734
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 222,
+ 80,
+ 389,
+ 113
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 227,
+ 80,
+ 383,
+ 92
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 227,
+ 80,
+ 383,
+ 92
+ ],
+ "score": 1.0,
+ "content": "fc(1000), relu, batchnorm, dropout(0.5),",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 227,
+ 90,
+ 383,
+ 104
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 227,
+ 90,
+ 383,
+ 104
+ ],
+ "score": 1.0,
+ "content": "fc(1000), relu, batchnorm, dropout(0.5),",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 228,
+ 100,
+ 338,
+ 113
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 228,
+ 100,
+ 306,
+ 113
+ ],
+ "score": 1.0,
+ "content": "dense(135), reshape",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 306,
+ 102,
+ 336,
+ 112
+ ],
+ "score": 0.83,
+ "content": "( 9 \\times 1 5 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 336,
+ 100,
+ 338,
+ 113
+ ],
+ "score": 0.0,
+ "content": "",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ }
+ ],
+ "index": 1
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 123,
+ 504,
+ 145
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 121,
+ 506,
+ 137
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 121,
+ 222,
+ 137
+ ],
+ "score": 1.0,
+ "content": "The last layer is then split into",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 222,
+ 124,
+ 293,
+ 134
+ ],
+ "score": 0.27,
+ "content": "9 \\times 9 , 9 \\times 3 , 9 \\times 3",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 293,
+ 121,
+ 506,
+ 137
+ ],
+ "score": 1.0,
+ "content": "matrices and separately activated by softmax, reflecting",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 133,
+ 204,
+ 147
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 133,
+ 204,
+ 147
+ ],
+ "score": 1.0,
+ "content": "the input dataset (Fig. 1).",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ }
+ ],
+ "index": 3.5
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 162,
+ 301,
+ 174
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 162,
+ 301,
+ 175
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 162,
+ 301,
+ 175
+ ],
+ "score": 1.0,
+ "content": "6.2 NETWORK MODEL FOR BLOCKSWOLRD",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ }
+ ],
+ "index": 5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 183,
+ 505,
+ 227
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 184,
+ 505,
+ 196
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 184,
+ 424,
+ 196
+ ],
+ "score": 1.0,
+ "content": "The same network as the 8-puzzle was used, except that the input and the output is a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 424,
+ 185,
+ 458,
+ 194
+ ],
+ "score": 0.88,
+ "content": "5 \\times 1 2 2 4",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 458,
+ 184,
+ 505,
+ 196
+ ],
+ "score": 1.0,
+ "content": "matrix. The",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 106,
+ 195,
+ 505,
+ 207
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 195,
+ 505,
+ 207
+ ],
+ "score": 1.0,
+ "content": "activations of the last layer is different: The first 1024 features are activated by a sigmoid function, while",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 204,
+ 505,
+ 218
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 204,
+ 505,
+ 218
+ ],
+ "score": 1.0,
+ "content": "the 200 features are divided into 40, 60, 40, 60 dimensions (for the one-hot bounding box information)",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 106,
+ 216,
+ 261,
+ 228
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 216,
+ 261,
+ 228
+ ],
+ "score": 1.0,
+ "content": "and are separately activated by softmax.",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ }
+ ],
+ "index": 7.5
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 107,
+ 244,
+ 320,
+ 255
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 243,
+ 321,
+ 256
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 243,
+ 321,
+ 256
+ ],
+ "score": 1.0,
+ "content": "6.3 FEATURE EXTRACTION FOR BLOCKSWORLD",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ }
+ ],
+ "index": 10
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 265,
+ 505,
+ 298
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 265,
+ 505,
+ 277
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 265,
+ 505,
+ 277
+ ],
+ "score": 1.0,
+ "content": "The 32x32 RGB image patches in the Blocksworld states are compressed into the feature vectors that are",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 106,
+ 276,
+ 505,
+ 288
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 276,
+ 505,
+ 288
+ ],
+ "score": 1.0,
+ "content": "later used as the input. The image features are learned by a convolutional autoencoder depicted in Fig. 4",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 104,
+ 285,
+ 150,
+ 300
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 285,
+ 150,
+ 300
+ ],
+ "score": 1.0,
+ "content": "and Fig. 5.",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ }
+ ],
+ "index": 12
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 236,
+ 311,
+ 377,
+ 422
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 237,
+ 311,
+ 321,
+ 324
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 311,
+ 262,
+ 324
+ ],
+ "score": 1.0,
+ "content": "Input",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 262,
+ 312,
+ 316,
+ 323
+ ],
+ "score": 0.33,
+ "content": "3 2 \\times 3 2 \\times 3 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 317,
+ 311,
+ 321,
+ 324
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 237,
+ 322,
+ 322,
+ 335
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 322,
+ 322,
+ 335
+ ],
+ "score": 1.0,
+ "content": "GaussianNoise(0.1),",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 237,
+ 333,
+ 373,
+ 346
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 333,
+ 289,
+ 346
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 289,
+ 334,
+ 306,
+ 344
+ ],
+ "score": 0.43,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 306,
+ 333,
+ 334,
+ 346
+ ],
+ "score": 1.0,
+ "content": ", kerne",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 334,
+ 334,
+ 365,
+ 344
+ ],
+ "score": 0.38,
+ "content": "\\mathsf { 1 { = } 3 \\times 3 , }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 366,
+ 333,
+ 373,
+ 346
+ ],
+ "score": 1.0,
+ "content": "),",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 236,
+ 344,
+ 259,
+ 357
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 344,
+ 259,
+ 357
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 237,
+ 355,
+ 331,
+ 367
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 355,
+ 291,
+ 367
+ ],
+ "score": 1.0,
+ "content": "MaxPooling",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 291,
+ 356,
+ 327,
+ 367
+ ],
+ "score": 0.36,
+ "content": "{ \\mathfrak { Q } } ( 2 \\times 2 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 327,
+ 355,
+ 331,
+ 367
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 237,
+ 366,
+ 374,
+ 379
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 366,
+ 289,
+ 379
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 367,
+ 306,
+ 377
+ ],
+ "score": 0.4,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 307,
+ 366,
+ 334,
+ 379
+ ],
+ "score": 1.0,
+ "content": ", kerne",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 334,
+ 367,
+ 365,
+ 377
+ ],
+ "score": 0.54,
+ "content": "\\mathrm { { \\Omega } | = 3 \\times 3 . }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 366,
+ 374,
+ 379
+ ],
+ "score": 1.0,
+ "content": ",),",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 236,
+ 376,
+ 259,
+ 389
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 376,
+ 259,
+ 389
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 237,
+ 388,
+ 331,
+ 401
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 388,
+ 289,
+ 401
+ ],
+ "score": 1.0,
+ "content": "MaxPooling",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 389,
+ 327,
+ 400
+ ],
+ "score": 0.35,
+ "content": "2 { \\mathrm { d } } ( 2 \\times 2 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 328,
+ 388,
+ 331,
+ 401
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 237,
+ 399,
+ 373,
+ 411
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 399,
+ 289,
+ 411
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 400,
+ 306,
+ 410
+ ],
+ "score": 0.44,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 306,
+ 399,
+ 335,
+ 411
+ ],
+ "score": 1.0,
+ "content": ", kernel",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 335,
+ 400,
+ 365,
+ 410
+ ],
+ "score": 0.38,
+ "content": "\\mathrm { = 3 \\times 3 }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 399,
+ 373,
+ 411
+ ],
+ "score": 1.0,
+ "content": ",),",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 237,
+ 410,
+ 274,
+ 424
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 410,
+ 274,
+ 424
+ ],
+ "score": 1.0,
+ "content": "sigmoid",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ }
+ ],
+ "index": 18.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 105,
+ 431,
+ 504,
+ 443
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 429,
+ 505,
+ 444
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 429,
+ 434,
+ 444
+ ],
+ "score": 1.0,
+ "content": "Figure 4: The implementation of the encoder for feature selection, which outputs a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 434,
+ 432,
+ 475,
+ 442
+ ],
+ "score": 0.9,
+ "content": "8 \\times 8 \\times 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 476,
+ 429,
+ 505,
+ 444
+ ],
+ "score": 1.0,
+ "content": "tensor.",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ }
+ ],
+ "index": 24
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 234,
+ 466,
+ 378,
+ 600
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 237,
+ 466,
+ 316,
+ 479
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 466,
+ 316,
+ 479
+ ],
+ "score": 1.0,
+ "content": "Input(8 × 8 × 16),",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 237,
+ 477,
+ 373,
+ 490
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 477,
+ 289,
+ 490
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 289,
+ 479,
+ 306,
+ 488
+ ],
+ "score": 0.27,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 307,
+ 477,
+ 373,
+ 490
+ ],
+ "score": 1.0,
+ "content": ", kernel=3 × 3,),",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 236,
+ 487,
+ 259,
+ 501
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 487,
+ 259,
+ 501
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 237,
+ 500,
+ 333,
+ 512
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 500,
+ 299,
+ 512
+ ],
+ "score": 1.0,
+ "content": "UpSampling2d",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 300,
+ 500,
+ 328,
+ 511
+ ],
+ "score": 0.35,
+ "content": "( 2 \\times 2 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 328,
+ 500,
+ 333,
+ 512
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 237,
+ 510,
+ 373,
+ 523
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 510,
+ 289,
+ 523
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 511,
+ 306,
+ 521
+ ],
+ "score": 0.39,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 306,
+ 510,
+ 334,
+ 523
+ ],
+ "score": 1.0,
+ "content": ", kerne",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 335,
+ 511,
+ 365,
+ 521
+ ],
+ "score": 0.61,
+ "content": "\\mathrm { = } 3 \\times 3 ,",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 510,
+ 373,
+ 523
+ ],
+ "score": 1.0,
+ "content": ",),",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 237,
+ 520,
+ 260,
+ 533
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 520,
+ 260,
+ 533
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 236,
+ 532,
+ 333,
+ 545
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 532,
+ 290,
+ 545
+ ],
+ "score": 1.0,
+ "content": "UpSampling",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 533,
+ 329,
+ 543
+ ],
+ "score": 0.33,
+ "content": "2 { \\mathrm { d } } ( 2 \\times 2 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 329,
+ 532,
+ 333,
+ 545
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 237,
+ 542,
+ 373,
+ 555
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 542,
+ 289,
+ 555
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 544,
+ 306,
+ 554
+ ],
+ "score": 0.39,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 307,
+ 542,
+ 335,
+ 555
+ ],
+ "score": 1.0,
+ "content": ", kernel",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 336,
+ 544,
+ 364,
+ 554
+ ],
+ "score": 0.52,
+ "content": "= 3 \\times 3 .",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 542,
+ 373,
+ 555
+ ],
+ "score": 1.0,
+ "content": ",),",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 237,
+ 554,
+ 259,
+ 567
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 554,
+ 259,
+ 567
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 236,
+ 563,
+ 278,
+ 578
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 563,
+ 278,
+ 578
+ ],
+ "score": 1.0,
+ "content": "fc(3072),",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 236,
+ 576,
+ 276,
+ 588
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 576,
+ 276,
+ 588
+ ],
+ "score": 1.0,
+ "content": "sigmoid,",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 237,
+ 586,
+ 325,
+ 600
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 586,
+ 270,
+ 600
+ ],
+ "score": 1.0,
+ "content": "reshape",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 270,
+ 587,
+ 325,
+ 599
+ ],
+ "score": 0.45,
+ "content": "( 3 2 \\times 3 2 \\times 3 )",
+ "type": "inline_equation"
+ }
+ ],
+ "index": 36
+ }
+ ],
+ "index": 30.5
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 646,
+ 305,
+ 658
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 645,
+ 307,
+ 659
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 645,
+ 307,
+ 659
+ ],
+ "score": 1.0,
+ "content": "6.4 NETWORK MODEL FOR RULE LEARNING",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ }
+ ],
+ "index": 37
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 668,
+ 505,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 667,
+ 505,
+ 681
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 667,
+ 505,
+ 681
+ ],
+ "score": 1.0,
+ "content": "We removed the encoder and the latent layer from the above models, and connected the input directly",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 105,
+ 678,
+ 505,
+ 691
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 678,
+ 493,
+ 691
+ ],
+ "score": 1.0,
+ "content": "to the decoder. While the decoder has the same types of layers, the width is shrinked to 400. In the",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 494,
+ 681,
+ 501,
+ 689
+ ],
+ "score": 0.54,
+ "content": "_ n",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 501,
+ 678,
+ 505,
+ 691
+ ],
+ "score": 1.0,
+ "content": "-",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 689,
+ 506,
+ 702
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 689,
+ 231,
+ 702
+ ],
+ "score": 1.0,
+ "content": "neighbor scenario, the input is a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 231,
+ 690,
+ 290,
+ 701
+ ],
+ "score": 0.92,
+ "content": "2 + 1 6 3 ( n + 1 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 290,
+ 689,
+ 506,
+ 702
+ ],
+ "score": 1.0,
+ "content": "vector, which consists of a one-hot label of 2 categories",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 712
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 699,
+ 236,
+ 712
+ ],
+ "score": 1.0,
+ "content": "for the predicate of the head, and",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 237,
+ 701,
+ 260,
+ 710
+ ],
+ "score": 0.87,
+ "content": "n + 1",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 261,
+ 699,
+ 505,
+ 712
+ ],
+ "score": 1.0,
+ "content": "one-hot labels of 163 categories for the arguments of the head.",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 106,
+ 710,
+ 505,
+ 723
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 710,
+ 505,
+ 723
+ ],
+ "score": 1.0,
+ "content": "163 categories corresponds to the number of countries in the Countries dataset (Bouchard et al., 2015).",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 106,
+ 721,
+ 478,
+ 733
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 721,
+ 165,
+ 733
+ ],
+ "score": 1.0,
+ "content": "The output is a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 166,
+ 721,
+ 195,
+ 732
+ ],
+ "score": 0.62,
+ "content": "[ n , 3 2 8 ]",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 195,
+ 721,
+ 402,
+ 733
+ ],
+ "score": 1.0,
+ "content": "matrix, where each row represents a binary predicate",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 402,
+ 721,
+ 471,
+ 731
+ ],
+ "score": 0.87,
+ "content": "3 2 8 = 2 + 2 \\cdot 1 6 3",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 472,
+ 721,
+ 478,
+ 733
+ ],
+ "score": 1.0,
+ "content": ").",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ }
+ ],
+ "index": 40.5
+ }
+ ],
+ "page_idx": 13,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 106,
+ 27,
+ 308,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 300,
+ 751,
+ 311,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 764
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 313,
+ 764
+ ],
+ "score": 1.0,
+ "content": "14",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 222,
+ 80,
+ 389,
+ 113
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 227,
+ 80,
+ 383,
+ 92
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 227,
+ 80,
+ 383,
+ 92
+ ],
+ "score": 1.0,
+ "content": "fc(1000), relu, batchnorm, dropout(0.5),",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 227,
+ 90,
+ 383,
+ 104
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 227,
+ 90,
+ 383,
+ 104
+ ],
+ "score": 1.0,
+ "content": "fc(1000), relu, batchnorm, dropout(0.5),",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 228,
+ 100,
+ 338,
+ 113
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 228,
+ 100,
+ 306,
+ 113
+ ],
+ "score": 1.0,
+ "content": "dense(135), reshape",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 306,
+ 102,
+ 336,
+ 112
+ ],
+ "score": 0.83,
+ "content": "( 9 \\times 1 5 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 336,
+ 100,
+ 338,
+ 113
+ ],
+ "score": 0.0,
+ "content": "",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ }
+ ],
+ "index": 1,
+ "bbox_fs": [
+ 227,
+ 80,
+ 383,
+ 113
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 123,
+ 504,
+ 145
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 121,
+ 506,
+ 137
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 121,
+ 222,
+ 137
+ ],
+ "score": 1.0,
+ "content": "The last layer is then split into",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 222,
+ 124,
+ 293,
+ 134
+ ],
+ "score": 0.27,
+ "content": "9 \\times 9 , 9 \\times 3 , 9 \\times 3",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 293,
+ 121,
+ 506,
+ 137
+ ],
+ "score": 1.0,
+ "content": "matrices and separately activated by softmax, reflecting",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 133,
+ 204,
+ 147
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 133,
+ 204,
+ 147
+ ],
+ "score": 1.0,
+ "content": "the input dataset (Fig. 1).",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ }
+ ],
+ "index": 3.5,
+ "bbox_fs": [
+ 105,
+ 121,
+ 506,
+ 147
+ ]
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 162,
+ 301,
+ 174
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 162,
+ 301,
+ 175
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 162,
+ 301,
+ 175
+ ],
+ "score": 1.0,
+ "content": "6.2 NETWORK MODEL FOR BLOCKSWOLRD",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ }
+ ],
+ "index": 5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 183,
+ 505,
+ 227
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 184,
+ 505,
+ 196
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 184,
+ 424,
+ 196
+ ],
+ "score": 1.0,
+ "content": "The same network as the 8-puzzle was used, except that the input and the output is a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 424,
+ 185,
+ 458,
+ 194
+ ],
+ "score": 0.88,
+ "content": "5 \\times 1 2 2 4",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 458,
+ 184,
+ 505,
+ 196
+ ],
+ "score": 1.0,
+ "content": "matrix. The",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 106,
+ 195,
+ 505,
+ 207
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 195,
+ 505,
+ 207
+ ],
+ "score": 1.0,
+ "content": "activations of the last layer is different: The first 1024 features are activated by a sigmoid function, while",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 204,
+ 505,
+ 218
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 204,
+ 505,
+ 218
+ ],
+ "score": 1.0,
+ "content": "the 200 features are divided into 40, 60, 40, 60 dimensions (for the one-hot bounding box information)",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 106,
+ 216,
+ 261,
+ 228
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 216,
+ 261,
+ 228
+ ],
+ "score": 1.0,
+ "content": "and are separately activated by softmax.",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ }
+ ],
+ "index": 7.5,
+ "bbox_fs": [
+ 105,
+ 184,
+ 505,
+ 228
+ ]
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 107,
+ 244,
+ 320,
+ 255
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 243,
+ 321,
+ 256
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 243,
+ 321,
+ 256
+ ],
+ "score": 1.0,
+ "content": "6.3 FEATURE EXTRACTION FOR BLOCKSWORLD",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ }
+ ],
+ "index": 10
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 265,
+ 505,
+ 298
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 265,
+ 505,
+ 277
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 265,
+ 505,
+ 277
+ ],
+ "score": 1.0,
+ "content": "The 32x32 RGB image patches in the Blocksworld states are compressed into the feature vectors that are",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 106,
+ 276,
+ 505,
+ 288
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 276,
+ 505,
+ 288
+ ],
+ "score": 1.0,
+ "content": "later used as the input. The image features are learned by a convolutional autoencoder depicted in Fig. 4",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 104,
+ 285,
+ 150,
+ 300
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 285,
+ 150,
+ 300
+ ],
+ "score": 1.0,
+ "content": "and Fig. 5.",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ }
+ ],
+ "index": 12,
+ "bbox_fs": [
+ 104,
+ 265,
+ 505,
+ 300
+ ]
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 236,
+ 311,
+ 377,
+ 422
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 237,
+ 311,
+ 321,
+ 324
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 311,
+ 262,
+ 324
+ ],
+ "score": 1.0,
+ "content": "Input",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 262,
+ 312,
+ 316,
+ 323
+ ],
+ "score": 0.33,
+ "content": "3 2 \\times 3 2 \\times 3 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 317,
+ 311,
+ 321,
+ 324
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 14,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 322,
+ 322,
+ 335
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 322,
+ 322,
+ 335
+ ],
+ "score": 1.0,
+ "content": "GaussianNoise(0.1),",
+ "type": "text"
+ }
+ ],
+ "index": 15,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 333,
+ 373,
+ 346
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 333,
+ 289,
+ 346
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 289,
+ 334,
+ 306,
+ 344
+ ],
+ "score": 0.43,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 306,
+ 333,
+ 334,
+ 346
+ ],
+ "score": 1.0,
+ "content": ", kerne",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 334,
+ 334,
+ 365,
+ 344
+ ],
+ "score": 0.38,
+ "content": "\\mathsf { 1 { = } 3 \\times 3 , }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 366,
+ 333,
+ 373,
+ 346
+ ],
+ "score": 1.0,
+ "content": "),",
+ "type": "text"
+ }
+ ],
+ "index": 16,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 236,
+ 344,
+ 259,
+ 357
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 344,
+ 259,
+ 357
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 17,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 355,
+ 331,
+ 367
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 355,
+ 291,
+ 367
+ ],
+ "score": 1.0,
+ "content": "MaxPooling",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 291,
+ 356,
+ 327,
+ 367
+ ],
+ "score": 0.36,
+ "content": "{ \\mathfrak { Q } } ( 2 \\times 2 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 327,
+ 355,
+ 331,
+ 367
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 18,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 366,
+ 374,
+ 379
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 366,
+ 289,
+ 379
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 367,
+ 306,
+ 377
+ ],
+ "score": 0.4,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 307,
+ 366,
+ 334,
+ 379
+ ],
+ "score": 1.0,
+ "content": ", kerne",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 334,
+ 367,
+ 365,
+ 377
+ ],
+ "score": 0.54,
+ "content": "\\mathrm { { \\Omega } | = 3 \\times 3 . }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 366,
+ 374,
+ 379
+ ],
+ "score": 1.0,
+ "content": ",),",
+ "type": "text"
+ }
+ ],
+ "index": 19,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 236,
+ 376,
+ 259,
+ 389
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 376,
+ 259,
+ 389
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 20,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 388,
+ 331,
+ 401
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 388,
+ 289,
+ 401
+ ],
+ "score": 1.0,
+ "content": "MaxPooling",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 389,
+ 327,
+ 400
+ ],
+ "score": 0.35,
+ "content": "2 { \\mathrm { d } } ( 2 \\times 2 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 328,
+ 388,
+ 331,
+ 401
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 21,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 399,
+ 373,
+ 411
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 399,
+ 289,
+ 411
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 400,
+ 306,
+ 410
+ ],
+ "score": 0.44,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 306,
+ 399,
+ 335,
+ 411
+ ],
+ "score": 1.0,
+ "content": ", kernel",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 335,
+ 400,
+ 365,
+ 410
+ ],
+ "score": 0.38,
+ "content": "\\mathrm { = 3 \\times 3 }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 399,
+ 373,
+ 411
+ ],
+ "score": 1.0,
+ "content": ",),",
+ "type": "text"
+ }
+ ],
+ "index": 22,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 410,
+ 274,
+ 424
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 410,
+ 274,
+ 424
+ ],
+ "score": 1.0,
+ "content": "sigmoid",
+ "type": "text"
+ }
+ ],
+ "index": 23,
+ "is_list_start_line": true
+ }
+ ],
+ "index": 18.5,
+ "bbox_fs": [
+ 236,
+ 311,
+ 374,
+ 424
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 105,
+ 431,
+ 504,
+ 443
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 429,
+ 505,
+ 444
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 429,
+ 434,
+ 444
+ ],
+ "score": 1.0,
+ "content": "Figure 4: The implementation of the encoder for feature selection, which outputs a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 434,
+ 432,
+ 475,
+ 442
+ ],
+ "score": 0.9,
+ "content": "8 \\times 8 \\times 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 476,
+ 429,
+ 505,
+ 444
+ ],
+ "score": 1.0,
+ "content": "tensor.",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ }
+ ],
+ "index": 24,
+ "bbox_fs": [
+ 105,
+ 429,
+ 505,
+ 444
+ ]
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 234,
+ 466,
+ 378,
+ 600
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 237,
+ 466,
+ 316,
+ 479
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 466,
+ 316,
+ 479
+ ],
+ "score": 1.0,
+ "content": "Input(8 × 8 × 16),",
+ "type": "text"
+ }
+ ],
+ "index": 25,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 477,
+ 373,
+ 490
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 477,
+ 289,
+ 490
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 289,
+ 479,
+ 306,
+ 488
+ ],
+ "score": 0.27,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 307,
+ 477,
+ 373,
+ 490
+ ],
+ "score": 1.0,
+ "content": ", kernel=3 × 3,),",
+ "type": "text"
+ }
+ ],
+ "index": 26,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 236,
+ 487,
+ 259,
+ 501
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 487,
+ 259,
+ 501
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 27,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 500,
+ 333,
+ 512
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 500,
+ 299,
+ 512
+ ],
+ "score": 1.0,
+ "content": "UpSampling2d",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 300,
+ 500,
+ 328,
+ 511
+ ],
+ "score": 0.35,
+ "content": "( 2 \\times 2 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 328,
+ 500,
+ 333,
+ 512
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 28,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 510,
+ 373,
+ 523
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 510,
+ 289,
+ 523
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 511,
+ 306,
+ 521
+ ],
+ "score": 0.39,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 306,
+ 510,
+ 334,
+ 523
+ ],
+ "score": 1.0,
+ "content": ", kerne",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 335,
+ 511,
+ 365,
+ 521
+ ],
+ "score": 0.61,
+ "content": "\\mathrm { = } 3 \\times 3 ,",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 510,
+ 373,
+ 523
+ ],
+ "score": 1.0,
+ "content": ",),",
+ "type": "text"
+ }
+ ],
+ "index": 29,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 520,
+ 260,
+ 533
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 520,
+ 260,
+ 533
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 30,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 236,
+ 532,
+ 333,
+ 545
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 532,
+ 290,
+ 545
+ ],
+ "score": 1.0,
+ "content": "UpSampling",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 533,
+ 329,
+ 543
+ ],
+ "score": 0.33,
+ "content": "2 { \\mathrm { d } } ( 2 \\times 2 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 329,
+ 532,
+ 333,
+ 545
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 31,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 542,
+ 373,
+ 555
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 542,
+ 289,
+ 555
+ ],
+ "score": 1.0,
+ "content": "conv2d(filte",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 290,
+ 544,
+ 306,
+ 554
+ ],
+ "score": 0.39,
+ "content": "{ = } 1 6",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 307,
+ 542,
+ 335,
+ 555
+ ],
+ "score": 1.0,
+ "content": ", kernel",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 336,
+ 544,
+ 364,
+ 554
+ ],
+ "score": 0.52,
+ "content": "= 3 \\times 3 .",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 365,
+ 542,
+ 373,
+ 555
+ ],
+ "score": 1.0,
+ "content": ",),",
+ "type": "text"
+ }
+ ],
+ "index": 32,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 554,
+ 259,
+ 567
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 554,
+ 259,
+ 567
+ ],
+ "score": 1.0,
+ "content": "relu,",
+ "type": "text"
+ }
+ ],
+ "index": 33,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 236,
+ 563,
+ 278,
+ 578
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 563,
+ 278,
+ 578
+ ],
+ "score": 1.0,
+ "content": "fc(3072),",
+ "type": "text"
+ }
+ ],
+ "index": 34,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 236,
+ 576,
+ 276,
+ 588
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 236,
+ 576,
+ 276,
+ 588
+ ],
+ "score": 1.0,
+ "content": "sigmoid,",
+ "type": "text"
+ }
+ ],
+ "index": 35,
+ "is_list_start_line": true
+ },
+ {
+ "bbox": [
+ 237,
+ 586,
+ 325,
+ 600
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 237,
+ 586,
+ 270,
+ 600
+ ],
+ "score": 1.0,
+ "content": "reshape",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 270,
+ 587,
+ 325,
+ 599
+ ],
+ "score": 0.45,
+ "content": "( 3 2 \\times 3 2 \\times 3 )",
+ "type": "inline_equation"
+ }
+ ],
+ "index": 36,
+ "is_list_start_line": true
+ }
+ ],
+ "index": 30.5,
+ "bbox_fs": [
+ 236,
+ 466,
+ 373,
+ 600
+ ]
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 646,
+ 305,
+ 658
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 645,
+ 307,
+ 659
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 645,
+ 307,
+ 659
+ ],
+ "score": 1.0,
+ "content": "6.4 NETWORK MODEL FOR RULE LEARNING",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ }
+ ],
+ "index": 37
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 668,
+ 505,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 667,
+ 505,
+ 681
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 667,
+ 505,
+ 681
+ ],
+ "score": 1.0,
+ "content": "We removed the encoder and the latent layer from the above models, and connected the input directly",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 105,
+ 678,
+ 505,
+ 691
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 678,
+ 493,
+ 691
+ ],
+ "score": 1.0,
+ "content": "to the decoder. While the decoder has the same types of layers, the width is shrinked to 400. In the",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 494,
+ 681,
+ 501,
+ 689
+ ],
+ "score": 0.54,
+ "content": "_ n",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 501,
+ 678,
+ 505,
+ 691
+ ],
+ "score": 1.0,
+ "content": "-",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 689,
+ 506,
+ 702
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 689,
+ 231,
+ 702
+ ],
+ "score": 1.0,
+ "content": "neighbor scenario, the input is a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 231,
+ 690,
+ 290,
+ 701
+ ],
+ "score": 0.92,
+ "content": "2 + 1 6 3 ( n + 1 )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 290,
+ 689,
+ 506,
+ 702
+ ],
+ "score": 1.0,
+ "content": "vector, which consists of a one-hot label of 2 categories",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 712
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 699,
+ 236,
+ 712
+ ],
+ "score": 1.0,
+ "content": "for the predicate of the head, and",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 237,
+ 701,
+ 260,
+ 710
+ ],
+ "score": 0.87,
+ "content": "n + 1",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 261,
+ 699,
+ 505,
+ 712
+ ],
+ "score": 1.0,
+ "content": "one-hot labels of 163 categories for the arguments of the head.",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 106,
+ 710,
+ 505,
+ 723
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 710,
+ 505,
+ 723
+ ],
+ "score": 1.0,
+ "content": "163 categories corresponds to the number of countries in the Countries dataset (Bouchard et al., 2015).",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 106,
+ 721,
+ 478,
+ 733
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 721,
+ 165,
+ 733
+ ],
+ "score": 1.0,
+ "content": "The output is a",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 166,
+ 721,
+ 195,
+ 732
+ ],
+ "score": 0.62,
+ "content": "[ n , 3 2 8 ]",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 195,
+ 721,
+ 402,
+ 733
+ ],
+ "score": 1.0,
+ "content": "matrix, where each row represents a binary predicate",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 402,
+ 721,
+ 471,
+ 731
+ ],
+ "score": 0.87,
+ "content": "3 2 8 = 2 + 2 \\cdot 1 6 3",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 472,
+ 721,
+ 478,
+ 733
+ ],
+ "score": 1.0,
+ "content": ").",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ }
+ ],
+ "index": 40.5,
+ "bbox_fs": [
+ 105,
+ 667,
+ 506,
+ 733
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "title",
+ "bbox": [
+ 106,
+ 82,
+ 473,
+ 104
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 82,
+ 474,
+ 94
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 82,
+ 474,
+ 94
+ ],
+ "score": 1.0,
+ "content": "6.5 EXAMPLE APPLICATION OF THE PERMUTATION-INVARIANT REPRESENTATION &",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 130,
+ 94,
+ 212,
+ 105
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 130,
+ 94,
+ 212,
+ 105
+ ],
+ "score": 1.0,
+ "content": "RECONSTRUCTION",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 0.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 114,
+ 505,
+ 210
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 115,
+ 504,
+ 127
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 115,
+ 504,
+ 127
+ ],
+ "score": 1.0,
+ "content": "To address the practical utility of “set reconstruction” or “set autoencoding”, we added a new experiment.",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 106,
+ 125,
+ 505,
+ 137
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 125,
+ 505,
+ 137
+ ],
+ "score": 1.0,
+ "content": "We modified Latplan (Asai & Fukunaga, 2018) neural-symbolic classical planning system, a system that",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 135,
+ 506,
+ 149
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 135,
+ 430,
+ 149
+ ],
+ "score": 1.0,
+ "content": "operates on a discrete symbolic latent space of the real-valued inputs and runs Dijkstra",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 430,
+ 136,
+ 450,
+ 146
+ ],
+ "score": 0.51,
+ "content": "\\mathrm { \\Phi _ { s / A ^ { * } } }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 450,
+ 135,
+ 506,
+ 149
+ ],
+ "score": 1.0,
+ "content": "search using a",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 106,
+ 147,
+ 505,
+ 158
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 147,
+ 505,
+ 158
+ ],
+ "score": 1.0,
+ "content": "state-of-the-art symbolic classical planning solver. We modified Latplan to take the set-of-object-feature-",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 157,
+ 505,
+ 170
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 157,
+ 505,
+ 170
+ ],
+ "score": 1.0,
+ "content": "vector input rather than images. It is a high-level task planner (unlike motion planning / actuator control)",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 168,
+ 505,
+ 180
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 168,
+ 505,
+ 180
+ ],
+ "score": 1.0,
+ "content": "that has implications on robotic systems, which perceives a set of inputs already preprocessed by the",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 178,
+ 504,
+ 190
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 178,
+ 504,
+ 190
+ ],
+ "score": 1.0,
+ "content": "external system. For example, the image input is first fed into Object Recognition system (e.g. YOLO,",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 187,
+ 506,
+ 201
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 187,
+ 506,
+ 201
+ ],
+ "score": 1.0,
+ "content": "(Redmon et al., 2016)) and the planner receives a set of feature vectors extracted from the image patches",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 199,
+ 484,
+ 212
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 199,
+ 484,
+ 212
+ ],
+ "score": 1.0,
+ "content": "segmented from the raw image, rather than feeding the image input directly to the planning system.",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ }
+ ],
+ "index": 6
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 215,
+ 505,
+ 289
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 215,
+ 505,
+ 228
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 215,
+ 505,
+ 228
+ ],
+ "score": 1.0,
+ "content": "Latplan system learns the binary latent space of an arbitrary raw input (e.g. images) with a Gumbel-",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 105,
+ 225,
+ 506,
+ 238
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 225,
+ 506,
+ 238
+ ],
+ "score": 1.0,
+ "content": "Softmax variational autoencoder, learns a discrete state space from the transition examples, and runs a",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 236,
+ 506,
+ 248
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 236,
+ 331,
+ 248
+ ],
+ "score": 1.0,
+ "content": "symbolic, systematic search algorithm such as Dijkstra or",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 331,
+ 237,
+ 344,
+ 246
+ ],
+ "score": 0.85,
+ "content": "\\mathbf { A } ^ { * }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 345,
+ 236,
+ 506,
+ 248
+ ],
+ "score": 1.0,
+ "content": "search which guarantee the optimality of",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 246,
+ 505,
+ 259
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 246,
+ 505,
+ 259
+ ],
+ "score": 1.0,
+ "content": "the solution. Unlike RL-based planning systems, the search agent does not contain the learning aspects.",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 256,
+ 505,
+ 270
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 256,
+ 505,
+ 270
+ ],
+ "score": 1.0,
+ "content": "The discrete plan in the latent space is mapped back to the raw image visualization of the plan execution,",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 267,
+ 506,
+ 280
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 267,
+ 506,
+ 280
+ ],
+ "score": 1.0,
+ "content": "which requires the reconstruction capability of (V)AE. A similar system replacing Gumbel Softmax VAE",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 278,
+ 356,
+ 290
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 278,
+ 356,
+ 290
+ ],
+ "score": 1.0,
+ "content": "with Causal InfoGAN was later proposed (Kurutach et al., 2018).",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ }
+ ],
+ "index": 14
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 294,
+ 505,
+ 326
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 294,
+ 505,
+ 306
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 294,
+ 505,
+ 306
+ ],
+ "score": 1.0,
+ "content": "We replaced Latplan’s Gumbel-Softmax VAE with our autoencoder used in the 8-Puzzle and the",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 304,
+ 505,
+ 317
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 304,
+ 505,
+ 317
+ ],
+ "score": 1.0,
+ "content": "Blocksworld experiments (Appendix, Sec. 6.1,Sec. 6.2). Our autoencoder also uses Gumbel Softmax in",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 315,
+ 465,
+ 329
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 315,
+ 465,
+ 329
+ ],
+ "score": 1.0,
+ "content": "the latent layer, but it uses (Zaheer et al., 2017) encoder and is trained with Set Cross Entropy.",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ }
+ ],
+ "index": 19
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 331,
+ 505,
+ 405
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 331,
+ 505,
+ 343
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 331,
+ 505,
+ 343
+ ],
+ "score": 1.0,
+ "content": "When the network learned the representation, it guarantees that the planner finds a solution because the",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 342,
+ 505,
+ 354
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 342,
+ 505,
+ 354
+ ],
+ "score": 1.0,
+ "content": "search algorithm being used (e.g. Dijkstra) is a complete, systematic, symbolic search algorithm, which",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 352,
+ 505,
+ 363
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 352,
+ 505,
+ 363
+ ],
+ "score": 1.0,
+ "content": "guarantees to find a solution whenever it is reachable in the state space. If the network cannot learn",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 363,
+ 505,
+ 375
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 363,
+ 505,
+ 375
+ ],
+ "score": 1.0,
+ "content": "the permutation-invariant representation, the system cannot solve the problem and/or return the human-",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 374,
+ 505,
+ 385
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 374,
+ 505,
+ 385
+ ],
+ "score": 1.0,
+ "content": "comprehensive visualization. This makes the specific permutation-invariant representation using (Zaheer",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 104,
+ 383,
+ 506,
+ 397
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 383,
+ 506,
+ 397
+ ],
+ "score": 1.0,
+ "content": "et al., 2017) and the proposed Set Cross Entropy necessary when the input is given as a set of future",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 394,
+ 139,
+ 407
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 394,
+ 139,
+ 407
+ ],
+ "score": 1.0,
+ "content": "vectors.",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ }
+ ],
+ "index": 24
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 107,
+ 420,
+ 149,
+ 432
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 420,
+ 151,
+ 433
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 420,
+ 151,
+ 433
+ ],
+ "score": 1.0,
+ "content": "8 PUZZLE",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ }
+ ],
+ "index": 28
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 441,
+ 504,
+ 483
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 441,
+ 506,
+ 454
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 441,
+ 506,
+ 454
+ ],
+ "score": 1.0,
+ "content": "First, the training was performed on a dataset in which the object vector ordering is randomized. The",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 106,
+ 452,
+ 505,
+ 464
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 452,
+ 216,
+ 464
+ ],
+ "score": 1.0,
+ "content": "autoencoder compresses the",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 216,
+ 452,
+ 270,
+ 462
+ ],
+ "score": 0.9,
+ "content": "1 5 \\times 9 = 1 3 5",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 270,
+ 452,
+ 505,
+ 464
+ ],
+ "score": 1.0,
+ "content": "-bit binary representation (object vectors) into a permutation-",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 460,
+ 506,
+ 475
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 460,
+ 506,
+ 475
+ ],
+ "score": 1.0,
+ "content": "invariant 100-bit discrete latent binary representation. We provided 5000 states for training the autoen-",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 472,
+ 433,
+ 484
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 472,
+ 262,
+ 484
+ ],
+ "score": 1.0,
+ "content": "coder, while the search space consists of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 262,
+ 473,
+ 316,
+ 483
+ ],
+ "score": 0.28,
+ "content": "3 6 2 8 8 0 ( = 9 ! )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 317,
+ 472,
+ 433,
+ 484
+ ],
+ "score": 1.0,
+ "content": "states and 967680 transitions.",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ }
+ ],
+ "index": 30.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 105,
+ 489,
+ 503,
+ 510
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 487,
+ 505,
+ 501
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 487,
+ 505,
+ 501
+ ],
+ "score": 1.0,
+ "content": "Note that each state have 9! variations due to the permutations in the order the tiles and the locations are",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 498,
+ 392,
+ 511
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 498,
+ 363,
+ 511
+ ],
+ "score": 1.0,
+ "content": "reported. This also increases the number of transition quadratically",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 364,
+ 499,
+ 386,
+ 511
+ ],
+ "score": 0.48,
+ "content": "( ( 9 ! ) ^ { 2 } ,",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 386,
+ 498,
+ 392,
+ 511
+ ],
+ "score": 1.0,
+ "content": ").",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ }
+ ],
+ "index": 33.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 516,
+ 505,
+ 558
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 515,
+ 505,
+ 528
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 515,
+ 505,
+ 528
+ ],
+ "score": 1.0,
+ "content": "We generated 40 problem instances of 8-puzzle each generated by a random walk from the goal state. 40",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 525,
+ 505,
+ 540
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 525,
+ 505,
+ 540
+ ],
+ "score": 1.0,
+ "content": "instances consist of 20 instances each generated by a 7-steps random walk and another 20 by 14 steps.",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 106,
+ 536,
+ 505,
+ 549
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 536,
+ 505,
+ 549
+ ],
+ "score": 1.0,
+ "content": "We solved 40 instances using Fast Downward classical planner Helmert (2004) with blind heuristics in",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 106,
+ 548,
+ 258,
+ 559
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 548,
+ 258,
+ 559
+ ],
+ "score": 1.0,
+ "content": "order to remove the effect of heuristics.",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ }
+ ],
+ "index": 36.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 563,
+ 505,
+ 626
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 563,
+ 505,
+ 576
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 563,
+ 505,
+ 576
+ ],
+ "score": 1.0,
+ "content": "We compared the number of problems successfully solved by two variations of Latplan where each uses",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 574,
+ 506,
+ 587
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 574,
+ 506,
+ 587
+ ],
+ "score": 1.0,
+ "content": "the autoencoder trained with Set Average and Set Cross Entropy, respectively, for encoding the input",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 585,
+ 505,
+ 597
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 585,
+ 505,
+ 597
+ ],
+ "score": 1.0,
+ "content": "into binary latent space. Both version managed to solve all instances because both Set Average and Set",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 106,
+ 595,
+ 505,
+ 608
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 595,
+ 505,
+ 608
+ ],
+ "score": 1.0,
+ "content": "Cross Entropy managed to train the AE from 5000 examples with a sufficient accuracy. All solutions were",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 605,
+ 505,
+ 618
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 605,
+ 505,
+ 618
+ ],
+ "score": 1.0,
+ "content": "correct (checked manually). Since the search algorithm being used is optimal, the quality of the solution",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 105,
+ 616,
+ 178,
+ 627
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 616,
+ 178,
+ 627
+ ],
+ "score": 1.0,
+ "content": "was also identical.",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ }
+ ],
+ "index": 41.5
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 643,
+ 175,
+ 653
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 107,
+ 643,
+ 176,
+ 654
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 643,
+ 176,
+ 654
+ ],
+ "score": 1.0,
+ "content": "BLOCKSWORLD",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ }
+ ],
+ "index": 45
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 663,
+ 504,
+ 704
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 662,
+ 505,
+ 675
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 662,
+ 505,
+ 675
+ ],
+ "score": 1.0,
+ "content": "We solved 30 planning instances in a 4-blocks, 3-stacks environment. The instances are generated by",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 106,
+ 673,
+ 505,
+ 685
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 673,
+ 505,
+ 685
+ ],
+ "score": 1.0,
+ "content": "taking a random initial state and choosing a goal state by the 3, 7, or 14 steps random walks (10 instances",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 105,
+ 683,
+ 505,
+ 696
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 683,
+ 505,
+ 696
+ ],
+ "score": 1.0,
+ "content": "each). The correctness of the plans are again checked manually. The same planner configuration was used",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ },
+ {
+ "bbox": [
+ 106,
+ 693,
+ 171,
+ 706
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 693,
+ 171,
+ 706
+ ],
+ "score": 1.0,
+ "content": "for all instances.",
+ "type": "text"
+ }
+ ],
+ "index": 49
+ }
+ ],
+ "index": 47.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 710,
+ 504,
+ 731
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 709,
+ 505,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 709,
+ 505,
+ 722
+ ],
+ "score": 1.0,
+ "content": "The search space consists of 5760 states and 34560 transitions, and each state have 4! variations due to",
+ "type": "text"
+ }
+ ],
+ "index": 50
+ },
+ {
+ "bbox": [
+ 105,
+ 720,
+ 482,
+ 733
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 720,
+ 482,
+ 733
+ ],
+ "score": 1.0,
+ "content": "permutations of 4 blocks. We provided 1000 randomly selected states for training the autoencoder.",
+ "type": "text"
+ }
+ ],
+ "index": 51
+ }
+ ],
+ "index": 50.5
+ }
+ ],
+ "page_idx": 14,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 308,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 107,
+ 26,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 26,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2019",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 301,
+ 751,
+ 311,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 312,
+ 764
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 299,
+ 750,
+ 312,
+ 764
+ ],
+ "score": 1.0,
+ "content": "",
+ "type": "text",
+ "height": 14,
+ "width": 13
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "title",
+ "bbox": [
+ 106,
+ 82,
+ 473,
+ 104
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 82,
+ 474,
+ 94
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 82,
+ 474,
+ 94
+ ],
+ "score": 1.0,
+ "content": "6.5 EXAMPLE APPLICATION OF THE PERMUTATION-INVARIANT REPRESENTATION &",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 130,
+ 94,
+ 212,
+ 105
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 130,
+ 94,
+ 212,
+ 105
+ ],
+ "score": 1.0,
+ "content": "RECONSTRUCTION",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 0.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 114,
+ 505,
+ 210
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 115,
+ 504,
+ 127
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 115,
+ 504,
+ 127
+ ],
+ "score": 1.0,
+ "content": "To address the practical utility of “set reconstruction” or “set autoencoding”, we added a new experiment.",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 106,
+ 125,
+ 505,
+ 137
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 125,
+ 505,
+ 137
+ ],
+ "score": 1.0,
+ "content": "We modified Latplan (Asai & Fukunaga, 2018) neural-symbolic classical planning system, a system that",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 135,
+ 506,
+ 149
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 135,
+ 430,
+ 149
+ ],
+ "score": 1.0,
+ "content": "operates on a discrete symbolic latent space of the real-valued inputs and runs Dijkstra",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 430,
+ 136,
+ 450,
+ 146
+ ],
+ "score": 0.51,
+ "content": "\\mathrm { \\Phi _ { s / A ^ { * } } }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 450,
+ 135,
+ 506,
+ 149
+ ],
+ "score": 1.0,
+ "content": "search using a",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 106,
+ 147,
+ 505,
+ 158
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 147,
+ 505,
+ 158
+ ],
+ "score": 1.0,
+ "content": "state-of-the-art symbolic classical planning solver. We modified Latplan to take the set-of-object-feature-",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 157,
+ 505,
+ 170
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 157,
+ 505,
+ 170
+ ],
+ "score": 1.0,
+ "content": "vector input rather than images. It is a high-level task planner (unlike motion planning / actuator control)",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 168,
+ 505,
+ 180
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 168,
+ 505,
+ 180
+ ],
+ "score": 1.0,
+ "content": "that has implications on robotic systems, which perceives a set of inputs already preprocessed by the",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 178,
+ 504,
+ 190
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 178,
+ 504,
+ 190
+ ],
+ "score": 1.0,
+ "content": "external system. For example, the image input is first fed into Object Recognition system (e.g. YOLO,",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 187,
+ 506,
+ 201
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 187,
+ 506,
+ 201
+ ],
+ "score": 1.0,
+ "content": "(Redmon et al., 2016)) and the planner receives a set of feature vectors extracted from the image patches",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 199,
+ 484,
+ 212
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 199,
+ 484,
+ 212
+ ],
+ "score": 1.0,
+ "content": "segmented from the raw image, rather than feeding the image input directly to the planning system.",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ }
+ ],
+ "index": 6,
+ "bbox_fs": [
+ 105,
+ 115,
+ 506,
+ 212
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 215,
+ 505,
+ 289
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 215,
+ 505,
+ 228
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 215,
+ 505,
+ 228
+ ],
+ "score": 1.0,
+ "content": "Latplan system learns the binary latent space of an arbitrary raw input (e.g. images) with a Gumbel-",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 105,
+ 225,
+ 506,
+ 238
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 225,
+ 506,
+ 238
+ ],
+ "score": 1.0,
+ "content": "Softmax variational autoencoder, learns a discrete state space from the transition examples, and runs a",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 236,
+ 506,
+ 248
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 236,
+ 331,
+ 248
+ ],
+ "score": 1.0,
+ "content": "symbolic, systematic search algorithm such as Dijkstra or",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 331,
+ 237,
+ 344,
+ 246
+ ],
+ "score": 0.85,
+ "content": "\\mathbf { A } ^ { * }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 345,
+ 236,
+ 506,
+ 248
+ ],
+ "score": 1.0,
+ "content": "search which guarantee the optimality of",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 246,
+ 505,
+ 259
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 246,
+ 505,
+ 259
+ ],
+ "score": 1.0,
+ "content": "the solution. Unlike RL-based planning systems, the search agent does not contain the learning aspects.",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 256,
+ 505,
+ 270
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 256,
+ 505,
+ 270
+ ],
+ "score": 1.0,
+ "content": "The discrete plan in the latent space is mapped back to the raw image visualization of the plan execution,",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 267,
+ 506,
+ 280
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 267,
+ 506,
+ 280
+ ],
+ "score": 1.0,
+ "content": "which requires the reconstruction capability of (V)AE. A similar system replacing Gumbel Softmax VAE",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 278,
+ 356,
+ 290
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 278,
+ 356,
+ 290
+ ],
+ "score": 1.0,
+ "content": "with Causal InfoGAN was later proposed (Kurutach et al., 2018).",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ }
+ ],
+ "index": 14,
+ "bbox_fs": [
+ 105,
+ 215,
+ 506,
+ 290
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 294,
+ 505,
+ 326
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 294,
+ 505,
+ 306
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 294,
+ 505,
+ 306
+ ],
+ "score": 1.0,
+ "content": "We replaced Latplan’s Gumbel-Softmax VAE with our autoencoder used in the 8-Puzzle and the",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 304,
+ 505,
+ 317
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 304,
+ 505,
+ 317
+ ],
+ "score": 1.0,
+ "content": "Blocksworld experiments (Appendix, Sec. 6.1,Sec. 6.2). Our autoencoder also uses Gumbel Softmax in",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 315,
+ 465,
+ 329
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 315,
+ 465,
+ 329
+ ],
+ "score": 1.0,
+ "content": "the latent layer, but it uses (Zaheer et al., 2017) encoder and is trained with Set Cross Entropy.",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ }
+ ],
+ "index": 19,
+ "bbox_fs": [
+ 105,
+ 294,
+ 505,
+ 329
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 331,
+ 505,
+ 405
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 331,
+ 505,
+ 343
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 331,
+ 505,
+ 343
+ ],
+ "score": 1.0,
+ "content": "When the network learned the representation, it guarantees that the planner finds a solution because the",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 342,
+ 505,
+ 354
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 342,
+ 505,
+ 354
+ ],
+ "score": 1.0,
+ "content": "search algorithm being used (e.g. Dijkstra) is a complete, systematic, symbolic search algorithm, which",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 352,
+ 505,
+ 363
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 352,
+ 505,
+ 363
+ ],
+ "score": 1.0,
+ "content": "guarantees to find a solution whenever it is reachable in the state space. If the network cannot learn",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 363,
+ 505,
+ 375
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 363,
+ 505,
+ 375
+ ],
+ "score": 1.0,
+ "content": "the permutation-invariant representation, the system cannot solve the problem and/or return the human-",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 374,
+ 505,
+ 385
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 374,
+ 505,
+ 385
+ ],
+ "score": 1.0,
+ "content": "comprehensive visualization. This makes the specific permutation-invariant representation using (Zaheer",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 104,
+ 383,
+ 506,
+ 397
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 383,
+ 506,
+ 397
+ ],
+ "score": 1.0,
+ "content": "et al., 2017) and the proposed Set Cross Entropy necessary when the input is given as a set of future",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 394,
+ 139,
+ 407
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 394,
+ 139,
+ 407
+ ],
+ "score": 1.0,
+ "content": "vectors.",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ }
+ ],
+ "index": 24,
+ "bbox_fs": [
+ 104,
+ 331,
+ 506,
+ 407
+ ]
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 107,
+ 420,
+ 149,
+ 432
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 420,
+ 151,
+ 433
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 420,
+ 151,
+ 433
+ ],
+ "score": 1.0,
+ "content": "8 PUZZLE",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ }
+ ],
+ "index": 28
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 441,
+ 504,
+ 483
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 441,
+ 506,
+ 454
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 441,
+ 506,
+ 454
+ ],
+ "score": 1.0,
+ "content": "First, the training was performed on a dataset in which the object vector ordering is randomized. The",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 106,
+ 452,
+ 505,
+ 464
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 452,
+ 216,
+ 464
+ ],
+ "score": 1.0,
+ "content": "autoencoder compresses the",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 216,
+ 452,
+ 270,
+ 462
+ ],
+ "score": 0.9,
+ "content": "1 5 \\times 9 = 1 3 5",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 270,
+ 452,
+ 505,
+ 464
+ ],
+ "score": 1.0,
+ "content": "-bit binary representation (object vectors) into a permutation-",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 460,
+ 506,
+ 475
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 460,
+ 506,
+ 475
+ ],
+ "score": 1.0,
+ "content": "invariant 100-bit discrete latent binary representation. We provided 5000 states for training the autoen-",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 472,
+ 433,
+ 484
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 472,
+ 262,
+ 484
+ ],
+ "score": 1.0,
+ "content": "coder, while the search space consists of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 262,
+ 473,
+ 316,
+ 483
+ ],
+ "score": 0.28,
+ "content": "3 6 2 8 8 0 ( = 9 ! )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 317,
+ 472,
+ 433,
+ 484
+ ],
+ "score": 1.0,
+ "content": "states and 967680 transitions.",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ }
+ ],
+ "index": 30.5,
+ "bbox_fs": [
+ 105,
+ 441,
+ 506,
+ 484
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 105,
+ 489,
+ 503,
+ 510
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 487,
+ 505,
+ 501
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 487,
+ 505,
+ 501
+ ],
+ "score": 1.0,
+ "content": "Note that each state have 9! variations due to the permutations in the order the tiles and the locations are",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 498,
+ 392,
+ 511
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 498,
+ 363,
+ 511
+ ],
+ "score": 1.0,
+ "content": "reported. This also increases the number of transition quadratically",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 364,
+ 499,
+ 386,
+ 511
+ ],
+ "score": 0.48,
+ "content": "( ( 9 ! ) ^ { 2 } ,",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 386,
+ 498,
+ 392,
+ 511
+ ],
+ "score": 1.0,
+ "content": ").",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ }
+ ],
+ "index": 33.5,
+ "bbox_fs": [
+ 105,
+ 487,
+ 505,
+ 511
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 516,
+ 505,
+ 558
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 515,
+ 505,
+ 528
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 515,
+ 505,
+ 528
+ ],
+ "score": 1.0,
+ "content": "We generated 40 problem instances of 8-puzzle each generated by a random walk from the goal state. 40",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 525,
+ 505,
+ 540
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 525,
+ 505,
+ 540
+ ],
+ "score": 1.0,
+ "content": "instances consist of 20 instances each generated by a 7-steps random walk and another 20 by 14 steps.",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 106,
+ 536,
+ 505,
+ 549
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 536,
+ 505,
+ 549
+ ],
+ "score": 1.0,
+ "content": "We solved 40 instances using Fast Downward classical planner Helmert (2004) with blind heuristics in",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 106,
+ 548,
+ 258,
+ 559
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 548,
+ 258,
+ 559
+ ],
+ "score": 1.0,
+ "content": "order to remove the effect of heuristics.",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ }
+ ],
+ "index": 36.5,
+ "bbox_fs": [
+ 105,
+ 515,
+ 505,
+ 559
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 563,
+ 505,
+ 626
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 563,
+ 505,
+ 576
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 563,
+ 505,
+ 576
+ ],
+ "score": 1.0,
+ "content": "We compared the number of problems successfully solved by two variations of Latplan where each uses",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 574,
+ 506,
+ 587
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 574,
+ 506,
+ 587
+ ],
+ "score": 1.0,
+ "content": "the autoencoder trained with Set Average and Set Cross Entropy, respectively, for encoding the input",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 585,
+ 505,
+ 597
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 585,
+ 505,
+ 597
+ ],
+ "score": 1.0,
+ "content": "into binary latent space. Both version managed to solve all instances because both Set Average and Set",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 106,
+ 595,
+ 505,
+ 608
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 595,
+ 505,
+ 608
+ ],
+ "score": 1.0,
+ "content": "Cross Entropy managed to train the AE from 5000 examples with a sufficient accuracy. All solutions were",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 605,
+ 505,
+ 618
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 605,
+ 505,
+ 618
+ ],
+ "score": 1.0,
+ "content": "correct (checked manually). Since the search algorithm being used is optimal, the quality of the solution",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 105,
+ 616,
+ 178,
+ 627
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 616,
+ 178,
+ 627
+ ],
+ "score": 1.0,
+ "content": "was also identical.",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ }
+ ],
+ "index": 41.5,
+ "bbox_fs": [
+ 105,
+ 563,
+ 506,
+ 627
+ ]
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 643,
+ 175,
+ 653
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 107,
+ 643,
+ 176,
+ 654
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 643,
+ 176,
+ 654
+ ],
+ "score": 1.0,
+ "content": "BLOCKSWORLD",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ }
+ ],
+ "index": 45
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 663,
+ 504,
+ 704
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 662,
+ 505,
+ 675
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 662,
+ 505,
+ 675
+ ],
+ "score": 1.0,
+ "content": "We solved 30 planning instances in a 4-blocks, 3-stacks environment. The instances are generated by",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 106,
+ 673,
+ 505,
+ 685
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 673,
+ 505,
+ 685
+ ],
+ "score": 1.0,
+ "content": "taking a random initial state and choosing a goal state by the 3, 7, or 14 steps random walks (10 instances",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 105,
+ 683,
+ 505,
+ 696
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 683,
+ 505,
+ 696
+ ],
+ "score": 1.0,
+ "content": "each). The correctness of the plans are again checked manually. The same planner configuration was used",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ },
+ {
+ "bbox": [
+ 106,
+ 693,
+ 171,
+ 706
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 693,
+ 171,
+ 706
+ ],
+ "score": 1.0,
+ "content": "for all instances.",
+ "type": "text"
+ }
+ ],
+ "index": 49
+ }
+ ],
+ "index": 47.5,
+ "bbox_fs": [
+ 105,
+ 662,
+ 505,
+ 706
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 108,
+ 710,
+ 504,
+ 731
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 709,
+ 505,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 709,
+ 505,
+ 722
+ ],
+ "score": 1.0,
+ "content": "The search space consists of 5760 states and 34560 transitions, and each state have 4! variations due to",
+ "type": "text"
+ }
+ ],
+ "index": 50
+ },
+ {
+ "bbox": [
+ 105,
+ 720,
+ 482,
+ 733
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 720,
+ 482,
+ 733
+ ],
+ "score": 1.0,
+ "content": "permutations of 4 blocks. We provided 1000 randomly selected states for training the autoencoder.",
+ "type": "text"
+ }
+ ],
+ "index": 51
+ }
+ ],
+ "index": 50.5,
+ "bbox_fs": [
+ 105,
+ 709,
+ 505,
+ 733
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "image",
+ "bbox": [
+ 309,
+ 105,
+ 495,
+ 167
+ ],
+ "blocks": [
+ {
+ "type": "image_body",
+ "bbox": [
+ 309,
+ 105,
+ 495,
+ 167
+ ],
+ "group_id": 1,
+ "lines": [
+ {
+ "bbox": [
+ 309,
+ 105,
+ 495,
+ 167
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 309,
+ 105,
+ 495,
+ 167
+ ],
+ "score": 0.269,
+ "type": "image",
+ "image_path": "621af72adc23d14c4b28f2afa847ccd90aaba22caeaa51c7890c8dc90150fe21.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 2.5,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 309,
+ 105,
+ 495,
+ 120.5
+ ],
+ "spans": [],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 309,
+ 120.5,
+ 495,
+ 136.0
+ ],
+ "spans": [],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 309,
+ 136.0,
+ 495,
+ 151.5
+ ],
+ "spans": [],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 309,
+ 151.5,
+ 495,
+ 167.0
+ ],
+ "spans": [],
+ "index": 4
+ }
+ ]
+ }
+ ],
+ "index": 2.5
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 197,
+ 79,
+ 221,
+ 190
+ ],
+ "blocks": [
+ {
+ "type": "image_body",
+ "bbox": [
+ 197,
+ 79,
+ 221,
+ 190
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 197,
+ 79,
+ 221,
+ 190
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 197,
+ 79,
+ 221,
+ 190
+ ],
+ "score": 0.701,
+ "type": "image",
+ "image_path": "75a2ab5601ad767c6e9f8540ba5250aa4daa56431c7aa98b701962e33e106c96.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 0,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 197,
+ 79,
+ 221,
+ 190
+ ],
+ "spans": [],
+ "index": 0
+ }
+ ]
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 106,
+ 198,
+ 505,
+ 243
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 198,
+ 505,
+ 212
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 198,
+ 505,
+ 212
+ ],
+ "score": 1.0,
+ "content": "Figure 6: (Left) An example plan in a set-of-object-vector form, decoded from its binary latent rep-",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 210,
+ 505,
+ 222
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 210,
+ 505,
+ 222
+ ],
+ "score": 1.0,
+ "content": "resentation using the permutation-invariant autoencoder (the plan is executed from top to bottom).",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 106,
+ 221,
+ 505,
+ 233
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 221,
+ 505,
+ 233
+ ],
+ "score": 1.0,
+ "content": "(Right) Its visualization using the tile images (taken from MNIST) pasted onto a black canvas (The",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 106,
+ 232,
+ 306,
+ 244
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 232,
+ 306,
+ 244
+ ],
+ "score": 1.0,
+ "content": "plan is executed from left to right, top to bottom).",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ }
+ ],
+ "index": 6.5
+ }
+ ],
+ "index": 3.25
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 263,
+ 505,
+ 317
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 264,
+ 505,
+ 276
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 264,
+ 505,
+ 276
+ ],
+ "score": 1.0,
+ "content": "We compared the number of problems successfully solved by Latplan between two variations of Latplan",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 274,
+ 506,
+ 287
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 274,
+ 506,
+ 287
+ ],
+ "score": 1.0,
+ "content": "using the autoencoder trained with Set Average and Set Cross Entropy, respectively. For the total of",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 105,
+ 284,
+ 505,
+ 298
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 284,
+ 209,
+ 298
+ ],
+ "score": 1.0,
+ "content": "30 instances, both Latplan",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 210,
+ 285,
+ 229,
+ 295
+ ],
+ "score": 0.36,
+ "content": "\\mathbf { \\Gamma } _ { \\mathrm { + } \\mathrm { S e t } }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 229,
+ 284,
+ 296,
+ 298
+ ],
+ "score": 1.0,
+ "content": "Avg and Latplan",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 296,
+ 285,
+ 320,
+ 295
+ ],
+ "score": 0.49,
+ "content": "\\mathrm { \\mathbf { \\Omega } _ { 1 + } S C E }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 321,
+ 284,
+ 505,
+ 298
+ ],
+ "score": 1.0,
+ "content": "returned plans, however the plans returned by",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 105,
+ 295,
+ 505,
+ 307
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 295,
+ 136,
+ 307
+ ],
+ "score": 1.0,
+ "content": "Latplan",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 136,
+ 296,
+ 154,
+ 305
+ ],
+ "score": 0.3,
+ "content": "+ \\mathrm { S e t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 155,
+ 295,
+ 336,
+ 307
+ ],
+ "score": 1.0,
+ "content": "Avg were correct in 11 instnaces, while Latplan",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 336,
+ 295,
+ 360,
+ 306
+ ],
+ "score": 0.61,
+ "content": "+ \\mathrm { S C E }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 361,
+ 295,
+ 505,
+ 307
+ ],
+ "score": 1.0,
+ "content": "returned 14 correct instances (Details",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 306,
+ 152,
+ 317
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 306,
+ 152,
+ 317
+ ],
+ "score": 1.0,
+ "content": "in Table 7).",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ }
+ ],
+ "index": 11
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 322,
+ 505,
+ 365
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 321,
+ 505,
+ 335
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 321,
+ 505,
+ 335
+ ],
+ "score": 1.0,
+ "content": "As the autoencoder trained by Set Average had larger reconstruction error, it sometimes fails to capture",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 332,
+ 505,
+ 345
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 332,
+ 505,
+ 345
+ ],
+ "score": 1.0,
+ "content": "the essential feature of the input, causing the system to return an invalid plan. The common error was",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 342,
+ 505,
+ 357
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 342,
+ 505,
+ 357
+ ],
+ "score": 1.0,
+ "content": "changing the surface of the blocks or swapping the blocks without a proper action needed, e.g., moving",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 353,
+ 438,
+ 366
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 353,
+ 438,
+ 366
+ ],
+ "score": 1.0,
+ "content": "more than two blocks, move a block and polish another block in a single time step, etc.",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ }
+ ],
+ "index": 15.5
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 165,
+ 374,
+ 446,
+ 443
+ ],
+ "blocks": [
+ {
+ "type": "table_body",
+ "bbox": [
+ 165,
+ 374,
+ 446,
+ 443
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 165,
+ 374,
+ 446,
+ 443
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 165,
+ 374,
+ 446,
+ 443
+ ],
+ "score": 0.976,
+ "html": " | The rate of correct answering on the test set,10 runs |
| n = 2, neighbor2(a,b,c):-neighborOf(a,b), neighborOf(b,c) Dataset: 2858 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Target ordering | Fixed | Random |
| Best 0.32 | Worst 0.23 | Median 0.29 | Mean 0.28 | Best 0.36 | Worst 0.25 | Median 0.31 | Mean 0.31 |
| H SH | 0.96 | 0.90 | 0.91 | 0.92 | 0.94 | 0.88 | 0.91 | 0.91 |
| A1H | 0.91 | 0.79 | 0.86 | 0.86 | 0.94 | 0.72 | 0.88 | 0.87 |
| H1H | 0.87 | 0.66 | 0.82 | 0.80 | 0.85 | 0.66 | 0.83 | 0.81 |
| n = 3, neighbor3(a,b,c,d):-.. |
| Target ordering | Dataset: 11000 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst 0.06 | Median | Mean |
| H | 0.10 | 0.04 | 0.06 | 0.06 | 0.10 | 0.07 | 0.07 |
| SH | 0.72 | 0.55 | 0.61 | 0.62 | 0.70 | 0.53 | 0.66 | 0.64 |
| A1H | 0.61 0.55 | 0.52 0.31 | 0.55 | 0.56 | 0.60 | 0.53 | 0.57 | 0.57 |
| H1H | | | 0.44 | 0.44 | 0.57 | 0.37 | 0.43 | 0.45 |
| Target ordering | n =4,neighbor4(a,b,c,d,e):-.. |
| Dataset: 39878 ground clauses; Training: 2250 clauses; Test: 250 clauses. |
| Best | Worst | Fixed Median | Mean | Best | Random Worst | Median | Mean |
| H | 0.02 | 0.00 | 0.01 | 0.01 | 0.03 0.00 | 0.02 | 0.02 |
| SH | 0.38 | 0.24 | 0.33 | 0.32 | 0.36 | 0.28 0.32 | 0.32 |
| A1H | 0.33 | 0.22 | 0.27 | 0.26 | 0.34 | 0.22 0.26 | 0.26 |
| H1H | 0.22 | 0.12 | 0.18 | 0.18 | 0.24 | 0.13 0.18 | 0.18 |
| n = 4, neighbor4(a,b,c,d,e):-... Dataset: 39878 ground clauses; Training: 90o0 clauses; Test: 1000 clauses. |
| Target ordering H | | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst Median | Mean |
| 0.04 | 0.03 | 0.04 | 0.03 | 0.04 | 0.02 0.03 | 0.03 |
| 0.87 | 0.81 | 0.82 | 0.83 | 0.86 | 0.77 0.82 | 0.82 |
| SH | | 0.77 | 0.76 | 0.79 | 0.59 | 0.73 | 0.72 |
| A1H | 0.81 0.50 | 0.71 | | | | 0.42 | 0.41 |
| H1H | 0.12 | 0.40 | 0.37 n = 5, neighbor5(a,b,c,d,e,f):-... | 0.53 | 0.24 | | |
|
| Target ordering H | Dataset: 137738 ground clauses; Training: 2250 clauses; Test: 250 clauses. | Fixed | | | | Random | |
| Best | Worst | Median | Mean | Best | Worst | Median Mean |
| 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 0.00 | 0.00 |
| SH | 0.17 | 0.10 0.11 | 0.12 | 0.15 | 0.06 | 0.11 | 0.11 |
| A1H | 0.13 | 0.06 0.10 | 0.10 | 0.13 | 0.06 | 0.11 | 0.10 |
| H1H | 0.06 | 0.01 0.04 | 0.04 | 0.06 | 0.04 | 0.05 | 0.05 |
| | | n = 5, neighbor5(a,b,c,d,e,f):-... | | | | |
| Target ordering | Dataset: 137738 ground clauses; Training: 9000 clauses; Test: 1000 clauses. | |
| Fixed | | | | Random | |
| H | Best Worst | Median 0.00 | Mean 0.00 | Best 0.01 | Worst | Median 0.01 | Mean 0.01 |
| SH | 0.01 | 0.00 | | | 0.00 0.50 | | 0.55 |
| A1H | 0.65 0.53 | 0.52 0.46 | 0.55 0.48 | 0.56 0.48 | 0.60 | 0.56 0.50 | 0.50 |
| | | | 0.56 | 0.46 | | |
| H1H | 0.20 | 0.04 | 0.11 | 0.11 | 0.18 0.07 | 0.13 | 0.13 |
| | | | | | | |
"
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 297,
+ 75,
+ 858,
+ 75,
+ 858,
+ 105,
+ 297,
+ 105
+ ],
+ "score": 0.912
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 836,
+ 2088,
+ 863,
+ 2088,
+ 863,
+ 2113,
+ 836,
+ 2113
+ ],
+ "score": 0.854
+ },
+ {
+ "category_id": 7,
+ "poly": [
+ 535,
+ 1874,
+ 1162,
+ 1874,
+ 1162,
+ 1907,
+ 535,
+ 1907
+ ],
+ "score": 0.801
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 745,
+ 1605,
+ 815,
+ 1605,
+ 815,
+ 1632,
+ 745,
+ 1632
+ ],
+ "score": 0.86,
+ "latex": "\\overline { { n = 5 } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 810,
+ 377,
+ 894,
+ 377,
+ 894,
+ 411,
+ 810,
+ 411
+ ],
+ "score": 0.85,
+ "latex": "\\textstyle { \\overline { { ( a , b , c ) } } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 758,
+ 1115,
+ 830,
+ 1115,
+ 830,
+ 1142,
+ 758,
+ 1142
+ ],
+ "score": 0.85,
+ "latex": "\\overline { { n = 4 } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 745,
+ 1360,
+ 815,
+ 1360,
+ 815,
+ 1387,
+ 745,
+ 1387
+ ],
+ "score": 0.84,
+ "latex": "\\overline { { n = 5 } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 771,
+ 626,
+ 842,
+ 626,
+ 842,
+ 653,
+ 771,
+ 653
+ ],
+ "score": 0.83,
+ "latex": "\\overline { { n = 3 } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 759,
+ 871,
+ 830,
+ 871,
+ 830,
+ 898,
+ 759,
+ 898
+ ],
+ "score": 0.83,
+ "latex": "\\overline { { n = 4 } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1033,
+ 377,
+ 1093,
+ 377,
+ 1093,
+ 411,
+ 1033,
+ 411
+ ],
+ "score": 0.82,
+ "latex": "\\textstyle { \\overline { { ( a , b ) } } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1229,
+ 378,
+ 1287,
+ 378,
+ 1287,
+ 411,
+ 1229,
+ 411
+ ],
+ "score": 0.75,
+ "latex": "\\overline { { ( b , c ) } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 615,
+ 380,
+ 686,
+ 380,
+ 686,
+ 408,
+ 615,
+ 408
+ ],
+ "score": 0.7,
+ "latex": "\\overline { { n = 2 } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 375,
+ 1051,
+ 429,
+ 1051,
+ 429,
+ 1082,
+ 375,
+ 1082
+ ],
+ "score": 0.66,
+ "latex": "A _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 373,
+ 1327,
+ 430,
+ 1327,
+ 430,
+ 1358,
+ 373,
+ 1358
+ ],
+ "score": 0.6,
+ "latex": "\\mathcal { H } _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 375,
+ 1541,
+ 429,
+ 1541,
+ 429,
+ 1571,
+ 375,
+ 1571
+ ],
+ "score": 0.56,
+ "latex": "A _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 373,
+ 1083,
+ 430,
+ 1083,
+ 430,
+ 1114,
+ 373,
+ 1114
+ ],
+ "score": 0.55,
+ "latex": "\\mathcal { H } _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 375,
+ 562,
+ 429,
+ 562,
+ 429,
+ 592,
+ 375,
+ 592
+ ],
+ "score": 0.53,
+ "latex": "A _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 373,
+ 594,
+ 430,
+ 594,
+ 430,
+ 625,
+ 373,
+ 625
+ ],
+ "score": 0.53,
+ "latex": "\\mathcal { H } _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 373,
+ 1572,
+ 430,
+ 1572,
+ 430,
+ 1603,
+ 373,
+ 1603
+ ],
+ "score": 0.48,
+ "latex": "\\mathcal { H } _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 375,
+ 1296,
+ 428,
+ 1296,
+ 428,
+ 1326,
+ 375,
+ 1326
+ ],
+ "score": 0.48,
+ "latex": "A _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 375,
+ 1785,
+ 429,
+ 1785,
+ 429,
+ 1815,
+ 375,
+ 1815
+ ],
+ "score": 0.47,
+ "latex": "A _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 375,
+ 807,
+ 429,
+ 807,
+ 429,
+ 837,
+ 375,
+ 837
+ ],
+ "score": 0.46,
+ "latex": "A _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 967,
+ 624,
+ 1126,
+ 624,
+ 1126,
+ 656,
+ 967,
+ 656
+ ],
+ "score": 0.4,
+ "latex": "( a , b , c , d ) \\div \\ldots"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 941,
+ 1357,
+ 1137,
+ 1357,
+ 1137,
+ 1390,
+ 941,
+ 1390
+ ],
+ "score": 0.35,
+ "latex": "( a , b , c , d , e , f ) \\colon ."
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 955,
+ 1113,
+ 1093,
+ 1113,
+ 1093,
+ 1145,
+ 955,
+ 1145
+ ],
+ "score": 0.31,
+ "latex": "( a , b , c , d , e )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 955,
+ 868,
+ 1140,
+ 868,
+ 1140,
+ 901,
+ 955,
+ 901
+ ],
+ "score": 0.31,
+ "latex": "( a , b , c , d , e ) \\colon - \\ldots ."
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 373,
+ 838,
+ 430,
+ 838,
+ 430,
+ 868,
+ 373,
+ 868
+ ],
+ "score": 0.29,
+ "latex": "\\mathcal { H } _ { \\mathrm { 1 H } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 941,
+ 1603,
+ 1155,
+ 1603,
+ 1155,
+ 1635,
+ 941,
+ 1635
+ ],
+ "score": 0.27,
+ "latex": "( a , b , c , d , e , f ) \\mathrel { \\mathop : } - \\mathrel { \\mathop . } + \\mathrel { \\mathop . }"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 73.0,
+ 858.0,
+ 73.0,
+ 858.0,
+ 108.0,
+ 297.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 832.0,
+ 2085.0,
+ 868.0,
+ 2085.0,
+ 868.0,
+ 2125.0,
+ 832.0,
+ 2125.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 533.0,
+ 1871.0,
+ 1166.0,
+ 1871.0,
+ 1166.0,
+ 1911.0,
+ 533.0,
+ 1911.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 10,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 231,
+ 1404,
+ 231,
+ 1404,
+ 536,
+ 298,
+ 536
+ ],
+ "score": 0.976
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 299,
+ 581,
+ 488,
+ 581,
+ 488,
+ 614,
+ 299,
+ 614
+ ],
+ "score": 0.879
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 298,
+ 76,
+ 857,
+ 76,
+ 857,
+ 104,
+ 298,
+ 104
+ ],
+ "score": 0.878
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 836,
+ 2088,
+ 865,
+ 2088,
+ 865,
+ 2112,
+ 836,
+ 2112
+ ],
+ "score": 0.834
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 291,
+ 607,
+ 1407,
+ 607,
+ 1407,
+ 2039,
+ 291,
+ 2039
+ ],
+ "score": 0.554
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 581.0,
+ 490.0,
+ 581.0,
+ 490.0,
+ 618.0,
+ 297.0,
+ 618.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 298.0,
+ 73.0,
+ 858.0,
+ 73.0,
+ 858.0,
+ 108.0,
+ 298.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 832.0,
+ 2085.0,
+ 870.0,
+ 2085.0,
+ 870.0,
+ 2124.0,
+ 832.0,
+ 2124.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 232.0,
+ 1404.0,
+ 232.0,
+ 1404.0,
+ 263.0,
+ 296.0,
+ 263.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 262.0,
+ 1405.0,
+ 262.0,
+ 1405.0,
+ 294.0,
+ 294.0,
+ 294.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 291.0,
+ 1404.0,
+ 291.0,
+ 1404.0,
+ 327.0,
+ 294.0,
+ 327.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 323.0,
+ 1405.0,
+ 323.0,
+ 1405.0,
+ 356.0,
+ 293.0,
+ 356.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 354.0,
+ 1404.0,
+ 354.0,
+ 1404.0,
+ 386.0,
+ 296.0,
+ 386.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 385.0,
+ 1404.0,
+ 385.0,
+ 1404.0,
+ 416.0,
+ 296.0,
+ 416.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 409.0,
+ 1406.0,
+ 409.0,
+ 1406.0,
+ 452.0,
+ 291.0,
+ 452.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 442.0,
+ 1404.0,
+ 442.0,
+ 1404.0,
+ 480.0,
+ 291.0,
+ 480.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 475.0,
+ 1406.0,
+ 475.0,
+ 1406.0,
+ 509.0,
+ 292.0,
+ 509.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 502.0,
+ 447.0,
+ 502.0,
+ 447.0,
+ 542.0,
+ 292.0,
+ 542.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 629.0,
+ 1406.0,
+ 629.0,
+ 1406.0,
+ 667.0,
+ 293.0,
+ 667.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 661.0,
+ 586.0,
+ 661.0,
+ 586.0,
+ 696.0,
+ 320.0,
+ 696.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 709.0,
+ 1402.0,
+ 709.0,
+ 1402.0,
+ 750.0,
+ 293.0,
+ 750.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 739.0,
+ 1403.0,
+ 739.0,
+ 1403.0,
+ 780.0,
+ 319.0,
+ 780.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 772.0,
+ 1238.0,
+ 772.0,
+ 1238.0,
+ 808.0,
+ 323.0,
+ 808.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 820.0,
+ 1406.0,
+ 820.0,
+ 1406.0,
+ 859.0,
+ 293.0,
+ 859.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 317.0,
+ 846.0,
+ 1406.0,
+ 846.0,
+ 1406.0,
+ 894.0,
+ 317.0,
+ 894.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 883.0,
+ 963.0,
+ 883.0,
+ 963.0,
+ 918.0,
+ 323.0,
+ 918.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 290.0,
+ 930.0,
+ 1408.0,
+ 930.0,
+ 1408.0,
+ 969.0,
+ 290.0,
+ 969.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 962.0,
+ 1406.0,
+ 962.0,
+ 1406.0,
+ 997.0,
+ 322.0,
+ 997.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 989.0,
+ 1405.0,
+ 989.0,
+ 1405.0,
+ 1025.0,
+ 322.0,
+ 1025.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 1021.0,
+ 1250.0,
+ 1021.0,
+ 1250.0,
+ 1056.0,
+ 322.0,
+ 1056.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 290.0,
+ 1066.0,
+ 1406.0,
+ 1066.0,
+ 1406.0,
+ 1111.0,
+ 290.0,
+ 1111.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 1100.0,
+ 1216.0,
+ 1100.0,
+ 1216.0,
+ 1138.0,
+ 319.0,
+ 1138.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1152.0,
+ 1405.0,
+ 1152.0,
+ 1405.0,
+ 1187.0,
+ 293.0,
+ 1187.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 325.0,
+ 1184.0,
+ 778.0,
+ 1184.0,
+ 778.0,
+ 1214.0,
+ 325.0,
+ 1214.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1234.0,
+ 1403.0,
+ 1234.0,
+ 1403.0,
+ 1269.0,
+ 293.0,
+ 1269.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 1264.0,
+ 1405.0,
+ 1264.0,
+ 1405.0,
+ 1299.0,
+ 322.0,
+ 1299.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 1291.0,
+ 391.0,
+ 1291.0,
+ 391.0,
+ 1325.0,
+ 322.0,
+ 1325.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1344.0,
+ 1406.0,
+ 1344.0,
+ 1406.0,
+ 1379.0,
+ 293.0,
+ 1379.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 1372.0,
+ 1403.0,
+ 1372.0,
+ 1403.0,
+ 1408.0,
+ 323.0,
+ 1408.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 1401.0,
+ 1083.0,
+ 1401.0,
+ 1083.0,
+ 1438.0,
+ 320.0,
+ 1438.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1454.0,
+ 1402.0,
+ 1454.0,
+ 1402.0,
+ 1489.0,
+ 295.0,
+ 1489.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 1481.0,
+ 459.0,
+ 1481.0,
+ 459.0,
+ 1514.0,
+ 321.0,
+ 1514.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1534.0,
+ 1406.0,
+ 1534.0,
+ 1406.0,
+ 1570.0,
+ 292.0,
+ 1570.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 1562.0,
+ 1405.0,
+ 1562.0,
+ 1405.0,
+ 1599.0,
+ 320.0,
+ 1599.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 325.0,
+ 1593.0,
+ 391.0,
+ 1593.0,
+ 391.0,
+ 1626.0,
+ 325.0,
+ 1626.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1641.0,
+ 1408.0,
+ 1641.0,
+ 1408.0,
+ 1682.0,
+ 292.0,
+ 1682.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 1669.0,
+ 1405.0,
+ 1669.0,
+ 1405.0,
+ 1716.0,
+ 319.0,
+ 1716.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 1701.0,
+ 569.0,
+ 1701.0,
+ 569.0,
+ 1736.0,
+ 323.0,
+ 1736.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1752.0,
+ 1403.0,
+ 1752.0,
+ 1403.0,
+ 1789.0,
+ 293.0,
+ 1789.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 1783.0,
+ 1050.0,
+ 1783.0,
+ 1050.0,
+ 1819.0,
+ 320.0,
+ 1819.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1830.0,
+ 1403.0,
+ 1830.0,
+ 1403.0,
+ 1874.0,
+ 292.0,
+ 1874.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 1866.0,
+ 1405.0,
+ 1866.0,
+ 1405.0,
+ 1901.0,
+ 320.0,
+ 1901.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 1894.0,
+ 752.0,
+ 1894.0,
+ 752.0,
+ 1929.0,
+ 323.0,
+ 1929.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1945.0,
+ 1403.0,
+ 1945.0,
+ 1403.0,
+ 1980.0,
+ 295.0,
+ 1980.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 1976.0,
+ 1402.0,
+ 1976.0,
+ 1402.0,
+ 2011.0,
+ 322.0,
+ 2011.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 321.0,
+ 2006.0,
+ 475.0,
+ 2006.0,
+ 475.0,
+ 2035.0,
+ 321.0,
+ 2035.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 11,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 299,
+ 1754,
+ 1403,
+ 1754,
+ 1403,
+ 1960,
+ 299,
+ 1960
+ ],
+ "score": 0.974
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 300,
+ 1680,
+ 1400,
+ 1680,
+ 1400,
+ 1739,
+ 300,
+ 1739
+ ],
+ "score": 0.936
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 300,
+ 1974,
+ 1401,
+ 1974,
+ 1401,
+ 2033,
+ 300,
+ 2033
+ ],
+ "score": 0.926
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 298,
+ 75,
+ 857,
+ 75,
+ 857,
+ 105,
+ 298,
+ 105
+ ],
+ "score": 0.897
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 302,
+ 1622,
+ 764,
+ 1622,
+ 764,
+ 1654,
+ 302,
+ 1654
+ ],
+ "score": 0.891
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 300,
+ 1557,
+ 449,
+ 1557,
+ 449,
+ 1590,
+ 300,
+ 1590
+ ],
+ "score": 0.839
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 837,
+ 2088,
+ 864,
+ 2088,
+ 864,
+ 2112,
+ 837,
+ 2112
+ ],
+ "score": 0.828
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 293,
+ 218,
+ 1406,
+ 218,
+ 1406,
+ 1515,
+ 293,
+ 1515
+ ],
+ "score": 0.665
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 625,
+ 1756,
+ 703,
+ 1756,
+ 703,
+ 1783,
+ 625,
+ 1783
+ ],
+ "score": 0.87,
+ "latex": "9 \\times 1 5"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1018,
+ 1817,
+ 1035,
+ 1817,
+ 1035,
+ 1843,
+ 1018,
+ 1843
+ ],
+ "score": 0.8,
+ "latex": "\\rho"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 943,
+ 452,
+ 960,
+ 452,
+ 960,
+ 474,
+ 943,
+ 474
+ ],
+ "score": 0.6,
+ "latex": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } } ="
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 298.0,
+ 73.0,
+ 858.0,
+ 73.0,
+ 858.0,
+ 108.0,
+ 298.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1622.0,
+ 769.0,
+ 1622.0,
+ 769.0,
+ 1658.0,
+ 296.0,
+ 1658.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1554.0,
+ 453.0,
+ 1554.0,
+ 453.0,
+ 1597.0,
+ 296.0,
+ 1597.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 830.0,
+ 2086.0,
+ 868.0,
+ 2086.0,
+ 868.0,
+ 2121.0,
+ 830.0,
+ 2121.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 1755.0,
+ 624.0,
+ 1755.0,
+ 624.0,
+ 1785.0,
+ 297.0,
+ 1785.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 704.0,
+ 1755.0,
+ 1404.0,
+ 1755.0,
+ 1404.0,
+ 1785.0,
+ 704.0,
+ 1785.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1784.0,
+ 1405.0,
+ 1784.0,
+ 1405.0,
+ 1814.0,
+ 295.0,
+ 1814.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1810.0,
+ 1017.0,
+ 1810.0,
+ 1017.0,
+ 1845.0,
+ 294.0,
+ 1845.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1036.0,
+ 1810.0,
+ 1405.0,
+ 1810.0,
+ 1405.0,
+ 1845.0,
+ 1036.0,
+ 1845.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1841.0,
+ 1408.0,
+ 1841.0,
+ 1408.0,
+ 1876.0,
+ 292.0,
+ 1876.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1869.0,
+ 1405.0,
+ 1869.0,
+ 1405.0,
+ 1907.0,
+ 292.0,
+ 1907.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1899.0,
+ 1405.0,
+ 1899.0,
+ 1405.0,
+ 1934.0,
+ 293.0,
+ 1934.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1930.0,
+ 856.0,
+ 1930.0,
+ 856.0,
+ 1963.0,
+ 295.0,
+ 1963.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1676.0,
+ 1403.0,
+ 1676.0,
+ 1403.0,
+ 1714.0,
+ 295.0,
+ 1714.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1707.0,
+ 506.0,
+ 1707.0,
+ 506.0,
+ 1740.0,
+ 292.0,
+ 1740.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1969.0,
+ 1406.0,
+ 1969.0,
+ 1406.0,
+ 2010.0,
+ 293.0,
+ 2010.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1998.0,
+ 378.0,
+ 1998.0,
+ 378.0,
+ 2039.0,
+ 292.0,
+ 2039.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 232.0,
+ 1406.0,
+ 232.0,
+ 1406.0,
+ 268.0,
+ 294.0,
+ 268.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 261.0,
+ 1355.0,
+ 261.0,
+ 1355.0,
+ 298.0,
+ 320.0,
+ 298.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 312.0,
+ 1404.0,
+ 312.0,
+ 1404.0,
+ 348.0,
+ 294.0,
+ 348.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 341.0,
+ 1377.0,
+ 341.0,
+ 1377.0,
+ 378.0,
+ 323.0,
+ 378.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 391.0,
+ 1405.0,
+ 391.0,
+ 1405.0,
+ 427.0,
+ 295.0,
+ 427.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 418.0,
+ 1406.0,
+ 418.0,
+ 1406.0,
+ 458.0,
+ 322.0,
+ 458.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 446.0,
+ 942.0,
+ 446.0,
+ 942.0,
+ 488.0,
+ 320.0,
+ 488.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 961.0,
+ 446.0,
+ 1116.0,
+ 446.0,
+ 1116.0,
+ 488.0,
+ 961.0,
+ 488.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 498.0,
+ 1405.0,
+ 498.0,
+ 1405.0,
+ 536.0,
+ 293.0,
+ 536.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 526.0,
+ 1406.0,
+ 526.0,
+ 1406.0,
+ 568.0,
+ 319.0,
+ 568.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 558.0,
+ 606.0,
+ 558.0,
+ 606.0,
+ 594.0,
+ 322.0,
+ 594.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 290.0,
+ 603.0,
+ 1406.0,
+ 603.0,
+ 1406.0,
+ 647.0,
+ 290.0,
+ 647.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 638.0,
+ 603.0,
+ 638.0,
+ 603.0,
+ 670.0,
+ 320.0,
+ 670.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 686.0,
+ 1405.0,
+ 686.0,
+ 1405.0,
+ 727.0,
+ 293.0,
+ 727.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 717.0,
+ 753.0,
+ 717.0,
+ 753.0,
+ 753.0,
+ 322.0,
+ 753.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 766.0,
+ 1405.0,
+ 766.0,
+ 1405.0,
+ 802.0,
+ 293.0,
+ 802.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 792.0,
+ 1406.0,
+ 792.0,
+ 1406.0,
+ 837.0,
+ 320.0,
+ 837.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 324.0,
+ 823.0,
+ 495.0,
+ 823.0,
+ 495.0,
+ 859.0,
+ 324.0,
+ 859.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 872.0,
+ 1404.0,
+ 872.0,
+ 1404.0,
+ 915.0,
+ 291.0,
+ 915.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 904.0,
+ 861.0,
+ 904.0,
+ 861.0,
+ 941.0,
+ 322.0,
+ 941.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 957.0,
+ 1402.0,
+ 957.0,
+ 1402.0,
+ 989.0,
+ 295.0,
+ 989.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 981.0,
+ 1406.0,
+ 981.0,
+ 1406.0,
+ 1025.0,
+ 319.0,
+ 1025.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 1013.0,
+ 594.0,
+ 1013.0,
+ 594.0,
+ 1050.0,
+ 323.0,
+ 1050.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1061.0,
+ 1404.0,
+ 1061.0,
+ 1404.0,
+ 1101.0,
+ 293.0,
+ 1101.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 1091.0,
+ 1405.0,
+ 1091.0,
+ 1405.0,
+ 1130.0,
+ 319.0,
+ 1130.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 1121.0,
+ 676.0,
+ 1121.0,
+ 676.0,
+ 1159.0,
+ 322.0,
+ 1159.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1174.0,
+ 1401.0,
+ 1174.0,
+ 1401.0,
+ 1206.0,
+ 295.0,
+ 1206.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 1203.0,
+ 1110.0,
+ 1203.0,
+ 1110.0,
+ 1239.0,
+ 322.0,
+ 1239.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 290.0,
+ 1248.0,
+ 1406.0,
+ 1248.0,
+ 1406.0,
+ 1291.0,
+ 290.0,
+ 1291.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 325.0,
+ 1283.0,
+ 819.0,
+ 1283.0,
+ 819.0,
+ 1315.0,
+ 325.0,
+ 1315.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1334.0,
+ 1402.0,
+ 1334.0,
+ 1402.0,
+ 1366.0,
+ 294.0,
+ 1366.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 322.0,
+ 1361.0,
+ 1405.0,
+ 1361.0,
+ 1405.0,
+ 1398.0,
+ 322.0,
+ 1398.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 323.0,
+ 1390.0,
+ 457.0,
+ 1390.0,
+ 457.0,
+ 1424.0,
+ 323.0,
+ 1424.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 1435.0,
+ 1406.0,
+ 1435.0,
+ 1406.0,
+ 1481.0,
+ 291.0,
+ 1481.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 319.0,
+ 1468.0,
+ 1107.0,
+ 1468.0,
+ 1107.0,
+ 1505.0,
+ 319.0,
+ 1505.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 12,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 1857,
+ 1405,
+ 1857,
+ 1405,
+ 2034,
+ 297,
+ 2034
+ ],
+ "score": 0.978
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 511,
+ 1405,
+ 511,
+ 1405,
+ 631,
+ 298,
+ 631
+ ],
+ "score": 0.977
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 738,
+ 1405,
+ 738,
+ 1405,
+ 828,
+ 298,
+ 828
+ ],
+ "score": 0.97
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 295,
+ 344,
+ 1402,
+ 344,
+ 1402,
+ 405,
+ 295,
+ 405
+ ],
+ "score": 0.945
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 619,
+ 223,
+ 1082,
+ 223,
+ 1082,
+ 315,
+ 619,
+ 315
+ ],
+ "score": 0.937
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 298,
+ 678,
+ 891,
+ 678,
+ 891,
+ 709,
+ 298,
+ 709
+ ],
+ "score": 0.919
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 294,
+ 1199,
+ 1400,
+ 1199,
+ 1400,
+ 1232,
+ 294,
+ 1232
+ ],
+ "score": 0.919
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 297,
+ 75,
+ 858,
+ 75,
+ 858,
+ 105,
+ 297,
+ 105
+ ],
+ "score": 0.909
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 300,
+ 451,
+ 837,
+ 451,
+ 837,
+ 484,
+ 300,
+ 484
+ ],
+ "score": 0.908
+ },
+ {
+ "category_id": 4,
+ "poly": [
+ 478,
+ 1691,
+ 1216,
+ 1691,
+ 1216,
+ 1724,
+ 478,
+ 1724
+ ],
+ "score": 0.898
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 300,
+ 1796,
+ 849,
+ 1796,
+ 849,
+ 1828,
+ 300,
+ 1828
+ ],
+ "score": 0.892
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 658,
+ 866,
+ 1048,
+ 866,
+ 1048,
+ 1174,
+ 658,
+ 1174
+ ],
+ "score": 0.865
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 836,
+ 2088,
+ 864,
+ 2088,
+ 864,
+ 2112,
+ 836,
+ 2112
+ ],
+ "score": 0.86
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 651,
+ 1296,
+ 1052,
+ 1296,
+ 1052,
+ 1667,
+ 651,
+ 1667
+ ],
+ "score": 0.653
+ },
+ {
+ "category_id": 3,
+ "poly": [
+ 651,
+ 1296,
+ 1052,
+ 1296,
+ 1052,
+ 1667,
+ 651,
+ 1667
+ ],
+ "score": 0.332
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 643,
+ 1917,
+ 806,
+ 1917,
+ 806,
+ 1948,
+ 643,
+ 1948
+ ],
+ "score": 0.92,
+ "latex": "2 + 1 6 3 ( n + 1 )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1207,
+ 1200,
+ 1322,
+ 1200,
+ 1322,
+ 1229,
+ 1207,
+ 1229
+ ],
+ "score": 0.9,
+ "latex": "8 \\times 8 \\times 1 6"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1179,
+ 514,
+ 1273,
+ 514,
+ 1273,
+ 541,
+ 1179,
+ 541
+ ],
+ "score": 0.88,
+ "latex": "5 \\times 1 2 2 4"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1118,
+ 2004,
+ 1311,
+ 2004,
+ 1311,
+ 2033,
+ 1118,
+ 2033
+ ],
+ "score": 0.87,
+ "latex": "3 2 8 = 2 + 2 \\cdot 1 6 3"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 659,
+ 1949,
+ 724,
+ 1949,
+ 724,
+ 1974,
+ 659,
+ 1974
+ ],
+ "score": 0.87,
+ "latex": "n + 1"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 851,
+ 284,
+ 934,
+ 284,
+ 934,
+ 312,
+ 851,
+ 312
+ ],
+ "score": 0.83,
+ "latex": "( 9 \\times 1 5 )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 620,
+ 346,
+ 678,
+ 346,
+ 678,
+ 373,
+ 620,
+ 373
+ ],
+ "score": 0.7,
+ "latex": "9 \\times 9"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 755,
+ 346,
+ 814,
+ 346,
+ 814,
+ 373,
+ 755,
+ 373
+ ],
+ "score": 0.69,
+ "latex": "9 \\times 3"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 462,
+ 2004,
+ 543,
+ 2004,
+ 543,
+ 2035,
+ 462,
+ 2035
+ ],
+ "score": 0.62,
+ "latex": "[ n , 3 2 8 ]"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 931,
+ 1421,
+ 1015,
+ 1421,
+ 1015,
+ 1449,
+ 931,
+ 1449
+ ],
+ "score": 0.61,
+ "latex": "\\mathrm { = } 3 \\times 3 ,"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 687,
+ 346,
+ 745,
+ 346,
+ 745,
+ 373,
+ 687,
+ 373
+ ],
+ "score": 0.58,
+ "latex": "9 \\times 3"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 930,
+ 1021,
+ 1014,
+ 1021,
+ 1014,
+ 1049,
+ 930,
+ 1049
+ ],
+ "score": 0.54,
+ "latex": "\\mathrm { { \\Omega } | = 3 \\times 3 . }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1373,
+ 1892,
+ 1392,
+ 1892,
+ 1392,
+ 1914,
+ 1373,
+ 1914
+ ],
+ "score": 0.54,
+ "latex": "_ n"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 934,
+ 1512,
+ 1013,
+ 1512,
+ 1013,
+ 1540,
+ 934,
+ 1540
+ ],
+ "score": 0.52,
+ "latex": "= 3 \\times 3 ."
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 751,
+ 1632,
+ 905,
+ 1632,
+ 905,
+ 1664,
+ 751,
+ 1664
+ ],
+ "score": 0.45,
+ "latex": "( 3 2 \\times 3 2 \\times 3 )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 806,
+ 1113,
+ 851,
+ 1113,
+ 851,
+ 1139,
+ 806,
+ 1139
+ ],
+ "score": 0.44,
+ "latex": "{ = } 1 6"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 805,
+ 930,
+ 851,
+ 930,
+ 851,
+ 957,
+ 805,
+ 957
+ ],
+ "score": 0.43,
+ "latex": "{ = } 1 6"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 806,
+ 1022,
+ 852,
+ 1022,
+ 852,
+ 1048,
+ 806,
+ 1048
+ ],
+ "score": 0.4,
+ "latex": "{ = } 1 6"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 806,
+ 1512,
+ 852,
+ 1512,
+ 852,
+ 1539,
+ 806,
+ 1539
+ ],
+ "score": 0.39,
+ "latex": "{ = } 1 6"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 806,
+ 1422,
+ 851,
+ 1422,
+ 851,
+ 1448,
+ 806,
+ 1448
+ ],
+ "score": 0.39,
+ "latex": "{ = } 1 6"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 932,
+ 1112,
+ 1014,
+ 1112,
+ 1014,
+ 1140,
+ 932,
+ 1140
+ ],
+ "score": 0.38,
+ "latex": "\\mathrm { = 3 \\times 3 }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 929,
+ 929,
+ 1016,
+ 929,
+ 1016,
+ 958,
+ 929,
+ 958
+ ],
+ "score": 0.38,
+ "latex": "\\mathsf { 1 { = } 3 \\times 3 , }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 810,
+ 989,
+ 910,
+ 989,
+ 910,
+ 1020,
+ 810,
+ 1020
+ ],
+ "score": 0.36,
+ "latex": "{ \\mathfrak { Q } } ( 2 \\times 2 )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 834,
+ 1390,
+ 912,
+ 1390,
+ 912,
+ 1420,
+ 834,
+ 1420
+ ],
+ "score": 0.35,
+ "latex": "( 2 \\times 2 )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 806,
+ 1081,
+ 911,
+ 1081,
+ 911,
+ 1112,
+ 806,
+ 1112
+ ],
+ "score": 0.35,
+ "latex": "2 { \\mathrm { d } } ( 2 \\times 2 )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 729,
+ 867,
+ 880,
+ 867,
+ 880,
+ 898,
+ 729,
+ 898
+ ],
+ "score": 0.33,
+ "latex": "3 2 \\times 3 2 \\times 3 )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 807,
+ 1481,
+ 914,
+ 1481,
+ 914,
+ 1511,
+ 807,
+ 1511
+ ],
+ "score": 0.33,
+ "latex": "2 { \\mathrm { d } } ( 2 \\times 2 )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 805,
+ 1331,
+ 852,
+ 1331,
+ 852,
+ 1357,
+ 805,
+ 1357
+ ],
+ "score": 0.27,
+ "latex": "{ = } 1 6"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 618,
+ 346,
+ 814,
+ 346,
+ 814,
+ 374,
+ 618,
+ 374
+ ],
+ "score": 0.27,
+ "latex": "9 \\times 9 , 9 \\times 3 , 9 \\times 3"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 676.0,
+ 893.0,
+ 676.0,
+ 893.0,
+ 713.0,
+ 294.0,
+ 713.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 73.0,
+ 858.0,
+ 73.0,
+ 858.0,
+ 108.0,
+ 297.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 451.0,
+ 838.0,
+ 451.0,
+ 838.0,
+ 487.0,
+ 296.0,
+ 487.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 478.0,
+ 1689.0,
+ 1220.0,
+ 1689.0,
+ 1220.0,
+ 1727.0,
+ 478.0,
+ 1727.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1794.0,
+ 854.0,
+ 1794.0,
+ 854.0,
+ 1832.0,
+ 295.0,
+ 1832.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 832.0,
+ 2085.0,
+ 870.0,
+ 2085.0,
+ 870.0,
+ 2123.0,
+ 832.0,
+ 2123.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 661.0,
+ 1297.0,
+ 879.0,
+ 1297.0,
+ 879.0,
+ 1331.0,
+ 661.0,
+ 1331.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1325.0,
+ 804.0,
+ 1325.0,
+ 804.0,
+ 1362.0,
+ 660.0,
+ 1362.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 853.0,
+ 1325.0,
+ 1037.0,
+ 1325.0,
+ 1037.0,
+ 1362.0,
+ 853.0,
+ 1362.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 658.0,
+ 1354.0,
+ 722.0,
+ 1354.0,
+ 722.0,
+ 1392.0,
+ 658.0,
+ 1392.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1389.0,
+ 833.0,
+ 1389.0,
+ 833.0,
+ 1424.0,
+ 660.0,
+ 1424.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 913.0,
+ 1389.0,
+ 926.0,
+ 1389.0,
+ 926.0,
+ 1424.0,
+ 913.0,
+ 1424.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1417.0,
+ 805.0,
+ 1417.0,
+ 805.0,
+ 1453.0,
+ 660.0,
+ 1453.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1417.0,
+ 930.0,
+ 1417.0,
+ 930.0,
+ 1453.0,
+ 852.0,
+ 1453.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1016.0,
+ 1417.0,
+ 1037.0,
+ 1417.0,
+ 1037.0,
+ 1453.0,
+ 1016.0,
+ 1453.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1446.0,
+ 723.0,
+ 1446.0,
+ 723.0,
+ 1483.0,
+ 659.0,
+ 1483.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 658.0,
+ 1479.0,
+ 806.0,
+ 1479.0,
+ 806.0,
+ 1514.0,
+ 658.0,
+ 1514.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 915.0,
+ 1479.0,
+ 926.0,
+ 1479.0,
+ 926.0,
+ 1514.0,
+ 915.0,
+ 1514.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1508.0,
+ 805.0,
+ 1508.0,
+ 805.0,
+ 1544.0,
+ 659.0,
+ 1544.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 853.0,
+ 1508.0,
+ 933.0,
+ 1508.0,
+ 933.0,
+ 1544.0,
+ 853.0,
+ 1544.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1014.0,
+ 1508.0,
+ 1038.0,
+ 1508.0,
+ 1038.0,
+ 1544.0,
+ 1014.0,
+ 1544.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1540.0,
+ 722.0,
+ 1540.0,
+ 722.0,
+ 1575.0,
+ 659.0,
+ 1575.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 657.0,
+ 1566.0,
+ 774.0,
+ 1566.0,
+ 774.0,
+ 1607.0,
+ 657.0,
+ 1607.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 658.0,
+ 1602.0,
+ 767.0,
+ 1602.0,
+ 767.0,
+ 1635.0,
+ 658.0,
+ 1635.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1630.0,
+ 750.0,
+ 1630.0,
+ 750.0,
+ 1667.0,
+ 659.0,
+ 1667.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 906.0,
+ 1630.0,
+ 910.0,
+ 1630.0,
+ 910.0,
+ 1667.0,
+ 906.0,
+ 1667.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1855.0,
+ 1405.0,
+ 1855.0,
+ 1405.0,
+ 1892.0,
+ 294.0,
+ 1892.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1885.0,
+ 1372.0,
+ 1885.0,
+ 1372.0,
+ 1922.0,
+ 292.0,
+ 1922.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1393.0,
+ 1885.0,
+ 1405.0,
+ 1885.0,
+ 1405.0,
+ 1922.0,
+ 1393.0,
+ 1922.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1916.0,
+ 642.0,
+ 1916.0,
+ 642.0,
+ 1950.0,
+ 294.0,
+ 1950.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 807.0,
+ 1916.0,
+ 1406.0,
+ 1916.0,
+ 1406.0,
+ 1950.0,
+ 807.0,
+ 1950.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1944.0,
+ 658.0,
+ 1944.0,
+ 658.0,
+ 1978.0,
+ 292.0,
+ 1978.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 725.0,
+ 1944.0,
+ 1405.0,
+ 1944.0,
+ 1405.0,
+ 1978.0,
+ 725.0,
+ 1978.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1974.0,
+ 1405.0,
+ 1974.0,
+ 1405.0,
+ 2009.0,
+ 295.0,
+ 2009.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 2004.0,
+ 461.0,
+ 2004.0,
+ 461.0,
+ 2038.0,
+ 295.0,
+ 2038.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 544.0,
+ 2004.0,
+ 1117.0,
+ 2004.0,
+ 1117.0,
+ 2038.0,
+ 544.0,
+ 2038.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1312.0,
+ 2004.0,
+ 1328.0,
+ 2004.0,
+ 1328.0,
+ 2038.0,
+ 1312.0,
+ 2038.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 512.0,
+ 1178.0,
+ 512.0,
+ 1178.0,
+ 546.0,
+ 297.0,
+ 546.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1274.0,
+ 512.0,
+ 1403.0,
+ 512.0,
+ 1403.0,
+ 546.0,
+ 1274.0,
+ 546.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 542.0,
+ 1403.0,
+ 542.0,
+ 1403.0,
+ 575.0,
+ 295.0,
+ 575.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 567.0,
+ 1405.0,
+ 567.0,
+ 1405.0,
+ 608.0,
+ 293.0,
+ 608.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 601.0,
+ 726.0,
+ 601.0,
+ 726.0,
+ 636.0,
+ 295.0,
+ 636.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 737.0,
+ 1405.0,
+ 737.0,
+ 1405.0,
+ 772.0,
+ 295.0,
+ 772.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 769.0,
+ 1405.0,
+ 769.0,
+ 1405.0,
+ 802.0,
+ 295.0,
+ 802.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 792.0,
+ 418.0,
+ 792.0,
+ 418.0,
+ 834.0,
+ 291.0,
+ 834.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 338.0,
+ 617.0,
+ 338.0,
+ 617.0,
+ 382.0,
+ 293.0,
+ 382.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 815.0,
+ 338.0,
+ 1406.0,
+ 338.0,
+ 1406.0,
+ 382.0,
+ 815.0,
+ 382.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 371.0,
+ 567.0,
+ 371.0,
+ 567.0,
+ 410.0,
+ 294.0,
+ 410.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 633.0,
+ 223.0,
+ 1066.0,
+ 223.0,
+ 1066.0,
+ 256.0,
+ 633.0,
+ 256.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 632.0,
+ 250.0,
+ 1066.0,
+ 250.0,
+ 1066.0,
+ 289.0,
+ 632.0,
+ 289.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 635.0,
+ 280.0,
+ 850.0,
+ 280.0,
+ 850.0,
+ 316.0,
+ 635.0,
+ 316.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 935.0,
+ 280.0,
+ 941.0,
+ 280.0,
+ 941.0,
+ 316.0,
+ 935.0,
+ 316.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1193.0,
+ 1206.0,
+ 1193.0,
+ 1206.0,
+ 1236.0,
+ 294.0,
+ 1236.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1323.0,
+ 1193.0,
+ 1405.0,
+ 1193.0,
+ 1405.0,
+ 1236.0,
+ 1323.0,
+ 1236.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 661.0,
+ 866.0,
+ 728.0,
+ 866.0,
+ 728.0,
+ 900.0,
+ 661.0,
+ 900.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 881.0,
+ 866.0,
+ 892.0,
+ 866.0,
+ 892.0,
+ 900.0,
+ 881.0,
+ 900.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 895.0,
+ 896.0,
+ 895.0,
+ 896.0,
+ 932.0,
+ 660.0,
+ 932.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 926.0,
+ 804.0,
+ 926.0,
+ 804.0,
+ 962.0,
+ 659.0,
+ 962.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 926.0,
+ 928.0,
+ 926.0,
+ 928.0,
+ 962.0,
+ 852.0,
+ 962.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1017.0,
+ 926.0,
+ 1038.0,
+ 926.0,
+ 1038.0,
+ 962.0,
+ 1017.0,
+ 962.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 658.0,
+ 957.0,
+ 721.0,
+ 957.0,
+ 721.0,
+ 992.0,
+ 658.0,
+ 992.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 988.0,
+ 809.0,
+ 988.0,
+ 809.0,
+ 1022.0,
+ 660.0,
+ 1022.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 911.0,
+ 988.0,
+ 922.0,
+ 988.0,
+ 922.0,
+ 1022.0,
+ 911.0,
+ 1022.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1017.0,
+ 805.0,
+ 1017.0,
+ 805.0,
+ 1053.0,
+ 659.0,
+ 1053.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 853.0,
+ 1017.0,
+ 929.0,
+ 1017.0,
+ 929.0,
+ 1053.0,
+ 853.0,
+ 1053.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1015.0,
+ 1017.0,
+ 1039.0,
+ 1017.0,
+ 1039.0,
+ 1053.0,
+ 1015.0,
+ 1053.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 658.0,
+ 1046.0,
+ 722.0,
+ 1046.0,
+ 722.0,
+ 1083.0,
+ 658.0,
+ 1083.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1080.0,
+ 805.0,
+ 1080.0,
+ 805.0,
+ 1114.0,
+ 660.0,
+ 1114.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 912.0,
+ 1080.0,
+ 922.0,
+ 1080.0,
+ 922.0,
+ 1114.0,
+ 912.0,
+ 1114.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 661.0,
+ 1111.0,
+ 805.0,
+ 1111.0,
+ 805.0,
+ 1143.0,
+ 661.0,
+ 1143.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1111.0,
+ 931.0,
+ 1111.0,
+ 931.0,
+ 1143.0,
+ 852.0,
+ 1143.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1015.0,
+ 1111.0,
+ 1038.0,
+ 1111.0,
+ 1038.0,
+ 1143.0,
+ 1015.0,
+ 1143.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1140.0,
+ 763.0,
+ 1140.0,
+ 763.0,
+ 1179.0,
+ 659.0,
+ 1179.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 661.0,
+ 1297.0,
+ 879.0,
+ 1297.0,
+ 879.0,
+ 1331.0,
+ 661.0,
+ 1331.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1325.0,
+ 804.0,
+ 1325.0,
+ 804.0,
+ 1362.0,
+ 660.0,
+ 1362.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 853.0,
+ 1325.0,
+ 1037.0,
+ 1325.0,
+ 1037.0,
+ 1362.0,
+ 853.0,
+ 1362.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 658.0,
+ 1354.0,
+ 722.0,
+ 1354.0,
+ 722.0,
+ 1392.0,
+ 658.0,
+ 1392.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1389.0,
+ 833.0,
+ 1389.0,
+ 833.0,
+ 1424.0,
+ 660.0,
+ 1424.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 913.0,
+ 1389.0,
+ 926.0,
+ 1389.0,
+ 926.0,
+ 1424.0,
+ 913.0,
+ 1424.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 660.0,
+ 1417.0,
+ 805.0,
+ 1417.0,
+ 805.0,
+ 1453.0,
+ 660.0,
+ 1453.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 852.0,
+ 1417.0,
+ 930.0,
+ 1417.0,
+ 930.0,
+ 1453.0,
+ 852.0,
+ 1453.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1016.0,
+ 1417.0,
+ 1037.0,
+ 1417.0,
+ 1037.0,
+ 1453.0,
+ 1016.0,
+ 1453.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1446.0,
+ 723.0,
+ 1446.0,
+ 723.0,
+ 1483.0,
+ 659.0,
+ 1483.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 658.0,
+ 1479.0,
+ 806.0,
+ 1479.0,
+ 806.0,
+ 1514.0,
+ 658.0,
+ 1514.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 915.0,
+ 1479.0,
+ 926.0,
+ 1479.0,
+ 926.0,
+ 1514.0,
+ 915.0,
+ 1514.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1508.0,
+ 805.0,
+ 1508.0,
+ 805.0,
+ 1544.0,
+ 659.0,
+ 1544.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 853.0,
+ 1508.0,
+ 933.0,
+ 1508.0,
+ 933.0,
+ 1544.0,
+ 853.0,
+ 1544.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1014.0,
+ 1508.0,
+ 1038.0,
+ 1508.0,
+ 1038.0,
+ 1544.0,
+ 1014.0,
+ 1544.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1540.0,
+ 722.0,
+ 1540.0,
+ 722.0,
+ 1575.0,
+ 659.0,
+ 1575.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 657.0,
+ 1566.0,
+ 774.0,
+ 1566.0,
+ 774.0,
+ 1607.0,
+ 657.0,
+ 1607.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 658.0,
+ 1602.0,
+ 767.0,
+ 1602.0,
+ 767.0,
+ 1635.0,
+ 658.0,
+ 1635.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 659.0,
+ 1630.0,
+ 750.0,
+ 1630.0,
+ 750.0,
+ 1667.0,
+ 659.0,
+ 1667.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 906.0,
+ 1630.0,
+ 910.0,
+ 1630.0,
+ 910.0,
+ 1667.0,
+ 906.0,
+ 1667.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 13,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 319,
+ 1404,
+ 319,
+ 1404,
+ 584,
+ 298,
+ 584
+ ],
+ "score": 0.98
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 599,
+ 1403,
+ 599,
+ 1403,
+ 804,
+ 298,
+ 804
+ ],
+ "score": 0.977
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 299,
+ 1566,
+ 1403,
+ 1566,
+ 1403,
+ 1741,
+ 299,
+ 1741
+ ],
+ "score": 0.976
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 299,
+ 1226,
+ 1402,
+ 1226,
+ 1402,
+ 1343,
+ 299,
+ 1343
+ ],
+ "score": 0.975
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 922,
+ 1403,
+ 922,
+ 1403,
+ 1127,
+ 298,
+ 1127
+ ],
+ "score": 0.975
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 300,
+ 1842,
+ 1402,
+ 1842,
+ 1402,
+ 1958,
+ 300,
+ 1958
+ ],
+ "score": 0.973
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 299,
+ 1434,
+ 1403,
+ 1434,
+ 1403,
+ 1550,
+ 299,
+ 1550
+ ],
+ "score": 0.973
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 300,
+ 819,
+ 1403,
+ 819,
+ 1403,
+ 907,
+ 300,
+ 907
+ ],
+ "score": 0.971
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 294,
+ 1359,
+ 1399,
+ 1359,
+ 1399,
+ 1419,
+ 294,
+ 1419
+ ],
+ "score": 0.948
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 300,
+ 1974,
+ 1400,
+ 1974,
+ 1400,
+ 2033,
+ 300,
+ 2033
+ ],
+ "score": 0.945
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 298,
+ 76,
+ 857,
+ 76,
+ 857,
+ 104,
+ 298,
+ 104
+ ],
+ "score": 0.877
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 300,
+ 1787,
+ 487,
+ 1787,
+ 487,
+ 1815,
+ 300,
+ 1815
+ ],
+ "score": 0.865
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 837,
+ 2088,
+ 864,
+ 2088,
+ 864,
+ 2112,
+ 837,
+ 2112
+ ],
+ "score": 0.839
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 299,
+ 1169,
+ 416,
+ 1169,
+ 416,
+ 1200,
+ 299,
+ 1200
+ ],
+ "score": 0.766
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 295,
+ 230,
+ 1315,
+ 230,
+ 1315,
+ 291,
+ 295,
+ 291
+ ],
+ "score": 0.577
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 295,
+ 230,
+ 1315,
+ 230,
+ 1315,
+ 291,
+ 295,
+ 291
+ ],
+ "score": 0.421
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 299,
+ 1169,
+ 416,
+ 1169,
+ 416,
+ 1200,
+ 299,
+ 1200
+ ],
+ "score": 0.111
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 601,
+ 1257,
+ 751,
+ 1257,
+ 751,
+ 1284,
+ 601,
+ 1284
+ ],
+ "score": 0.9,
+ "latex": "1 5 \\times 9 = 1 3 5"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 921,
+ 659,
+ 958,
+ 659,
+ 958,
+ 685,
+ 921,
+ 685
+ ],
+ "score": 0.85,
+ "latex": "\\mathbf { A } ^ { * }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 820,
+ 1315,
+ 874,
+ 1315,
+ 874,
+ 1342,
+ 820,
+ 1342
+ ],
+ "score": 0.56,
+ "latex": "( = 9 !"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1196,
+ 380,
+ 1250,
+ 380,
+ 1250,
+ 407,
+ 1196,
+ 407
+ ],
+ "score": 0.51,
+ "latex": "\\mathrm { \\Phi _ { s / A ^ { * } } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1012,
+ 1387,
+ 1073,
+ 1387,
+ 1073,
+ 1420,
+ 1012,
+ 1420
+ ],
+ "score": 0.48,
+ "latex": "( ( 9 ! ) ^ { 2 } ,"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 730,
+ 1314,
+ 880,
+ 1314,
+ 880,
+ 1344,
+ 730,
+ 1344
+ ],
+ "score": 0.28,
+ "latex": "3 6 2 8 8 0 ( = 9 ! )"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 298.0,
+ 73.0,
+ 858.0,
+ 73.0,
+ 858.0,
+ 108.0,
+ 298.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 298.0,
+ 1788.0,
+ 489.0,
+ 1788.0,
+ 489.0,
+ 1817.0,
+ 298.0,
+ 1817.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 833.0,
+ 2085.0,
+ 869.0,
+ 2085.0,
+ 869.0,
+ 2124.0,
+ 833.0,
+ 2124.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1168.0,
+ 420.0,
+ 1168.0,
+ 420.0,
+ 1204.0,
+ 295.0,
+ 1204.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 229.0,
+ 1318.0,
+ 229.0,
+ 1318.0,
+ 263.0,
+ 296.0,
+ 263.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 363.0,
+ 262.0,
+ 591.0,
+ 262.0,
+ 591.0,
+ 293.0,
+ 363.0,
+ 293.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 321.0,
+ 1402.0,
+ 321.0,
+ 1402.0,
+ 353.0,
+ 297.0,
+ 353.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 348.0,
+ 1405.0,
+ 348.0,
+ 1405.0,
+ 383.0,
+ 296.0,
+ 383.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 377.0,
+ 1195.0,
+ 377.0,
+ 1195.0,
+ 416.0,
+ 293.0,
+ 416.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1251.0,
+ 377.0,
+ 1406.0,
+ 377.0,
+ 1406.0,
+ 416.0,
+ 1251.0,
+ 416.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 410.0,
+ 1405.0,
+ 410.0,
+ 1405.0,
+ 441.0,
+ 296.0,
+ 441.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 438.0,
+ 1404.0,
+ 438.0,
+ 1404.0,
+ 473.0,
+ 294.0,
+ 473.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 467.0,
+ 1405.0,
+ 467.0,
+ 1405.0,
+ 502.0,
+ 294.0,
+ 502.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 496.0,
+ 1401.0,
+ 496.0,
+ 1401.0,
+ 528.0,
+ 294.0,
+ 528.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 522.0,
+ 1406.0,
+ 522.0,
+ 1406.0,
+ 559.0,
+ 293.0,
+ 559.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 554.0,
+ 1347.0,
+ 554.0,
+ 1347.0,
+ 590.0,
+ 294.0,
+ 590.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 598.0,
+ 1405.0,
+ 598.0,
+ 1405.0,
+ 635.0,
+ 292.0,
+ 635.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 626.0,
+ 1408.0,
+ 626.0,
+ 1408.0,
+ 662.0,
+ 293.0,
+ 662.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 657.0,
+ 920.0,
+ 657.0,
+ 920.0,
+ 691.0,
+ 294.0,
+ 691.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 959.0,
+ 657.0,
+ 1407.0,
+ 657.0,
+ 1407.0,
+ 691.0,
+ 959.0,
+ 691.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 685.0,
+ 1405.0,
+ 685.0,
+ 1405.0,
+ 721.0,
+ 293.0,
+ 721.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 712.0,
+ 1404.0,
+ 712.0,
+ 1404.0,
+ 750.0,
+ 292.0,
+ 750.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 743.0,
+ 1407.0,
+ 743.0,
+ 1407.0,
+ 780.0,
+ 293.0,
+ 780.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 774.0,
+ 991.0,
+ 774.0,
+ 991.0,
+ 808.0,
+ 294.0,
+ 808.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1565.0,
+ 1405.0,
+ 1565.0,
+ 1405.0,
+ 1601.0,
+ 294.0,
+ 1601.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1595.0,
+ 1407.0,
+ 1595.0,
+ 1407.0,
+ 1631.0,
+ 293.0,
+ 1631.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1625.0,
+ 1405.0,
+ 1625.0,
+ 1405.0,
+ 1660.0,
+ 294.0,
+ 1660.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1655.0,
+ 1405.0,
+ 1655.0,
+ 1405.0,
+ 1689.0,
+ 295.0,
+ 1689.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1683.0,
+ 1405.0,
+ 1683.0,
+ 1405.0,
+ 1717.0,
+ 294.0,
+ 1717.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1713.0,
+ 496.0,
+ 1713.0,
+ 496.0,
+ 1742.0,
+ 294.0,
+ 1742.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1225.0,
+ 1406.0,
+ 1225.0,
+ 1406.0,
+ 1263.0,
+ 294.0,
+ 1263.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1256.0,
+ 600.0,
+ 1256.0,
+ 600.0,
+ 1290.0,
+ 295.0,
+ 1290.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 752.0,
+ 1256.0,
+ 1403.0,
+ 1256.0,
+ 1403.0,
+ 1290.0,
+ 752.0,
+ 1290.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1280.0,
+ 1406.0,
+ 1280.0,
+ 1406.0,
+ 1321.0,
+ 293.0,
+ 1321.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1312.0,
+ 729.0,
+ 1312.0,
+ 729.0,
+ 1347.0,
+ 294.0,
+ 1347.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 881.0,
+ 1312.0,
+ 1204.0,
+ 1312.0,
+ 1204.0,
+ 1347.0,
+ 881.0,
+ 1347.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 922.0,
+ 1405.0,
+ 922.0,
+ 1405.0,
+ 955.0,
+ 296.0,
+ 955.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 952.0,
+ 1405.0,
+ 952.0,
+ 1405.0,
+ 985.0,
+ 294.0,
+ 985.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 980.0,
+ 1405.0,
+ 980.0,
+ 1405.0,
+ 1011.0,
+ 293.0,
+ 1011.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1010.0,
+ 1405.0,
+ 1010.0,
+ 1405.0,
+ 1044.0,
+ 294.0,
+ 1044.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1039.0,
+ 1404.0,
+ 1039.0,
+ 1404.0,
+ 1072.0,
+ 294.0,
+ 1072.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 1066.0,
+ 1407.0,
+ 1066.0,
+ 1407.0,
+ 1104.0,
+ 291.0,
+ 1104.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1097.0,
+ 388.0,
+ 1097.0,
+ 388.0,
+ 1131.0,
+ 293.0,
+ 1131.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1841.0,
+ 1403.0,
+ 1841.0,
+ 1403.0,
+ 1877.0,
+ 295.0,
+ 1877.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1872.0,
+ 1404.0,
+ 1872.0,
+ 1404.0,
+ 1905.0,
+ 295.0,
+ 1905.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1899.0,
+ 1404.0,
+ 1899.0,
+ 1404.0,
+ 1934.0,
+ 294.0,
+ 1934.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1927.0,
+ 477.0,
+ 1927.0,
+ 477.0,
+ 1962.0,
+ 296.0,
+ 1962.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1433.0,
+ 1405.0,
+ 1433.0,
+ 1405.0,
+ 1468.0,
+ 294.0,
+ 1468.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1460.0,
+ 1405.0,
+ 1460.0,
+ 1405.0,
+ 1500.0,
+ 293.0,
+ 1500.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1489.0,
+ 1404.0,
+ 1489.0,
+ 1404.0,
+ 1526.0,
+ 295.0,
+ 1526.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 1523.0,
+ 717.0,
+ 1523.0,
+ 717.0,
+ 1553.0,
+ 297.0,
+ 1553.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 818.0,
+ 1405.0,
+ 818.0,
+ 1405.0,
+ 851.0,
+ 296.0,
+ 851.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 845.0,
+ 1405.0,
+ 845.0,
+ 1405.0,
+ 883.0,
+ 293.0,
+ 883.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 875.0,
+ 1294.0,
+ 875.0,
+ 1294.0,
+ 914.0,
+ 293.0,
+ 914.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1355.0,
+ 1404.0,
+ 1355.0,
+ 1404.0,
+ 1393.0,
+ 293.0,
+ 1393.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1385.0,
+ 1011.0,
+ 1385.0,
+ 1011.0,
+ 1421.0,
+ 292.0,
+ 1421.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1074.0,
+ 1385.0,
+ 1091.0,
+ 1385.0,
+ 1091.0,
+ 1421.0,
+ 1074.0,
+ 1421.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1972.0,
+ 1405.0,
+ 1972.0,
+ 1405.0,
+ 2008.0,
+ 295.0,
+ 2008.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 2001.0,
+ 1340.0,
+ 2001.0,
+ 1340.0,
+ 2038.0,
+ 292.0,
+ 2038.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 229.0,
+ 1318.0,
+ 229.0,
+ 1318.0,
+ 263.0,
+ 296.0,
+ 263.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 363.0,
+ 262.0,
+ 591.0,
+ 262.0,
+ 591.0,
+ 293.0,
+ 363.0,
+ 293.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1168.0,
+ 420.0,
+ 1168.0,
+ 420.0,
+ 1204.0,
+ 295.0,
+ 1204.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 14,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 733,
+ 1404,
+ 733,
+ 1404,
+ 881,
+ 297,
+ 881
+ ],
+ "score": 0.976
+ },
+ {
+ "category_id": 5,
+ "poly": [
+ 460,
+ 1040,
+ 1240,
+ 1040,
+ 1240,
+ 1232,
+ 460,
+ 1232
+ ],
+ "score": 0.976,
+ "html": "| Algorithm1Minibatch stochastic gradient descent training of explainable graph generative adver- sarial nets.The number of steps to apply to the generator, w,is a hyperparameter.We used ω = 3. |
| 1:for number of training iterations do | |
| 2: | Sample minibatch of m samples {e(1),..,x(m)} from data distribution pdata |
| 3: 4: 5: | Sample the respective m shadow walks {s(1),...,s(m)} Update S model weights: |
| m K 0m M £ s(e) log S(s()] i=1 =1 |
| 6: 7: | Generate minibatch of m shadow walks {s(1),...,s(m)} with model S |
| 8: | Sample minibatch of m noise samples {z(1),..,z(m)} from N(0,Id) Update G model weights: |
| 9: | |
| 10: | M 0gm 1 [log(1-D(G(z(𝑖)|s()))] =1 |
| 11: 12: | for w steps do Update D model weights: |
| m 1 |
| 13: | 0dm ∑[logD(x(i) | g(𝑖) + log(1-D(G(z(𝑖)|s(i)))] =1 |
| 14: end for | end for |
| |
+
+Shadow Caster The shadow caster $S$ is a sequence-to-sequence model that learns arrays of contiguous node properties from sampled shadow walks on the shadow. The network predicts a sequence of inputs one at a time when some sequence is observed. We model $S$ with a long short-term memory (LSTM) (Hochreiter & Schmidhuber, 1997) neural network. Given sampled sequences of shadow walks $( \pmb { s } _ { 1 } , \dots , \pmb { s } _ { T } )$ from the shadow as inputs, the shadow caster $S$ then generates synthetic shadow walks $\big ( \tilde { s } _ { 1 } , \dots , \tilde { s } _ { T } \big )$ to mimic the sampled walks.
+
+Generator The generator $G$ is a probabilistic sequential learning model that generates conditional graph random walks $( { \pmb v } _ { 1 } , \dots , { \pmb v } _ { T } ) \sim G$ . We model $G$ using another parameterized LSTM network $f _ { \theta }$ . At each step $t$ , $f _ { \theta }$ takes as input the previous memory state $_ { { \mathbf { } } m _ { t - 1 } }$ of the LSTM model, the current additional information $\tilde { \mathbf { \ b { s } } } _ { t }$ , and the last node ${ \mathbf { } } v _ { t - 1 }$ . The model produces two values $( p _ { t } , m _ { t } )$ , where ${ \mathbf { } } p _ { t }$ denotes the probability distribution over the current node and ${ \mathbf { } } m _ { t }$ the current memory state. Next, the current node ${ \mathbf { } } v _ { t }$ is sampled from a categorical distribution $\mathbf { } \mathbf { v } _ { t } \sim C a t ( \sigma ( \mathbf { p } _ { t } ) )$ using a one-hot vector representation, where $\sigma ( \cdot )$ is the softmax function.
+
+In order to initialize the model, we draw a latent noise from a multivariate standard normal distribution $\mathbf { \boldsymbol { z } } \sim \mathcal { N } ( \mathbf { 0 } , \mathbf { \boldsymbol { I } } _ { d } )$ and pass it through a hyperbolic tangent function $g _ { \theta ^ { \prime } } ( z )$ to compute memory state $m _ { 0 }$ . Generator $G$ takes as inputs the noise $_ { z }$ and sampled shadow walks $\pmb { s }$ , and outputs graph random walks $( \pmb { v } _ { 1 } , \dots , \pmb { v } _ { T } )$ . Through this process, we generate fake random walks.
+
+At this point, we find that our model is closely related to the recently introduced random walk graph generative model (Bojchevski et al., 2018). In addition to random noise model initialization, the generator greatly benefits from the auxiliary information $\tilde { \mathbf { \boldsymbol { s } } } _ { t }$ , modeling a more accurate representation of the original graph (see Appendix for details).
+
+Discriminator The discriminator $D$ is a binary classification LSTM model. The goal of $D$ is to discriminate between real walks sampled from walking on the original graph and fake walks generated by $G$ . At each time-step $t$ , the discriminator takes two inputs: the current node ${ \mathbf { } } v _ { t }$ and the associated shadow $\mathbf { \boldsymbol { s } } _ { t }$ , both represented as one-hot vectors. After processing each presented sequence of shadow and graph walks, $D$ outputs a score between 0 and 1, indicating the probability of a real walk.
+
+After training the model, we have a shadow caster $S$ and a generator $G$ that can produce synthetic graphs. The shadow caster first constructs shadow walks $\big ( \tilde { s } _ { 1 } , \dots , \tilde { s } _ { T } \big )$ of some user-defined class distribution (a relatively small number of shadow walks, e.g., 10,000). The generator then takes $\big ( \tilde { s } _ { 1 } , \dots , \tilde { s } _ { T } \big )$ and generates a large set of random graph walks (a much larger number of random walks than for training, e.g., 10M). We construct a score matrix $_ { s }$ by counting how often an edge appears in the set of graph walks. Next, we convert $\pmb { S }$ into a binary adjacency matrix $\hat { A }$ by first setting $s _ { i j } = s _ { j i } = \operatorname* { m a x } \{ s _ { i j } , s _ { j i } \}$ to get a symmetric matrix. Next, we could use simple binarization strategies such as thresholding or choosing top- $k$ entries. However, we follow a probabilistic strategy, introduced in Bojchevski et al. (2018), that mitigates the issue of leaving out the low-degree nodes and producing singletons because the starting nodes of every walk is random.
+
+# 2.3 EXPLAINING GENERATED GRAPHS
+
+Different from existing approaches, our model takes shadow walks—a series of random walks on the node properties graph—as inputs to the generator, and creates graphs with various densities. To answer questions like: “Why did the model generate such graphs? Could we modify it to our desire?”, we generate graphs that are more explainable by controlling these shadow walk inputs. Our goal is to provide insight into how black-box generative models produce graphs. For any desired graph, we first build a Markov chain to model and construct sequences of node properties based on some user-specified transition distribution. These sequences are then injected into the shadow caster $S$ to generate shadow walks $\big ( \tilde { s } _ { 1 } , \dots , \tilde { s } _ { T } \big )$ that mimic the original shadow. Next, given a trained SHADOWCAST model $\Theta$ and the shadow walks $( \tilde { s } _ { 1 } , \dots , \tilde { s } _ { T } )$ , the generator $G$ produces desired graphs $\tilde { \mathcal { G } }$ ’s. Through this process, one can control the shadow distributions and study the generated graphs by comparing the results.
+
+# 3 RELATED WORK
+
+Although many existing works study the generalizability of graph generation methods, explaining generated graphs remains an open question. From a broader point of view, we can consider the related problems of (1) constructing generative models for graph-structured data and (2) interpreting machine learning models and understanding their results.
+
+Graph Generation Most existing graph generation models are designed to generate graphs mimicking the structure of observed graphs. So far, no generative method that shapes graphs into new desired states have been proposed. In general, we can group these graph generative models into two main families—those that directly model the graph structure (Cao & Kipf, 2018; Liu et al., 2017; Tavakoli et al., 2017; Zhou et al., 2019; Ma et al., 2018; Simonovsky & Komodakis, 2018) and others that study the graph in the context of node representations (Kipf & Welling, 2016; Wang et al., 2018; Grover et al., 2019; Zou & Lerman, 2019). While modeling of graph structures approximates the distribution of graphs with minimal assumptions about their structure, modeling node embedding estimates the probabilities of each edge’s existence, which effectively models the relational structure of large graphs. Another series of tangential work, graph translation (Guo et al., 2019; Jin et al., 2019; Guo et al., 2018), attempts to learn a translation mapping from the input domain to the target domain graph. However, the methods are designed to mainly generate graphs that match the structural characteristics of any given graph.
+
+Recently, some works in graph generation have started exploring network structures of various conditions. These works employ graph-level condition information. In one work, Li et al. (2018) produce some conditional generation results, where the conditions are graph properties such as the number of nodes and edges. Another work, CondGEN (Yang et al., 2019), injects semantics into the graphs by conditioning the model on supplementary contextual information. The model mainly considers multiple small graphs, each with an accompanying semantic condition to learn a distribution over graphs. While GraphRNN (You et al., 2018) is not a direct conditional model, it decomposes the generative process into sequences of nodes and edges, which potentially allows for explicit conditioning. However, these methods only generate graphs mimicking the observed graphs.
+
+To allow state manipulation and controllable graph generation, our model borrows the concept from NetGAN (Bojchevski et al., 2018), which adapts the standard LSTM to learn a distribution of random walks and exploit sparsity in real-world graphs. In contrast to NetGAN, we integrate a condition-based control mechanism to learn a model that generates explainable graphs. Due to the challenging nature of the problem, to the best of our knowledge, no work has definitively considered shaping graphs into new desired states.
+
+Explainable AI Explainable AI studies the task of improving the interpretability of AI systems. While proxy model methods (Huysmans et al., 2011; Augasta & Kathirvalavakumar, 2011; Zilke et al., 2016; Lakkaraju et al., 2017) often resort to learning local approximations of predictions using sets of rules in applying conditions on the prediction, advances in interpretability methods (Adadi & Berrada, 2018; Guidotti et al., 2018; Koh & Liang, 2017) treat black-box models as such and query them for information. Among the many recently developed interpretable models, Graph Neural Network (GNN) models have been studied to explain predictions on graph-structured data via attention mechanisms (Velickovi ˇ c et al., 2018; Neil et al., 2018; Xie & Grossman, 2018). These ap- ´ proaches learn important graph structures by predicting and assigning attention values to the edges. The attention values are the same for all nodes in the same structure, limiting the predictive power.
+
+Moreover, these models cannot explain predictions by combining node feature information with the graph structure. To circumvent the limitations of attention-based GNN models, GNNExplainer (Ying et al., 2019) considers both graph structure and node features to explain predictions. However, explainable GNN models identify explanations in graph structures and node features, which are suitable for link prediction, node/graph classification tasks but not graph generation.
+
+# 4 EXPERIMENTS
+
+In this section, we first compare and evaluate our approach with other baseline graph generation methods on three datasets to establish our model’s ability to generate high-quality graphs of complex networks. Next, we demonstrate the explainability of SHADOWCAST by controlling the generative process to create graphs according to specification. Note that generating graphs mimicking any given graph as closely as possible is not our goal. Our objective is to introduce a more explainable graph generative approach. Through our experiments, we not only demonstrate that SHADOWCAST exhibits competitive performance in the task of graph generation, but we also show that our model can generate graphs of different density distributions by controlling the shadows.
+
+Datasets We consider three real-world graphs in social and information networks, where each node belongs to one of the ground-truth communities. Two of the datasets are email communication networks EUcore-top ( $N = 3 4 8$ , $E = 3 3 4 2$ , $K = 5$ ) and Enron ( $N = 1 5 4$ , $E = 1 8 4 3$ , $K = 3$ ). The other dataset Cora-ML $N = 2 8 1 0$ , $E = 7 9 8 1$ , $K = 7$ ) is a commonly used subset of a large author citation dataset. We provide the links to datasets used in our experiments (see Appendix for details).
+
+We study communication networks: (1) EUcore-top is a network that consists of the top five largest departments in the EUcore email dataset that was created using anonymized emails from a large European research institution. (2) Enron is a dataset of the Enron email corpus where nodes are employees labeled according to their department information. The citation network: (3) Cora-ML is a popular benchmark citation dataset. Nodes labeled according to their paper topic are authors, and edges between them indicate that an author cited another author’s paper.
+
+Baselines Since controlling the generative process to provide explainable graph generation is a novel task, and no such method is developed, we compare our approach against four current stateof-the-art graph generation baseline methods—GraphRNN (You et al., 2018), GVAE (Simonovsky & Komodakis, 2018), NetGAN (Bojchevski et al., 2018), and CondGEN (Yang et al., 2019). We randomly select $8 5 \%$ of the edges in each graph for training and use the remaining $1 5 \%$ for validation and testing. We refer readers to the Appendix for more details about the model implementation settings, baseline models, datasets, and explainable generated visualizations.
+
+Performance We evaluate SHADOWCAST against existing benchmark generative models (You et al., 2018; Simonovsky & Komodakis, 2018; Bojchevski et al., 2018; Yang et al., 2019) and present the comparison statistics 1 (Table 1). By comparing the statistics of the real graphs and those generated by each method, closer mean values indicate greater resemblance to the original graphs, thus better performance. In general, baseline methods succeed at replicating the graphs that are directly modeled. Unsurprisingly, GVAE, designed for generating small graphs, performs well in the smaller Enron and EUcore-top datasets. However, it does not recover statistics of the larger graph Cora-ML well. On the other hand, our model captures all graph properties of the datasets, especially excelling in preserving properties of larger graphs, as shown in its generation of the Cora-ML dataset.
+
+| Algorithm1Minibatch stochastic gradient descent training of explainable graph generative adver- sarial nets.The number of steps to apply to the generator, w,is a hyperparameter.We used ω = 3. |
| 1:for number of training iterations do | |
| 2: | Sample minibatch of m samples {e(1),..,x(m)} from data distribution pdata |
| 3: 4: 5: | Sample the respective m shadow walks {s(1),...,s(m)} Update S model weights: |
| m K 0m M £ s(e) log S(s()] i=1 =1 |
| 6: 7: | Generate minibatch of m shadow walks {s(1),...,s(m)} with model S |
| 8: | Sample minibatch of m noise samples {z(1),..,z(m)} from N(0,Id) Update G model weights: |
| 9: | |
| 10: | M 0gm 1 [log(1-D(G(z(𝑖)|s()))] =1 |
| 11: 12: | for w steps do Update D model weights: |
| m 1 |
| 13: | 0dm ∑[logD(x(i) | g(𝑖) + log(1-D(G(z(𝑖)|s(i)))] =1 |
| 14: end for | end for |
| |
",
+ "bbox": [
+ 243,
+ 405,
+ 758,
+ 671
+ ],
+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "Shadow Caster The shadow caster $S$ is a sequence-to-sequence model that learns arrays of contiguous node properties from sampled shadow walks on the shadow. The network predicts a sequence of inputs one at a time when some sequence is observed. We model $S$ with a long short-term memory (LSTM) (Hochreiter & Schmidhuber, 1997) neural network. Given sampled sequences of shadow walks $( \\pmb { s } _ { 1 } , \\dots , \\pmb { s } _ { T } )$ from the shadow as inputs, the shadow caster $S$ then generates synthetic shadow walks $\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )$ to mimic the sampled walks. ",
+ "bbox": [
+ 173,
+ 693,
+ 825,
+ 776
+ ],
+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "Generator The generator $G$ is a probabilistic sequential learning model that generates conditional graph random walks $( { \\pmb v } _ { 1 } , \\dots , { \\pmb v } _ { T } ) \\sim G$ . We model $G$ using another parameterized LSTM network $f _ { \\theta }$ . At each step $t$ , $f _ { \\theta }$ takes as input the previous memory state $_ { { \\mathbf { } } m _ { t - 1 } }$ of the LSTM model, the current additional information $\\tilde { \\mathbf { \\ b { s } } } _ { t }$ , and the last node ${ \\mathbf { } } v _ { t - 1 }$ . The model produces two values $( p _ { t } , m _ { t } )$ , where ${ \\mathbf { } } p _ { t }$ denotes the probability distribution over the current node and ${ \\mathbf { } } m _ { t }$ the current memory state. Next, the current node ${ \\mathbf { } } v _ { t }$ is sampled from a categorical distribution $\\mathbf { } \\mathbf { v } _ { t } \\sim C a t ( \\sigma ( \\mathbf { p } _ { t } ) )$ using a one-hot vector representation, where $\\sigma ( \\cdot )$ is the softmax function. ",
+ "bbox": [
+ 173,
+ 790,
+ 825,
+ 890
+ ],
+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "In order to initialize the model, we draw a latent noise from a multivariate standard normal distribution $\\mathbf { \\boldsymbol { z } } \\sim \\mathcal { N } ( \\mathbf { 0 } , \\mathbf { \\boldsymbol { I } } _ { d } )$ and pass it through a hyperbolic tangent function $g _ { \\theta ^ { \\prime } } ( z )$ to compute memory state $m _ { 0 }$ . Generator $G$ takes as inputs the noise $_ { z }$ and sampled shadow walks $\\pmb { s }$ , and outputs graph random walks $( \\pmb { v } _ { 1 } , \\dots , \\pmb { v } _ { T } )$ . Through this process, we generate fake random walks. ",
+ "bbox": [
+ 173,
+ 895,
+ 821,
+ 924
+ ],
+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "",
+ "bbox": [
+ 171,
+ 103,
+ 821,
+ 132
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "At this point, we find that our model is closely related to the recently introduced random walk graph generative model (Bojchevski et al., 2018). In addition to random noise model initialization, the generator greatly benefits from the auxiliary information $\\tilde { \\mathbf { \\boldsymbol { s } } } _ { t }$ , modeling a more accurate representation of the original graph (see Appendix for details). ",
+ "bbox": [
+ 174,
+ 138,
+ 823,
+ 194
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Discriminator The discriminator $D$ is a binary classification LSTM model. The goal of $D$ is to discriminate between real walks sampled from walking on the original graph and fake walks generated by $G$ . At each time-step $t$ , the discriminator takes two inputs: the current node ${ \\mathbf { } } v _ { t }$ and the associated shadow $\\mathbf { \\boldsymbol { s } } _ { t }$ , both represented as one-hot vectors. After processing each presented sequence of shadow and graph walks, $D$ outputs a score between 0 and 1, indicating the probability of a real walk. ",
+ "bbox": [
+ 174,
+ 212,
+ 825,
+ 295
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "After training the model, we have a shadow caster $S$ and a generator $G$ that can produce synthetic graphs. The shadow caster first constructs shadow walks $\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )$ of some user-defined class distribution (a relatively small number of shadow walks, e.g., 10,000). The generator then takes $\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )$ and generates a large set of random graph walks (a much larger number of random walks than for training, e.g., 10M). We construct a score matrix $_ { s }$ by counting how often an edge appears in the set of graph walks. Next, we convert $\\pmb { S }$ into a binary adjacency matrix $\\hat { A }$ by first setting $s _ { i j } = s _ { j i } = \\operatorname* { m a x } \\{ s _ { i j } , s _ { j i } \\}$ to get a symmetric matrix. Next, we could use simple binarization strategies such as thresholding or choosing top- $k$ entries. However, we follow a probabilistic strategy, introduced in Bojchevski et al. (2018), that mitigates the issue of leaving out the low-degree nodes and producing singletons because the starting nodes of every walk is random. ",
+ "bbox": [
+ 174,
+ 303,
+ 825,
+ 444
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "2.3 EXPLAINING GENERATED GRAPHS ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 462,
+ 457,
+ 476
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Different from existing approaches, our model takes shadow walks—a series of random walks on the node properties graph—as inputs to the generator, and creates graphs with various densities. To answer questions like: “Why did the model generate such graphs? Could we modify it to our desire?”, we generate graphs that are more explainable by controlling these shadow walk inputs. Our goal is to provide insight into how black-box generative models produce graphs. For any desired graph, we first build a Markov chain to model and construct sequences of node properties based on some user-specified transition distribution. These sequences are then injected into the shadow caster $S$ to generate shadow walks $\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )$ that mimic the original shadow. Next, given a trained SHADOWCAST model $\\Theta$ and the shadow walks $( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } )$ , the generator $G$ produces desired graphs $\\tilde { \\mathcal { G } }$ ’s. Through this process, one can control the shadow distributions and study the generated graphs by comparing the results. ",
+ "bbox": [
+ 174,
+ 488,
+ 825,
+ 643
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "3 RELATED WORK ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 665,
+ 344,
+ 681
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Although many existing works study the generalizability of graph generation methods, explaining generated graphs remains an open question. From a broader point of view, we can consider the related problems of (1) constructing generative models for graph-structured data and (2) interpreting machine learning models and understanding their results. ",
+ "bbox": [
+ 174,
+ 698,
+ 825,
+ 753
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Graph Generation Most existing graph generation models are designed to generate graphs mimicking the structure of observed graphs. So far, no generative method that shapes graphs into new desired states have been proposed. In general, we can group these graph generative models into two main families—those that directly model the graph structure (Cao & Kipf, 2018; Liu et al., 2017; Tavakoli et al., 2017; Zhou et al., 2019; Ma et al., 2018; Simonovsky & Komodakis, 2018) and others that study the graph in the context of node representations (Kipf & Welling, 2016; Wang et al., 2018; Grover et al., 2019; Zou & Lerman, 2019). While modeling of graph structures approximates the distribution of graphs with minimal assumptions about their structure, modeling node embedding estimates the probabilities of each edge’s existence, which effectively models the relational structure of large graphs. Another series of tangential work, graph translation (Guo et al., 2019; Jin et al., 2019; Guo et al., 2018), attempts to learn a translation mapping from the input domain to the target domain graph. However, the methods are designed to mainly generate graphs that match the structural characteristics of any given graph. ",
+ "bbox": [
+ 174,
+ 770,
+ 825,
+ 924
+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "",
+ "bbox": [
+ 173,
+ 103,
+ 823,
+ 132
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Recently, some works in graph generation have started exploring network structures of various conditions. These works employ graph-level condition information. In one work, Li et al. (2018) produce some conditional generation results, where the conditions are graph properties such as the number of nodes and edges. Another work, CondGEN (Yang et al., 2019), injects semantics into the graphs by conditioning the model on supplementary contextual information. The model mainly considers multiple small graphs, each with an accompanying semantic condition to learn a distribution over graphs. While GraphRNN (You et al., 2018) is not a direct conditional model, it decomposes the generative process into sequences of nodes and edges, which potentially allows for explicit conditioning. However, these methods only generate graphs mimicking the observed graphs. ",
+ "bbox": [
+ 174,
+ 138,
+ 825,
+ 263
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "To allow state manipulation and controllable graph generation, our model borrows the concept from NetGAN (Bojchevski et al., 2018), which adapts the standard LSTM to learn a distribution of random walks and exploit sparsity in real-world graphs. In contrast to NetGAN, we integrate a condition-based control mechanism to learn a model that generates explainable graphs. Due to the challenging nature of the problem, to the best of our knowledge, no work has definitively considered shaping graphs into new desired states. ",
+ "bbox": [
+ 174,
+ 271,
+ 825,
+ 354
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Explainable AI Explainable AI studies the task of improving the interpretability of AI systems. While proxy model methods (Huysmans et al., 2011; Augasta & Kathirvalavakumar, 2011; Zilke et al., 2016; Lakkaraju et al., 2017) often resort to learning local approximations of predictions using sets of rules in applying conditions on the prediction, advances in interpretability methods (Adadi & Berrada, 2018; Guidotti et al., 2018; Koh & Liang, 2017) treat black-box models as such and query them for information. Among the many recently developed interpretable models, Graph Neural Network (GNN) models have been studied to explain predictions on graph-structured data via attention mechanisms (Velickovi ˇ c et al., 2018; Neil et al., 2018; Xie & Grossman, 2018). These ap- ´ proaches learn important graph structures by predicting and assigning attention values to the edges. The attention values are the same for all nodes in the same structure, limiting the predictive power. ",
+ "bbox": [
+ 174,
+ 369,
+ 825,
+ 508
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Moreover, these models cannot explain predictions by combining node feature information with the graph structure. To circumvent the limitations of attention-based GNN models, GNNExplainer (Ying et al., 2019) considers both graph structure and node features to explain predictions. However, explainable GNN models identify explanations in graph structures and node features, which are suitable for link prediction, node/graph classification tasks but not graph generation. ",
+ "bbox": [
+ 174,
+ 516,
+ 825,
+ 585
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4 EXPERIMENTS ",
+ "text_level": 1,
+ "bbox": [
+ 176,
+ 606,
+ 326,
+ 621
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "In this section, we first compare and evaluate our approach with other baseline graph generation methods on three datasets to establish our model’s ability to generate high-quality graphs of complex networks. Next, we demonstrate the explainability of SHADOWCAST by controlling the generative process to create graphs according to specification. Note that generating graphs mimicking any given graph as closely as possible is not our goal. Our objective is to introduce a more explainable graph generative approach. Through our experiments, we not only demonstrate that SHADOWCAST exhibits competitive performance in the task of graph generation, but we also show that our model can generate graphs of different density distributions by controlling the shadows. ",
+ "bbox": [
+ 174,
+ 637,
+ 825,
+ 748
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Datasets We consider three real-world graphs in social and information networks, where each node belongs to one of the ground-truth communities. Two of the datasets are email communication networks EUcore-top ( $N = 3 4 8$ , $E = 3 3 4 2$ , $K = 5$ ) and Enron ( $N = 1 5 4$ , $E = 1 8 4 3$ , $K = 3$ ). The other dataset Cora-ML $N = 2 8 1 0$ , $E = 7 9 8 1$ , $K = 7$ ) is a commonly used subset of a large author citation dataset. We provide the links to datasets used in our experiments (see Appendix for details). ",
+ "bbox": [
+ 174,
+ 763,
+ 823,
+ 833
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "We study communication networks: (1) EUcore-top is a network that consists of the top five largest departments in the EUcore email dataset that was created using anonymized emails from a large European research institution. (2) Enron is a dataset of the Enron email corpus where nodes are employees labeled according to their department information. The citation network: (3) Cora-ML is a popular benchmark citation dataset. Nodes labeled according to their paper topic are authors, and edges between them indicate that an author cited another author’s paper. ",
+ "bbox": [
+ 174,
+ 840,
+ 825,
+ 924
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Baselines Since controlling the generative process to provide explainable graph generation is a novel task, and no such method is developed, we compare our approach against four current stateof-the-art graph generation baseline methods—GraphRNN (You et al., 2018), GVAE (Simonovsky & Komodakis, 2018), NetGAN (Bojchevski et al., 2018), and CondGEN (Yang et al., 2019). We randomly select $8 5 \\%$ of the edges in each graph for training and use the remaining $1 5 \\%$ for validation and testing. We refer readers to the Appendix for more details about the model implementation settings, baseline models, datasets, and explainable generated visualizations. ",
+ "bbox": [
+ 173,
+ 103,
+ 825,
+ 200
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "Performance We evaluate SHADOWCAST against existing benchmark generative models (You et al., 2018; Simonovsky & Komodakis, 2018; Bojchevski et al., 2018; Yang et al., 2019) and present the comparison statistics 1 (Table 1). By comparing the statistics of the real graphs and those generated by each method, closer mean values indicate greater resemblance to the original graphs, thus better performance. In general, baseline methods succeed at replicating the graphs that are directly modeled. Unsurprisingly, GVAE, designed for generating small graphs, performs well in the smaller Enron and EUcore-top datasets. However, it does not recover statistics of the larger graph Cora-ML well. On the other hand, our model captures all graph properties of the datasets, especially excelling in preserving properties of larger graphs, as shown in its generation of the Cora-ML dataset. ",
+ "bbox": [
+ 173,
+ 218,
+ 825,
+ 343
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "table",
+ "img_path": "images/28c0f41a473a8bec9380e569787705e985254c7f8c129517b6e40f8da008d658.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Algorithm1Minibatch stochastic gradient descent training of explainable graph generative adver- sarial nets.The number of steps to apply to the generator, w,is a hyperparameter.We used ω = 3. |
| 1:for number of training iterations do | |
| 2: | Sample minibatch of m samples {e(1),..,x(m)} from data distribution pdata |
| 3: 4: 5: | Sample the respective m shadow walks {s(1),...,s(m)} Update S model weights: |
| m K 0m M £ s(e) log S(s()] i=1 =1 |
| 6: 7: | Generate minibatch of m shadow walks {s(1),...,s(m)} with model S |
| 8: | Sample minibatch of m noise samples {z(1),..,z(m)} from N(0,Id) Update G model weights: |
| 9: | |
| 10: | M 0gm 1 [log(1-D(G(z(𝑖)|s()))] =1 |
| 11: 12: | for w steps do Update D model weights: |
| m 1 |
| 13: | 0dm ∑[logD(x(i) | g(𝑖) + log(1-D(G(z(𝑖)|s(i)))] =1 |
| 14: end for | end for |
| |
",
+ "type": "table",
+ "image_path": "fed73649867fccc02ef902c54c11a97e3b6b3ac70ab1caeed2e7cb8cd707addd.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 19,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 149,
+ 321,
+ 464,
+ 391.3333333333333
+ ],
+ "spans": [],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 149,
+ 391.3333333333333,
+ 464,
+ 461.66666666666663
+ ],
+ "spans": [],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 149,
+ 461.66666666666663,
+ 464,
+ 532.0
+ ],
+ "spans": [],
+ "index": 20
+ }
+ ]
+ }
+ ],
+ "index": 19
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 549,
+ 505,
+ 615
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 548,
+ 505,
+ 561
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 548,
+ 258,
+ 561
+ ],
+ "score": 1.0,
+ "content": "Shadow Caster The shadow caster",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 258,
+ 550,
+ 266,
+ 559
+ ],
+ "score": 0.8,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 267,
+ 548,
+ 505,
+ 561
+ ],
+ "score": 1.0,
+ "content": "is a sequence-to-sequence model that learns arrays of con-",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 106,
+ 560,
+ 505,
+ 573
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 560,
+ 505,
+ 573
+ ],
+ "score": 1.0,
+ "content": "tiguous node properties from sampled shadow walks on the shadow. The network predicts a se-",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 571,
+ 505,
+ 583
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 571,
+ 405,
+ 583
+ ],
+ "score": 1.0,
+ "content": "quence of inputs one at a time when some sequence is observed. We model",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 406,
+ 571,
+ 414,
+ 581
+ ],
+ "score": 0.79,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 414,
+ 571,
+ 505,
+ 583
+ ],
+ "score": 1.0,
+ "content": "with a long short-term",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 582,
+ 506,
+ 594
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 582,
+ 506,
+ 594
+ ],
+ "score": 1.0,
+ "content": "memory (LSTM) (Hochreiter & Schmidhuber, 1997) neural network. Given sampled sequences of",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 591,
+ 506,
+ 606
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 591,
+ 165,
+ 606
+ ],
+ "score": 1.0,
+ "content": "shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 165,
+ 593,
+ 216,
+ 604
+ ],
+ "score": 0.91,
+ "content": "( \\pmb { s } _ { 1 } , \\dots , \\pmb { s } _ { T } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 217,
+ 591,
+ 398,
+ 606
+ ],
+ "score": 1.0,
+ "content": "from the shadow as inputs, the shadow caster",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 398,
+ 593,
+ 406,
+ 603
+ ],
+ "score": 0.81,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 407,
+ 591,
+ 506,
+ 606
+ ],
+ "score": 1.0,
+ "content": "then generates synthetic",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 603,
+ 336,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 603,
+ 165,
+ 617
+ ],
+ "score": 1.0,
+ "content": "shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 165,
+ 605,
+ 217,
+ 616
+ ],
+ "score": 0.89,
+ "content": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 217,
+ 603,
+ 336,
+ 617
+ ],
+ "score": 1.0,
+ "content": "to mimic the sampled walks.",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ }
+ ],
+ "index": 23.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 626,
+ 505,
+ 705
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 626,
+ 505,
+ 640
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 626,
+ 218,
+ 640
+ ],
+ "score": 1.0,
+ "content": "Generator The generator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 218,
+ 627,
+ 227,
+ 637
+ ],
+ "score": 0.82,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 228,
+ 626,
+ 505,
+ 640
+ ],
+ "score": 1.0,
+ "content": "is a probabilistic sequential learning model that generates conditional",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 637,
+ 506,
+ 651
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 637,
+ 191,
+ 651
+ ],
+ "score": 1.0,
+ "content": "graph random walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 191,
+ 638,
+ 266,
+ 650
+ ],
+ "score": 0.91,
+ "content": "( { \\pmb v } _ { 1 } , \\dots , { \\pmb v } _ { T } ) \\sim G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 266,
+ 637,
+ 314,
+ 651
+ ],
+ "score": 1.0,
+ "content": ". We model",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 314,
+ 639,
+ 324,
+ 648
+ ],
+ "score": 0.81,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 324,
+ 637,
+ 506,
+ 651
+ ],
+ "score": 1.0,
+ "content": "using another parameterized LSTM network",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 107,
+ 649,
+ 505,
+ 661
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 649,
+ 117,
+ 660
+ ],
+ "score": 0.84,
+ "content": "f _ { \\theta }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 117,
+ 649,
+ 179,
+ 661
+ ],
+ "score": 1.0,
+ "content": ". At each step",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 180,
+ 650,
+ 185,
+ 659
+ ],
+ "score": 0.63,
+ "content": "t",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 185,
+ 649,
+ 189,
+ 661
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 189,
+ 650,
+ 200,
+ 660
+ ],
+ "score": 0.83,
+ "content": "f _ { \\theta }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 200,
+ 649,
+ 374,
+ 661
+ ],
+ "score": 1.0,
+ "content": "takes as input the previous memory state",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 374,
+ 650,
+ 399,
+ 660
+ ],
+ "score": 0.89,
+ "content": "_ { { \\mathbf { } } m _ { t - 1 } }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 399,
+ 649,
+ 505,
+ 661
+ ],
+ "score": 1.0,
+ "content": "of the LSTM model, the",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 105,
+ 659,
+ 505,
+ 673
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 659,
+ 228,
+ 673
+ ],
+ "score": 1.0,
+ "content": "current additional information",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 228,
+ 660,
+ 239,
+ 671
+ ],
+ "score": 0.88,
+ "content": "\\tilde { \\mathbf { \\ b { s } } } _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 239,
+ 659,
+ 311,
+ 673
+ ],
+ "score": 1.0,
+ "content": ", and the last node",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 312,
+ 661,
+ 332,
+ 672
+ ],
+ "score": 0.89,
+ "content": "{ \\mathbf { } } v _ { t - 1 }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 332,
+ 659,
+ 465,
+ 673
+ ],
+ "score": 1.0,
+ "content": ". The model produces two values",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 465,
+ 660,
+ 501,
+ 672
+ ],
+ "score": 0.92,
+ "content": "( p _ { t } , m _ { t } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 501,
+ 659,
+ 505,
+ 673
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 670,
+ 505,
+ 684
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 670,
+ 134,
+ 684
+ ],
+ "score": 1.0,
+ "content": "where",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 134,
+ 672,
+ 145,
+ 682
+ ],
+ "score": 0.84,
+ "content": "{ \\mathbf { } } p _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 146,
+ 670,
+ 404,
+ 684
+ ],
+ "score": 1.0,
+ "content": "denotes the probability distribution over the current node and",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 404,
+ 672,
+ 419,
+ 682
+ ],
+ "score": 0.85,
+ "content": "{ \\mathbf { } } m _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 419,
+ 670,
+ 505,
+ 684
+ ],
+ "score": 1.0,
+ "content": "the current memory",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 681,
+ 506,
+ 694
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 682,
+ 222,
+ 694
+ ],
+ "score": 1.0,
+ "content": "state. Next, the current node",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 222,
+ 683,
+ 232,
+ 693
+ ],
+ "score": 0.86,
+ "content": "{ \\mathbf { } } v _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 232,
+ 682,
+ 401,
+ 694
+ ],
+ "score": 1.0,
+ "content": "is sampled from a categorical distribution",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 402,
+ 681,
+ 472,
+ 694
+ ],
+ "score": 0.93,
+ "content": "\\mathbf { } \\mathbf { v } _ { t } \\sim C a t ( \\sigma ( \\mathbf { p } _ { t } ) )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 473,
+ 682,
+ 506,
+ 694
+ ],
+ "score": 1.0,
+ "content": "using a",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 106,
+ 693,
+ 370,
+ 705
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 693,
+ 255,
+ 705
+ ],
+ "score": 1.0,
+ "content": "one-hot vector representation, where",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 255,
+ 693,
+ 272,
+ 705
+ ],
+ "score": 0.91,
+ "content": "\\sigma ( \\cdot )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 273,
+ 693,
+ 370,
+ 705
+ ],
+ "score": 1.0,
+ "content": "is the softmax function.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ }
+ ],
+ "index": 30
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 709,
+ 503,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 709,
+ 505,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 709,
+ 505,
+ 722
+ ],
+ "score": 1.0,
+ "content": "In order to initialize the model, we draw a latent noise from a multivariate standard normal distri-",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 720,
+ 505,
+ 734
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 720,
+ 134,
+ 734
+ ],
+ "score": 1.0,
+ "content": "bution",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 135,
+ 720,
+ 195,
+ 732
+ ],
+ "score": 0.94,
+ "content": "\\mathbf { \\boldsymbol { z } } \\sim \\mathcal { N } ( \\mathbf { 0 } , \\mathbf { \\boldsymbol { I } } _ { d } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 195,
+ 720,
+ 394,
+ 734
+ ],
+ "score": 1.0,
+ "content": "and pass it through a hyperbolic tangent function",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 394,
+ 721,
+ 421,
+ 732
+ ],
+ "score": 0.93,
+ "content": "g _ { \\theta ^ { \\prime } } ( z )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 421,
+ 720,
+ 505,
+ 734
+ ],
+ "score": 1.0,
+ "content": "to compute memory",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ }
+ ],
+ "index": 34.5
+ }
+ ],
+ "page_idx": 3,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 307,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 25,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 25,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2021",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 302,
+ 752,
+ 308,
+ 759
+ ],
+ "lines": []
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 82,
+ 505,
+ 138
+ ],
+ "lines": [],
+ "index": 2,
+ "bbox_fs": [
+ 105,
+ 82,
+ 506,
+ 139
+ ],
+ "lines_deleted": true
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 143,
+ 503,
+ 165
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 142,
+ 505,
+ 156
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 142,
+ 505,
+ 156
+ ],
+ "score": 1.0,
+ "content": "Following Mirza & Osindero (2014), we introduce the conditional GAN training for graph shadow",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 106,
+ 154,
+ 254,
+ 166
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 154,
+ 254,
+ 166
+ ],
+ "score": 1.0,
+ "content": "random walks and define the loss as:",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ }
+ ],
+ "index": 5.5,
+ "bbox_fs": [
+ 105,
+ 142,
+ 505,
+ 166
+ ]
+ },
+ {
+ "type": "interline_equation",
+ "bbox": [
+ 206,
+ 168,
+ 405,
+ 182
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 206,
+ 168,
+ 405,
+ 182
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 206,
+ 168,
+ 405,
+ 182
+ ],
+ "score": 0.89,
+ "content": "\\mathcal { L } _ { c g a n } = \\log ( D ( \\pmb { x } \\mid \\pmb { s } ) ) + \\log ( 1 - D ( G ( \\pmb { z } \\mid \\pmb { s } ) ) )",
+ "type": "interline_equation",
+ "image_path": "ea7d5b1a9648932d430af07af58df911d36ce6d48f0a84d6cbea16b75321c855.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 7,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 206,
+ 168,
+ 405,
+ 182
+ ],
+ "spans": [],
+ "index": 7
+ }
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 190,
+ 505,
+ 301
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 189,
+ 505,
+ 205
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 189,
+ 134,
+ 205
+ ],
+ "score": 1.0,
+ "content": "where",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 134,
+ 191,
+ 198,
+ 203
+ ],
+ "score": 0.92,
+ "content": "\\boldsymbol { z } \\sim \\mathcal { N } ( \\mathbf { 0 } , \\boldsymbol { I } _ { d } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 198,
+ 189,
+ 505,
+ 205
+ ],
+ "score": 1.0,
+ "content": "is a latent noise from a multivariate standard normal distribution. We rep-",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 203,
+ 504,
+ 214
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 203,
+ 342,
+ 214
+ ],
+ "score": 1.0,
+ "content": "resent a social transaction network as an input graph of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 343,
+ 203,
+ 353,
+ 212
+ ],
+ "score": 0.82,
+ "content": "N",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 354,
+ 203,
+ 504,
+ 214
+ ],
+ "score": 1.0,
+ "content": "nodes as a binary adjacency matrix",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 107,
+ 209,
+ 504,
+ 227
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 212,
+ 174,
+ 225
+ ],
+ "score": 0.93,
+ "content": "\\pmb { A } \\in \\{ 0 , 1 \\} ^ { N \\times N }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 174,
+ 209,
+ 366,
+ 227
+ ],
+ "score": 1.0,
+ "content": ". We then sample sets of random walks of length",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 366,
+ 214,
+ 375,
+ 223
+ ],
+ "score": 0.79,
+ "content": "T",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 375,
+ 209,
+ 397,
+ 227
+ ],
+ "score": 1.0,
+ "content": "from",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 398,
+ 214,
+ 407,
+ 223
+ ],
+ "score": 0.73,
+ "content": "\\pmb { A }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 407,
+ 209,
+ 496,
+ 227
+ ],
+ "score": 1.0,
+ "content": "to use as training data",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 496,
+ 215,
+ 504,
+ 223
+ ],
+ "score": 0.68,
+ "content": "_ { \\textbf { \\em x } }",
+ "type": "inline_equation"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 105,
+ 224,
+ 505,
+ 236
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 224,
+ 505,
+ 236
+ ],
+ "score": 1.0,
+ "content": "for our model. Following Bojchevski et al. (2018), we use a biased second-order random walk sam-",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 105,
+ 235,
+ 505,
+ 247
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 235,
+ 200,
+ 247
+ ],
+ "score": 1.0,
+ "content": "pling strategy (Grover",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 200,
+ 236,
+ 209,
+ 245
+ ],
+ "score": 0.27,
+ "content": "\\&",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 209,
+ 235,
+ 505,
+ 247
+ ],
+ "score": 1.0,
+ "content": "Leskovec, 2016)—one of the advantageous properties of random walks",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 247,
+ 504,
+ 258
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 247,
+ 504,
+ 258
+ ],
+ "score": 1.0,
+ "content": "is their invariance under node reordering—in order to better capture both global and local graph",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 104,
+ 256,
+ 506,
+ 271
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 256,
+ 506,
+ 271
+ ],
+ "score": 1.0,
+ "content": "structures. Another advantage of random walks is that the walks only include connected nodes,",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 268,
+ 505,
+ 281
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 268,
+ 505,
+ 281
+ ],
+ "score": 1.0,
+ "content": "which efficiently exploits the sparsity of real-world graphs by including nonzero values of the adja-",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 279,
+ 505,
+ 292
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 279,
+ 162,
+ 292
+ ],
+ "score": 1.0,
+ "content": "cency matrix",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 162,
+ 280,
+ 170,
+ 289
+ ],
+ "score": 0.69,
+ "content": "A",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 171,
+ 279,
+ 505,
+ 292
+ ],
+ "score": 1.0,
+ "content": ". In the rest of this section, we describe in detail each stage of the SHADOWCAST",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 290,
+ 387,
+ 302
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 290,
+ 387,
+ 302
+ ],
+ "score": 1.0,
+ "content": "generation process and formally present the procedure (Algorithm 1).",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ }
+ ],
+ "index": 12.5,
+ "bbox_fs": [
+ 104,
+ 189,
+ 506,
+ 302
+ ]
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 149,
+ 321,
+ 464,
+ 532
+ ],
+ "blocks": [
+ {
+ "type": "table_body",
+ "bbox": [
+ 149,
+ 321,
+ 464,
+ 532
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 149,
+ 321,
+ 464,
+ 532
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 149,
+ 321,
+ 464,
+ 532
+ ],
+ "score": 0.942,
+ "html": "| Algorithm1Minibatch stochastic gradient descent training of explainable graph generative adver- sarial nets.The number of steps to apply to the generator, w,is a hyperparameter.We used ω = 3. |
| 1:for number of training iterations do | |
| 2: | Sample minibatch of m samples {e(1),..,x(m)} from data distribution pdata |
| 3: 4: 5: | Sample the respective m shadow walks {s(1),...,s(m)} Update S model weights: |
| m K 0m M £ s(e) log S(s()] i=1 =1 |
| 6: 7: | Generate minibatch of m shadow walks {s(1),...,s(m)} with model S |
| 8: | Sample minibatch of m noise samples {z(1),..,z(m)} from N(0,Id) Update G model weights: |
| 9: | |
| 10: | M 0gm 1 [log(1-D(G(z(𝑖)|s()))] =1 |
| 11: 12: | for w steps do Update D model weights: |
| m 1 |
| 13: | 0dm ∑[logD(x(i) | g(𝑖) + log(1-D(G(z(𝑖)|s(i)))] =1 |
| 14: end for | end for |
| |
",
+ "type": "table",
+ "image_path": "fed73649867fccc02ef902c54c11a97e3b6b3ac70ab1caeed2e7cb8cd707addd.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 19,
+ "virtual_lines": [
+ {
+ "bbox": [
+ 149,
+ 321,
+ 464,
+ 391.3333333333333
+ ],
+ "spans": [],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 149,
+ 391.3333333333333,
+ 464,
+ 461.66666666666663
+ ],
+ "spans": [],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 149,
+ 461.66666666666663,
+ 464,
+ 532.0
+ ],
+ "spans": [],
+ "index": 20
+ }
+ ]
+ }
+ ],
+ "index": 19
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 549,
+ 505,
+ 615
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 548,
+ 505,
+ 561
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 548,
+ 258,
+ 561
+ ],
+ "score": 1.0,
+ "content": "Shadow Caster The shadow caster",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 258,
+ 550,
+ 266,
+ 559
+ ],
+ "score": 0.8,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 267,
+ 548,
+ 505,
+ 561
+ ],
+ "score": 1.0,
+ "content": "is a sequence-to-sequence model that learns arrays of con-",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 106,
+ 560,
+ 505,
+ 573
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 560,
+ 505,
+ 573
+ ],
+ "score": 1.0,
+ "content": "tiguous node properties from sampled shadow walks on the shadow. The network predicts a se-",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 571,
+ 505,
+ 583
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 571,
+ 405,
+ 583
+ ],
+ "score": 1.0,
+ "content": "quence of inputs one at a time when some sequence is observed. We model",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 406,
+ 571,
+ 414,
+ 581
+ ],
+ "score": 0.79,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 414,
+ 571,
+ 505,
+ 583
+ ],
+ "score": 1.0,
+ "content": "with a long short-term",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 582,
+ 506,
+ 594
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 582,
+ 506,
+ 594
+ ],
+ "score": 1.0,
+ "content": "memory (LSTM) (Hochreiter & Schmidhuber, 1997) neural network. Given sampled sequences of",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 591,
+ 506,
+ 606
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 591,
+ 165,
+ 606
+ ],
+ "score": 1.0,
+ "content": "shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 165,
+ 593,
+ 216,
+ 604
+ ],
+ "score": 0.91,
+ "content": "( \\pmb { s } _ { 1 } , \\dots , \\pmb { s } _ { T } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 217,
+ 591,
+ 398,
+ 606
+ ],
+ "score": 1.0,
+ "content": "from the shadow as inputs, the shadow caster",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 398,
+ 593,
+ 406,
+ 603
+ ],
+ "score": 0.81,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 407,
+ 591,
+ 506,
+ 606
+ ],
+ "score": 1.0,
+ "content": "then generates synthetic",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 603,
+ 336,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 603,
+ 165,
+ 617
+ ],
+ "score": 1.0,
+ "content": "shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 165,
+ 605,
+ 217,
+ 616
+ ],
+ "score": 0.89,
+ "content": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 217,
+ 603,
+ 336,
+ 617
+ ],
+ "score": 1.0,
+ "content": "to mimic the sampled walks.",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ }
+ ],
+ "index": 23.5,
+ "bbox_fs": [
+ 105,
+ 548,
+ 506,
+ 617
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 626,
+ 505,
+ 705
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 626,
+ 505,
+ 640
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 626,
+ 218,
+ 640
+ ],
+ "score": 1.0,
+ "content": "Generator The generator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 218,
+ 627,
+ 227,
+ 637
+ ],
+ "score": 0.82,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 228,
+ 626,
+ 505,
+ 640
+ ],
+ "score": 1.0,
+ "content": "is a probabilistic sequential learning model that generates conditional",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 637,
+ 506,
+ 651
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 637,
+ 191,
+ 651
+ ],
+ "score": 1.0,
+ "content": "graph random walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 191,
+ 638,
+ 266,
+ 650
+ ],
+ "score": 0.91,
+ "content": "( { \\pmb v } _ { 1 } , \\dots , { \\pmb v } _ { T } ) \\sim G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 266,
+ 637,
+ 314,
+ 651
+ ],
+ "score": 1.0,
+ "content": ". We model",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 314,
+ 639,
+ 324,
+ 648
+ ],
+ "score": 0.81,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 324,
+ 637,
+ 506,
+ 651
+ ],
+ "score": 1.0,
+ "content": "using another parameterized LSTM network",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 107,
+ 649,
+ 505,
+ 661
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 649,
+ 117,
+ 660
+ ],
+ "score": 0.84,
+ "content": "f _ { \\theta }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 117,
+ 649,
+ 179,
+ 661
+ ],
+ "score": 1.0,
+ "content": ". At each step",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 180,
+ 650,
+ 185,
+ 659
+ ],
+ "score": 0.63,
+ "content": "t",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 185,
+ 649,
+ 189,
+ 661
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 189,
+ 650,
+ 200,
+ 660
+ ],
+ "score": 0.83,
+ "content": "f _ { \\theta }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 200,
+ 649,
+ 374,
+ 661
+ ],
+ "score": 1.0,
+ "content": "takes as input the previous memory state",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 374,
+ 650,
+ 399,
+ 660
+ ],
+ "score": 0.89,
+ "content": "_ { { \\mathbf { } } m _ { t - 1 } }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 399,
+ 649,
+ 505,
+ 661
+ ],
+ "score": 1.0,
+ "content": "of the LSTM model, the",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 105,
+ 659,
+ 505,
+ 673
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 659,
+ 228,
+ 673
+ ],
+ "score": 1.0,
+ "content": "current additional information",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 228,
+ 660,
+ 239,
+ 671
+ ],
+ "score": 0.88,
+ "content": "\\tilde { \\mathbf { \\ b { s } } } _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 239,
+ 659,
+ 311,
+ 673
+ ],
+ "score": 1.0,
+ "content": ", and the last node",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 312,
+ 661,
+ 332,
+ 672
+ ],
+ "score": 0.89,
+ "content": "{ \\mathbf { } } v _ { t - 1 }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 332,
+ 659,
+ 465,
+ 673
+ ],
+ "score": 1.0,
+ "content": ". The model produces two values",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 465,
+ 660,
+ 501,
+ 672
+ ],
+ "score": 0.92,
+ "content": "( p _ { t } , m _ { t } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 501,
+ 659,
+ 505,
+ 673
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 670,
+ 505,
+ 684
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 670,
+ 134,
+ 684
+ ],
+ "score": 1.0,
+ "content": "where",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 134,
+ 672,
+ 145,
+ 682
+ ],
+ "score": 0.84,
+ "content": "{ \\mathbf { } } p _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 146,
+ 670,
+ 404,
+ 684
+ ],
+ "score": 1.0,
+ "content": "denotes the probability distribution over the current node and",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 404,
+ 672,
+ 419,
+ 682
+ ],
+ "score": 0.85,
+ "content": "{ \\mathbf { } } m _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 419,
+ 670,
+ 505,
+ 684
+ ],
+ "score": 1.0,
+ "content": "the current memory",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 681,
+ 506,
+ 694
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 682,
+ 222,
+ 694
+ ],
+ "score": 1.0,
+ "content": "state. Next, the current node",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 222,
+ 683,
+ 232,
+ 693
+ ],
+ "score": 0.86,
+ "content": "{ \\mathbf { } } v _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 232,
+ 682,
+ 401,
+ 694
+ ],
+ "score": 1.0,
+ "content": "is sampled from a categorical distribution",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 402,
+ 681,
+ 472,
+ 694
+ ],
+ "score": 0.93,
+ "content": "\\mathbf { } \\mathbf { v } _ { t } \\sim C a t ( \\sigma ( \\mathbf { p } _ { t } ) )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 473,
+ 682,
+ 506,
+ 694
+ ],
+ "score": 1.0,
+ "content": "using a",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 106,
+ 693,
+ 370,
+ 705
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 693,
+ 255,
+ 705
+ ],
+ "score": 1.0,
+ "content": "one-hot vector representation, where",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 255,
+ 693,
+ 272,
+ 705
+ ],
+ "score": 0.91,
+ "content": "\\sigma ( \\cdot )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 273,
+ 693,
+ 370,
+ 705
+ ],
+ "score": 1.0,
+ "content": "is the softmax function.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ }
+ ],
+ "index": 30,
+ "bbox_fs": [
+ 105,
+ 626,
+ 506,
+ 705
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 709,
+ 503,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 709,
+ 505,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 709,
+ 505,
+ 722
+ ],
+ "score": 1.0,
+ "content": "In order to initialize the model, we draw a latent noise from a multivariate standard normal distri-",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 720,
+ 505,
+ 734
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 720,
+ 134,
+ 734
+ ],
+ "score": 1.0,
+ "content": "bution",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 135,
+ 720,
+ 195,
+ 732
+ ],
+ "score": 0.94,
+ "content": "\\mathbf { \\boldsymbol { z } } \\sim \\mathcal { N } ( \\mathbf { 0 } , \\mathbf { \\boldsymbol { I } } _ { d } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 195,
+ 720,
+ 394,
+ 734
+ ],
+ "score": 1.0,
+ "content": "and pass it through a hyperbolic tangent function",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 394,
+ 721,
+ 421,
+ 732
+ ],
+ "score": 0.93,
+ "content": "g _ { \\theta ^ { \\prime } } ( z )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 421,
+ 720,
+ 505,
+ 734
+ ],
+ "score": 1.0,
+ "content": "to compute memory",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 81,
+ 505,
+ 96
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 81,
+ 127,
+ 96
+ ],
+ "score": 1.0,
+ "content": "state",
+ "type": "text",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 127,
+ 84,
+ 143,
+ 94
+ ],
+ "score": 0.85,
+ "content": "m _ { 0 }",
+ "type": "inline_equation",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 144,
+ 81,
+ 190,
+ 96
+ ],
+ "score": 1.0,
+ "content": ". Generator",
+ "type": "text",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 191,
+ 83,
+ 200,
+ 92
+ ],
+ "score": 0.81,
+ "content": "G",
+ "type": "inline_equation",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 200,
+ 81,
+ 300,
+ 96
+ ],
+ "score": 1.0,
+ "content": "takes as inputs the noise",
+ "type": "text",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 300,
+ 84,
+ 308,
+ 92
+ ],
+ "score": 0.74,
+ "content": "_ { z }",
+ "type": "inline_equation",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 308,
+ 81,
+ 420,
+ 96
+ ],
+ "score": 1.0,
+ "content": "and sampled shadow walks",
+ "type": "text",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 421,
+ 85,
+ 427,
+ 92
+ ],
+ "score": 0.63,
+ "content": "\\pmb { s }",
+ "type": "inline_equation",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 427,
+ 81,
+ 505,
+ 96
+ ],
+ "score": 1.0,
+ "content": ", and outputs graph",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 106,
+ 93,
+ 442,
+ 106
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 93,
+ 165,
+ 106
+ ],
+ "score": 1.0,
+ "content": "random walks",
+ "type": "text",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 166,
+ 94,
+ 218,
+ 106
+ ],
+ "score": 0.91,
+ "content": "( \\pmb { v } _ { 1 } , \\dots , \\pmb { v } _ { T } )",
+ "type": "inline_equation",
+ "cross_page": true
+ },
+ {
+ "bbox": [
+ 218,
+ 93,
+ 442,
+ 106
+ ],
+ "score": 1.0,
+ "content": ". Through this process, we generate fake random walks.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 34.5,
+ "bbox_fs": [
+ 105,
+ 709,
+ 505,
+ 734
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 105,
+ 82,
+ 503,
+ 105
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 81,
+ 505,
+ 96
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 81,
+ 127,
+ 96
+ ],
+ "score": 1.0,
+ "content": "state",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 127,
+ 84,
+ 143,
+ 94
+ ],
+ "score": 0.85,
+ "content": "m _ { 0 }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 144,
+ 81,
+ 190,
+ 96
+ ],
+ "score": 1.0,
+ "content": ". Generator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 191,
+ 83,
+ 200,
+ 92
+ ],
+ "score": 0.81,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 200,
+ 81,
+ 300,
+ 96
+ ],
+ "score": 1.0,
+ "content": "takes as inputs the noise",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 300,
+ 84,
+ 308,
+ 92
+ ],
+ "score": 0.74,
+ "content": "_ { z }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 308,
+ 81,
+ 420,
+ 96
+ ],
+ "score": 1.0,
+ "content": "and sampled shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 421,
+ 85,
+ 427,
+ 92
+ ],
+ "score": 0.63,
+ "content": "\\pmb { s }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 427,
+ 81,
+ 505,
+ 96
+ ],
+ "score": 1.0,
+ "content": ", and outputs graph",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 106,
+ 93,
+ 442,
+ 106
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 93,
+ 165,
+ 106
+ ],
+ "score": 1.0,
+ "content": "random walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 166,
+ 94,
+ 218,
+ 106
+ ],
+ "score": 0.91,
+ "content": "( \\pmb { v } _ { 1 } , \\dots , \\pmb { v } _ { T } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 218,
+ 93,
+ 442,
+ 106
+ ],
+ "score": 1.0,
+ "content": ". Through this process, we generate fake random walks.",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 0.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 110,
+ 504,
+ 154
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 110,
+ 506,
+ 123
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 110,
+ 506,
+ 123
+ ],
+ "score": 1.0,
+ "content": "At this point, we find that our model is closely related to the recently introduced random walk graph",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 104,
+ 121,
+ 506,
+ 135
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 121,
+ 506,
+ 135
+ ],
+ "score": 1.0,
+ "content": "generative model (Bojchevski et al., 2018). In addition to random noise model initialization, the gen-",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 132,
+ 505,
+ 145
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 132,
+ 323,
+ 145
+ ],
+ "score": 1.0,
+ "content": "erator greatly benefits from the auxiliary information",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 324,
+ 133,
+ 334,
+ 144
+ ],
+ "score": 0.86,
+ "content": "\\tilde { \\mathbf { \\boldsymbol { s } } } _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 334,
+ 132,
+ 505,
+ 145
+ ],
+ "score": 1.0,
+ "content": ", modeling a more accurate representation",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 106,
+ 144,
+ 299,
+ 156
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 144,
+ 299,
+ 156
+ ],
+ "score": 1.0,
+ "content": "of the original graph (see Appendix for details).",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ }
+ ],
+ "index": 3.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 168,
+ 505,
+ 234
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 168,
+ 505,
+ 181
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 168,
+ 252,
+ 181
+ ],
+ "score": 1.0,
+ "content": "Discriminator The discriminator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 252,
+ 169,
+ 262,
+ 178
+ ],
+ "score": 0.81,
+ "content": "D",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 262,
+ 168,
+ 484,
+ 181
+ ],
+ "score": 1.0,
+ "content": "is a binary classification LSTM model. The goal of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 484,
+ 169,
+ 493,
+ 178
+ ],
+ "score": 0.81,
+ "content": "D",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 494,
+ 168,
+ 505,
+ 181
+ ],
+ "score": 1.0,
+ "content": "is",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 179,
+ 505,
+ 192
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 179,
+ 505,
+ 192
+ ],
+ "score": 1.0,
+ "content": "to discriminate between real walks sampled from walking on the original graph and fake walks",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 190,
+ 506,
+ 203
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 190,
+ 162,
+ 203
+ ],
+ "score": 1.0,
+ "content": "generated by",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 162,
+ 190,
+ 171,
+ 200
+ ],
+ "score": 0.75,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 171,
+ 190,
+ 251,
+ 203
+ ],
+ "score": 1.0,
+ "content": ". At each time-step",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 252,
+ 191,
+ 257,
+ 200
+ ],
+ "score": 0.62,
+ "content": "t",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 257,
+ 190,
+ 475,
+ 203
+ ],
+ "score": 1.0,
+ "content": ", the discriminator takes two inputs: the current node",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 476,
+ 191,
+ 486,
+ 201
+ ],
+ "score": 0.84,
+ "content": "{ \\mathbf { } } v _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 487,
+ 190,
+ 506,
+ 203
+ ],
+ "score": 1.0,
+ "content": "and",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 106,
+ 201,
+ 505,
+ 213
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 201,
+ 200,
+ 213
+ ],
+ "score": 1.0,
+ "content": "the associated shadow",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 201,
+ 203,
+ 211,
+ 212
+ ],
+ "score": 0.85,
+ "content": "\\mathbf { \\boldsymbol { s } } _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 211,
+ 201,
+ 505,
+ 213
+ ],
+ "score": 1.0,
+ "content": ", both represented as one-hot vectors. After processing each presented",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 211,
+ 505,
+ 225
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 211,
+ 259,
+ 225
+ ],
+ "score": 1.0,
+ "content": "sequence of shadow and graph walks,",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 259,
+ 213,
+ 269,
+ 222
+ ],
+ "score": 0.8,
+ "content": "D",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 269,
+ 211,
+ 505,
+ 225
+ ],
+ "score": 1.0,
+ "content": "outputs a score between 0 and 1, indicating the probability",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 105,
+ 223,
+ 166,
+ 234
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 223,
+ 166,
+ 234
+ ],
+ "score": 1.0,
+ "content": "of a real walk.",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ }
+ ],
+ "index": 8.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 240,
+ 505,
+ 352
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 240,
+ 505,
+ 252
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 240,
+ 312,
+ 252
+ ],
+ "score": 1.0,
+ "content": "After training the model, we have a shadow caster",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 312,
+ 240,
+ 320,
+ 250
+ ],
+ "score": 0.8,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 320,
+ 240,
+ 386,
+ 252
+ ],
+ "score": 1.0,
+ "content": "and a generator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 387,
+ 240,
+ 396,
+ 250
+ ],
+ "score": 0.79,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 396,
+ 240,
+ 505,
+ 252
+ ],
+ "score": 1.0,
+ "content": "that can produce synthetic",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 250,
+ 506,
+ 264
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 250,
+ 341,
+ 264
+ ],
+ "score": 1.0,
+ "content": "graphs. The shadow caster first constructs shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 342,
+ 251,
+ 393,
+ 263
+ ],
+ "score": 0.91,
+ "content": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 393,
+ 250,
+ 506,
+ 264
+ ],
+ "score": 1.0,
+ "content": "of some user-defined class",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 261,
+ 505,
+ 275
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 261,
+ 505,
+ 275
+ ],
+ "score": 1.0,
+ "content": "distribution (a relatively small number of shadow walks, e.g., 10,000). The generator then takes",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 107,
+ 273,
+ 505,
+ 285
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 273,
+ 159,
+ 285
+ ],
+ "score": 0.9,
+ "content": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 159,
+ 273,
+ 505,
+ 285
+ ],
+ "score": 1.0,
+ "content": "and generates a large set of random graph walks (a much larger number of random",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 284,
+ 505,
+ 297
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 284,
+ 367,
+ 297
+ ],
+ "score": 1.0,
+ "content": "walks than for training, e.g., 10M). We construct a score matrix",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 367,
+ 284,
+ 376,
+ 294
+ ],
+ "score": 0.78,
+ "content": "_ { s }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 376,
+ 284,
+ 505,
+ 297
+ ],
+ "score": 1.0,
+ "content": "by counting how often an edge",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 295,
+ 506,
+ 308
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 297,
+ 323,
+ 308
+ ],
+ "score": 1.0,
+ "content": "appears in the set of graph walks. Next, we convert",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 324,
+ 297,
+ 332,
+ 307
+ ],
+ "score": 0.77,
+ "content": "\\pmb { S }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 333,
+ 297,
+ 461,
+ 308
+ ],
+ "score": 1.0,
+ "content": "into a binary adjacency matrix",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 462,
+ 295,
+ 472,
+ 306
+ ],
+ "score": 0.85,
+ "content": "\\hat { A }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 472,
+ 297,
+ 506,
+ 308
+ ],
+ "score": 1.0,
+ "content": "by first",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 105,
+ 307,
+ 505,
+ 320
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 307,
+ 136,
+ 320
+ ],
+ "score": 1.0,
+ "content": "setting",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 136,
+ 307,
+ 246,
+ 320
+ ],
+ "score": 0.92,
+ "content": "s _ { i j } = s _ { j i } = \\operatorname* { m a x } \\{ s _ { i j } , s _ { j i } \\}",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 246,
+ 307,
+ 505,
+ 320
+ ],
+ "score": 1.0,
+ "content": "to get a symmetric matrix. Next, we could use simple binariza-",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 318,
+ 505,
+ 331
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 318,
+ 318,
+ 331
+ ],
+ "score": 1.0,
+ "content": "tion strategies such as thresholding or choosing top-",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 318,
+ 319,
+ 325,
+ 329
+ ],
+ "score": 0.79,
+ "content": "k",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 325,
+ 318,
+ 505,
+ 331
+ ],
+ "score": 1.0,
+ "content": "entries. However, we follow a probabilistic",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 329,
+ 505,
+ 342
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 329,
+ 505,
+ 342
+ ],
+ "score": 1.0,
+ "content": "strategy, introduced in Bojchevski et al. (2018), that mitigates the issue of leaving out the low-degree",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 106,
+ 341,
+ 442,
+ 352
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 341,
+ 442,
+ 352
+ ],
+ "score": 1.0,
+ "content": "nodes and producing singletons because the starting nodes of every walk is random.",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ }
+ ],
+ "index": 16.5
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 366,
+ 280,
+ 377
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 366,
+ 281,
+ 379
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 366,
+ 281,
+ 379
+ ],
+ "score": 1.0,
+ "content": "2.3 EXPLAINING GENERATED GRAPHS",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ }
+ ],
+ "index": 22
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 387,
+ 505,
+ 510
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 386,
+ 505,
+ 401
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 386,
+ 505,
+ 401
+ ],
+ "score": 1.0,
+ "content": "Different from existing approaches, our model takes shadow walks—a series of random walks on",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 398,
+ 505,
+ 411
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 398,
+ 505,
+ 411
+ ],
+ "score": 1.0,
+ "content": "the node properties graph—as inputs to the generator, and creates graphs with various densities.",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 409,
+ 504,
+ 422
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 409,
+ 504,
+ 422
+ ],
+ "score": 1.0,
+ "content": "To answer questions like: “Why did the model generate such graphs? Could we modify it to our",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 420,
+ 505,
+ 434
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 420,
+ 505,
+ 434
+ ],
+ "score": 1.0,
+ "content": "desire?”, we generate graphs that are more explainable by controlling these shadow walk inputs. Our",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 431,
+ 506,
+ 444
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 431,
+ 506,
+ 444
+ ],
+ "score": 1.0,
+ "content": "goal is to provide insight into how black-box generative models produce graphs. For any desired",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 442,
+ 506,
+ 455
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 442,
+ 506,
+ 455
+ ],
+ "score": 1.0,
+ "content": "graph, we first build a Markov chain to model and construct sequences of node properties based on",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 453,
+ 505,
+ 465
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 453,
+ 505,
+ 465
+ ],
+ "score": 1.0,
+ "content": "some user-specified transition distribution. These sequences are then injected into the shadow caster",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 107,
+ 463,
+ 506,
+ 477
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 465,
+ 114,
+ 474
+ ],
+ "score": 0.82,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 115,
+ 463,
+ 226,
+ 477
+ ],
+ "score": 1.0,
+ "content": "to generate shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 226,
+ 464,
+ 278,
+ 476
+ ],
+ "score": 0.92,
+ "content": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 278,
+ 463,
+ 506,
+ 477
+ ],
+ "score": 1.0,
+ "content": "that mimic the original shadow. Next, given a trained",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 474,
+ 506,
+ 488
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 474,
+ 201,
+ 488
+ ],
+ "score": 1.0,
+ "content": "SHADOWCAST model",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 201,
+ 475,
+ 212,
+ 485
+ ],
+ "score": 0.77,
+ "content": "\\Theta",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 212,
+ 474,
+ 308,
+ 488
+ ],
+ "score": 1.0,
+ "content": "and the shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 308,
+ 475,
+ 360,
+ 487
+ ],
+ "score": 0.93,
+ "content": "( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 361,
+ 474,
+ 422,
+ 488
+ ],
+ "score": 1.0,
+ "content": ", the generator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 423,
+ 475,
+ 432,
+ 485
+ ],
+ "score": 0.78,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 432,
+ 474,
+ 506,
+ 488
+ ],
+ "score": 1.0,
+ "content": "produces desired",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 486,
+ 506,
+ 501
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 487,
+ 135,
+ 501
+ ],
+ "score": 1.0,
+ "content": "graphs",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 136,
+ 486,
+ 144,
+ 499
+ ],
+ "score": 0.82,
+ "content": "\\tilde { \\mathcal { G } }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 144,
+ 487,
+ 506,
+ 501
+ ],
+ "score": 1.0,
+ "content": "’s. Through this process, one can control the shadow distributions and study the generated",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 105,
+ 499,
+ 239,
+ 511
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 499,
+ 239,
+ 511
+ ],
+ "score": 1.0,
+ "content": "graphs by comparing the results.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ }
+ ],
+ "index": 28
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 527,
+ 211,
+ 540
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 526,
+ 213,
+ 542
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 526,
+ 213,
+ 542
+ ],
+ "score": 1.0,
+ "content": "3 RELATED WORK",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ }
+ ],
+ "index": 34
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 553,
+ 505,
+ 597
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 553,
+ 505,
+ 566
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 553,
+ 505,
+ 566
+ ],
+ "score": 1.0,
+ "content": "Although many existing works study the generalizability of graph generation methods, explaining",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 565,
+ 505,
+ 576
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 565,
+ 505,
+ 576
+ ],
+ "score": 1.0,
+ "content": "generated graphs remains an open question. From a broader point of view, we can consider the",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 574,
+ 505,
+ 588
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 574,
+ 505,
+ 588
+ ],
+ "score": 1.0,
+ "content": "related problems of (1) constructing generative models for graph-structured data and (2) interpreting",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 587,
+ 336,
+ 599
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 587,
+ 336,
+ 599
+ ],
+ "score": 1.0,
+ "content": "machine learning models and understanding their results.",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ }
+ ],
+ "index": 36.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 610,
+ 505,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 610,
+ 505,
+ 624
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 610,
+ 505,
+ 624
+ ],
+ "score": 1.0,
+ "content": "Graph Generation Most existing graph generation models are designed to generate graphs mim-",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 622,
+ 505,
+ 635
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 622,
+ 505,
+ 635
+ ],
+ "score": 1.0,
+ "content": "icking the structure of observed graphs. So far, no generative method that shapes graphs into new",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 632,
+ 506,
+ 646
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 632,
+ 506,
+ 646
+ ],
+ "score": 1.0,
+ "content": "desired states have been proposed. In general, we can group these graph generative models into two",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 105,
+ 644,
+ 505,
+ 657
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 644,
+ 505,
+ 657
+ ],
+ "score": 1.0,
+ "content": "main families—those that directly model the graph structure (Cao & Kipf, 2018; Liu et al., 2017;",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 655,
+ 505,
+ 667
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 655,
+ 505,
+ 667
+ ],
+ "score": 1.0,
+ "content": "Tavakoli et al., 2017; Zhou et al., 2019; Ma et al., 2018; Simonovsky & Komodakis, 2018) and oth-",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "score": 1.0,
+ "content": "ers that study the graph in the context of node representations (Kipf & Welling, 2016; Wang et al.,",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ },
+ {
+ "bbox": [
+ 105,
+ 676,
+ 505,
+ 689
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 676,
+ 505,
+ 689
+ ],
+ "score": 1.0,
+ "content": "2018; Grover et al., 2019; Zou & Lerman, 2019). While modeling of graph structures approximates",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ },
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "score": 1.0,
+ "content": "the distribution of graphs with minimal assumptions about their structure, modeling node embed-",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "score": 1.0,
+ "content": "ding estimates the probabilities of each edge’s existence, which effectively models the relational",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 105,
+ 709,
+ 505,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 709,
+ 505,
+ 722
+ ],
+ "score": 1.0,
+ "content": "structure of large graphs. Another series of tangential work, graph translation (Guo et al., 2019; Jin",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ },
+ {
+ "bbox": [
+ 105,
+ 721,
+ 505,
+ 733
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 721,
+ 505,
+ 733
+ ],
+ "score": 1.0,
+ "content": "et al., 2019; Guo et al., 2018), attempts to learn a translation mapping from the input domain to the",
+ "type": "text"
+ }
+ ],
+ "index": 49
+ }
+ ],
+ "index": 44
+ }
+ ],
+ "page_idx": 4,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 108,
+ 27,
+ 306,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2021",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 302,
+ 751,
+ 308,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 302,
+ 750,
+ 309,
+ 763
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 302,
+ 750,
+ 309,
+ 763
+ ],
+ "score": 1.0,
+ "content": "5",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 105,
+ 82,
+ 503,
+ 105
+ ],
+ "lines": [],
+ "index": 0.5,
+ "bbox_fs": [
+ 105,
+ 81,
+ 505,
+ 106
+ ],
+ "lines_deleted": true
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 110,
+ 504,
+ 154
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 110,
+ 506,
+ 123
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 110,
+ 506,
+ 123
+ ],
+ "score": 1.0,
+ "content": "At this point, we find that our model is closely related to the recently introduced random walk graph",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 104,
+ 121,
+ 506,
+ 135
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 121,
+ 506,
+ 135
+ ],
+ "score": 1.0,
+ "content": "generative model (Bojchevski et al., 2018). In addition to random noise model initialization, the gen-",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 132,
+ 505,
+ 145
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 132,
+ 323,
+ 145
+ ],
+ "score": 1.0,
+ "content": "erator greatly benefits from the auxiliary information",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 324,
+ 133,
+ 334,
+ 144
+ ],
+ "score": 0.86,
+ "content": "\\tilde { \\mathbf { \\boldsymbol { s } } } _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 334,
+ 132,
+ 505,
+ 145
+ ],
+ "score": 1.0,
+ "content": ", modeling a more accurate representation",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 106,
+ 144,
+ 299,
+ 156
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 144,
+ 299,
+ 156
+ ],
+ "score": 1.0,
+ "content": "of the original graph (see Appendix for details).",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ }
+ ],
+ "index": 3.5,
+ "bbox_fs": [
+ 104,
+ 110,
+ 506,
+ 156
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 168,
+ 505,
+ 234
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 168,
+ 505,
+ 181
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 168,
+ 252,
+ 181
+ ],
+ "score": 1.0,
+ "content": "Discriminator The discriminator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 252,
+ 169,
+ 262,
+ 178
+ ],
+ "score": 0.81,
+ "content": "D",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 262,
+ 168,
+ 484,
+ 181
+ ],
+ "score": 1.0,
+ "content": "is a binary classification LSTM model. The goal of",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 484,
+ 169,
+ 493,
+ 178
+ ],
+ "score": 0.81,
+ "content": "D",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 494,
+ 168,
+ 505,
+ 181
+ ],
+ "score": 1.0,
+ "content": "is",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 179,
+ 505,
+ 192
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 179,
+ 505,
+ 192
+ ],
+ "score": 1.0,
+ "content": "to discriminate between real walks sampled from walking on the original graph and fake walks",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 190,
+ 506,
+ 203
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 190,
+ 162,
+ 203
+ ],
+ "score": 1.0,
+ "content": "generated by",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 162,
+ 190,
+ 171,
+ 200
+ ],
+ "score": 0.75,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 171,
+ 190,
+ 251,
+ 203
+ ],
+ "score": 1.0,
+ "content": ". At each time-step",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 252,
+ 191,
+ 257,
+ 200
+ ],
+ "score": 0.62,
+ "content": "t",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 257,
+ 190,
+ 475,
+ 203
+ ],
+ "score": 1.0,
+ "content": ", the discriminator takes two inputs: the current node",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 476,
+ 191,
+ 486,
+ 201
+ ],
+ "score": 0.84,
+ "content": "{ \\mathbf { } } v _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 487,
+ 190,
+ 506,
+ 203
+ ],
+ "score": 1.0,
+ "content": "and",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 106,
+ 201,
+ 505,
+ 213
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 201,
+ 200,
+ 213
+ ],
+ "score": 1.0,
+ "content": "the associated shadow",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 201,
+ 203,
+ 211,
+ 212
+ ],
+ "score": 0.85,
+ "content": "\\mathbf { \\boldsymbol { s } } _ { t }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 211,
+ 201,
+ 505,
+ 213
+ ],
+ "score": 1.0,
+ "content": ", both represented as one-hot vectors. After processing each presented",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 211,
+ 505,
+ 225
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 211,
+ 259,
+ 225
+ ],
+ "score": 1.0,
+ "content": "sequence of shadow and graph walks,",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 259,
+ 213,
+ 269,
+ 222
+ ],
+ "score": 0.8,
+ "content": "D",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 269,
+ 211,
+ 505,
+ 225
+ ],
+ "score": 1.0,
+ "content": "outputs a score between 0 and 1, indicating the probability",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 105,
+ 223,
+ 166,
+ 234
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 223,
+ 166,
+ 234
+ ],
+ "score": 1.0,
+ "content": "of a real walk.",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ }
+ ],
+ "index": 8.5,
+ "bbox_fs": [
+ 105,
+ 168,
+ 506,
+ 234
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 240,
+ 505,
+ 352
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 240,
+ 505,
+ 252
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 240,
+ 312,
+ 252
+ ],
+ "score": 1.0,
+ "content": "After training the model, we have a shadow caster",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 312,
+ 240,
+ 320,
+ 250
+ ],
+ "score": 0.8,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 320,
+ 240,
+ 386,
+ 252
+ ],
+ "score": 1.0,
+ "content": "and a generator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 387,
+ 240,
+ 396,
+ 250
+ ],
+ "score": 0.79,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 396,
+ 240,
+ 505,
+ 252
+ ],
+ "score": 1.0,
+ "content": "that can produce synthetic",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 250,
+ 506,
+ 264
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 250,
+ 341,
+ 264
+ ],
+ "score": 1.0,
+ "content": "graphs. The shadow caster first constructs shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 342,
+ 251,
+ 393,
+ 263
+ ],
+ "score": 0.91,
+ "content": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 393,
+ 250,
+ 506,
+ 264
+ ],
+ "score": 1.0,
+ "content": "of some user-defined class",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 261,
+ 505,
+ 275
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 261,
+ 505,
+ 275
+ ],
+ "score": 1.0,
+ "content": "distribution (a relatively small number of shadow walks, e.g., 10,000). The generator then takes",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 107,
+ 273,
+ 505,
+ 285
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 273,
+ 159,
+ 285
+ ],
+ "score": 0.9,
+ "content": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 159,
+ 273,
+ 505,
+ 285
+ ],
+ "score": 1.0,
+ "content": "and generates a large set of random graph walks (a much larger number of random",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 284,
+ 505,
+ 297
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 284,
+ 367,
+ 297
+ ],
+ "score": 1.0,
+ "content": "walks than for training, e.g., 10M). We construct a score matrix",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 367,
+ 284,
+ 376,
+ 294
+ ],
+ "score": 0.78,
+ "content": "_ { s }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 376,
+ 284,
+ 505,
+ 297
+ ],
+ "score": 1.0,
+ "content": "by counting how often an edge",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ },
+ {
+ "bbox": [
+ 105,
+ 295,
+ 506,
+ 308
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 297,
+ 323,
+ 308
+ ],
+ "score": 1.0,
+ "content": "appears in the set of graph walks. Next, we convert",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 324,
+ 297,
+ 332,
+ 307
+ ],
+ "score": 0.77,
+ "content": "\\pmb { S }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 333,
+ 297,
+ 461,
+ 308
+ ],
+ "score": 1.0,
+ "content": "into a binary adjacency matrix",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 462,
+ 295,
+ 472,
+ 306
+ ],
+ "score": 0.85,
+ "content": "\\hat { A }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 472,
+ 297,
+ 506,
+ 308
+ ],
+ "score": 1.0,
+ "content": "by first",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 105,
+ 307,
+ 505,
+ 320
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 307,
+ 136,
+ 320
+ ],
+ "score": 1.0,
+ "content": "setting",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 136,
+ 307,
+ 246,
+ 320
+ ],
+ "score": 0.92,
+ "content": "s _ { i j } = s _ { j i } = \\operatorname* { m a x } \\{ s _ { i j } , s _ { j i } \\}",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 246,
+ 307,
+ 505,
+ 320
+ ],
+ "score": 1.0,
+ "content": "to get a symmetric matrix. Next, we could use simple binariza-",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 105,
+ 318,
+ 505,
+ 331
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 318,
+ 318,
+ 331
+ ],
+ "score": 1.0,
+ "content": "tion strategies such as thresholding or choosing top-",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 318,
+ 319,
+ 325,
+ 329
+ ],
+ "score": 0.79,
+ "content": "k",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 325,
+ 318,
+ 505,
+ 331
+ ],
+ "score": 1.0,
+ "content": "entries. However, we follow a probabilistic",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 329,
+ 505,
+ 342
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 329,
+ 505,
+ 342
+ ],
+ "score": 1.0,
+ "content": "strategy, introduced in Bojchevski et al. (2018), that mitigates the issue of leaving out the low-degree",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 106,
+ 341,
+ 442,
+ 352
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 341,
+ 442,
+ 352
+ ],
+ "score": 1.0,
+ "content": "nodes and producing singletons because the starting nodes of every walk is random.",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ }
+ ],
+ "index": 16.5,
+ "bbox_fs": [
+ 105,
+ 240,
+ 506,
+ 352
+ ]
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 366,
+ 280,
+ 377
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 366,
+ 281,
+ 379
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 366,
+ 281,
+ 379
+ ],
+ "score": 1.0,
+ "content": "2.3 EXPLAINING GENERATED GRAPHS",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ }
+ ],
+ "index": 22
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 387,
+ 505,
+ 510
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 386,
+ 505,
+ 401
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 386,
+ 505,
+ 401
+ ],
+ "score": 1.0,
+ "content": "Different from existing approaches, our model takes shadow walks—a series of random walks on",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 398,
+ 505,
+ 411
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 398,
+ 505,
+ 411
+ ],
+ "score": 1.0,
+ "content": "the node properties graph—as inputs to the generator, and creates graphs with various densities.",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 409,
+ 504,
+ 422
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 409,
+ 504,
+ 422
+ ],
+ "score": 1.0,
+ "content": "To answer questions like: “Why did the model generate such graphs? Could we modify it to our",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 105,
+ 420,
+ 505,
+ 434
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 420,
+ 505,
+ 434
+ ],
+ "score": 1.0,
+ "content": "desire?”, we generate graphs that are more explainable by controlling these shadow walk inputs. Our",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ },
+ {
+ "bbox": [
+ 105,
+ 431,
+ 506,
+ 444
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 431,
+ 506,
+ 444
+ ],
+ "score": 1.0,
+ "content": "goal is to provide insight into how black-box generative models produce graphs. For any desired",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 105,
+ 442,
+ 506,
+ 455
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 442,
+ 506,
+ 455
+ ],
+ "score": 1.0,
+ "content": "graph, we first build a Markov chain to model and construct sequences of node properties based on",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 453,
+ 505,
+ 465
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 453,
+ 505,
+ 465
+ ],
+ "score": 1.0,
+ "content": "some user-specified transition distribution. These sequences are then injected into the shadow caster",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 107,
+ 463,
+ 506,
+ 477
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 107,
+ 465,
+ 114,
+ 474
+ ],
+ "score": 0.82,
+ "content": "S",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 115,
+ 463,
+ 226,
+ 477
+ ],
+ "score": 1.0,
+ "content": "to generate shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 226,
+ 464,
+ 278,
+ 476
+ ],
+ "score": 0.92,
+ "content": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 278,
+ 463,
+ 506,
+ 477
+ ],
+ "score": 1.0,
+ "content": "that mimic the original shadow. Next, given a trained",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 105,
+ 474,
+ 506,
+ 488
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 474,
+ 201,
+ 488
+ ],
+ "score": 1.0,
+ "content": "SHADOWCAST model",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 201,
+ 475,
+ 212,
+ 485
+ ],
+ "score": 0.77,
+ "content": "\\Theta",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 212,
+ 474,
+ 308,
+ 488
+ ],
+ "score": 1.0,
+ "content": "and the shadow walks",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 308,
+ 475,
+ 360,
+ 487
+ ],
+ "score": 0.93,
+ "content": "( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } )",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 361,
+ 474,
+ 422,
+ 488
+ ],
+ "score": 1.0,
+ "content": ", the generator",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 423,
+ 475,
+ 432,
+ 485
+ ],
+ "score": 0.78,
+ "content": "G",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 432,
+ 474,
+ 506,
+ 488
+ ],
+ "score": 1.0,
+ "content": "produces desired",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ },
+ {
+ "bbox": [
+ 105,
+ 486,
+ 506,
+ 501
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 487,
+ 135,
+ 501
+ ],
+ "score": 1.0,
+ "content": "graphs",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 136,
+ 486,
+ 144,
+ 499
+ ],
+ "score": 0.82,
+ "content": "\\tilde { \\mathcal { G } }",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 144,
+ 487,
+ 506,
+ 501
+ ],
+ "score": 1.0,
+ "content": "’s. Through this process, one can control the shadow distributions and study the generated",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ },
+ {
+ "bbox": [
+ 105,
+ 499,
+ 239,
+ 511
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 499,
+ 239,
+ 511
+ ],
+ "score": 1.0,
+ "content": "graphs by comparing the results.",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ }
+ ],
+ "index": 28,
+ "bbox_fs": [
+ 105,
+ 386,
+ 506,
+ 511
+ ]
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 527,
+ 211,
+ 540
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 526,
+ 213,
+ 542
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 526,
+ 213,
+ 542
+ ],
+ "score": 1.0,
+ "content": "3 RELATED WORK",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ }
+ ],
+ "index": 34
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 553,
+ 505,
+ 597
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 553,
+ 505,
+ 566
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 553,
+ 505,
+ 566
+ ],
+ "score": 1.0,
+ "content": "Although many existing works study the generalizability of graph generation methods, explaining",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 105,
+ 565,
+ 505,
+ 576
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 565,
+ 505,
+ 576
+ ],
+ "score": 1.0,
+ "content": "generated graphs remains an open question. From a broader point of view, we can consider the",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 574,
+ 505,
+ 588
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 574,
+ 505,
+ 588
+ ],
+ "score": 1.0,
+ "content": "related problems of (1) constructing generative models for graph-structured data and (2) interpreting",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 587,
+ 336,
+ 599
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 587,
+ 336,
+ 599
+ ],
+ "score": 1.0,
+ "content": "machine learning models and understanding their results.",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ }
+ ],
+ "index": 36.5,
+ "bbox_fs": [
+ 105,
+ 553,
+ 505,
+ 599
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 610,
+ 505,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 610,
+ 505,
+ 624
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 610,
+ 505,
+ 624
+ ],
+ "score": 1.0,
+ "content": "Graph Generation Most existing graph generation models are designed to generate graphs mim-",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 622,
+ 505,
+ 635
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 622,
+ 505,
+ 635
+ ],
+ "score": 1.0,
+ "content": "icking the structure of observed graphs. So far, no generative method that shapes graphs into new",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ },
+ {
+ "bbox": [
+ 105,
+ 632,
+ 506,
+ 646
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 632,
+ 506,
+ 646
+ ],
+ "score": 1.0,
+ "content": "desired states have been proposed. In general, we can group these graph generative models into two",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 105,
+ 644,
+ 505,
+ 657
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 644,
+ 505,
+ 657
+ ],
+ "score": 1.0,
+ "content": "main families—those that directly model the graph structure (Cao & Kipf, 2018; Liu et al., 2017;",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 655,
+ 505,
+ 667
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 655,
+ 505,
+ 667
+ ],
+ "score": 1.0,
+ "content": "Tavakoli et al., 2017; Zhou et al., 2019; Ma et al., 2018; Simonovsky & Komodakis, 2018) and oth-",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 666,
+ 505,
+ 678
+ ],
+ "score": 1.0,
+ "content": "ers that study the graph in the context of node representations (Kipf & Welling, 2016; Wang et al.,",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ },
+ {
+ "bbox": [
+ 105,
+ 676,
+ 505,
+ 689
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 676,
+ 505,
+ 689
+ ],
+ "score": 1.0,
+ "content": "2018; Grover et al., 2019; Zou & Lerman, 2019). While modeling of graph structures approximates",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ },
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "score": 1.0,
+ "content": "the distribution of graphs with minimal assumptions about their structure, modeling node embed-",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "score": 1.0,
+ "content": "ding estimates the probabilities of each edge’s existence, which effectively models the relational",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 105,
+ 709,
+ 505,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 709,
+ 505,
+ 722
+ ],
+ "score": 1.0,
+ "content": "structure of large graphs. Another series of tangential work, graph translation (Guo et al., 2019; Jin",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ },
+ {
+ "bbox": [
+ 105,
+ 721,
+ 505,
+ 733
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 721,
+ 505,
+ 733
+ ],
+ "score": 1.0,
+ "content": "et al., 2019; Guo et al., 2018), attempts to learn a translation mapping from the input domain to the",
+ "type": "text"
+ }
+ ],
+ "index": 49
+ },
+ {
+ "bbox": [
+ 106,
+ 82,
+ 505,
+ 95
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 82,
+ 505,
+ 95
+ ],
+ "score": 1.0,
+ "content": "target domain graph. However, the methods are designed to mainly generate graphs that match the",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 105,
+ 93,
+ 285,
+ 106
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 93,
+ 285,
+ 106
+ ],
+ "score": 1.0,
+ "content": "structural characteristics of any given graph.",
+ "type": "text",
+ "cross_page": true
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 44,
+ "bbox_fs": [
+ 105,
+ 610,
+ 506,
+ 733
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 82,
+ 504,
+ 105
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 82,
+ 505,
+ 95
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 82,
+ 505,
+ 95
+ ],
+ "score": 1.0,
+ "content": "target domain graph. However, the methods are designed to mainly generate graphs that match the",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 105,
+ 93,
+ 285,
+ 106
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 93,
+ 285,
+ 106
+ ],
+ "score": 1.0,
+ "content": "structural characteristics of any given graph.",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "index": 0.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 110,
+ 505,
+ 209
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 111,
+ 505,
+ 123
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 111,
+ 505,
+ 123
+ ],
+ "score": 1.0,
+ "content": "Recently, some works in graph generation have started exploring network structures of various con-",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 105,
+ 121,
+ 505,
+ 134
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 121,
+ 505,
+ 134
+ ],
+ "score": 1.0,
+ "content": "ditions. These works employ graph-level condition information. In one work, Li et al. (2018)",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 132,
+ 505,
+ 145
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 132,
+ 505,
+ 145
+ ],
+ "score": 1.0,
+ "content": "produce some conditional generation results, where the conditions are graph properties such as the",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 105,
+ 143,
+ 505,
+ 156
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 143,
+ 505,
+ 156
+ ],
+ "score": 1.0,
+ "content": "number of nodes and edges. Another work, CondGEN (Yang et al., 2019), injects semantics into the",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 154,
+ 505,
+ 167
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 154,
+ 505,
+ 167
+ ],
+ "score": 1.0,
+ "content": "graphs by conditioning the model on supplementary contextual information. The model mainly con-",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 165,
+ 505,
+ 178
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 165,
+ 505,
+ 178
+ ],
+ "score": 1.0,
+ "content": "siders multiple small graphs, each with an accompanying semantic condition to learn a distribution",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 175,
+ 506,
+ 190
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 175,
+ 506,
+ 190
+ ],
+ "score": 1.0,
+ "content": "over graphs. While GraphRNN (You et al., 2018) is not a direct conditional model, it decomposes",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 187,
+ 505,
+ 201
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 187,
+ 505,
+ 201
+ ],
+ "score": 1.0,
+ "content": "the generative process into sequences of nodes and edges, which potentially allows for explicit con-",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 198,
+ 462,
+ 212
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 198,
+ 462,
+ 212
+ ],
+ "score": 1.0,
+ "content": "ditioning. However, these methods only generate graphs mimicking the observed graphs.",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ }
+ ],
+ "index": 6
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 215,
+ 505,
+ 281
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 214,
+ 505,
+ 228
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 214,
+ 505,
+ 228
+ ],
+ "score": 1.0,
+ "content": "To allow state manipulation and controllable graph generation, our model borrows the concept",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 106,
+ 226,
+ 505,
+ 238
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 226,
+ 505,
+ 238
+ ],
+ "score": 1.0,
+ "content": "from NetGAN (Bojchevski et al., 2018), which adapts the standard LSTM to learn a distribution",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 235,
+ 507,
+ 250
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 235,
+ 507,
+ 250
+ ],
+ "score": 1.0,
+ "content": "of random walks and exploit sparsity in real-world graphs. In contrast to NetGAN, we integrate a",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 247,
+ 505,
+ 260
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 247,
+ 505,
+ 260
+ ],
+ "score": 1.0,
+ "content": "condition-based control mechanism to learn a model that generates explainable graphs. Due to the",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 259,
+ 505,
+ 271
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 259,
+ 505,
+ 271
+ ],
+ "score": 1.0,
+ "content": "challenging nature of the problem, to the best of our knowledge, no work has definitively considered",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 270,
+ 264,
+ 281
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 270,
+ 264,
+ 281
+ ],
+ "score": 1.0,
+ "content": "shaping graphs into new desired states.",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ }
+ ],
+ "index": 13.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 293,
+ 505,
+ 403
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 292,
+ 505,
+ 306
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 292,
+ 505,
+ 306
+ ],
+ "score": 1.0,
+ "content": "Explainable AI Explainable AI studies the task of improving the interpretability of AI systems.",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 105,
+ 304,
+ 504,
+ 317
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 304,
+ 504,
+ 317
+ ],
+ "score": 1.0,
+ "content": "While proxy model methods (Huysmans et al., 2011; Augasta & Kathirvalavakumar, 2011; Zilke",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 104,
+ 313,
+ 505,
+ 329
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 313,
+ 505,
+ 329
+ ],
+ "score": 1.0,
+ "content": "et al., 2016; Lakkaraju et al., 2017) often resort to learning local approximations of predictions using",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 326,
+ 504,
+ 339
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 326,
+ 504,
+ 339
+ ],
+ "score": 1.0,
+ "content": "sets of rules in applying conditions on the prediction, advances in interpretability methods (Adadi",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 105,
+ 337,
+ 505,
+ 349
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 337,
+ 505,
+ 349
+ ],
+ "score": 1.0,
+ "content": "& Berrada, 2018; Guidotti et al., 2018; Koh & Liang, 2017) treat black-box models as such and",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 348,
+ 505,
+ 361
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 348,
+ 505,
+ 361
+ ],
+ "score": 1.0,
+ "content": "query them for information. Among the many recently developed interpretable models, Graph Neu-",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 358,
+ 506,
+ 372
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 358,
+ 506,
+ 372
+ ],
+ "score": 1.0,
+ "content": "ral Network (GNN) models have been studied to explain predictions on graph-structured data via",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 369,
+ 505,
+ 384
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 369,
+ 505,
+ 384
+ ],
+ "score": 1.0,
+ "content": "attention mechanisms (Velickovi ˇ c et al., 2018; Neil et al., 2018; Xie & Grossman, 2018). These ap- ´",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 381,
+ 504,
+ 394
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 381,
+ 504,
+ 394
+ ],
+ "score": 1.0,
+ "content": "proaches learn important graph structures by predicting and assigning attention values to the edges.",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 106,
+ 390,
+ 502,
+ 405
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 390,
+ 502,
+ 405
+ ],
+ "score": 1.0,
+ "content": "The attention values are the same for all nodes in the same structure, limiting the predictive power.",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ }
+ ],
+ "index": 21.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 409,
+ 505,
+ 464
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 409,
+ 505,
+ 421
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 409,
+ 505,
+ 421
+ ],
+ "score": 1.0,
+ "content": "Moreover, these models cannot explain predictions by combining node feature information with",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 106,
+ 420,
+ 505,
+ 432
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 420,
+ 505,
+ 432
+ ],
+ "score": 1.0,
+ "content": "the graph structure. To circumvent the limitations of attention-based GNN models, GNNEx-",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 430,
+ 505,
+ 444
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 430,
+ 505,
+ 444
+ ],
+ "score": 1.0,
+ "content": "plainer (Ying et al., 2019) considers both graph structure and node features to explain predictions.",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 105,
+ 441,
+ 505,
+ 455
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 441,
+ 505,
+ 455
+ ],
+ "score": 1.0,
+ "content": "However, explainable GNN models identify explanations in graph structures and node features,",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 106,
+ 453,
+ 485,
+ 465
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 453,
+ 485,
+ 465
+ ],
+ "score": 1.0,
+ "content": "which are suitable for link prediction, node/graph classification tasks but not graph generation.",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ }
+ ],
+ "index": 29
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 480,
+ 200,
+ 492
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 479,
+ 201,
+ 495
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 479,
+ 201,
+ 495
+ ],
+ "score": 1.0,
+ "content": "4 EXPERIMENTS",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ }
+ ],
+ "index": 32
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 505,
+ 505,
+ 593
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 504,
+ 505,
+ 518
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 504,
+ 505,
+ 518
+ ],
+ "score": 1.0,
+ "content": "In this section, we first compare and evaluate our approach with other baseline graph generation",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 516,
+ 505,
+ 528
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 516,
+ 505,
+ 528
+ ],
+ "score": 1.0,
+ "content": "methods on three datasets to establish our model’s ability to generate high-quality graphs of complex",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 527,
+ 505,
+ 539
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 527,
+ 505,
+ 539
+ ],
+ "score": 1.0,
+ "content": "networks. Next, we demonstrate the explainability of SHADOWCAST by controlling the generative",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 104,
+ 537,
+ 505,
+ 552
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 537,
+ 505,
+ 552
+ ],
+ "score": 1.0,
+ "content": "process to create graphs according to specification. Note that generating graphs mimicking any",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 549,
+ 506,
+ 561
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 549,
+ 506,
+ 561
+ ],
+ "score": 1.0,
+ "content": "given graph as closely as possible is not our goal. Our objective is to introduce a more explainable",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 559,
+ 506,
+ 572
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 559,
+ 506,
+ 572
+ ],
+ "score": 1.0,
+ "content": "graph generative approach. Through our experiments, we not only demonstrate that SHADOWCAST",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 105,
+ 570,
+ 506,
+ 584
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 570,
+ 506,
+ 584
+ ],
+ "score": 1.0,
+ "content": "exhibits competitive performance in the task of graph generation, but we also show that our model",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 582,
+ 432,
+ 594
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 582,
+ 432,
+ 594
+ ],
+ "score": 1.0,
+ "content": "can generate graphs of different density distributions by controlling the shadows.",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ }
+ ],
+ "index": 36.5
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 605,
+ 504,
+ 660
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 605,
+ 505,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 605,
+ 505,
+ 617
+ ],
+ "score": 1.0,
+ "content": "Datasets We consider three real-world graphs in social and information networks, where each",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 106,
+ 616,
+ 505,
+ 628
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 616,
+ 505,
+ 628
+ ],
+ "score": 1.0,
+ "content": "node belongs to one of the ground-truth communities. Two of the datasets are email communication",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 626,
+ 506,
+ 639
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 626,
+ 199,
+ 639
+ ],
+ "score": 1.0,
+ "content": "networks EUcore-top (",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 199,
+ 627,
+ 236,
+ 637
+ ],
+ "score": 0.87,
+ "content": "N = 3 4 8",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 236,
+ 626,
+ 240,
+ 639
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 240,
+ 627,
+ 280,
+ 637
+ ],
+ "score": 0.87,
+ "content": "E = 3 3 4 2",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 280,
+ 626,
+ 285,
+ 639
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 285,
+ 627,
+ 312,
+ 637
+ ],
+ "score": 0.88,
+ "content": "K = 5",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 313,
+ 626,
+ 365,
+ 639
+ ],
+ "score": 1.0,
+ "content": ") and Enron (",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 365,
+ 627,
+ 402,
+ 637
+ ],
+ "score": 0.86,
+ "content": "N = 1 5 4",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 402,
+ 626,
+ 406,
+ 639
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 406,
+ 627,
+ 447,
+ 637
+ ],
+ "score": 0.84,
+ "content": "E = 1 8 4 3",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 447,
+ 626,
+ 451,
+ 639
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 451,
+ 627,
+ 479,
+ 638
+ ],
+ "score": 0.81,
+ "content": "K = 3",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 479,
+ 626,
+ 506,
+ 639
+ ],
+ "score": 1.0,
+ "content": "). The",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 105,
+ 638,
+ 506,
+ 651
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 638,
+ 203,
+ 651
+ ],
+ "score": 1.0,
+ "content": "other dataset Cora-ML",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 204,
+ 638,
+ 245,
+ 649
+ ],
+ "score": 0.84,
+ "content": "N = 2 8 1 0",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 246,
+ 638,
+ 249,
+ 651
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 249,
+ 638,
+ 289,
+ 649
+ ],
+ "score": 0.84,
+ "content": "E = 7 9 8 1",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 290,
+ 638,
+ 294,
+ 651
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 294,
+ 639,
+ 321,
+ 649
+ ],
+ "score": 0.84,
+ "content": "K = 7",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 321,
+ 638,
+ 506,
+ 651
+ ],
+ "score": 1.0,
+ "content": ") is a commonly used subset of a large author",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ },
+ {
+ "bbox": [
+ 105,
+ 648,
+ 506,
+ 663
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 648,
+ 506,
+ 663
+ ],
+ "score": 1.0,
+ "content": "citation dataset. We provide the links to datasets used in our experiments (see Appendix for details).",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ }
+ ],
+ "index": 43
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 666,
+ 505,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 665,
+ 505,
+ 678
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 665,
+ 505,
+ 678
+ ],
+ "score": 1.0,
+ "content": "We study communication networks: (1) EUcore-top is a network that consists of the top five largest",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 105,
+ 676,
+ 505,
+ 690
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 676,
+ 505,
+ 690
+ ],
+ "score": 1.0,
+ "content": "departments in the EUcore email dataset that was created using anonymized emails from a large",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "score": 1.0,
+ "content": "European research institution. (2) Enron is a dataset of the Enron email corpus where nodes are",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ },
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "score": 1.0,
+ "content": "employees labeled according to their department information. The citation network: (3) Cora-ML is",
+ "type": "text"
+ }
+ ],
+ "index": 49
+ },
+ {
+ "bbox": [
+ 104,
+ 709,
+ 506,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 709,
+ 506,
+ 722
+ ],
+ "score": 1.0,
+ "content": "a popular benchmark citation dataset. Nodes labeled according to their paper topic are authors, and",
+ "type": "text"
+ }
+ ],
+ "index": 50
+ },
+ {
+ "bbox": [
+ 105,
+ 720,
+ 397,
+ 734
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 720,
+ 397,
+ 734
+ ],
+ "score": 1.0,
+ "content": "edges between them indicate that an author cited another author’s paper.",
+ "type": "text"
+ }
+ ],
+ "index": 51
+ }
+ ],
+ "index": 48.5
+ }
+ ],
+ "page_idx": 5,
+ "page_size": [
+ 612,
+ 792
+ ],
+ "discarded_blocks": [
+ {
+ "type": "discarded",
+ "bbox": [
+ 302,
+ 752,
+ 308,
+ 760
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 302,
+ 751,
+ 309,
+ 762
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 302,
+ 751,
+ 309,
+ 762
+ ],
+ "score": 1.0,
+ "content": "6",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ },
+ {
+ "type": "discarded",
+ "bbox": [
+ 107,
+ 27,
+ 307,
+ 37
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 308,
+ 38
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 26,
+ 308,
+ 38
+ ],
+ "score": 1.0,
+ "content": "Under review as a conference paper at ICLR 2021",
+ "type": "text"
+ }
+ ]
+ }
+ ]
+ }
+ ],
+ "para_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 82,
+ 504,
+ 105
+ ],
+ "lines": [],
+ "index": 0.5,
+ "bbox_fs": [
+ 105,
+ 82,
+ 505,
+ 106
+ ],
+ "lines_deleted": true
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 110,
+ 505,
+ 209
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 111,
+ 505,
+ 123
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 111,
+ 505,
+ 123
+ ],
+ "score": 1.0,
+ "content": "Recently, some works in graph generation have started exploring network structures of various con-",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 105,
+ 121,
+ 505,
+ 134
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 121,
+ 505,
+ 134
+ ],
+ "score": 1.0,
+ "content": "ditions. These works employ graph-level condition information. In one work, Li et al. (2018)",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 132,
+ 505,
+ 145
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 132,
+ 505,
+ 145
+ ],
+ "score": 1.0,
+ "content": "produce some conditional generation results, where the conditions are graph properties such as the",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 105,
+ 143,
+ 505,
+ 156
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 143,
+ 505,
+ 156
+ ],
+ "score": 1.0,
+ "content": "number of nodes and edges. Another work, CondGEN (Yang et al., 2019), injects semantics into the",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 105,
+ 154,
+ 505,
+ 167
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 154,
+ 505,
+ 167
+ ],
+ "score": 1.0,
+ "content": "graphs by conditioning the model on supplementary contextual information. The model mainly con-",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
+ 105,
+ 165,
+ 505,
+ 178
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 165,
+ 505,
+ 178
+ ],
+ "score": 1.0,
+ "content": "siders multiple small graphs, each with an accompanying semantic condition to learn a distribution",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 175,
+ 506,
+ 190
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 175,
+ 506,
+ 190
+ ],
+ "score": 1.0,
+ "content": "over graphs. While GraphRNN (You et al., 2018) is not a direct conditional model, it decomposes",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 187,
+ 505,
+ 201
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 187,
+ 505,
+ 201
+ ],
+ "score": 1.0,
+ "content": "the generative process into sequences of nodes and edges, which potentially allows for explicit con-",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 198,
+ 462,
+ 212
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 198,
+ 462,
+ 212
+ ],
+ "score": 1.0,
+ "content": "ditioning. However, these methods only generate graphs mimicking the observed graphs.",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ }
+ ],
+ "index": 6,
+ "bbox_fs": [
+ 105,
+ 111,
+ 506,
+ 212
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 215,
+ 505,
+ 281
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 214,
+ 505,
+ 228
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 214,
+ 505,
+ 228
+ ],
+ "score": 1.0,
+ "content": "To allow state manipulation and controllable graph generation, our model borrows the concept",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 106,
+ 226,
+ 505,
+ 238
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 226,
+ 505,
+ 238
+ ],
+ "score": 1.0,
+ "content": "from NetGAN (Bojchevski et al., 2018), which adapts the standard LSTM to learn a distribution",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 235,
+ 507,
+ 250
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 235,
+ 507,
+ 250
+ ],
+ "score": 1.0,
+ "content": "of random walks and exploit sparsity in real-world graphs. In contrast to NetGAN, we integrate a",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 247,
+ 505,
+ 260
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 247,
+ 505,
+ 260
+ ],
+ "score": 1.0,
+ "content": "condition-based control mechanism to learn a model that generates explainable graphs. Due to the",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 259,
+ 505,
+ 271
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 259,
+ 505,
+ 271
+ ],
+ "score": 1.0,
+ "content": "challenging nature of the problem, to the best of our knowledge, no work has definitively considered",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ },
+ {
+ "bbox": [
+ 105,
+ 270,
+ 264,
+ 281
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 270,
+ 264,
+ 281
+ ],
+ "score": 1.0,
+ "content": "shaping graphs into new desired states.",
+ "type": "text"
+ }
+ ],
+ "index": 16
+ }
+ ],
+ "index": 13.5,
+ "bbox_fs": [
+ 105,
+ 214,
+ 507,
+ 281
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 293,
+ 505,
+ 403
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 292,
+ 505,
+ 306
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 292,
+ 505,
+ 306
+ ],
+ "score": 1.0,
+ "content": "Explainable AI Explainable AI studies the task of improving the interpretability of AI systems.",
+ "type": "text"
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 105,
+ 304,
+ 504,
+ 317
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 304,
+ 504,
+ 317
+ ],
+ "score": 1.0,
+ "content": "While proxy model methods (Huysmans et al., 2011; Augasta & Kathirvalavakumar, 2011; Zilke",
+ "type": "text"
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
+ 104,
+ 313,
+ 505,
+ 329
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 313,
+ 505,
+ 329
+ ],
+ "score": 1.0,
+ "content": "et al., 2016; Lakkaraju et al., 2017) often resort to learning local approximations of predictions using",
+ "type": "text"
+ }
+ ],
+ "index": 19
+ },
+ {
+ "bbox": [
+ 105,
+ 326,
+ 504,
+ 339
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 326,
+ 504,
+ 339
+ ],
+ "score": 1.0,
+ "content": "sets of rules in applying conditions on the prediction, advances in interpretability methods (Adadi",
+ "type": "text"
+ }
+ ],
+ "index": 20
+ },
+ {
+ "bbox": [
+ 105,
+ 337,
+ 505,
+ 349
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 337,
+ 505,
+ 349
+ ],
+ "score": 1.0,
+ "content": "& Berrada, 2018; Guidotti et al., 2018; Koh & Liang, 2017) treat black-box models as such and",
+ "type": "text"
+ }
+ ],
+ "index": 21
+ },
+ {
+ "bbox": [
+ 105,
+ 348,
+ 505,
+ 361
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 348,
+ 505,
+ 361
+ ],
+ "score": 1.0,
+ "content": "query them for information. Among the many recently developed interpretable models, Graph Neu-",
+ "type": "text"
+ }
+ ],
+ "index": 22
+ },
+ {
+ "bbox": [
+ 105,
+ 358,
+ 506,
+ 372
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 358,
+ 506,
+ 372
+ ],
+ "score": 1.0,
+ "content": "ral Network (GNN) models have been studied to explain predictions on graph-structured data via",
+ "type": "text"
+ }
+ ],
+ "index": 23
+ },
+ {
+ "bbox": [
+ 105,
+ 369,
+ 505,
+ 384
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 369,
+ 505,
+ 384
+ ],
+ "score": 1.0,
+ "content": "attention mechanisms (Velickovi ˇ c et al., 2018; Neil et al., 2018; Xie & Grossman, 2018). These ap- ´",
+ "type": "text"
+ }
+ ],
+ "index": 24
+ },
+ {
+ "bbox": [
+ 105,
+ 381,
+ 504,
+ 394
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 381,
+ 504,
+ 394
+ ],
+ "score": 1.0,
+ "content": "proaches learn important graph structures by predicting and assigning attention values to the edges.",
+ "type": "text"
+ }
+ ],
+ "index": 25
+ },
+ {
+ "bbox": [
+ 106,
+ 390,
+ 502,
+ 405
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 390,
+ 502,
+ 405
+ ],
+ "score": 1.0,
+ "content": "The attention values are the same for all nodes in the same structure, limiting the predictive power.",
+ "type": "text"
+ }
+ ],
+ "index": 26
+ }
+ ],
+ "index": 21.5,
+ "bbox_fs": [
+ 104,
+ 292,
+ 506,
+ 405
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 409,
+ 505,
+ 464
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 409,
+ 505,
+ 421
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 409,
+ 505,
+ 421
+ ],
+ "score": 1.0,
+ "content": "Moreover, these models cannot explain predictions by combining node feature information with",
+ "type": "text"
+ }
+ ],
+ "index": 27
+ },
+ {
+ "bbox": [
+ 106,
+ 420,
+ 505,
+ 432
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 420,
+ 505,
+ 432
+ ],
+ "score": 1.0,
+ "content": "the graph structure. To circumvent the limitations of attention-based GNN models, GNNEx-",
+ "type": "text"
+ }
+ ],
+ "index": 28
+ },
+ {
+ "bbox": [
+ 105,
+ 430,
+ 505,
+ 444
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 430,
+ 505,
+ 444
+ ],
+ "score": 1.0,
+ "content": "plainer (Ying et al., 2019) considers both graph structure and node features to explain predictions.",
+ "type": "text"
+ }
+ ],
+ "index": 29
+ },
+ {
+ "bbox": [
+ 105,
+ 441,
+ 505,
+ 455
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 441,
+ 505,
+ 455
+ ],
+ "score": 1.0,
+ "content": "However, explainable GNN models identify explanations in graph structures and node features,",
+ "type": "text"
+ }
+ ],
+ "index": 30
+ },
+ {
+ "bbox": [
+ 106,
+ 453,
+ 485,
+ 465
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 453,
+ 485,
+ 465
+ ],
+ "score": 1.0,
+ "content": "which are suitable for link prediction, node/graph classification tasks but not graph generation.",
+ "type": "text"
+ }
+ ],
+ "index": 31
+ }
+ ],
+ "index": 29,
+ "bbox_fs": [
+ 105,
+ 409,
+ 505,
+ 465
+ ]
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 108,
+ 480,
+ 200,
+ 492
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 479,
+ 201,
+ 495
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 479,
+ 201,
+ 495
+ ],
+ "score": 1.0,
+ "content": "4 EXPERIMENTS",
+ "type": "text"
+ }
+ ],
+ "index": 32
+ }
+ ],
+ "index": 32
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 505,
+ 505,
+ 593
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 504,
+ 505,
+ 518
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 504,
+ 505,
+ 518
+ ],
+ "score": 1.0,
+ "content": "In this section, we first compare and evaluate our approach with other baseline graph generation",
+ "type": "text"
+ }
+ ],
+ "index": 33
+ },
+ {
+ "bbox": [
+ 105,
+ 516,
+ 505,
+ 528
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 516,
+ 505,
+ 528
+ ],
+ "score": 1.0,
+ "content": "methods on three datasets to establish our model’s ability to generate high-quality graphs of complex",
+ "type": "text"
+ }
+ ],
+ "index": 34
+ },
+ {
+ "bbox": [
+ 105,
+ 527,
+ 505,
+ 539
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 527,
+ 505,
+ 539
+ ],
+ "score": 1.0,
+ "content": "networks. Next, we demonstrate the explainability of SHADOWCAST by controlling the generative",
+ "type": "text"
+ }
+ ],
+ "index": 35
+ },
+ {
+ "bbox": [
+ 104,
+ 537,
+ 505,
+ 552
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 537,
+ 505,
+ 552
+ ],
+ "score": 1.0,
+ "content": "process to create graphs according to specification. Note that generating graphs mimicking any",
+ "type": "text"
+ }
+ ],
+ "index": 36
+ },
+ {
+ "bbox": [
+ 105,
+ 549,
+ 506,
+ 561
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 549,
+ 506,
+ 561
+ ],
+ "score": 1.0,
+ "content": "given graph as closely as possible is not our goal. Our objective is to introduce a more explainable",
+ "type": "text"
+ }
+ ],
+ "index": 37
+ },
+ {
+ "bbox": [
+ 105,
+ 559,
+ 506,
+ 572
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 559,
+ 506,
+ 572
+ ],
+ "score": 1.0,
+ "content": "graph generative approach. Through our experiments, we not only demonstrate that SHADOWCAST",
+ "type": "text"
+ }
+ ],
+ "index": 38
+ },
+ {
+ "bbox": [
+ 105,
+ 570,
+ 506,
+ 584
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 570,
+ 506,
+ 584
+ ],
+ "score": 1.0,
+ "content": "exhibits competitive performance in the task of graph generation, but we also show that our model",
+ "type": "text"
+ }
+ ],
+ "index": 39
+ },
+ {
+ "bbox": [
+ 105,
+ 582,
+ 432,
+ 594
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 582,
+ 432,
+ 594
+ ],
+ "score": 1.0,
+ "content": "can generate graphs of different density distributions by controlling the shadows.",
+ "type": "text"
+ }
+ ],
+ "index": 40
+ }
+ ],
+ "index": 36.5,
+ "bbox_fs": [
+ 104,
+ 504,
+ 506,
+ 594
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 605,
+ 504,
+ 660
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 605,
+ 505,
+ 617
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 605,
+ 505,
+ 617
+ ],
+ "score": 1.0,
+ "content": "Datasets We consider three real-world graphs in social and information networks, where each",
+ "type": "text"
+ }
+ ],
+ "index": 41
+ },
+ {
+ "bbox": [
+ 106,
+ 616,
+ 505,
+ 628
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 616,
+ 505,
+ 628
+ ],
+ "score": 1.0,
+ "content": "node belongs to one of the ground-truth communities. Two of the datasets are email communication",
+ "type": "text"
+ }
+ ],
+ "index": 42
+ },
+ {
+ "bbox": [
+ 105,
+ 626,
+ 506,
+ 639
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 626,
+ 199,
+ 639
+ ],
+ "score": 1.0,
+ "content": "networks EUcore-top (",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 199,
+ 627,
+ 236,
+ 637
+ ],
+ "score": 0.87,
+ "content": "N = 3 4 8",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 236,
+ 626,
+ 240,
+ 639
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 240,
+ 627,
+ 280,
+ 637
+ ],
+ "score": 0.87,
+ "content": "E = 3 3 4 2",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 280,
+ 626,
+ 285,
+ 639
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 285,
+ 627,
+ 312,
+ 637
+ ],
+ "score": 0.88,
+ "content": "K = 5",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 313,
+ 626,
+ 365,
+ 639
+ ],
+ "score": 1.0,
+ "content": ") and Enron (",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 365,
+ 627,
+ 402,
+ 637
+ ],
+ "score": 0.86,
+ "content": "N = 1 5 4",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 402,
+ 626,
+ 406,
+ 639
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 406,
+ 627,
+ 447,
+ 637
+ ],
+ "score": 0.84,
+ "content": "E = 1 8 4 3",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 447,
+ 626,
+ 451,
+ 639
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 451,
+ 627,
+ 479,
+ 638
+ ],
+ "score": 0.81,
+ "content": "K = 3",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 479,
+ 626,
+ 506,
+ 639
+ ],
+ "score": 1.0,
+ "content": "). The",
+ "type": "text"
+ }
+ ],
+ "index": 43
+ },
+ {
+ "bbox": [
+ 105,
+ 638,
+ 506,
+ 651
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 638,
+ 203,
+ 651
+ ],
+ "score": 1.0,
+ "content": "other dataset Cora-ML",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 204,
+ 638,
+ 245,
+ 649
+ ],
+ "score": 0.84,
+ "content": "N = 2 8 1 0",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 246,
+ 638,
+ 249,
+ 651
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 249,
+ 638,
+ 289,
+ 649
+ ],
+ "score": 0.84,
+ "content": "E = 7 9 8 1",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 290,
+ 638,
+ 294,
+ 651
+ ],
+ "score": 1.0,
+ "content": ",",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 294,
+ 639,
+ 321,
+ 649
+ ],
+ "score": 0.84,
+ "content": "K = 7",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 321,
+ 638,
+ 506,
+ 651
+ ],
+ "score": 1.0,
+ "content": ") is a commonly used subset of a large author",
+ "type": "text"
+ }
+ ],
+ "index": 44
+ },
+ {
+ "bbox": [
+ 105,
+ 648,
+ 506,
+ 663
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 648,
+ 506,
+ 663
+ ],
+ "score": 1.0,
+ "content": "citation dataset. We provide the links to datasets used in our experiments (see Appendix for details).",
+ "type": "text"
+ }
+ ],
+ "index": 45
+ }
+ ],
+ "index": 43,
+ "bbox_fs": [
+ 105,
+ 605,
+ 506,
+ 663
+ ]
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 107,
+ 666,
+ 505,
+ 732
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 665,
+ 505,
+ 678
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 665,
+ 505,
+ 678
+ ],
+ "score": 1.0,
+ "content": "We study communication networks: (1) EUcore-top is a network that consists of the top five largest",
+ "type": "text"
+ }
+ ],
+ "index": 46
+ },
+ {
+ "bbox": [
+ 105,
+ 676,
+ 505,
+ 690
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 676,
+ 505,
+ 690
+ ],
+ "score": 1.0,
+ "content": "departments in the EUcore email dataset that was created using anonymized emails from a large",
+ "type": "text"
+ }
+ ],
+ "index": 47
+ },
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 687,
+ 505,
+ 700
+ ],
+ "score": 1.0,
+ "content": "European research institution. (2) Enron is a dataset of the Enron email corpus where nodes are",
+ "type": "text"
+ }
+ ],
+ "index": 48
+ },
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 699,
+ 505,
+ 711
+ ],
+ "score": 1.0,
+ "content": "employees labeled according to their department information. The citation network: (3) Cora-ML is",
+ "type": "text"
+ }
+ ],
+ "index": 49
+ },
+ {
+ "bbox": [
+ 104,
+ 709,
+ 506,
+ 722
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 104,
+ 709,
+ 506,
+ 722
+ ],
+ "score": 1.0,
+ "content": "a popular benchmark citation dataset. Nodes labeled according to their paper topic are authors, and",
+ "type": "text"
+ }
+ ],
+ "index": 50
+ },
+ {
+ "bbox": [
+ 105,
+ 720,
+ 397,
+ 734
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 720,
+ 397,
+ 734
+ ],
+ "score": 1.0,
+ "content": "edges between them indicate that an author cited another author’s paper.",
+ "type": "text"
+ }
+ ],
+ "index": 51
+ }
+ ],
+ "index": 48.5,
+ "bbox_fs": [
+ 104,
+ 665,
+ 506,
+ 734
+ ]
+ }
+ ]
+ },
+ {
+ "preproc_blocks": [
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 82,
+ 505,
+ 159
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 82,
+ 506,
+ 96
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 82,
+ 506,
+ 96
+ ],
+ "score": 1.0,
+ "content": "Baselines Since controlling the generative process to provide explainable graph generation is a",
+ "type": "text"
+ }
+ ],
+ "index": 0
+ },
+ {
+ "bbox": [
+ 105,
+ 94,
+ 505,
+ 106
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 94,
+ 505,
+ 106
+ ],
+ "score": 1.0,
+ "content": "novel task, and no such method is developed, we compare our approach against four current state-",
+ "type": "text"
+ }
+ ],
+ "index": 1
+ },
+ {
+ "bbox": [
+ 105,
+ 103,
+ 505,
+ 118
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 103,
+ 505,
+ 118
+ ],
+ "score": 1.0,
+ "content": "of-the-art graph generation baseline methods—GraphRNN (You et al., 2018), GVAE (Simonovsky",
+ "type": "text"
+ }
+ ],
+ "index": 2
+ },
+ {
+ "bbox": [
+ 106,
+ 116,
+ 505,
+ 127
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 116,
+ 505,
+ 127
+ ],
+ "score": 1.0,
+ "content": "& Komodakis, 2018), NetGAN (Bojchevski et al., 2018), and CondGEN (Yang et al., 2019). We",
+ "type": "text"
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
+ 105,
+ 126,
+ 505,
+ 140
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 126,
+ 171,
+ 140
+ ],
+ "score": 1.0,
+ "content": "randomly select",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 171,
+ 126,
+ 191,
+ 137
+ ],
+ "score": 0.88,
+ "content": "8 5 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 191,
+ 126,
+ 429,
+ 140
+ ],
+ "score": 1.0,
+ "content": "of the edges in each graph for training and use the remaining",
+ "type": "text"
+ },
+ {
+ "bbox": [
+ 429,
+ 126,
+ 449,
+ 137
+ ],
+ "score": 0.88,
+ "content": "1 5 \\%",
+ "type": "inline_equation"
+ },
+ {
+ "bbox": [
+ 449,
+ 126,
+ 505,
+ 140
+ ],
+ "score": 1.0,
+ "content": "for validation",
+ "type": "text"
+ }
+ ],
+ "index": 4
+ },
+ {
+ "bbox": [
+ 106,
+ 137,
+ 505,
+ 150
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 137,
+ 505,
+ 150
+ ],
+ "score": 1.0,
+ "content": "and testing. We refer readers to the Appendix for more details about the model implementation",
+ "type": "text"
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 106,
+ 149,
+ 414,
+ 161
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 149,
+ 414,
+ 161
+ ],
+ "score": 1.0,
+ "content": "settings, baseline models, datasets, and explainable generated visualizations.",
+ "type": "text"
+ }
+ ],
+ "index": 6
+ }
+ ],
+ "index": 3
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 106,
+ 173,
+ 505,
+ 272
+ ],
+ "lines": [
+ {
+ "bbox": [
+ 105,
+ 173,
+ 505,
+ 186
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 173,
+ 505,
+ 186
+ ],
+ "score": 1.0,
+ "content": "Performance We evaluate SHADOWCAST against existing benchmark generative models (You",
+ "type": "text"
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
+ 105,
+ 183,
+ 505,
+ 197
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 183,
+ 505,
+ 197
+ ],
+ "score": 1.0,
+ "content": "et al., 2018; Simonovsky & Komodakis, 2018; Bojchevski et al., 2018; Yang et al., 2019) and present",
+ "type": "text"
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 105,
+ 194,
+ 506,
+ 209
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 194,
+ 506,
+ 209
+ ],
+ "score": 1.0,
+ "content": "the comparison statistics 1 (Table 1). By comparing the statistics of the real graphs and those gen-",
+ "type": "text"
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
+ 105,
+ 206,
+ 505,
+ 219
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 206,
+ 505,
+ 219
+ ],
+ "score": 1.0,
+ "content": "erated by each method, closer mean values indicate greater resemblance to the original graphs, thus",
+ "type": "text"
+ }
+ ],
+ "index": 10
+ },
+ {
+ "bbox": [
+ 106,
+ 217,
+ 505,
+ 230
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 217,
+ 505,
+ 230
+ ],
+ "score": 1.0,
+ "content": "better performance. In general, baseline methods succeed at replicating the graphs that are directly",
+ "type": "text"
+ }
+ ],
+ "index": 11
+ },
+ {
+ "bbox": [
+ 106,
+ 228,
+ 505,
+ 241
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 228,
+ 505,
+ 241
+ ],
+ "score": 1.0,
+ "content": "modeled. Unsurprisingly, GVAE, designed for generating small graphs, performs well in the smaller",
+ "type": "text"
+ }
+ ],
+ "index": 12
+ },
+ {
+ "bbox": [
+ 105,
+ 238,
+ 506,
+ 252
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 238,
+ 506,
+ 252
+ ],
+ "score": 1.0,
+ "content": "Enron and EUcore-top datasets. However, it does not recover statistics of the larger graph Cora-ML",
+ "type": "text"
+ }
+ ],
+ "index": 13
+ },
+ {
+ "bbox": [
+ 105,
+ 249,
+ 505,
+ 263
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 249,
+ 505,
+ 263
+ ],
+ "score": 1.0,
+ "content": "well. On the other hand, our model captures all graph properties of the datasets, especially excelling",
+ "type": "text"
+ }
+ ],
+ "index": 14
+ },
+ {
+ "bbox": [
+ 105,
+ 261,
+ 475,
+ 273
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 105,
+ 261,
+ 475,
+ 273
+ ],
+ "score": 1.0,
+ "content": "in preserving properties of larger graphs, as shown in its generation of the Cora-ML dataset.",
+ "type": "text"
+ }
+ ],
+ "index": 15
+ }
+ ],
+ "index": 11
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 106,
+ 282,
+ 504,
+ 435
+ ],
+ "blocks": [
+ {
+ "type": "table_body",
+ "bbox": [
+ 106,
+ 282,
+ 504,
+ 435
+ ],
+ "group_id": 0,
+ "lines": [
+ {
+ "bbox": [
+ 106,
+ 282,
+ 504,
+ 435
+ ],
+ "spans": [
+ {
+ "bbox": [
+ 106,
+ 282,
+ 504,
+ 435
+ ],
+ "score": 0.982,
+ "html": "| Algorithm1Minibatch stochastic gradient descent training of explainable graph generative adver- sarial nets.The number of steps to apply to the generator, w,is a hyperparameter.We used ω = 3. |
| 1:for number of training iterations do | |
| 2: | Sample minibatch of m samples {e(1),..,x(m)} from data distribution pdata |
| 3: 4: 5: | Sample the respective m shadow walks {s(1),...,s(m)} Update S model weights: |
| m K 0m M £ s(e) log S(s()] i=1 =1 |
| 6: 7: | Generate minibatch of m shadow walks {s(1),...,s(m)} with model S |
| 8: | Sample minibatch of m noise samples {z(1),..,z(m)} from N(0,Id) Update G model weights: |
| 9: | |
| 10: | M 0gm 1 [log(1-D(G(z(𝑖)|s()))] =1 |
| 11: 12: | for w steps do Update D model weights: |
| m 1 |
| 13: | 0dm ∑[logD(x(i) | g(𝑖) + log(1-D(G(z(𝑖)|s(i)))] =1 |
| 14: end for | end for |
| |
"
+ },
+ {
+ "category_id": 8,
+ "poly": [
+ 573,
+ 469,
+ 1126,
+ 469,
+ 1126,
+ 508,
+ 573,
+ 508
+ ],
+ "score": 0.868
+ },
+ {
+ "category_id": 9,
+ "poly": [
+ 1366,
+ 474,
+ 1399,
+ 474,
+ 1399,
+ 503,
+ 1366,
+ 503
+ ],
+ "score": 0.863
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 299,
+ 75,
+ 854,
+ 75,
+ 854,
+ 104,
+ 299,
+ 104
+ ],
+ "score": 0.777
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 841,
+ 2089,
+ 858,
+ 2089,
+ 858,
+ 2111,
+ 841,
+ 2111
+ ],
+ "score": 0.767
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 300,
+ 76,
+ 852,
+ 76,
+ 852,
+ 104,
+ 300,
+ 104
+ ],
+ "score": 0.344
+ },
+ {
+ "category_id": 8,
+ "poly": [
+ 572,
+ 469,
+ 1126,
+ 469,
+ 1126,
+ 508,
+ 572,
+ 508
+ ],
+ "score": 0.168
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 375,
+ 2002,
+ 542,
+ 2002,
+ 542,
+ 2036,
+ 375,
+ 2036
+ ],
+ "score": 0.94,
+ "latex": "\\mathbf { \\boldsymbol { z } } \\sim \\mathcal { N } ( \\mathbf { 0 } , \\mathbf { \\boldsymbol { I } } _ { d } )"
+ },
+ {
+ "category_id": 14,
+ "poly": [
+ 696,
+ 1241,
+ 1040,
+ 1241,
+ 1040,
+ 1297,
+ 696,
+ 1297
+ ],
+ "score": 0.93,
+ "latex": "\\nabla _ { \\theta _ { g } } \\frac { 1 } { m } \\sum _ { i = 1 } ^ { m } [ \\log ( 1 - D ( G ( z ^ { ( i ) } \\mid \\tilde { \\pmb { s } } ^ { ( i ) } ) ) ) ]"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1117,
+ 1894,
+ 1313,
+ 1894,
+ 1313,
+ 1928,
+ 1117,
+ 1928
+ ],
+ "score": 0.93,
+ "latex": "\\mathbf { } \\mathbf { v } _ { t } \\sim C a t ( \\sigma ( \\mathbf { p } _ { t } ) )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 298,
+ 591,
+ 484,
+ 591,
+ 484,
+ 627,
+ 298,
+ 627
+ ],
+ "score": 0.93,
+ "latex": "\\pmb { A } \\in \\{ 0 , 1 \\} ^ { N \\times N }"
+ },
+ {
+ "category_id": 14,
+ "poly": [
+ 720,
+ 1078,
+ 1016,
+ 1078,
+ 1016,
+ 1137,
+ 720,
+ 1137
+ ],
+ "score": 0.93,
+ "latex": "\\nabla _ { \\boldsymbol { \\theta _ { s } } } \\frac { 1 } { m } \\sum _ { i = 1 } ^ { m } [ - \\sum _ { c = 1 } ^ { K } \\pmb { s } ^ { ( c ) } \\log \\pmb { S } ( \\pmb { s } ^ { ( c ) } ) ]"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1096,
+ 2003,
+ 1170,
+ 2003,
+ 1170,
+ 2036,
+ 1096,
+ 2036
+ ],
+ "score": 0.93,
+ "latex": "g _ { \\theta ^ { \\prime } } ( z )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 374,
+ 532,
+ 551,
+ 532,
+ 551,
+ 566,
+ 374,
+ 566
+ ],
+ "score": 0.92,
+ "latex": "\\boldsymbol { z } \\sim \\mathcal { N } ( \\mathbf { 0 } , \\boldsymbol { I } _ { d } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1293,
+ 1834,
+ 1393,
+ 1834,
+ 1393,
+ 1868,
+ 1293,
+ 1868
+ ],
+ "score": 0.92,
+ "latex": "( p _ { t } , m _ { t } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 460,
+ 1648,
+ 602,
+ 1648,
+ 602,
+ 1680,
+ 460,
+ 1680
+ ],
+ "score": 0.91,
+ "latex": "( \\pmb { s } _ { 1 } , \\dots , \\pmb { s } _ { T } )"
+ },
+ {
+ "category_id": 14,
+ "poly": [
+ 605,
+ 1366,
+ 1131,
+ 1366,
+ 1131,
+ 1424,
+ 605,
+ 1424
+ ],
+ "score": 0.91,
+ "latex": "\\nabla _ { \\theta _ { d } } \\frac { 1 } { m } \\sum _ { i = 1 } ^ { m } [ \\log D ( { \\pmb x } ^ { ( i ) } \\mid \\tilde { { \\pmb s } } ^ { ( i ) } ) + \\log ( 1 - D ( G ( { \\pmb z } ^ { ( i ) } \\mid \\tilde { { \\pmb s } } ^ { ( i ) } ) ) ) ]"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 710,
+ 1927,
+ 758,
+ 1927,
+ 758,
+ 1959,
+ 710,
+ 1959
+ ],
+ "score": 0.91,
+ "latex": "\\sigma ( \\cdot )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 533,
+ 1774,
+ 740,
+ 1774,
+ 740,
+ 1806,
+ 533,
+ 1806
+ ],
+ "score": 0.91,
+ "latex": "( { \\pmb v } _ { 1 } , \\dots , { \\pmb v } _ { T } ) \\sim G"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1027,
+ 1173,
+ 1110,
+ 1173,
+ 1110,
+ 1197,
+ 1027,
+ 1197
+ ],
+ "score": 0.9,
+ "latex": "\\mathcal { N } ( \\mathbf { 0 } , \\pmb { I } _ { d } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 772,
+ 978,
+ 927,
+ 978,
+ 927,
+ 1006,
+ 772,
+ 1006
+ ],
+ "score": 0.9,
+ "latex": "\\{ \\pmb { x } ^ { ( 1 ) } , \\ldots , \\pmb { x } ^ { ( m ) } \\}"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1040,
+ 1808,
+ 1110,
+ 1808,
+ 1110,
+ 1835,
+ 1040,
+ 1835
+ ],
+ "score": 0.89,
+ "latex": "_ { { \\mathbf { } } m _ { t - 1 } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 867,
+ 1838,
+ 923,
+ 1838,
+ 923,
+ 1867,
+ 867,
+ 1867
+ ],
+ "score": 0.89,
+ "latex": "{ \\mathbf { } } v _ { t - 1 }"
+ },
+ {
+ "category_id": 14,
+ "poly": [
+ 573,
+ 468,
+ 1126,
+ 468,
+ 1126,
+ 508,
+ 573,
+ 508
+ ],
+ "score": 0.89,
+ "latex": "\\mathcal { L } _ { c g a n } = \\log ( D ( \\pmb { x } \\mid \\pmb { s } ) ) + \\log ( 1 - D ( G ( \\pmb { z } \\mid \\pmb { s } ) ) )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 838,
+ 1143,
+ 987,
+ 1143,
+ 987,
+ 1169,
+ 838,
+ 1169
+ ],
+ "score": 0.89,
+ "latex": "\\{ \\tilde { s } ^ { ( 1 ) } , \\ldots , \\tilde { s } ^ { ( m ) } \\}"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 834,
+ 1006,
+ 983,
+ 1006,
+ 983,
+ 1034,
+ 834,
+ 1034
+ ],
+ "score": 0.89,
+ "latex": "\\{ s ^ { ( 1 ) } , \\ldots , s ^ { ( m ) } \\}"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 461,
+ 1681,
+ 604,
+ 1681,
+ 604,
+ 1712,
+ 461,
+ 1712
+ ],
+ "score": 0.89,
+ "latex": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 825,
+ 1170,
+ 975,
+ 1170,
+ 975,
+ 1197,
+ 825,
+ 1197
+ ],
+ "score": 0.88,
+ "latex": "\\{ z ^ { ( 1 ) } , \\dots , z ^ { ( m ) } \\}"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 636,
+ 1835,
+ 664,
+ 1835,
+ 664,
+ 1865,
+ 636,
+ 1865
+ ],
+ "score": 0.88,
+ "latex": "\\tilde { \\mathbf { \\ b { s } } } _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 553,
+ 1199,
+ 571,
+ 1199,
+ 571,
+ 1215,
+ 553,
+ 1215
+ ],
+ "score": 0.87,
+ "latex": "G"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 672,
+ 1180,
+ 692,
+ 1180,
+ 692,
+ 1191,
+ 672,
+ 1191
+ ],
+ "score": 0.86,
+ "latex": "m"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 618,
+ 1899,
+ 646,
+ 1899,
+ 646,
+ 1926,
+ 618,
+ 1926
+ ],
+ "score": 0.86,
+ "latex": "{ \\mathbf { } } v _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1210,
+ 920,
+ 1267,
+ 920,
+ 1267,
+ 942,
+ 1210,
+ 942
+ ],
+ "score": 0.85,
+ "latex": "\\omega = 3"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1124,
+ 1869,
+ 1165,
+ 1869,
+ 1165,
+ 1895,
+ 1124,
+ 1895
+ ],
+ "score": 0.85,
+ "latex": "{ \\mathbf { } } m _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 552,
+ 1035,
+ 569,
+ 1035,
+ 569,
+ 1052,
+ 552,
+ 1052
+ ],
+ "score": 0.85,
+ "latex": "S"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 374,
+ 1869,
+ 405,
+ 1869,
+ 405,
+ 1896,
+ 374,
+ 1896
+ ],
+ "score": 0.84,
+ "latex": "{ \\mathbf { } } p _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 298,
+ 1805,
+ 326,
+ 1805,
+ 326,
+ 1836,
+ 298,
+ 1836
+ ],
+ "score": 0.84,
+ "latex": "f _ { \\theta }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 527,
+ 1806,
+ 556,
+ 1806,
+ 556,
+ 1836,
+ 527,
+ 1836
+ ],
+ "score": 0.83,
+ "latex": "f _ { \\theta }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 608,
+ 1744,
+ 633,
+ 1744,
+ 633,
+ 1770,
+ 608,
+ 1770
+ ],
+ "score": 0.82,
+ "latex": "G"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 672,
+ 991,
+ 692,
+ 991,
+ 692,
+ 1001,
+ 672,
+ 1001
+ ],
+ "score": 0.82,
+ "latex": "_ { m }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 680,
+ 1017,
+ 701,
+ 1017,
+ 701,
+ 1028,
+ 680,
+ 1028
+ ],
+ "score": 0.82,
+ "latex": "m"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 953,
+ 564,
+ 983,
+ 564,
+ 983,
+ 590,
+ 953,
+ 590
+ ],
+ "score": 0.82,
+ "latex": "N"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1095,
+ 1147,
+ 1111,
+ 1147,
+ 1111,
+ 1164,
+ 1095,
+ 1164
+ ],
+ "score": 0.81,
+ "latex": "S"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 874,
+ 1775,
+ 900,
+ 1775,
+ 900,
+ 1802,
+ 874,
+ 1802
+ ],
+ "score": 0.81,
+ "latex": "G"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1108,
+ 1649,
+ 1130,
+ 1649,
+ 1130,
+ 1675,
+ 1108,
+ 1675
+ ],
+ "score": 0.81,
+ "latex": "S"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 719,
+ 1528,
+ 741,
+ 1528,
+ 741,
+ 1554,
+ 719,
+ 1554
+ ],
+ "score": 0.8,
+ "latex": "S"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 585,
+ 1324,
+ 605,
+ 1324,
+ 605,
+ 1343,
+ 585,
+ 1343
+ ],
+ "score": 0.8,
+ "latex": "D"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 685,
+ 1153,
+ 705,
+ 1153,
+ 705,
+ 1164,
+ 685,
+ 1164
+ ],
+ "score": 0.8,
+ "latex": "m"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1019,
+ 595,
+ 1043,
+ 595,
+ 1043,
+ 621,
+ 1019,
+ 621
+ ],
+ "score": 0.79,
+ "latex": "T"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1128,
+ 1588,
+ 1150,
+ 1588,
+ 1150,
+ 1615,
+ 1128,
+ 1615
+ ],
+ "score": 0.79,
+ "latex": "S"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1106,
+ 595,
+ 1132,
+ 595,
+ 1132,
+ 621,
+ 1106,
+ 621
+ ],
+ "score": 0.73,
+ "latex": "\\pmb { A }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 922,
+ 925,
+ 938,
+ 925,
+ 938,
+ 941,
+ 922,
+ 941
+ ],
+ "score": 0.71,
+ "latex": "\\omega"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 516,
+ 1302,
+ 533,
+ 1302,
+ 533,
+ 1319,
+ 516,
+ 1319
+ ],
+ "score": 0.7,
+ "latex": "\\omega"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 451,
+ 778,
+ 474,
+ 778,
+ 474,
+ 804,
+ 451,
+ 804
+ ],
+ "score": 0.69,
+ "latex": "A"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1380,
+ 599,
+ 1401,
+ 599,
+ 1401,
+ 621,
+ 1380,
+ 621
+ ],
+ "score": 0.68,
+ "latex": "_ { \\textbf { \\em x } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 500,
+ 1807,
+ 514,
+ 1807,
+ 514,
+ 1831,
+ 500,
+ 1831
+ ],
+ "score": 0.63,
+ "latex": "t"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 740,
+ 958,
+ 766,
+ 958,
+ 766,
+ 975,
+ 740,
+ 975
+ ],
+ "score": 0.27,
+ "latex": "\\mathbf { d o }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 557,
+ 656,
+ 582,
+ 656,
+ 582,
+ 683,
+ 557,
+ 683
+ ],
+ "score": 0.27,
+ "latex": "\\&"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 72.0,
+ 857.0,
+ 72.0,
+ 857.0,
+ 108.0,
+ 297.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 838.0,
+ 2086.0,
+ 862.0,
+ 2086.0,
+ 862.0,
+ 2118.0,
+ 838.0,
+ 2118.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 73.0,
+ 856.0,
+ 73.0,
+ 856.0,
+ 108.0,
+ 297.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 527.0,
+ 373.0,
+ 527.0,
+ 373.0,
+ 571.0,
+ 293.0,
+ 571.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 552.0,
+ 527.0,
+ 1404.0,
+ 527.0,
+ 1404.0,
+ 571.0,
+ 552.0,
+ 571.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 564.0,
+ 952.0,
+ 564.0,
+ 952.0,
+ 596.0,
+ 294.0,
+ 596.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 984.0,
+ 564.0,
+ 1402.0,
+ 564.0,
+ 1402.0,
+ 596.0,
+ 984.0,
+ 596.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 583.0,
+ 297.0,
+ 583.0,
+ 297.0,
+ 633.0,
+ 291.0,
+ 633.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 485.0,
+ 583.0,
+ 1018.0,
+ 583.0,
+ 1018.0,
+ 633.0,
+ 485.0,
+ 633.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1044.0,
+ 583.0,
+ 1105.0,
+ 583.0,
+ 1105.0,
+ 633.0,
+ 1044.0,
+ 633.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1133.0,
+ 583.0,
+ 1379.0,
+ 583.0,
+ 1379.0,
+ 633.0,
+ 1133.0,
+ 633.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1402.0,
+ 583.0,
+ 1410.0,
+ 583.0,
+ 1410.0,
+ 633.0,
+ 1402.0,
+ 633.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 623.0,
+ 1404.0,
+ 623.0,
+ 1404.0,
+ 658.0,
+ 293.0,
+ 658.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 655.0,
+ 556.0,
+ 655.0,
+ 556.0,
+ 688.0,
+ 293.0,
+ 688.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 583.0,
+ 655.0,
+ 1404.0,
+ 655.0,
+ 1404.0,
+ 688.0,
+ 583.0,
+ 688.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 687.0,
+ 1402.0,
+ 687.0,
+ 1402.0,
+ 718.0,
+ 294.0,
+ 718.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 712.0,
+ 1406.0,
+ 712.0,
+ 1406.0,
+ 753.0,
+ 291.0,
+ 753.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 745.0,
+ 1404.0,
+ 745.0,
+ 1404.0,
+ 781.0,
+ 294.0,
+ 781.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 776.0,
+ 450.0,
+ 776.0,
+ 450.0,
+ 812.0,
+ 294.0,
+ 812.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 475.0,
+ 776.0,
+ 1405.0,
+ 776.0,
+ 1405.0,
+ 812.0,
+ 475.0,
+ 812.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 808.0,
+ 1075.0,
+ 808.0,
+ 1075.0,
+ 841.0,
+ 293.0,
+ 841.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1524.0,
+ 718.0,
+ 1524.0,
+ 718.0,
+ 1561.0,
+ 294.0,
+ 1561.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 742.0,
+ 1524.0,
+ 1405.0,
+ 1524.0,
+ 1405.0,
+ 1561.0,
+ 742.0,
+ 1561.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1557.0,
+ 1405.0,
+ 1557.0,
+ 1405.0,
+ 1592.0,
+ 295.0,
+ 1592.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1587.0,
+ 1127.0,
+ 1587.0,
+ 1127.0,
+ 1621.0,
+ 293.0,
+ 1621.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1151.0,
+ 1587.0,
+ 1405.0,
+ 1587.0,
+ 1405.0,
+ 1621.0,
+ 1151.0,
+ 1621.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1617.0,
+ 1406.0,
+ 1617.0,
+ 1406.0,
+ 1652.0,
+ 294.0,
+ 1652.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1644.0,
+ 459.0,
+ 1644.0,
+ 459.0,
+ 1684.0,
+ 293.0,
+ 1684.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 603.0,
+ 1644.0,
+ 1107.0,
+ 1644.0,
+ 1107.0,
+ 1684.0,
+ 603.0,
+ 1684.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1131.0,
+ 1644.0,
+ 1406.0,
+ 1644.0,
+ 1406.0,
+ 1684.0,
+ 1131.0,
+ 1684.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1675.0,
+ 460.0,
+ 1675.0,
+ 460.0,
+ 1714.0,
+ 294.0,
+ 1714.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 605.0,
+ 1675.0,
+ 934.0,
+ 1675.0,
+ 934.0,
+ 1714.0,
+ 605.0,
+ 1714.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 228.0,
+ 1406.0,
+ 228.0,
+ 1406.0,
+ 266.0,
+ 292.0,
+ 266.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 260.0,
+ 1406.0,
+ 260.0,
+ 1406.0,
+ 297.0,
+ 294.0,
+ 297.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 290.0,
+ 1407.0,
+ 290.0,
+ 1407.0,
+ 327.0,
+ 292.0,
+ 327.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 320.0,
+ 1404.0,
+ 320.0,
+ 1404.0,
+ 357.0,
+ 293.0,
+ 357.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 353.0,
+ 740.0,
+ 353.0,
+ 740.0,
+ 387.0,
+ 297.0,
+ 387.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1741.0,
+ 607.0,
+ 1741.0,
+ 607.0,
+ 1780.0,
+ 295.0,
+ 1780.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 634.0,
+ 1741.0,
+ 1405.0,
+ 1741.0,
+ 1405.0,
+ 1780.0,
+ 634.0,
+ 1780.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1772.0,
+ 532.0,
+ 1772.0,
+ 532.0,
+ 1811.0,
+ 294.0,
+ 1811.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 741.0,
+ 1772.0,
+ 873.0,
+ 1772.0,
+ 873.0,
+ 1811.0,
+ 741.0,
+ 1811.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 901.0,
+ 1772.0,
+ 1406.0,
+ 1772.0,
+ 1406.0,
+ 1811.0,
+ 901.0,
+ 1811.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 327.0,
+ 1803.0,
+ 499.0,
+ 1803.0,
+ 499.0,
+ 1838.0,
+ 327.0,
+ 1838.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 515.0,
+ 1803.0,
+ 526.0,
+ 1803.0,
+ 526.0,
+ 1838.0,
+ 515.0,
+ 1838.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 557.0,
+ 1803.0,
+ 1039.0,
+ 1803.0,
+ 1039.0,
+ 1838.0,
+ 557.0,
+ 1838.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1111.0,
+ 1803.0,
+ 1405.0,
+ 1803.0,
+ 1405.0,
+ 1838.0,
+ 1111.0,
+ 1838.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1832.0,
+ 635.0,
+ 1832.0,
+ 635.0,
+ 1871.0,
+ 294.0,
+ 1871.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 665.0,
+ 1832.0,
+ 866.0,
+ 1832.0,
+ 866.0,
+ 1871.0,
+ 665.0,
+ 1871.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 924.0,
+ 1832.0,
+ 1292.0,
+ 1832.0,
+ 1292.0,
+ 1871.0,
+ 924.0,
+ 1871.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1394.0,
+ 1832.0,
+ 1404.0,
+ 1832.0,
+ 1404.0,
+ 1871.0,
+ 1394.0,
+ 1871.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1863.0,
+ 373.0,
+ 1863.0,
+ 373.0,
+ 1901.0,
+ 294.0,
+ 1901.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 406.0,
+ 1863.0,
+ 1123.0,
+ 1863.0,
+ 1123.0,
+ 1901.0,
+ 406.0,
+ 1901.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1166.0,
+ 1863.0,
+ 1404.0,
+ 1863.0,
+ 1404.0,
+ 1901.0,
+ 1166.0,
+ 1901.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1896.0,
+ 617.0,
+ 1896.0,
+ 617.0,
+ 1930.0,
+ 294.0,
+ 1930.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 647.0,
+ 1896.0,
+ 1116.0,
+ 1896.0,
+ 1116.0,
+ 1930.0,
+ 647.0,
+ 1930.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1314.0,
+ 1896.0,
+ 1406.0,
+ 1896.0,
+ 1406.0,
+ 1930.0,
+ 1314.0,
+ 1930.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1926.0,
+ 709.0,
+ 1926.0,
+ 709.0,
+ 1960.0,
+ 295.0,
+ 1960.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 759.0,
+ 1926.0,
+ 1030.0,
+ 1926.0,
+ 1030.0,
+ 1960.0,
+ 759.0,
+ 1960.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1971.0,
+ 1404.0,
+ 1971.0,
+ 1404.0,
+ 2007.0,
+ 295.0,
+ 2007.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 2000.0,
+ 374.0,
+ 2000.0,
+ 374.0,
+ 2039.0,
+ 294.0,
+ 2039.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 543.0,
+ 2000.0,
+ 1095.0,
+ 2000.0,
+ 1095.0,
+ 2039.0,
+ 543.0,
+ 2039.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1171.0,
+ 2000.0,
+ 1403.0,
+ 2000.0,
+ 1403.0,
+ 2039.0,
+ 1171.0,
+ 2039.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 395.0,
+ 1403.0,
+ 395.0,
+ 1403.0,
+ 435.0,
+ 294.0,
+ 435.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 430.0,
+ 708.0,
+ 430.0,
+ 708.0,
+ 462.0,
+ 296.0,
+ 462.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 3,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1076,
+ 1404,
+ 1076,
+ 1404,
+ 1418,
+ 298,
+ 1418
+ ],
+ "score": 0.985
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 667,
+ 1404,
+ 667,
+ 1404,
+ 978,
+ 298,
+ 978
+ ],
+ "score": 0.983
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1697,
+ 1404,
+ 1697,
+ 1404,
+ 2034,
+ 298,
+ 2034
+ ],
+ "score": 0.982
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 467,
+ 1403,
+ 467,
+ 1403,
+ 650,
+ 298,
+ 650
+ ],
+ "score": 0.978
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1537,
+ 1403,
+ 1537,
+ 1403,
+ 1660,
+ 298,
+ 1660
+ ],
+ "score": 0.976
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 299,
+ 308,
+ 1402,
+ 308,
+ 1402,
+ 430,
+ 299,
+ 430
+ ],
+ "score": 0.975
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 294,
+ 229,
+ 1399,
+ 229,
+ 1399,
+ 293,
+ 294,
+ 293
+ ],
+ "score": 0.953
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 301,
+ 1465,
+ 587,
+ 1465,
+ 587,
+ 1502,
+ 301,
+ 1502
+ ],
+ "score": 0.902
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 302,
+ 1018,
+ 778,
+ 1018,
+ 778,
+ 1049,
+ 302,
+ 1049
+ ],
+ "score": 0.888
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 300,
+ 76,
+ 852,
+ 76,
+ 852,
+ 104,
+ 300,
+ 104
+ ],
+ "score": 0.78
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 841,
+ 2088,
+ 858,
+ 2088,
+ 858,
+ 2112,
+ 841,
+ 2112
+ ],
+ "score": 0.718
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 858,
+ 1320,
+ 1002,
+ 1320,
+ 1002,
+ 1354,
+ 858,
+ 1354
+ ],
+ "score": 0.93,
+ "latex": "( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 379,
+ 855,
+ 684,
+ 855,
+ 684,
+ 889,
+ 379,
+ 889
+ ],
+ "score": 0.92,
+ "latex": "s _ { i j } = s _ { j i } = \\operatorname* { m a x } \\{ s _ { i j } , s _ { j i } \\}"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 630,
+ 1290,
+ 773,
+ 1290,
+ 773,
+ 1323,
+ 630,
+ 1323
+ ],
+ "score": 0.92,
+ "latex": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 462,
+ 262,
+ 606,
+ 262,
+ 606,
+ 295,
+ 462,
+ 295
+ ],
+ "score": 0.91,
+ "latex": "( \\pmb { v } _ { 1 } , \\dots , \\pmb { v } _ { T } )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 950,
+ 698,
+ 1093,
+ 698,
+ 1093,
+ 731,
+ 950,
+ 731
+ ],
+ "score": 0.91,
+ "latex": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 298,
+ 759,
+ 442,
+ 759,
+ 442,
+ 793,
+ 298,
+ 793
+ ],
+ "score": 0.9,
+ "latex": "\\big ( \\tilde { s } _ { 1 } , \\dots , \\tilde { s } _ { T } \\big )"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 900,
+ 370,
+ 928,
+ 370,
+ 928,
+ 400,
+ 900,
+ 400
+ ],
+ "score": 0.86,
+ "latex": "\\tilde { \\mathbf { \\boldsymbol { s } } } _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 355,
+ 236,
+ 399,
+ 236,
+ 399,
+ 262,
+ 355,
+ 262
+ ],
+ "score": 0.85,
+ "latex": "m _ { 0 }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 559,
+ 564,
+ 587,
+ 564,
+ 587,
+ 591,
+ 559,
+ 591
+ ],
+ "score": 0.85,
+ "latex": "\\mathbf { \\boldsymbol { s } } _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1284,
+ 820,
+ 1312,
+ 820,
+ 1312,
+ 852,
+ 1284,
+ 852
+ ],
+ "score": 0.85,
+ "latex": "\\hat { A }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1323,
+ 533,
+ 1352,
+ 533,
+ 1352,
+ 560,
+ 1323,
+ 560
+ ],
+ "score": 0.84,
+ "latex": "{ \\mathbf { } } v _ { t }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 298,
+ 1292,
+ 319,
+ 1292,
+ 319,
+ 1318,
+ 298,
+ 1318
+ ],
+ "score": 0.82,
+ "latex": "S"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 378,
+ 1352,
+ 400,
+ 1352,
+ 400,
+ 1387,
+ 378,
+ 1387
+ ],
+ "score": 0.82,
+ "latex": "\\tilde { \\mathcal { G } }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 702,
+ 470,
+ 729,
+ 470,
+ 729,
+ 496,
+ 702,
+ 496
+ ],
+ "score": 0.81,
+ "latex": "D"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1346,
+ 470,
+ 1372,
+ 470,
+ 1372,
+ 496,
+ 1346,
+ 496
+ ],
+ "score": 0.81,
+ "latex": "D"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 531,
+ 232,
+ 556,
+ 232,
+ 556,
+ 258,
+ 531,
+ 258
+ ],
+ "score": 0.81,
+ "latex": "G"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 868,
+ 669,
+ 890,
+ 669,
+ 890,
+ 696,
+ 868,
+ 696
+ ],
+ "score": 0.8,
+ "latex": "S"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 721,
+ 592,
+ 748,
+ 592,
+ 748,
+ 618,
+ 721,
+ 618
+ ],
+ "score": 0.8,
+ "latex": "D"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 885,
+ 887,
+ 904,
+ 887,
+ 904,
+ 914,
+ 885,
+ 914
+ ],
+ "score": 0.79,
+ "latex": "k"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1075,
+ 669,
+ 1100,
+ 669,
+ 1100,
+ 696,
+ 1075,
+ 696
+ ],
+ "score": 0.79,
+ "latex": "G"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1175,
+ 1322,
+ 1201,
+ 1322,
+ 1201,
+ 1349,
+ 1175,
+ 1349
+ ],
+ "score": 0.78,
+ "latex": "G"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1022,
+ 791,
+ 1045,
+ 791,
+ 1045,
+ 818,
+ 1022,
+ 818
+ ],
+ "score": 0.78,
+ "latex": "_ { s }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 900,
+ 825,
+ 924,
+ 825,
+ 924,
+ 853,
+ 900,
+ 853
+ ],
+ "score": 0.77,
+ "latex": "\\pmb { S }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 560,
+ 1322,
+ 589,
+ 1322,
+ 589,
+ 1349,
+ 560,
+ 1349
+ ],
+ "score": 0.77,
+ "latex": "\\Theta"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 451,
+ 530,
+ 475,
+ 530,
+ 475,
+ 557,
+ 451,
+ 557
+ ],
+ "score": 0.75,
+ "latex": "G"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 835,
+ 236,
+ 856,
+ 236,
+ 856,
+ 258,
+ 835,
+ 258
+ ],
+ "score": 0.74,
+ "latex": "_ { z }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1170,
+ 237,
+ 1187,
+ 237,
+ 1187,
+ 258,
+ 1170,
+ 258
+ ],
+ "score": 0.63,
+ "latex": "\\pmb { s }"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 700,
+ 533,
+ 715,
+ 533,
+ 715,
+ 558,
+ 700,
+ 558
+ ],
+ "score": 0.62,
+ "latex": "t"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1463.0,
+ 593.0,
+ 1463.0,
+ 593.0,
+ 1507.0,
+ 292.0,
+ 1507.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1017.0,
+ 781.0,
+ 1017.0,
+ 781.0,
+ 1053.0,
+ 296.0,
+ 1053.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 73.0,
+ 856.0,
+ 73.0,
+ 856.0,
+ 108.0,
+ 297.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 839.0,
+ 2085.0,
+ 861.0,
+ 2085.0,
+ 861.0,
+ 2120.0,
+ 839.0,
+ 2120.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1074.0,
+ 1405.0,
+ 1074.0,
+ 1405.0,
+ 1114.0,
+ 292.0,
+ 1114.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1108.0,
+ 1404.0,
+ 1108.0,
+ 1404.0,
+ 1143.0,
+ 294.0,
+ 1143.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1138.0,
+ 1402.0,
+ 1138.0,
+ 1402.0,
+ 1173.0,
+ 294.0,
+ 1173.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1168.0,
+ 1405.0,
+ 1168.0,
+ 1405.0,
+ 1207.0,
+ 293.0,
+ 1207.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1198.0,
+ 1406.0,
+ 1198.0,
+ 1406.0,
+ 1234.0,
+ 292.0,
+ 1234.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1228.0,
+ 1406.0,
+ 1228.0,
+ 1406.0,
+ 1266.0,
+ 292.0,
+ 1266.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1260.0,
+ 1405.0,
+ 1260.0,
+ 1405.0,
+ 1293.0,
+ 293.0,
+ 1293.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1287.0,
+ 297.0,
+ 1287.0,
+ 297.0,
+ 1327.0,
+ 292.0,
+ 1327.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 320.0,
+ 1287.0,
+ 629.0,
+ 1287.0,
+ 629.0,
+ 1327.0,
+ 320.0,
+ 1327.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 774.0,
+ 1287.0,
+ 1406.0,
+ 1287.0,
+ 1406.0,
+ 1327.0,
+ 774.0,
+ 1327.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1317.0,
+ 559.0,
+ 1317.0,
+ 559.0,
+ 1358.0,
+ 293.0,
+ 1358.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 590.0,
+ 1317.0,
+ 857.0,
+ 1317.0,
+ 857.0,
+ 1358.0,
+ 590.0,
+ 1358.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1003.0,
+ 1317.0,
+ 1174.0,
+ 1317.0,
+ 1174.0,
+ 1358.0,
+ 1003.0,
+ 1358.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1202.0,
+ 1317.0,
+ 1406.0,
+ 1317.0,
+ 1406.0,
+ 1358.0,
+ 1202.0,
+ 1358.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1355.0,
+ 377.0,
+ 1355.0,
+ 377.0,
+ 1393.0,
+ 292.0,
+ 1393.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 401.0,
+ 1355.0,
+ 1406.0,
+ 1355.0,
+ 1406.0,
+ 1393.0,
+ 401.0,
+ 1393.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1388.0,
+ 664.0,
+ 1388.0,
+ 664.0,
+ 1420.0,
+ 293.0,
+ 1420.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 668.0,
+ 867.0,
+ 668.0,
+ 867.0,
+ 700.0,
+ 296.0,
+ 700.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 891.0,
+ 668.0,
+ 1074.0,
+ 668.0,
+ 1074.0,
+ 700.0,
+ 891.0,
+ 700.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1101.0,
+ 668.0,
+ 1404.0,
+ 668.0,
+ 1404.0,
+ 700.0,
+ 1101.0,
+ 700.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 697.0,
+ 949.0,
+ 697.0,
+ 949.0,
+ 734.0,
+ 292.0,
+ 734.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1094.0,
+ 697.0,
+ 1407.0,
+ 697.0,
+ 1407.0,
+ 734.0,
+ 1094.0,
+ 734.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 725.0,
+ 1405.0,
+ 725.0,
+ 1405.0,
+ 765.0,
+ 293.0,
+ 765.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 760.0,
+ 297.0,
+ 760.0,
+ 297.0,
+ 793.0,
+ 293.0,
+ 793.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 443.0,
+ 760.0,
+ 1404.0,
+ 760.0,
+ 1404.0,
+ 793.0,
+ 443.0,
+ 793.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 789.0,
+ 1021.0,
+ 789.0,
+ 1021.0,
+ 825.0,
+ 294.0,
+ 825.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1046.0,
+ 789.0,
+ 1405.0,
+ 789.0,
+ 1405.0,
+ 825.0,
+ 1046.0,
+ 825.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 825.0,
+ 899.0,
+ 825.0,
+ 899.0,
+ 858.0,
+ 293.0,
+ 858.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 925.0,
+ 825.0,
+ 1283.0,
+ 825.0,
+ 1283.0,
+ 858.0,
+ 925.0,
+ 858.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1313.0,
+ 825.0,
+ 1406.0,
+ 825.0,
+ 1406.0,
+ 858.0,
+ 1313.0,
+ 858.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 853.0,
+ 378.0,
+ 853.0,
+ 378.0,
+ 891.0,
+ 292.0,
+ 891.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 685.0,
+ 853.0,
+ 1405.0,
+ 853.0,
+ 1405.0,
+ 891.0,
+ 685.0,
+ 891.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 884.0,
+ 884.0,
+ 884.0,
+ 884.0,
+ 920.0,
+ 292.0,
+ 920.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 905.0,
+ 884.0,
+ 1404.0,
+ 884.0,
+ 1404.0,
+ 920.0,
+ 905.0,
+ 920.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 915.0,
+ 1404.0,
+ 915.0,
+ 1404.0,
+ 951.0,
+ 294.0,
+ 951.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 948.0,
+ 1230.0,
+ 948.0,
+ 1230.0,
+ 980.0,
+ 296.0,
+ 980.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1697.0,
+ 1403.0,
+ 1697.0,
+ 1403.0,
+ 1734.0,
+ 295.0,
+ 1734.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1729.0,
+ 1405.0,
+ 1729.0,
+ 1405.0,
+ 1764.0,
+ 294.0,
+ 1764.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1757.0,
+ 1406.0,
+ 1757.0,
+ 1406.0,
+ 1795.0,
+ 293.0,
+ 1795.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1790.0,
+ 1405.0,
+ 1790.0,
+ 1405.0,
+ 1825.0,
+ 293.0,
+ 1825.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1820.0,
+ 1404.0,
+ 1820.0,
+ 1404.0,
+ 1854.0,
+ 294.0,
+ 1854.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1851.0,
+ 1404.0,
+ 1851.0,
+ 1404.0,
+ 1885.0,
+ 293.0,
+ 1885.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1879.0,
+ 1405.0,
+ 1879.0,
+ 1405.0,
+ 1916.0,
+ 293.0,
+ 1916.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1911.0,
+ 1404.0,
+ 1911.0,
+ 1404.0,
+ 1946.0,
+ 294.0,
+ 1946.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1942.0,
+ 1405.0,
+ 1942.0,
+ 1405.0,
+ 1977.0,
+ 294.0,
+ 1977.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1972.0,
+ 1405.0,
+ 1972.0,
+ 1405.0,
+ 2006.0,
+ 293.0,
+ 2006.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 2003.0,
+ 1405.0,
+ 2003.0,
+ 1405.0,
+ 2038.0,
+ 293.0,
+ 2038.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 468.0,
+ 701.0,
+ 468.0,
+ 701.0,
+ 503.0,
+ 294.0,
+ 503.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 730.0,
+ 468.0,
+ 1345.0,
+ 468.0,
+ 1345.0,
+ 503.0,
+ 730.0,
+ 503.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1373.0,
+ 468.0,
+ 1405.0,
+ 468.0,
+ 1405.0,
+ 503.0,
+ 1373.0,
+ 503.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 499.0,
+ 1405.0,
+ 499.0,
+ 1405.0,
+ 534.0,
+ 294.0,
+ 534.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 528.0,
+ 450.0,
+ 528.0,
+ 450.0,
+ 565.0,
+ 292.0,
+ 565.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 476.0,
+ 528.0,
+ 699.0,
+ 528.0,
+ 699.0,
+ 565.0,
+ 476.0,
+ 565.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 716.0,
+ 528.0,
+ 1322.0,
+ 528.0,
+ 1322.0,
+ 565.0,
+ 716.0,
+ 565.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1353.0,
+ 528.0,
+ 1406.0,
+ 528.0,
+ 1406.0,
+ 565.0,
+ 1353.0,
+ 565.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 561.0,
+ 558.0,
+ 561.0,
+ 558.0,
+ 593.0,
+ 296.0,
+ 593.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 588.0,
+ 561.0,
+ 1404.0,
+ 561.0,
+ 1404.0,
+ 593.0,
+ 588.0,
+ 593.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 588.0,
+ 720.0,
+ 588.0,
+ 720.0,
+ 627.0,
+ 292.0,
+ 627.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 749.0,
+ 588.0,
+ 1403.0,
+ 588.0,
+ 1403.0,
+ 627.0,
+ 749.0,
+ 627.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 620.0,
+ 463.0,
+ 620.0,
+ 463.0,
+ 652.0,
+ 294.0,
+ 652.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1537.0,
+ 1405.0,
+ 1537.0,
+ 1405.0,
+ 1573.0,
+ 294.0,
+ 1573.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1570.0,
+ 1405.0,
+ 1570.0,
+ 1405.0,
+ 1602.0,
+ 292.0,
+ 1602.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1597.0,
+ 1404.0,
+ 1597.0,
+ 1404.0,
+ 1636.0,
+ 292.0,
+ 1636.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1631.0,
+ 936.0,
+ 1631.0,
+ 936.0,
+ 1664.0,
+ 294.0,
+ 1664.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 308.0,
+ 1406.0,
+ 308.0,
+ 1406.0,
+ 344.0,
+ 294.0,
+ 344.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 290.0,
+ 337.0,
+ 1407.0,
+ 337.0,
+ 1407.0,
+ 375.0,
+ 290.0,
+ 375.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 368.0,
+ 899.0,
+ 368.0,
+ 899.0,
+ 405.0,
+ 293.0,
+ 405.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 929.0,
+ 368.0,
+ 1404.0,
+ 368.0,
+ 1404.0,
+ 405.0,
+ 929.0,
+ 405.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 401.0,
+ 832.0,
+ 401.0,
+ 832.0,
+ 434.0,
+ 295.0,
+ 434.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 226.0,
+ 354.0,
+ 226.0,
+ 354.0,
+ 267.0,
+ 293.0,
+ 267.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 400.0,
+ 226.0,
+ 530.0,
+ 226.0,
+ 530.0,
+ 267.0,
+ 400.0,
+ 267.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 557.0,
+ 226.0,
+ 834.0,
+ 226.0,
+ 834.0,
+ 267.0,
+ 557.0,
+ 267.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 857.0,
+ 226.0,
+ 1169.0,
+ 226.0,
+ 1169.0,
+ 267.0,
+ 857.0,
+ 267.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1188.0,
+ 226.0,
+ 1404.0,
+ 226.0,
+ 1404.0,
+ 267.0,
+ 1188.0,
+ 267.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 261.0,
+ 461.0,
+ 261.0,
+ 461.0,
+ 297.0,
+ 295.0,
+ 297.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 607.0,
+ 261.0,
+ 1229.0,
+ 261.0,
+ 1229.0,
+ 297.0,
+ 607.0,
+ 297.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 4,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 308,
+ 1403,
+ 308,
+ 1403,
+ 583,
+ 298,
+ 583
+ ],
+ "score": 0.982
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 814,
+ 1404,
+ 814,
+ 1404,
+ 1120,
+ 298,
+ 1120
+ ],
+ "score": 0.981
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1403,
+ 1403,
+ 1403,
+ 1403,
+ 1648,
+ 298,
+ 1648
+ ],
+ "score": 0.98
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 598,
+ 1404,
+ 598,
+ 1404,
+ 781,
+ 298,
+ 781
+ ],
+ "score": 0.979
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 299,
+ 1137,
+ 1403,
+ 1137,
+ 1403,
+ 1290,
+ 299,
+ 1290
+ ],
+ "score": 0.978
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1850,
+ 1403,
+ 1850,
+ 1403,
+ 2034,
+ 298,
+ 2034
+ ],
+ "score": 0.978
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 298,
+ 1681,
+ 1402,
+ 1681,
+ 1402,
+ 1835,
+ 298,
+ 1835
+ ],
+ "score": 0.976
+ },
+ {
+ "category_id": 1,
+ "poly": [
+ 297,
+ 230,
+ 1400,
+ 230,
+ 1400,
+ 294,
+ 297,
+ 294
+ ],
+ "score": 0.953
+ },
+ {
+ "category_id": 0,
+ "poly": [
+ 300,
+ 1335,
+ 557,
+ 1335,
+ 557,
+ 1369,
+ 300,
+ 1369
+ ],
+ "score": 0.887
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 840,
+ 2089,
+ 858,
+ 2089,
+ 858,
+ 2112,
+ 840,
+ 2112
+ ],
+ "score": 0.778
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 300,
+ 76,
+ 852,
+ 76,
+ 852,
+ 104,
+ 300,
+ 104
+ ],
+ "score": 0.733
+ },
+ {
+ "category_id": 2,
+ "poly": [
+ 299,
+ 76,
+ 854,
+ 76,
+ 854,
+ 104,
+ 299,
+ 104
+ ],
+ "score": 0.175
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 793,
+ 1743,
+ 869,
+ 1743,
+ 869,
+ 1772,
+ 793,
+ 1772
+ ],
+ "score": 0.88,
+ "latex": "K = 5"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 668,
+ 1743,
+ 779,
+ 1743,
+ 779,
+ 1771,
+ 668,
+ 1771
+ ],
+ "score": 0.87,
+ "latex": "E = 3 3 4 2"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 554,
+ 1743,
+ 656,
+ 1743,
+ 656,
+ 1771,
+ 554,
+ 1771
+ ],
+ "score": 0.87,
+ "latex": "N = 3 4 8"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1015,
+ 1743,
+ 1117,
+ 1743,
+ 1117,
+ 1772,
+ 1015,
+ 1772
+ ],
+ "score": 0.86,
+ "latex": "N = 1 5 4"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1129,
+ 1743,
+ 1242,
+ 1743,
+ 1242,
+ 1772,
+ 1129,
+ 1772
+ ],
+ "score": 0.84,
+ "latex": "E = 1 8 4 3"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 818,
+ 1775,
+ 892,
+ 1775,
+ 892,
+ 1803,
+ 818,
+ 1803
+ ],
+ "score": 0.84,
+ "latex": "K = 7"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 567,
+ 1774,
+ 683,
+ 1774,
+ 683,
+ 1803,
+ 567,
+ 1803
+ ],
+ "score": 0.84,
+ "latex": "N = 2 8 1 0"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 694,
+ 1774,
+ 805,
+ 1774,
+ 805,
+ 1803,
+ 694,
+ 1803
+ ],
+ "score": 0.84,
+ "latex": "E = 7 9 8 1"
+ },
+ {
+ "category_id": 13,
+ "poly": [
+ 1254,
+ 1743,
+ 1331,
+ 1743,
+ 1331,
+ 1773,
+ 1254,
+ 1773
+ ],
+ "score": 0.81,
+ "latex": "K = 3"
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1332.0,
+ 561.0,
+ 1332.0,
+ 561.0,
+ 1375.0,
+ 293.0,
+ 1375.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 840.0,
+ 2087.0,
+ 861.0,
+ 2087.0,
+ 861.0,
+ 2118.0,
+ 840.0,
+ 2118.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 73.0,
+ 856.0,
+ 73.0,
+ 856.0,
+ 108.0,
+ 297.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 73.0,
+ 857.0,
+ 73.0,
+ 857.0,
+ 108.0,
+ 297.0,
+ 108.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 310.0,
+ 1404.0,
+ 310.0,
+ 1404.0,
+ 343.0,
+ 296.0,
+ 343.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 337.0,
+ 1405.0,
+ 337.0,
+ 1405.0,
+ 374.0,
+ 294.0,
+ 374.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 369.0,
+ 1405.0,
+ 369.0,
+ 1405.0,
+ 404.0,
+ 293.0,
+ 404.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 399.0,
+ 1405.0,
+ 399.0,
+ 1405.0,
+ 435.0,
+ 294.0,
+ 435.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 429.0,
+ 1405.0,
+ 429.0,
+ 1405.0,
+ 466.0,
+ 292.0,
+ 466.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 459.0,
+ 1404.0,
+ 459.0,
+ 1404.0,
+ 495.0,
+ 294.0,
+ 495.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 488.0,
+ 1407.0,
+ 488.0,
+ 1407.0,
+ 529.0,
+ 293.0,
+ 529.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 520.0,
+ 1405.0,
+ 520.0,
+ 1405.0,
+ 560.0,
+ 293.0,
+ 560.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 550.0,
+ 1286.0,
+ 550.0,
+ 1286.0,
+ 589.0,
+ 293.0,
+ 589.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 812.0,
+ 1404.0,
+ 812.0,
+ 1404.0,
+ 852.0,
+ 293.0,
+ 852.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 845.0,
+ 1402.0,
+ 845.0,
+ 1402.0,
+ 881.0,
+ 294.0,
+ 881.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 872.0,
+ 1405.0,
+ 872.0,
+ 1405.0,
+ 916.0,
+ 291.0,
+ 916.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 907.0,
+ 1402.0,
+ 907.0,
+ 1402.0,
+ 943.0,
+ 293.0,
+ 943.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 937.0,
+ 1404.0,
+ 937.0,
+ 1404.0,
+ 972.0,
+ 294.0,
+ 972.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 968.0,
+ 1405.0,
+ 968.0,
+ 1405.0,
+ 1005.0,
+ 292.0,
+ 1005.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 996.0,
+ 1406.0,
+ 996.0,
+ 1406.0,
+ 1034.0,
+ 293.0,
+ 1034.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1025.0,
+ 1404.0,
+ 1025.0,
+ 1404.0,
+ 1069.0,
+ 292.0,
+ 1069.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1060.0,
+ 1402.0,
+ 1060.0,
+ 1402.0,
+ 1095.0,
+ 294.0,
+ 1095.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1086.0,
+ 1395.0,
+ 1086.0,
+ 1395.0,
+ 1127.0,
+ 295.0,
+ 1127.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1401.0,
+ 1405.0,
+ 1401.0,
+ 1405.0,
+ 1439.0,
+ 292.0,
+ 1439.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1436.0,
+ 1403.0,
+ 1436.0,
+ 1403.0,
+ 1469.0,
+ 294.0,
+ 1469.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1466.0,
+ 1403.0,
+ 1466.0,
+ 1403.0,
+ 1499.0,
+ 294.0,
+ 1499.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 1492.0,
+ 1405.0,
+ 1492.0,
+ 1405.0,
+ 1534.0,
+ 291.0,
+ 1534.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1526.0,
+ 1406.0,
+ 1526.0,
+ 1406.0,
+ 1560.0,
+ 293.0,
+ 1560.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1554.0,
+ 1408.0,
+ 1554.0,
+ 1408.0,
+ 1591.0,
+ 292.0,
+ 1591.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1585.0,
+ 1407.0,
+ 1585.0,
+ 1407.0,
+ 1623.0,
+ 292.0,
+ 1623.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1617.0,
+ 1201.0,
+ 1617.0,
+ 1201.0,
+ 1652.0,
+ 292.0,
+ 1652.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 596.0,
+ 1405.0,
+ 596.0,
+ 1405.0,
+ 634.0,
+ 295.0,
+ 634.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 630.0,
+ 1405.0,
+ 630.0,
+ 1405.0,
+ 662.0,
+ 296.0,
+ 662.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 655.0,
+ 1409.0,
+ 655.0,
+ 1409.0,
+ 697.0,
+ 292.0,
+ 697.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 688.0,
+ 1405.0,
+ 688.0,
+ 1405.0,
+ 724.0,
+ 294.0,
+ 724.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 720.0,
+ 1405.0,
+ 720.0,
+ 1405.0,
+ 755.0,
+ 294.0,
+ 755.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 751.0,
+ 735.0,
+ 751.0,
+ 735.0,
+ 783.0,
+ 294.0,
+ 783.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 1137.0,
+ 1404.0,
+ 1137.0,
+ 1404.0,
+ 1170.0,
+ 295.0,
+ 1170.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 1167.0,
+ 1403.0,
+ 1167.0,
+ 1403.0,
+ 1200.0,
+ 297.0,
+ 1200.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1195.0,
+ 1404.0,
+ 1195.0,
+ 1404.0,
+ 1235.0,
+ 293.0,
+ 1235.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1225.0,
+ 1405.0,
+ 1225.0,
+ 1405.0,
+ 1265.0,
+ 294.0,
+ 1265.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 297.0,
+ 1260.0,
+ 1348.0,
+ 1260.0,
+ 1348.0,
+ 1293.0,
+ 297.0,
+ 1293.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1849.0,
+ 1405.0,
+ 1849.0,
+ 1405.0,
+ 1885.0,
+ 296.0,
+ 1885.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1880.0,
+ 1404.0,
+ 1880.0,
+ 1404.0,
+ 1918.0,
+ 293.0,
+ 1918.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1910.0,
+ 1405.0,
+ 1910.0,
+ 1405.0,
+ 1947.0,
+ 292.0,
+ 1947.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1942.0,
+ 1405.0,
+ 1942.0,
+ 1405.0,
+ 1976.0,
+ 293.0,
+ 1976.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 291.0,
+ 1971.0,
+ 1406.0,
+ 1971.0,
+ 1406.0,
+ 2008.0,
+ 291.0,
+ 2008.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 2000.0,
+ 1104.0,
+ 2000.0,
+ 1104.0,
+ 2041.0,
+ 292.0,
+ 2041.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1683.0,
+ 1404.0,
+ 1683.0,
+ 1404.0,
+ 1716.0,
+ 296.0,
+ 1716.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 296.0,
+ 1713.0,
+ 1404.0,
+ 1713.0,
+ 1404.0,
+ 1746.0,
+ 296.0,
+ 1746.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 292.0,
+ 1741.0,
+ 553.0,
+ 1741.0,
+ 553.0,
+ 1777.0,
+ 292.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 657.0,
+ 1741.0,
+ 667.0,
+ 1741.0,
+ 667.0,
+ 1777.0,
+ 657.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 780.0,
+ 1741.0,
+ 792.0,
+ 1741.0,
+ 792.0,
+ 1777.0,
+ 780.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 870.0,
+ 1741.0,
+ 1014.0,
+ 1741.0,
+ 1014.0,
+ 1777.0,
+ 870.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1118.0,
+ 1741.0,
+ 1128.0,
+ 1741.0,
+ 1128.0,
+ 1777.0,
+ 1118.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1243.0,
+ 1741.0,
+ 1253.0,
+ 1741.0,
+ 1253.0,
+ 1777.0,
+ 1243.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 1332.0,
+ 1741.0,
+ 1406.0,
+ 1741.0,
+ 1406.0,
+ 1777.0,
+ 1332.0,
+ 1777.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 294.0,
+ 1773.0,
+ 566.0,
+ 1773.0,
+ 566.0,
+ 1810.0,
+ 294.0,
+ 1810.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 684.0,
+ 1773.0,
+ 693.0,
+ 1773.0,
+ 693.0,
+ 1810.0,
+ 684.0,
+ 1810.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 806.0,
+ 1773.0,
+ 817.0,
+ 1773.0,
+ 817.0,
+ 1810.0,
+ 806.0,
+ 1810.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 893.0,
+ 1773.0,
+ 1406.0,
+ 1773.0,
+ 1406.0,
+ 1810.0,
+ 893.0,
+ 1810.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 1802.0,
+ 1406.0,
+ 1802.0,
+ 1406.0,
+ 1843.0,
+ 293.0,
+ 1843.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 295.0,
+ 229.0,
+ 1404.0,
+ 229.0,
+ 1404.0,
+ 265.0,
+ 295.0,
+ 265.0
+ ],
+ "score": 1.0,
+ "text": ""
+ },
+ {
+ "category_id": 15,
+ "poly": [
+ 293.0,
+ 259.0,
+ 793.0,
+ 259.0,
+ 793.0,
+ 297.0,
+ 293.0,
+ 297.0
+ ],
+ "score": 1.0,
+ "text": ""
+ }
+ ],
+ "page_info": {
+ "page_no": 5,
+ "width": 1700,
+ "height": 2200
+ }
+ },
+ {
+ "layout_dets": [
+ {
+ "category_id": 5,
+ "poly": [
+ 296,
+ 786,
+ 1400,
+ 786,
+ 1400,
+ 1210,
+ 296,
+ 1210
+ ],
+ "score": 0.982,
+ "html": "