{ "pdf_info": [ { "preproc_blocks": [ { "type": "title", "bbox": [ 107, 79, 506, 115 ], "lines": [ { "bbox": [ 105, 78, 508, 98 ], "spans": [ { "bbox": [ 105, 78, 508, 98 ], "score": 1.0, "content": "LOCAL AUGMENTATION FOR GRAPH NEURAL NET-", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 100, 162, 118 ], "spans": [ { "bbox": [ 105, 100, 162, 118 ], "score": 1.0, "content": "WORKS", "type": "text" } ], "index": 1 } ], "index": 0.5 }, { "type": "text", "bbox": [ 112, 135, 244, 157 ], "lines": [ { "bbox": [ 113, 135, 201, 147 ], "spans": [ { "bbox": [ 113, 135, 201, 147 ], "score": 1.0, "content": "Anonymous authors", "type": "text" } ], "index": 2 }, { "bbox": [ 111, 146, 245, 158 ], "spans": [ { "bbox": [ 111, 146, 245, 158 ], "score": 1.0, "content": "Paper under double-blind review", "type": "text" } ], "index": 3 } ], "index": 2.5 }, { "type": "title", "bbox": [ 278, 186, 333, 199 ], "lines": [ { "bbox": [ 277, 186, 335, 200 ], "spans": [ { "bbox": [ 277, 186, 335, 200 ], "score": 1.0, "content": "ABSTRACT", "type": "text" } ], "index": 4 } ], "index": 4 }, { "type": "text", "bbox": [ 143, 210, 469, 385 ], "lines": [ { "bbox": [ 141, 209, 470, 223 ], "spans": [ { "bbox": [ 141, 209, 470, 223 ], "score": 1.0, "content": "Data augmentation has been widely used in image data and linguistic data but", "type": "text" } ], "index": 5 }, { "bbox": [ 141, 221, 469, 234 ], "spans": [ { "bbox": [ 141, 221, 469, 234 ], "score": 1.0, "content": "remains under-explored for Graph Neural Networks (GNNs). Existing methods", "type": "text" } ], "index": 6 }, { "bbox": [ 141, 232, 469, 245 ], "spans": [ { "bbox": [ 141, 232, 469, 245 ], "score": 1.0, "content": "focus on augmenting the graph data from a global perspective and largely fall", "type": "text" } ], "index": 7 }, { "bbox": [ 141, 243, 469, 255 ], "spans": [ { "bbox": [ 141, 243, 469, 255 ], "score": 1.0, "content": "into two genres: structural manipulation and adversarial training with feature", "type": "text" } ], "index": 8 }, { "bbox": [ 141, 254, 469, 267 ], "spans": [ { "bbox": [ 141, 254, 469, 267 ], "score": 1.0, "content": "noise injection. However, recent graph data augmentation methods ignore the", "type": "text" } ], "index": 9 }, { "bbox": [ 141, 265, 470, 277 ], "spans": [ { "bbox": [ 141, 265, 470, 277 ], "score": 1.0, "content": "importance of local information for the GNNs’ message passing mechanism. In", "type": "text" } ], "index": 10 }, { "bbox": [ 141, 276, 470, 288 ], "spans": [ { "bbox": [ 141, 276, 470, 288 ], "score": 1.0, "content": "this work, we introduce the local augmentation, which enhances the locality of", "type": "text" } ], "index": 11 }, { "bbox": [ 141, 288, 470, 299 ], "spans": [ { "bbox": [ 141, 288, 470, 299 ], "score": 1.0, "content": "node representations by their subgraph structures. Specifically, we model the data", "type": "text" } ], "index": 12 }, { "bbox": [ 141, 299, 469, 309 ], "spans": [ { "bbox": [ 141, 299, 469, 309 ], "score": 1.0, "content": "augmentation as a feature generation process. Given a node’s features, our local", "type": "text" } ], "index": 13 }, { "bbox": [ 141, 309, 470, 321 ], "spans": [ { "bbox": [ 141, 309, 470, 321 ], "score": 1.0, "content": "augmentation approach learns the conditional distribution of its neighbors’ features", "type": "text" } ], "index": 14 }, { "bbox": [ 142, 321, 470, 332 ], "spans": [ { "bbox": [ 142, 321, 470, 332 ], "score": 1.0, "content": "and generates more neighbors’ features to boost the performance of downstream", "type": "text" } ], "index": 15 }, { "bbox": [ 141, 330, 471, 344 ], "spans": [ { "bbox": [ 141, 330, 471, 344 ], "score": 1.0, "content": "tasks. Based on the local augmentation, we further design a novel framework:", "type": "text" } ], "index": 16 }, { "bbox": [ 141, 342, 470, 354 ], "spans": [ { "bbox": [ 141, 342, 470, 354 ], "score": 1.0, "content": "LA-GNN, which can apply to any GNN models in a plug-and-play manner. Ex-", "type": "text" } ], "index": 17 }, { "bbox": [ 141, 353, 469, 365 ], "spans": [ { "bbox": [ 141, 353, 469, 365 ], "score": 1.0, "content": "tensive experiments and analyses show that local augmentation consistently yields", "type": "text" } ], "index": 18 }, { "bbox": [ 141, 363, 470, 376 ], "spans": [ { "bbox": [ 141, 363, 470, 376 ], "score": 1.0, "content": "performance improvement for various GNN architectures across a diverse set of", "type": "text" } ], "index": 19 }, { "bbox": [ 142, 376, 195, 385 ], "spans": [ { "bbox": [ 142, 376, 195, 385 ], "score": 1.0, "content": "benchmarks.", "type": "text" } ], "index": 20 } ], "index": 12.5 }, { "type": "title", "bbox": [ 108, 405, 206, 417 ], "lines": [ { "bbox": [ 105, 403, 208, 421 ], "spans": [ { "bbox": [ 105, 403, 208, 421 ], "score": 1.0, "content": "1 INTRODUCTION", "type": "text" } ], "index": 21 } ], "index": 21 }, { "type": "text", "bbox": [ 107, 428, 505, 627 ], "lines": [ { "bbox": [ 106, 430, 506, 442 ], "spans": [ { "bbox": [ 106, 430, 506, 442 ], "score": 1.0, "content": "Graph Neural Networks (GNNs) and their variants (Abu-El-Haija et al., 2019; Kipf & Welling, 2017;", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 441, 505, 453 ], "spans": [ { "bbox": [ 106, 441, 505, 453 ], "score": 1.0, "content": "Velickovi ˇ c et al., 2018) have achieved state-of-the-art performance for many tasks on graphs such as ´", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 452, 506, 464 ], "spans": [ { "bbox": [ 105, 452, 506, 464 ], "score": 1.0, "content": "recommendation system (Ying et al., 2018) and traffic prediction (Guo et al., 2019). However, most", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 462, 505, 475 ], "spans": [ { "bbox": [ 105, 462, 505, 475 ], "score": 1.0, "content": "of the GNN models, such as GCN (Kipf & Welling, 2017) and GAT (Velickovi ˇ c et al., 2018), learn ´", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 473, 506, 486 ], "spans": [ { "bbox": [ 105, 473, 506, 486 ], "score": 1.0, "content": "the node representations by aggregating information over only the 2-hop neighborhood. Such shallow", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 484, 506, 498 ], "spans": [ { "bbox": [ 105, 484, 506, 498 ], "score": 1.0, "content": "architectures limit their ability to extract information from higher-layer neighborhoods (Wang &", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 495, 505, 508 ], "spans": [ { "bbox": [ 106, 495, 505, 508 ], "score": 1.0, "content": "Derr, 2021). But deep GNNs are prone to over-smoothing (Li et al., 2018), which suggests the node", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 506, 505, 519 ], "spans": [ { "bbox": [ 105, 506, 505, 519 ], "score": 1.0, "content": "representations tend to converge to a certain vector and thus become indistinguishable. One solution", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 517, 506, 530 ], "spans": [ { "bbox": [ 105, 517, 506, 530 ], "score": 1.0, "content": "to address this problem is to preserve the locality of node representations when increasing the number", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 528, 505, 541 ], "spans": [ { "bbox": [ 106, 528, 505, 541 ], "score": 1.0, "content": "of layers. For example, JKNet (Xu et al., 2018) densely connects (Huang et al., 2017) each hidden", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 538, 506, 553 ], "spans": [ { "bbox": [ 105, 538, 506, 553 ], "score": 1.0, "content": "layer to the final layer. GCNII (Chen et al., 2020) employs an initial residual to construct a skip", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 550, 506, 563 ], "spans": [ { "bbox": [ 105, 550, 506, 563 ], "score": 1.0, "content": "connection from the input layer. Besides, Zeng et al. (2021) pointed out that the key for GNN is", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 561, 506, 574 ], "spans": [ { "bbox": [ 106, 561, 506, 574 ], "score": 1.0, "content": "to smooth the local neighborhood into informative representation, no matter how deep it is. And", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 572, 506, 585 ], "spans": [ { "bbox": [ 106, 572, 506, 585 ], "score": 1.0, "content": "they decouple the depth and scope of GNNs to help capture local graph structure. Prior works have", "type": "text" } ], "index": 35 }, { "bbox": [ 106, 583, 505, 596 ], "spans": [ { "bbox": [ 106, 583, 505, 596 ], "score": 1.0, "content": "emphasized the importance of local information, but one property of the graph is that the number of", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 594, 505, 606 ], "spans": [ { "bbox": [ 105, 594, 505, 606 ], "score": 1.0, "content": "nodes in the local neighborhood is far fewer than higher-order neighbors. And this property limits the", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 605, 506, 618 ], "spans": [ { "bbox": [ 105, 605, 506, 618 ], "score": 1.0, "content": "expressive power of GNNs due to the limited neighbors in the local structure. A very intuitive idea is", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 617, 438, 628 ], "spans": [ { "bbox": [ 105, 617, 438, 628 ], "score": 1.0, "content": "to use data augmentation to increase the number of nodes in the local substructure.", "type": "text" } ], "index": 39 } ], "index": 30.5 }, { "type": "text", "bbox": [ 107, 633, 505, 732 ], "lines": [ { "bbox": [ 106, 633, 505, 646 ], "spans": [ { "bbox": [ 106, 633, 505, 646 ], "score": 1.0, "content": "However, existing graph data augmentation methods ignore the importance of local information", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 644, 504, 655 ], "spans": [ { "bbox": [ 106, 644, 504, 655 ], "score": 1.0, "content": "and only perturb at the topology-level and feature-level from a global perspective, which can be", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 654, 506, 668 ], "spans": [ { "bbox": [ 105, 654, 506, 668 ], "score": 1.0, "content": "divided into two categories: topology-level augmentation (Rong et al., 2020; Wang et al., 2020b; Zhao", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 666, 506, 678 ], "spans": [ { "bbox": [ 105, 666, 506, 678 ], "score": 1.0, "content": "et al., 2021) and feature-level augmentation (Deng et al., 2019; Feng et al., 2019; Kong et al., 2020).", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 676, 506, 690 ], "spans": [ { "bbox": [ 105, 676, 506, 690 ], "score": 1.0, "content": "Topology-level augmentation perturbs the adjacency matrix, yielding different graph structures. On", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "the other hand, existing feature-level augmentation mainly exploits perturbation of node attributes", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 698, 506, 712 ], "spans": [ { "bbox": [ 105, 698, 506, 712 ], "score": 1.0, "content": "guided by adversarial training (Deng et al., 2019; Feng et al., 2019; Kong et al., 2020). These", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 709, 506, 722 ], "spans": [ { "bbox": [ 105, 709, 506, 722 ], "score": 1.0, "content": "augmentation techniques have two drawbacks. 1) Some of they employ full-batch training for", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 720, 506, 733 ], "spans": [ { "bbox": [ 105, 720, 506, 733 ], "score": 1.0, "content": "augmentation, which is computationally expensive, and introduce some additional side effects such", "type": "text" } ], "index": 48 } ], "index": 44 } ], "page_idx": 0, "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 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 752, 308, 760 ], "lines": [ { "bbox": [ 302, 751, 309, 762 ], "spans": [ { "bbox": [ 302, 751, 309, 762 ], "score": 1.0, "content": "1", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "title", "bbox": [ 107, 79, 506, 115 ], "lines": [ { "bbox": [ 105, 78, 508, 98 ], "spans": [ { "bbox": [ 105, 78, 508, 98 ], "score": 1.0, "content": "LOCAL AUGMENTATION FOR GRAPH NEURAL NET-", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 100, 162, 118 ], "spans": [ { "bbox": [ 105, 100, 162, 118 ], "score": 1.0, "content": "WORKS", "type": "text" } ], "index": 1 } ], "index": 0.5 }, { "type": "text", "bbox": [ 112, 135, 244, 157 ], "lines": [ { "bbox": [ 113, 135, 201, 147 ], "spans": [ { "bbox": [ 113, 135, 201, 147 ], "score": 1.0, "content": "Anonymous authors", "type": "text" } ], "index": 2 }, { "bbox": [ 111, 146, 245, 158 ], "spans": [ { "bbox": [ 111, 146, 245, 158 ], "score": 1.0, "content": "Paper under double-blind review", "type": "text" } ], "index": 3 } ], "index": 2.5, "bbox_fs": [ 111, 135, 245, 158 ] }, { "type": "title", "bbox": [ 278, 186, 333, 199 ], "lines": [ { "bbox": [ 277, 186, 335, 200 ], "spans": [ { "bbox": [ 277, 186, 335, 200 ], "score": 1.0, "content": "ABSTRACT", "type": "text" } ], "index": 4 } ], "index": 4 }, { "type": "text", "bbox": [ 143, 210, 469, 385 ], "lines": [ { "bbox": [ 141, 209, 470, 223 ], "spans": [ { "bbox": [ 141, 209, 470, 223 ], "score": 1.0, "content": "Data augmentation has been widely used in image data and linguistic data but", "type": "text" } ], "index": 5 }, { "bbox": [ 141, 221, 469, 234 ], "spans": [ { "bbox": [ 141, 221, 469, 234 ], "score": 1.0, "content": "remains under-explored for Graph Neural Networks (GNNs). Existing methods", "type": "text" } ], "index": 6 }, { "bbox": [ 141, 232, 469, 245 ], "spans": [ { "bbox": [ 141, 232, 469, 245 ], "score": 1.0, "content": "focus on augmenting the graph data from a global perspective and largely fall", "type": "text" } ], "index": 7 }, { "bbox": [ 141, 243, 469, 255 ], "spans": [ { "bbox": [ 141, 243, 469, 255 ], "score": 1.0, "content": "into two genres: structural manipulation and adversarial training with feature", "type": "text" } ], "index": 8 }, { "bbox": [ 141, 254, 469, 267 ], "spans": [ { "bbox": [ 141, 254, 469, 267 ], "score": 1.0, "content": "noise injection. However, recent graph data augmentation methods ignore the", "type": "text" } ], "index": 9 }, { "bbox": [ 141, 265, 470, 277 ], "spans": [ { "bbox": [ 141, 265, 470, 277 ], "score": 1.0, "content": "importance of local information for the GNNs’ message passing mechanism. In", "type": "text" } ], "index": 10 }, { "bbox": [ 141, 276, 470, 288 ], "spans": [ { "bbox": [ 141, 276, 470, 288 ], "score": 1.0, "content": "this work, we introduce the local augmentation, which enhances the locality of", "type": "text" } ], "index": 11 }, { "bbox": [ 141, 288, 470, 299 ], "spans": [ { "bbox": [ 141, 288, 470, 299 ], "score": 1.0, "content": "node representations by their subgraph structures. Specifically, we model the data", "type": "text" } ], "index": 12 }, { "bbox": [ 141, 299, 469, 309 ], "spans": [ { "bbox": [ 141, 299, 469, 309 ], "score": 1.0, "content": "augmentation as a feature generation process. Given a node’s features, our local", "type": "text" } ], "index": 13 }, { "bbox": [ 141, 309, 470, 321 ], "spans": [ { "bbox": [ 141, 309, 470, 321 ], "score": 1.0, "content": "augmentation approach learns the conditional distribution of its neighbors’ features", "type": "text" } ], "index": 14 }, { "bbox": [ 142, 321, 470, 332 ], "spans": [ { "bbox": [ 142, 321, 470, 332 ], "score": 1.0, "content": "and generates more neighbors’ features to boost the performance of downstream", "type": "text" } ], "index": 15 }, { "bbox": [ 141, 330, 471, 344 ], "spans": [ { "bbox": [ 141, 330, 471, 344 ], "score": 1.0, "content": "tasks. Based on the local augmentation, we further design a novel framework:", "type": "text" } ], "index": 16 }, { "bbox": [ 141, 342, 470, 354 ], "spans": [ { "bbox": [ 141, 342, 470, 354 ], "score": 1.0, "content": "LA-GNN, which can apply to any GNN models in a plug-and-play manner. Ex-", "type": "text" } ], "index": 17 }, { "bbox": [ 141, 353, 469, 365 ], "spans": [ { "bbox": [ 141, 353, 469, 365 ], "score": 1.0, "content": "tensive experiments and analyses show that local augmentation consistently yields", "type": "text" } ], "index": 18 }, { "bbox": [ 141, 363, 470, 376 ], "spans": [ { "bbox": [ 141, 363, 470, 376 ], "score": 1.0, "content": "performance improvement for various GNN architectures across a diverse set of", "type": "text" } ], "index": 19 }, { "bbox": [ 142, 376, 195, 385 ], "spans": [ { "bbox": [ 142, 376, 195, 385 ], "score": 1.0, "content": "benchmarks.", "type": "text" } ], "index": 20 } ], "index": 12.5, "bbox_fs": [ 141, 209, 471, 385 ] }, { "type": "title", "bbox": [ 108, 405, 206, 417 ], "lines": [ { "bbox": [ 105, 403, 208, 421 ], "spans": [ { "bbox": [ 105, 403, 208, 421 ], "score": 1.0, "content": "1 INTRODUCTION", "type": "text" } ], "index": 21 } ], "index": 21 }, { "type": "text", "bbox": [ 107, 428, 505, 627 ], "lines": [ { "bbox": [ 106, 430, 506, 442 ], "spans": [ { "bbox": [ 106, 430, 506, 442 ], "score": 1.0, "content": "Graph Neural Networks (GNNs) and their variants (Abu-El-Haija et al., 2019; Kipf & Welling, 2017;", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 441, 505, 453 ], "spans": [ { "bbox": [ 106, 441, 505, 453 ], "score": 1.0, "content": "Velickovi ˇ c et al., 2018) have achieved state-of-the-art performance for many tasks on graphs such as ´", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 452, 506, 464 ], "spans": [ { "bbox": [ 105, 452, 506, 464 ], "score": 1.0, "content": "recommendation system (Ying et al., 2018) and traffic prediction (Guo et al., 2019). However, most", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 462, 505, 475 ], "spans": [ { "bbox": [ 105, 462, 505, 475 ], "score": 1.0, "content": "of the GNN models, such as GCN (Kipf & Welling, 2017) and GAT (Velickovi ˇ c et al., 2018), learn ´", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 473, 506, 486 ], "spans": [ { "bbox": [ 105, 473, 506, 486 ], "score": 1.0, "content": "the node representations by aggregating information over only the 2-hop neighborhood. Such shallow", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 484, 506, 498 ], "spans": [ { "bbox": [ 105, 484, 506, 498 ], "score": 1.0, "content": "architectures limit their ability to extract information from higher-layer neighborhoods (Wang &", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 495, 505, 508 ], "spans": [ { "bbox": [ 106, 495, 505, 508 ], "score": 1.0, "content": "Derr, 2021). But deep GNNs are prone to over-smoothing (Li et al., 2018), which suggests the node", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 506, 505, 519 ], "spans": [ { "bbox": [ 105, 506, 505, 519 ], "score": 1.0, "content": "representations tend to converge to a certain vector and thus become indistinguishable. One solution", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 517, 506, 530 ], "spans": [ { "bbox": [ 105, 517, 506, 530 ], "score": 1.0, "content": "to address this problem is to preserve the locality of node representations when increasing the number", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 528, 505, 541 ], "spans": [ { "bbox": [ 106, 528, 505, 541 ], "score": 1.0, "content": "of layers. For example, JKNet (Xu et al., 2018) densely connects (Huang et al., 2017) each hidden", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 538, 506, 553 ], "spans": [ { "bbox": [ 105, 538, 506, 553 ], "score": 1.0, "content": "layer to the final layer. GCNII (Chen et al., 2020) employs an initial residual to construct a skip", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 550, 506, 563 ], "spans": [ { "bbox": [ 105, 550, 506, 563 ], "score": 1.0, "content": "connection from the input layer. Besides, Zeng et al. (2021) pointed out that the key for GNN is", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 561, 506, 574 ], "spans": [ { "bbox": [ 106, 561, 506, 574 ], "score": 1.0, "content": "to smooth the local neighborhood into informative representation, no matter how deep it is. And", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 572, 506, 585 ], "spans": [ { "bbox": [ 106, 572, 506, 585 ], "score": 1.0, "content": "they decouple the depth and scope of GNNs to help capture local graph structure. Prior works have", "type": "text" } ], "index": 35 }, { "bbox": [ 106, 583, 505, 596 ], "spans": [ { "bbox": [ 106, 583, 505, 596 ], "score": 1.0, "content": "emphasized the importance of local information, but one property of the graph is that the number of", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 594, 505, 606 ], "spans": [ { "bbox": [ 105, 594, 505, 606 ], "score": 1.0, "content": "nodes in the local neighborhood is far fewer than higher-order neighbors. And this property limits the", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 605, 506, 618 ], "spans": [ { "bbox": [ 105, 605, 506, 618 ], "score": 1.0, "content": "expressive power of GNNs due to the limited neighbors in the local structure. A very intuitive idea is", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 617, 438, 628 ], "spans": [ { "bbox": [ 105, 617, 438, 628 ], "score": 1.0, "content": "to use data augmentation to increase the number of nodes in the local substructure.", "type": "text" } ], "index": 39 } ], "index": 30.5, "bbox_fs": [ 105, 430, 506, 628 ] }, { "type": "text", "bbox": [ 107, 633, 505, 732 ], "lines": [ { "bbox": [ 106, 633, 505, 646 ], "spans": [ { "bbox": [ 106, 633, 505, 646 ], "score": 1.0, "content": "However, existing graph data augmentation methods ignore the importance of local information", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 644, 504, 655 ], "spans": [ { "bbox": [ 106, 644, 504, 655 ], "score": 1.0, "content": "and only perturb at the topology-level and feature-level from a global perspective, which can be", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 654, 506, 668 ], "spans": [ { "bbox": [ 105, 654, 506, 668 ], "score": 1.0, "content": "divided into two categories: topology-level augmentation (Rong et al., 2020; Wang et al., 2020b; Zhao", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 666, 506, 678 ], "spans": [ { "bbox": [ 105, 666, 506, 678 ], "score": 1.0, "content": "et al., 2021) and feature-level augmentation (Deng et al., 2019; Feng et al., 2019; Kong et al., 2020).", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 676, 506, 690 ], "spans": [ { "bbox": [ 105, 676, 506, 690 ], "score": 1.0, "content": "Topology-level augmentation perturbs the adjacency matrix, yielding different graph structures. On", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "the other hand, existing feature-level augmentation mainly exploits perturbation of node attributes", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 698, 506, 712 ], "spans": [ { "bbox": [ 105, 698, 506, 712 ], "score": 1.0, "content": "guided by adversarial training (Deng et al., 2019; Feng et al., 2019; Kong et al., 2020). These", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 709, 506, 722 ], "spans": [ { "bbox": [ 105, 709, 506, 722 ], "score": 1.0, "content": "augmentation techniques have two drawbacks. 1) Some of they employ full-batch training for", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 720, 506, 733 ], "spans": [ { "bbox": [ 105, 720, 506, 733 ], "score": 1.0, "content": "augmentation, which is computationally expensive, and introduce some additional side effects such", "type": "text" } ], "index": 48 }, { "bbox": [ 105, 83, 505, 95 ], "spans": [ { "bbox": [ 105, 83, 505, 95 ], "score": 1.0, "content": "as over-smoothing. 2) The type of feature-level augmentation is coarse-grained, which focuses on", "type": "text", "cross_page": true } ], "index": 0 }, { "bbox": [ 105, 94, 505, 105 ], "spans": [ { "bbox": [ 105, 94, 505, 105 ], "score": 1.0, "content": "global augmentation and overlooks the local information of the neighborhood. Moreover, to our best", "type": "text", "cross_page": true } ], "index": 1 }, { "bbox": [ 105, 105, 505, 118 ], "spans": [ { "bbox": [ 105, 105, 505, 118 ], "score": 1.0, "content": "knowledge, none of the existing approaches combines both the feature representations and the graph", "type": "text", "cross_page": true } ], "index": 2 }, { "bbox": [ 105, 116, 448, 129 ], "spans": [ { "bbox": [ 105, 116, 448, 129 ], "score": 1.0, "content": "topology, especially the local subgraph structures, for graph-level data augmentation.", "type": "text", "cross_page": true } ], "index": 3 } ], "index": 44, "bbox_fs": [ 105, 633, 506, 733 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 107, 82, 505, 127 ], "lines": [ { "bbox": [ 105, 83, 505, 95 ], "spans": [ { "bbox": [ 105, 83, 505, 95 ], "score": 1.0, "content": "as over-smoothing. 2) The type of feature-level augmentation is coarse-grained, which focuses on", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 94, 505, 105 ], "spans": [ { "bbox": [ 105, 94, 505, 105 ], "score": 1.0, "content": "global augmentation and overlooks the local information of the neighborhood. Moreover, to our best", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 105, 505, 118 ], "spans": [ { "bbox": [ 105, 105, 505, 118 ], "score": 1.0, "content": "knowledge, none of the existing approaches combines both the feature representations and the graph", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 116, 448, 129 ], "spans": [ { "bbox": [ 105, 116, 448, 129 ], "score": 1.0, "content": "topology, especially the local subgraph structures, for graph-level data augmentation.", "type": "text" } ], "index": 3 } ], "index": 1.5 }, { "type": "text", "bbox": [ 107, 132, 506, 221 ], "lines": [ { "bbox": [ 105, 132, 507, 145 ], "spans": [ { "bbox": [ 105, 132, 507, 145 ], "score": 1.0, "content": "In this work, we propose a framework: Local Augmentation for Graph Neural Networks (LA-GNNs),", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 144, 507, 156 ], "spans": [ { "bbox": [ 105, 144, 507, 156 ], "score": 1.0, "content": "to further enhance the locality of node representations based on both the topology-level and feature-", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 154, 506, 166 ], "spans": [ { "bbox": [ 106, 154, 506, 166 ], "score": 1.0, "content": "level information in the substructure. The term \"local augmentation\" refers to the generation of", "type": "text" } ], "index": 6 }, { "bbox": [ 106, 165, 506, 178 ], "spans": [ { "bbox": [ 106, 165, 506, 178 ], "score": 1.0, "content": "neighborhood features via a generative model conditioned on local structures and node features.", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 176, 506, 189 ], "spans": [ { "bbox": [ 105, 176, 506, 189 ], "score": 1.0, "content": "Specifically, our proposed framework learns the conditional distribution of the connected neighbors’", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 187, 506, 200 ], "spans": [ { "bbox": [ 105, 187, 506, 200 ], "score": 1.0, "content": "representations given the representation of the central node, bearing some similarities with the Skip-", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 198, 506, 210 ], "spans": [ { "bbox": [ 105, 198, 506, 210 ], "score": 1.0, "content": "gram (Mikolov et al., 2013) and Deepwalk Perozzi et al. (2014), with the difference that our method", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 208, 284, 223 ], "spans": [ { "bbox": [ 105, 208, 284, 223 ], "score": 1.0, "content": "does not base on word or graph embedding.", "type": "text" } ], "index": 11 } ], "index": 7.5 }, { "type": "text", "bbox": [ 107, 226, 505, 380 ], "lines": [ { "bbox": [ 105, 225, 505, 239 ], "spans": [ { "bbox": [ 105, 225, 505, 239 ], "score": 1.0, "content": "The motivation behind this work concludes three-fold. 1) Existing feature-level augmentation works", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 237, 506, 249 ], "spans": [ { "bbox": [ 105, 237, 506, 249 ], "score": 1.0, "content": "primarily pay attention to global augmentation without considering the informative neighborhood. 2)", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 248, 506, 261 ], "spans": [ { "bbox": [ 106, 248, 506, 261 ], "score": 1.0, "content": "The distributions of the representations of the neighbors are closely connected to the central node,", "type": "text" } ], "index": 14 }, { "bbox": [ 106, 259, 506, 272 ], "spans": [ { "bbox": [ 106, 259, 506, 272 ], "score": 1.0, "content": "making ample room for feature augmentation. 3) Preserving the locality of node representations is", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 270, 506, 282 ], "spans": [ { "bbox": [ 105, 270, 237, 282 ], "score": 1.0, "content": "key to avoiding over-smoothing", "type": "text" }, { "bbox": [ 238, 270, 251, 280 ], "score": 0.27, "content": "\\mathrm { { X u } }", "type": "inline_equation" }, { "bbox": [ 252, 270, 506, 282 ], "score": 1.0, "content": "et al., 2018; Klicpera et al., 2019; Chen et al., 2020). And there", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 281, 506, 294 ], "spans": [ { "bbox": [ 105, 281, 506, 294 ], "score": 1.0, "content": "are several benefits in applying local augmentation for the GNN training. First, local augmentation is", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 291, 506, 304 ], "spans": [ { "bbox": [ 105, 291, 506, 304 ], "score": 1.0, "content": "essentially a data augmentation technique that can improve the generalization of the GNN models", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 302, 505, 315 ], "spans": [ { "bbox": [ 106, 302, 505, 315 ], "score": 1.0, "content": "and prevent over-fitting. Second, we can recover some missing contextual information of the local", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 314, 506, 326 ], "spans": [ { "bbox": [ 106, 314, 506, 326 ], "score": 1.0, "content": "neighborhood in an attributed graph via the generative model (Jia & Benson, 2020). Third, our", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 324, 506, 338 ], "spans": [ { "bbox": [ 105, 324, 506, 338 ], "score": 1.0, "content": "proposed framework is flexible and can be applied to various popular backbone networks such", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 335, 506, 348 ], "spans": [ { "bbox": [ 105, 335, 506, 348 ], "score": 1.0, "content": "as GCN (Kipf & Welling, 2017), GAT (Velickovi ˇ c et al., 2018), GCNII (Chen et al., 2020), and ´", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 346, 505, 360 ], "spans": [ { "bbox": [ 105, 346, 505, 360 ], "score": 1.0, "content": "GRAND (Feng et al., 2020) to enhance their performance. Extensive experimental results demonstrate", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 357, 506, 371 ], "spans": [ { "bbox": [ 105, 357, 506, 371 ], "score": 1.0, "content": "that our proposed framework could improve the performance of GNN variants on 7 benchmark", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 367, 144, 380 ], "spans": [ { "bbox": [ 105, 367, 144, 380 ], "score": 1.0, "content": "datasets.", "type": "text" } ], "index": 25 } ], "index": 18.5 }, { "type": "title", "bbox": [ 108, 395, 200, 408 ], "lines": [ { "bbox": [ 104, 394, 201, 411 ], "spans": [ { "bbox": [ 104, 394, 201, 411 ], "score": 1.0, "content": "2 BACKGROUND", "type": "text" } ], "index": 26 } ], "index": 26 }, { "type": "text", "bbox": [ 106, 418, 505, 502 ], "lines": [ { "bbox": [ 104, 416, 504, 434 ], "spans": [ { "bbox": [ 104, 416, 177, 434 ], "score": 1.0, "content": "Notations. Let", "type": "text" }, { "bbox": [ 177, 419, 230, 431 ], "score": 0.93, "content": "G = ( V , E )", "type": "inline_equation" }, { "bbox": [ 230, 416, 347, 434 ], "score": 1.0, "content": "represent the graph, where", "type": "text" }, { "bbox": [ 347, 420, 357, 429 ], "score": 0.8, "content": "V", "type": "inline_equation" }, { "bbox": [ 357, 416, 447, 434 ], "score": 1.0, "content": "is the set of vertices", "type": "text" }, { "bbox": [ 447, 419, 504, 431 ], "score": 0.78, "content": "\\{ v _ { 1 } , \\cdots , v _ { N } \\}", "type": "inline_equation" } ], "index": 27 }, { "bbox": [ 103, 428, 506, 444 ], "spans": [ { "bbox": [ 103, 428, 128, 444 ], "score": 1.0, "content": "with", "type": "text" }, { "bbox": [ 128, 430, 168, 442 ], "score": 0.91, "content": "| V | = N", "type": "inline_equation" }, { "bbox": [ 168, 428, 188, 444 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 189, 431, 198, 441 ], "score": 0.82, "content": "E", "type": "inline_equation" }, { "bbox": [ 198, 428, 432, 444 ], "score": 1.0, "content": "is the set of edges. The adjacency matrix is defined as", "type": "text" }, { "bbox": [ 432, 431, 503, 443 ], "score": 0.85, "content": "\\mathbf { A } \\in \\{ 0 , 1 \\} ^ { N \\times N }", "type": "inline_equation" }, { "bbox": [ 503, 428, 506, 444 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 28 }, { "bbox": [ 101, 440, 510, 471 ], "spans": [ { "bbox": [ 101, 440, 124, 471 ], "score": 1.0, "content": "and nod", "type": "text" }, { "bbox": [ 125, 442, 162, 453 ], "score": 0.91, "content": "\\mathbf { A } _ { i j } = 1", "type": "inline_equation" }, { "bbox": [ 169, 440, 221, 471 ], "score": 1.0, "content": "f and only if denote the d", "type": "text" }, { "bbox": [ 222, 442, 274, 454 ], "score": 0.93, "content": "( v _ { i } , v _ { j } ) \\in E", "type": "inline_equation" }, { "bbox": [ 274, 440, 297, 471 ], "score": 1.0, "content": ". Let ee ma", "type": "text" }, { "bbox": [ 297, 441, 383, 453 ], "score": 0.93, "content": "\\mathcal { N } _ { i } \\overset { \\cdot } { = } \\{ v _ { j } \\vert \\mathbf { A } _ { i j } = 1 \\}", "type": "inline_equation" }, { "bbox": [ 419, 440, 510, 471 ], "score": 1.0, "content": "the neighborhood of. The feature matrix", "type": "text" } ], "index": 29 }, { "bbox": [ 129, 452, 419, 466 ], "spans": [ { "bbox": [ 129, 455, 139, 464 ], "score": 0.85, "content": "v _ { i }", "type": "inline_equation" }, { "bbox": [ 159, 453, 169, 463 ], "score": 0.7, "content": "\\mathbf { D }", "type": "inline_equation" }, { "bbox": [ 345, 452, 419, 466 ], "score": 0.93, "content": "\\begin{array} { r } { \\dot { \\bf D } _ { i i } = \\dot { \\sum } _ { j = 1 } ^ { n } { \\bf A } _ { i j } } \\end{array}", "type": "inline_equation" } ], "index": 30 }, { "bbox": [ 104, 463, 506, 480 ], "spans": [ { "bbox": [ 104, 463, 163, 480 ], "score": 1.0, "content": "is denoted as", "type": "text" }, { "bbox": [ 164, 465, 215, 476 ], "score": 0.91, "content": "\\mathbf { X } \\in \\mathbb { R } ^ { N \\times F }", "type": "inline_equation" }, { "bbox": [ 215, 463, 289, 480 ], "score": 1.0, "content": "where each node", "type": "text" }, { "bbox": [ 290, 468, 297, 476 ], "score": 0.78, "content": "v", "type": "inline_equation" }, { "bbox": [ 297, 463, 382, 480 ], "score": 1.0, "content": "is associated with a", "type": "text" }, { "bbox": [ 382, 467, 391, 476 ], "score": 0.83, "content": "F", "type": "inline_equation" }, { "bbox": [ 391, 463, 506, 480 ], "score": 1.0, "content": "-dimensional feature vector", "type": "text" } ], "index": 31 }, { "bbox": [ 106, 474, 506, 490 ], "spans": [ { "bbox": [ 106, 477, 120, 488 ], "score": 0.82, "content": "\\mathbf { X } _ { v }", "type": "inline_equation" }, { "bbox": [ 121, 474, 125, 490 ], "score": 1.0, "content": ".", "type": "text" }, { "bbox": [ 126, 477, 192, 489 ], "score": 0.87, "content": "\\mathbf { Y } \\in \\{ 0 , 1 \\} ^ { N \\times C }", "type": "inline_equation" }, { "bbox": [ 192, 474, 352, 490 ], "score": 1.0, "content": "denote the one-hot label matrix, where", "type": "text" }, { "bbox": [ 353, 477, 408, 489 ], "score": 0.94, "content": "\\mathbf { Y } _ { i } \\in \\{ 0 , 1 \\} ^ { C }", "type": "inline_equation" }, { "bbox": [ 409, 474, 506, 490 ], "score": 1.0, "content": "is a one-hot vector and", "type": "text" } ], "index": 32 }, { "bbox": [ 107, 483, 239, 509 ], "spans": [ { "bbox": [ 107, 488, 168, 504 ], "score": 0.91, "content": "\\begin{array} { r } { \\sum _ { j = 1 } ^ { C } \\mathbf { Y } _ { i j } = 1 } \\end{array}", "type": "inline_equation" }, { "bbox": [ 168, 483, 200, 509 ], "score": 1.0, "content": "for any", "type": "text" }, { "bbox": [ 200, 491, 230, 501 ], "score": 0.91, "content": "v _ { i } \\in V", "type": "inline_equation" }, { "bbox": [ 230, 483, 239, 509 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 33 } ], "index": 30 }, { "type": "text", "bbox": [ 106, 514, 505, 548 ], "lines": [ { "bbox": [ 106, 514, 505, 527 ], "spans": [ { "bbox": [ 106, 514, 505, 527 ], "score": 1.0, "content": "GNN. Graph Neural Network (GNN) is a type of neural network that directly operates on the graph", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 525, 505, 538 ], "spans": [ { "bbox": [ 106, 525, 505, 538 ], "score": 1.0, "content": "structure, such as GCN and GAT (Kipf & Welling, 2017; Velickovi ˇ c et al., 2018), that capture the ´", "type": "text" } ], "index": 35 }, { "bbox": [ 106, 536, 410, 550 ], "spans": [ { "bbox": [ 106, 536, 410, 550 ], "score": 1.0, "content": "dependence of graphs via message passing between the nodes of a graph as", "type": "text" } ], "index": 36 } ], "index": 35 }, { "type": "interline_equation", "bbox": [ 258, 549, 351, 564 ], "lines": [ { "bbox": [ 258, 549, 351, 564 ], "spans": [ { "bbox": [ 258, 549, 351, 564 ], "score": 0.92, "content": "\\mathbf { H } ^ { ( \\ell ) } = f ( \\mathbf { A } , \\mathbf { H } ^ { ( \\ell - 1 ) } ) ,", "type": "interline_equation", "image_path": "a0a846dead3255d0f75f83845cabc54956e351f1d16184644971b29cc873b6b0.jpg" } ] } ], "index": 37, "virtual_lines": [ { "bbox": [ 258, 549, 351, 564 ], "spans": [], "index": 37 } ] }, { "type": "text", "bbox": [ 107, 566, 505, 606 ], "lines": [ { "bbox": [ 105, 565, 505, 580 ], "spans": [ { "bbox": [ 105, 565, 132, 580 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 568, 140, 578 ], "score": 0.85, "content": "f", "type": "inline_equation" }, { "bbox": [ 140, 565, 351, 580 ], "score": 1.0, "content": "denotes the specific GNN layer for different models,", "type": "text" }, { "bbox": [ 351, 566, 371, 577 ], "score": 0.9, "content": "\\mathbf { H } ^ { ( \\ell ) }", "type": "inline_equation" }, { "bbox": [ 371, 565, 487, 580 ], "score": 1.0, "content": "are the hidden vectors of the", "type": "text" }, { "bbox": [ 488, 568, 493, 577 ], "score": 0.7, "content": "\\ell", "type": "inline_equation" }, { "bbox": [ 493, 565, 505, 580 ], "score": 1.0, "content": "-th", "type": "text" } ], "index": 38 }, { "bbox": [ 104, 577, 506, 592 ], "spans": [ { "bbox": [ 104, 577, 145, 592 ], "score": 1.0, "content": "layer and", "type": "text" }, { "bbox": [ 145, 578, 188, 590 ], "score": 0.91, "content": "\\mathbf { H } ^ { ( 0 ) } = \\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 188, 577, 246, 592 ], "score": 1.0, "content": ". For example,", "type": "text" }, { "bbox": [ 246, 578, 339, 591 ], "score": 0.92, "content": "\\dot { f ( \\mathbf { A } , \\mathbf { H } ) } = \\sigma ( \\hat { \\mathbf { A } } \\mathbf { H } \\mathbf { W } )", "type": "inline_equation" }, { "bbox": [ 340, 577, 407, 592 ], "score": 1.0, "content": "for GCN, where", "type": "text" }, { "bbox": [ 407, 578, 483, 590 ], "score": 0.88, "content": "\\hat { \\mathbf { A } } = \\tilde { \\mathbf { D } } ^ { - \\frac { 1 } { 2 } } \\tilde { \\mathbf { A } } \\tilde { \\mathbf { D } } ^ { - \\frac { 1 } { 2 } } ,", "type": "inline_equation" }, { "bbox": [ 484, 578, 495, 590 ], "score": 0.47, "content": "\\tilde { \\bf D }", "type": "inline_equation" }, { "bbox": [ 495, 577, 506, 592 ], "score": 1.0, "content": "is", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 590, 356, 606 ], "spans": [ { "bbox": [ 105, 590, 189, 606 ], "score": 1.0, "content": "the degree matrix of", "type": "text" }, { "bbox": [ 190, 591, 199, 603 ], "score": 0.79, "content": "\\tilde { \\mathbf { A } }", "type": "inline_equation" }, { "bbox": [ 199, 590, 220, 606 ], "score": 1.0, "content": ", i.e.,", "type": "text" }, { "bbox": [ 220, 591, 281, 606 ], "score": 0.93, "content": "\\begin{array} { r } { \\tilde { \\bf D } _ { i i } = \\sum _ { j } \\tilde { \\bf A } _ { i j } } \\end{array}", "type": "inline_equation" }, { "bbox": [ 282, 590, 302, 606 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 303, 591, 351, 603 ], "score": 0.88, "content": "\\tilde { \\mathbf { A } } = \\mathbf { A } + \\mathbf { I }", "type": "inline_equation" }, { "bbox": [ 351, 590, 356, 606 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 40 } ], "index": 39 }, { "type": "text", "bbox": [ 106, 616, 506, 725 ], "lines": [ { "bbox": [ 106, 617, 506, 629 ], "spans": [ { "bbox": [ 106, 617, 432, 629 ], "score": 1.0, "content": "Topology-level Augmentation. Topology-level augmentation usually perturbs", "type": "text" }, { "bbox": [ 432, 617, 441, 627 ], "score": 0.42, "content": "\\mathbf { A }", "type": "inline_equation" }, { "bbox": [ 442, 617, 506, 629 ], "score": 1.0, "content": "to generate dif-", "type": "text" } ], "index": 41 }, { "bbox": [ 106, 627, 505, 640 ], "spans": [ { "bbox": [ 106, 627, 325, 640 ], "score": 1.0, "content": "ferent graph structures, which can be formulated as", "type": "text" }, { "bbox": [ 326, 627, 393, 639 ], "score": 0.91, "content": "\\mathbf { A } ^ { \\prime } = \\mathcal { F } ( \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 393, 627, 426, 640 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 426, 628, 446, 639 ], "score": 0.89, "content": "\\mathcal F ( \\cdot )", "type": "inline_equation" }, { "bbox": [ 447, 627, 505, 640 ], "score": 1.0, "content": "is a structure", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 638, 504, 652 ], "spans": [ { "bbox": [ 105, 638, 418, 652 ], "score": 1.0, "content": "perturbation function. For example, DropEdge (Rong et al., 2020) considers", "type": "text" }, { "bbox": [ 419, 639, 504, 650 ], "score": 0.91, "content": "\\mathcal { F } ( \\mathbf { A } , \\mathbf { X } ) = \\mathbf { A } - \\mathbf { A _ { s } }", "type": "inline_equation" } ], "index": 43 }, { "bbox": [ 106, 650, 506, 662 ], "spans": [ { "bbox": [ 106, 650, 204, 662 ], "score": 1.0, "content": "which is independent of", "type": "text" }, { "bbox": [ 204, 650, 213, 660 ], "score": 0.64, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 214, 650, 244, 662 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 244, 650, 258, 660 ], "score": 0.88, "content": "\\mathbf { A _ { s } }", "type": "inline_equation" }, { "bbox": [ 259, 650, 494, 662 ], "score": 1.0, "content": "is a sparse matrix consists of a subset of the original edges", "type": "text" }, { "bbox": [ 494, 650, 503, 659 ], "score": 0.8, "content": "E", "type": "inline_equation" }, { "bbox": [ 503, 650, 506, 662 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 659, 506, 675 ], "spans": [ { "bbox": [ 105, 659, 506, 675 ], "score": 1.0, "content": "GAUG-O (Zhao et al., 2021) leverages their proposed neural edge predictors to produce a different", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 672, 506, 691 ], "spans": [ { "bbox": [ 105, 672, 145, 690 ], "score": 1.0, "content": "structure", "type": "text" }, { "bbox": [ 145, 675, 158, 686 ], "score": 0.82, "content": "\\mathbf { A } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 158, 672, 187, 690 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 187, 672, 315, 691 ], "score": 0.87, "content": "\\begin{array} { r } { \\mathbf { A } _ { i j } ^ { \\prime } = \\left\\lfloor \\frac { 1 } { 1 + e ^ { - \\left( \\log \\mathbf { P } _ { i j } + G \\right) / \\tau } } + \\frac { 1 } { 2 } \\right\\rfloor } \\end{array}", "type": "inline_equation" }, { "bbox": [ 315, 674, 319, 689 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 320, 673, 435, 690 ], "score": 0.66, "content": "\\mathbf { P } _ { i j } = \\alpha \\mathbf { M } _ { i j } + ( 1 - \\alpha ) \\mathbf { A } _ { i j }", "type": "inline_equation" }, { "bbox": [ 435, 674, 438, 689 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 439, 673, 502, 688 ], "score": 0.91, "content": "\\mathbf { M } = { \\boldsymbol { \\sigma } } \\left( \\mathbf { Z } \\mathbf { Z } ^ { T } \\right)", "type": "inline_equation" }, { "bbox": [ 502, 674, 506, 689 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 46 }, { "bbox": [ 106, 689, 506, 703 ], "spans": [ { "bbox": [ 106, 690, 191, 703 ], "score": 0.88, "content": "\\mathbf { Z } = f \\left( \\mathbf { A } , f ( \\mathbf { A } , \\mathbf { X } ) \\right)", "type": "inline_equation" }, { "bbox": [ 191, 689, 195, 703 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 195, 693, 203, 701 ], "score": 0.72, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 203, 689, 409, 703 ], "score": 1.0, "content": "is the temperature of Gumbel-Softmax distribution,", "type": "text" }, { "bbox": [ 409, 690, 488, 703 ], "score": 0.88, "content": "G \\sim { \\mathrm { G u m b e l } } ( 0 , 1 )", "type": "inline_equation" }, { "bbox": [ 488, 689, 506, 703 ], "score": 1.0, "content": "is a", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 700, 506, 715 ], "spans": [ { "bbox": [ 105, 700, 222, 715 ], "score": 1.0, "content": "Gumbel random variate, and", "type": "text" }, { "bbox": [ 222, 703, 230, 711 ], "score": 0.81, "content": "\\alpha", "type": "inline_equation" }, { "bbox": [ 231, 700, 506, 715 ], "score": 1.0, "content": "is a hyperparameter mediating the influence of edge predictor on the", "type": "text" } ], "index": 48 }, { "bbox": [ 105, 712, 167, 725 ], "spans": [ { "bbox": [ 105, 712, 167, 725 ], "score": 1.0, "content": "original graph.", "type": "text" } ], "index": 49 } ], "index": 45 } ], "page_idx": 1, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 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 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 751, 309, 760 ], "lines": [ { "bbox": [ 301, 750, 310, 763 ], "spans": [ { "bbox": [ 301, 750, 310, 763 ], "score": 1.0, "content": "2", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 107, 82, 505, 127 ], "lines": [], "index": 1.5, "bbox_fs": [ 105, 83, 505, 129 ], "lines_deleted": true }, { "type": "text", "bbox": [ 107, 132, 506, 221 ], "lines": [ { "bbox": [ 105, 132, 507, 145 ], "spans": [ { "bbox": [ 105, 132, 507, 145 ], "score": 1.0, "content": "In this work, we propose a framework: Local Augmentation for Graph Neural Networks (LA-GNNs),", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 144, 507, 156 ], "spans": [ { "bbox": [ 105, 144, 507, 156 ], "score": 1.0, "content": "to further enhance the locality of node representations based on both the topology-level and feature-", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 154, 506, 166 ], "spans": [ { "bbox": [ 106, 154, 506, 166 ], "score": 1.0, "content": "level information in the substructure. The term \"local augmentation\" refers to the generation of", "type": "text" } ], "index": 6 }, { "bbox": [ 106, 165, 506, 178 ], "spans": [ { "bbox": [ 106, 165, 506, 178 ], "score": 1.0, "content": "neighborhood features via a generative model conditioned on local structures and node features.", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 176, 506, 189 ], "spans": [ { "bbox": [ 105, 176, 506, 189 ], "score": 1.0, "content": "Specifically, our proposed framework learns the conditional distribution of the connected neighbors’", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 187, 506, 200 ], "spans": [ { "bbox": [ 105, 187, 506, 200 ], "score": 1.0, "content": "representations given the representation of the central node, bearing some similarities with the Skip-", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 198, 506, 210 ], "spans": [ { "bbox": [ 105, 198, 506, 210 ], "score": 1.0, "content": "gram (Mikolov et al., 2013) and Deepwalk Perozzi et al. (2014), with the difference that our method", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 208, 284, 223 ], "spans": [ { "bbox": [ 105, 208, 284, 223 ], "score": 1.0, "content": "does not base on word or graph embedding.", "type": "text" } ], "index": 11 } ], "index": 7.5, "bbox_fs": [ 105, 132, 507, 223 ] }, { "type": "text", "bbox": [ 107, 226, 505, 380 ], "lines": [ { "bbox": [ 105, 225, 505, 239 ], "spans": [ { "bbox": [ 105, 225, 505, 239 ], "score": 1.0, "content": "The motivation behind this work concludes three-fold. 1) Existing feature-level augmentation works", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 237, 506, 249 ], "spans": [ { "bbox": [ 105, 237, 506, 249 ], "score": 1.0, "content": "primarily pay attention to global augmentation without considering the informative neighborhood. 2)", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 248, 506, 261 ], "spans": [ { "bbox": [ 106, 248, 506, 261 ], "score": 1.0, "content": "The distributions of the representations of the neighbors are closely connected to the central node,", "type": "text" } ], "index": 14 }, { "bbox": [ 106, 259, 506, 272 ], "spans": [ { "bbox": [ 106, 259, 506, 272 ], "score": 1.0, "content": "making ample room for feature augmentation. 3) Preserving the locality of node representations is", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 270, 506, 282 ], "spans": [ { "bbox": [ 105, 270, 237, 282 ], "score": 1.0, "content": "key to avoiding over-smoothing", "type": "text" }, { "bbox": [ 238, 270, 251, 280 ], "score": 0.27, "content": "\\mathrm { { X u } }", "type": "inline_equation" }, { "bbox": [ 252, 270, 506, 282 ], "score": 1.0, "content": "et al., 2018; Klicpera et al., 2019; Chen et al., 2020). And there", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 281, 506, 294 ], "spans": [ { "bbox": [ 105, 281, 506, 294 ], "score": 1.0, "content": "are several benefits in applying local augmentation for the GNN training. First, local augmentation is", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 291, 506, 304 ], "spans": [ { "bbox": [ 105, 291, 506, 304 ], "score": 1.0, "content": "essentially a data augmentation technique that can improve the generalization of the GNN models", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 302, 505, 315 ], "spans": [ { "bbox": [ 106, 302, 505, 315 ], "score": 1.0, "content": "and prevent over-fitting. Second, we can recover some missing contextual information of the local", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 314, 506, 326 ], "spans": [ { "bbox": [ 106, 314, 506, 326 ], "score": 1.0, "content": "neighborhood in an attributed graph via the generative model (Jia & Benson, 2020). Third, our", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 324, 506, 338 ], "spans": [ { "bbox": [ 105, 324, 506, 338 ], "score": 1.0, "content": "proposed framework is flexible and can be applied to various popular backbone networks such", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 335, 506, 348 ], "spans": [ { "bbox": [ 105, 335, 506, 348 ], "score": 1.0, "content": "as GCN (Kipf & Welling, 2017), GAT (Velickovi ˇ c et al., 2018), GCNII (Chen et al., 2020), and ´", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 346, 505, 360 ], "spans": [ { "bbox": [ 105, 346, 505, 360 ], "score": 1.0, "content": "GRAND (Feng et al., 2020) to enhance their performance. Extensive experimental results demonstrate", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 357, 506, 371 ], "spans": [ { "bbox": [ 105, 357, 506, 371 ], "score": 1.0, "content": "that our proposed framework could improve the performance of GNN variants on 7 benchmark", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 367, 144, 380 ], "spans": [ { "bbox": [ 105, 367, 144, 380 ], "score": 1.0, "content": "datasets.", "type": "text" } ], "index": 25 } ], "index": 18.5, "bbox_fs": [ 105, 225, 506, 380 ] }, { "type": "title", "bbox": [ 108, 395, 200, 408 ], "lines": [ { "bbox": [ 104, 394, 201, 411 ], "spans": [ { "bbox": [ 104, 394, 201, 411 ], "score": 1.0, "content": "2 BACKGROUND", "type": "text" } ], "index": 26 } ], "index": 26 }, { "type": "text", "bbox": [ 106, 418, 505, 502 ], "lines": [ { "bbox": [ 104, 416, 504, 434 ], "spans": [ { "bbox": [ 104, 416, 177, 434 ], "score": 1.0, "content": "Notations. Let", "type": "text" }, { "bbox": [ 177, 419, 230, 431 ], "score": 0.93, "content": "G = ( V , E )", "type": "inline_equation" }, { "bbox": [ 230, 416, 347, 434 ], "score": 1.0, "content": "represent the graph, where", "type": "text" }, { "bbox": [ 347, 420, 357, 429 ], "score": 0.8, "content": "V", "type": "inline_equation" }, { "bbox": [ 357, 416, 447, 434 ], "score": 1.0, "content": "is the set of vertices", "type": "text" }, { "bbox": [ 447, 419, 504, 431 ], "score": 0.78, "content": "\\{ v _ { 1 } , \\cdots , v _ { N } \\}", "type": "inline_equation" } ], "index": 27 }, { "bbox": [ 103, 428, 506, 444 ], "spans": [ { "bbox": [ 103, 428, 128, 444 ], "score": 1.0, "content": "with", "type": "text" }, { "bbox": [ 128, 430, 168, 442 ], "score": 0.91, "content": "| V | = N", "type": "inline_equation" }, { "bbox": [ 168, 428, 188, 444 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 189, 431, 198, 441 ], "score": 0.82, "content": "E", "type": "inline_equation" }, { "bbox": [ 198, 428, 432, 444 ], "score": 1.0, "content": "is the set of edges. The adjacency matrix is defined as", "type": "text" }, { "bbox": [ 432, 431, 503, 443 ], "score": 0.85, "content": "\\mathbf { A } \\in \\{ 0 , 1 \\} ^ { N \\times N }", "type": "inline_equation" }, { "bbox": [ 503, 428, 506, 444 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 28 }, { "bbox": [ 101, 440, 510, 471 ], "spans": [ { "bbox": [ 101, 440, 124, 471 ], "score": 1.0, "content": "and nod", "type": "text" }, { "bbox": [ 125, 442, 162, 453 ], "score": 0.91, "content": "\\mathbf { A } _ { i j } = 1", "type": "inline_equation" }, { "bbox": [ 169, 440, 221, 471 ], "score": 1.0, "content": "f and only if denote the d", "type": "text" }, { "bbox": [ 222, 442, 274, 454 ], "score": 0.93, "content": "( v _ { i } , v _ { j } ) \\in E", "type": "inline_equation" }, { "bbox": [ 274, 440, 297, 471 ], "score": 1.0, "content": ". Let ee ma", "type": "text" }, { "bbox": [ 297, 441, 383, 453 ], "score": 0.93, "content": "\\mathcal { N } _ { i } \\overset { \\cdot } { = } \\{ v _ { j } \\vert \\mathbf { A } _ { i j } = 1 \\}", "type": "inline_equation" }, { "bbox": [ 419, 440, 510, 471 ], "score": 1.0, "content": "the neighborhood of. The feature matrix", "type": "text" } ], "index": 29 }, { "bbox": [ 129, 452, 419, 466 ], "spans": [ { "bbox": [ 129, 455, 139, 464 ], "score": 0.85, "content": "v _ { i }", "type": "inline_equation" }, { "bbox": [ 159, 453, 169, 463 ], "score": 0.7, "content": "\\mathbf { D }", "type": "inline_equation" }, { "bbox": [ 345, 452, 419, 466 ], "score": 0.93, "content": "\\begin{array} { r } { \\dot { \\bf D } _ { i i } = \\dot { \\sum } _ { j = 1 } ^ { n } { \\bf A } _ { i j } } \\end{array}", "type": "inline_equation" } ], "index": 30 }, { "bbox": [ 104, 463, 506, 480 ], "spans": [ { "bbox": [ 104, 463, 163, 480 ], "score": 1.0, "content": "is denoted as", "type": "text" }, { "bbox": [ 164, 465, 215, 476 ], "score": 0.91, "content": "\\mathbf { X } \\in \\mathbb { R } ^ { N \\times F }", "type": "inline_equation" }, { "bbox": [ 215, 463, 289, 480 ], "score": 1.0, "content": "where each node", "type": "text" }, { "bbox": [ 290, 468, 297, 476 ], "score": 0.78, "content": "v", "type": "inline_equation" }, { "bbox": [ 297, 463, 382, 480 ], "score": 1.0, "content": "is associated with a", "type": "text" }, { "bbox": [ 382, 467, 391, 476 ], "score": 0.83, "content": "F", "type": "inline_equation" }, { "bbox": [ 391, 463, 506, 480 ], "score": 1.0, "content": "-dimensional feature vector", "type": "text" } ], "index": 31 }, { "bbox": [ 106, 474, 506, 490 ], "spans": [ { "bbox": [ 106, 477, 120, 488 ], "score": 0.82, "content": "\\mathbf { X } _ { v }", "type": "inline_equation" }, { "bbox": [ 121, 474, 125, 490 ], "score": 1.0, "content": ".", "type": "text" }, { "bbox": [ 126, 477, 192, 489 ], "score": 0.87, "content": "\\mathbf { Y } \\in \\{ 0 , 1 \\} ^ { N \\times C }", "type": "inline_equation" }, { "bbox": [ 192, 474, 352, 490 ], "score": 1.0, "content": "denote the one-hot label matrix, where", "type": "text" }, { "bbox": [ 353, 477, 408, 489 ], "score": 0.94, "content": "\\mathbf { Y } _ { i } \\in \\{ 0 , 1 \\} ^ { C }", "type": "inline_equation" }, { "bbox": [ 409, 474, 506, 490 ], "score": 1.0, "content": "is a one-hot vector and", "type": "text" } ], "index": 32 }, { "bbox": [ 107, 483, 239, 509 ], "spans": [ { "bbox": [ 107, 488, 168, 504 ], "score": 0.91, "content": "\\begin{array} { r } { \\sum _ { j = 1 } ^ { C } \\mathbf { Y } _ { i j } = 1 } \\end{array}", "type": "inline_equation" }, { "bbox": [ 168, 483, 200, 509 ], "score": 1.0, "content": "for any", "type": "text" }, { "bbox": [ 200, 491, 230, 501 ], "score": 0.91, "content": "v _ { i } \\in V", "type": "inline_equation" }, { "bbox": [ 230, 483, 239, 509 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 33 } ], "index": 30, "bbox_fs": [ 101, 416, 510, 509 ] }, { "type": "text", "bbox": [ 106, 514, 505, 548 ], "lines": [ { "bbox": [ 106, 514, 505, 527 ], "spans": [ { "bbox": [ 106, 514, 505, 527 ], "score": 1.0, "content": "GNN. Graph Neural Network (GNN) is a type of neural network that directly operates on the graph", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 525, 505, 538 ], "spans": [ { "bbox": [ 106, 525, 505, 538 ], "score": 1.0, "content": "structure, such as GCN and GAT (Kipf & Welling, 2017; Velickovi ˇ c et al., 2018), that capture the ´", "type": "text" } ], "index": 35 }, { "bbox": [ 106, 536, 410, 550 ], "spans": [ { "bbox": [ 106, 536, 410, 550 ], "score": 1.0, "content": "dependence of graphs via message passing between the nodes of a graph as", "type": "text" } ], "index": 36 } ], "index": 35, "bbox_fs": [ 106, 514, 505, 550 ] }, { "type": "interline_equation", "bbox": [ 258, 549, 351, 564 ], "lines": [ { "bbox": [ 258, 549, 351, 564 ], "spans": [ { "bbox": [ 258, 549, 351, 564 ], "score": 0.92, "content": "\\mathbf { H } ^ { ( \\ell ) } = f ( \\mathbf { A } , \\mathbf { H } ^ { ( \\ell - 1 ) } ) ,", "type": "interline_equation", "image_path": "a0a846dead3255d0f75f83845cabc54956e351f1d16184644971b29cc873b6b0.jpg" } ] } ], "index": 37, "virtual_lines": [ { "bbox": [ 258, 549, 351, 564 ], "spans": [], "index": 37 } ] }, { "type": "text", "bbox": [ 107, 566, 505, 606 ], "lines": [ { "bbox": [ 105, 565, 505, 580 ], "spans": [ { "bbox": [ 105, 565, 132, 580 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 568, 140, 578 ], "score": 0.85, "content": "f", "type": "inline_equation" }, { "bbox": [ 140, 565, 351, 580 ], "score": 1.0, "content": "denotes the specific GNN layer for different models,", "type": "text" }, { "bbox": [ 351, 566, 371, 577 ], "score": 0.9, "content": "\\mathbf { H } ^ { ( \\ell ) }", "type": "inline_equation" }, { "bbox": [ 371, 565, 487, 580 ], "score": 1.0, "content": "are the hidden vectors of the", "type": "text" }, { "bbox": [ 488, 568, 493, 577 ], "score": 0.7, "content": "\\ell", "type": "inline_equation" }, { "bbox": [ 493, 565, 505, 580 ], "score": 1.0, "content": "-th", "type": "text" } ], "index": 38 }, { "bbox": [ 104, 577, 506, 592 ], "spans": [ { "bbox": [ 104, 577, 145, 592 ], "score": 1.0, "content": "layer and", "type": "text" }, { "bbox": [ 145, 578, 188, 590 ], "score": 0.91, "content": "\\mathbf { H } ^ { ( 0 ) } = \\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 188, 577, 246, 592 ], "score": 1.0, "content": ". For example,", "type": "text" }, { "bbox": [ 246, 578, 339, 591 ], "score": 0.92, "content": "\\dot { f ( \\mathbf { A } , \\mathbf { H } ) } = \\sigma ( \\hat { \\mathbf { A } } \\mathbf { H } \\mathbf { W } )", "type": "inline_equation" }, { "bbox": [ 340, 577, 407, 592 ], "score": 1.0, "content": "for GCN, where", "type": "text" }, { "bbox": [ 407, 578, 483, 590 ], "score": 0.88, "content": "\\hat { \\mathbf { A } } = \\tilde { \\mathbf { D } } ^ { - \\frac { 1 } { 2 } } \\tilde { \\mathbf { A } } \\tilde { \\mathbf { D } } ^ { - \\frac { 1 } { 2 } } ,", "type": "inline_equation" }, { "bbox": [ 484, 578, 495, 590 ], "score": 0.47, "content": "\\tilde { \\bf D }", "type": "inline_equation" }, { "bbox": [ 495, 577, 506, 592 ], "score": 1.0, "content": "is", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 590, 356, 606 ], "spans": [ { "bbox": [ 105, 590, 189, 606 ], "score": 1.0, "content": "the degree matrix of", "type": "text" }, { "bbox": [ 190, 591, 199, 603 ], "score": 0.79, "content": "\\tilde { \\mathbf { A } }", "type": "inline_equation" }, { "bbox": [ 199, 590, 220, 606 ], "score": 1.0, "content": ", i.e.,", "type": "text" }, { "bbox": [ 220, 591, 281, 606 ], "score": 0.93, "content": "\\begin{array} { r } { \\tilde { \\bf D } _ { i i } = \\sum _ { j } \\tilde { \\bf A } _ { i j } } \\end{array}", "type": "inline_equation" }, { "bbox": [ 282, 590, 302, 606 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 303, 591, 351, 603 ], "score": 0.88, "content": "\\tilde { \\mathbf { A } } = \\mathbf { A } + \\mathbf { I }", "type": "inline_equation" }, { "bbox": [ 351, 590, 356, 606 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 40 } ], "index": 39, "bbox_fs": [ 104, 565, 506, 606 ] }, { "type": "text", "bbox": [ 106, 616, 506, 725 ], "lines": [ { "bbox": [ 106, 617, 506, 629 ], "spans": [ { "bbox": [ 106, 617, 432, 629 ], "score": 1.0, "content": "Topology-level Augmentation. Topology-level augmentation usually perturbs", "type": "text" }, { "bbox": [ 432, 617, 441, 627 ], "score": 0.42, "content": "\\mathbf { A }", "type": "inline_equation" }, { "bbox": [ 442, 617, 506, 629 ], "score": 1.0, "content": "to generate dif-", "type": "text" } ], "index": 41 }, { "bbox": [ 106, 627, 505, 640 ], "spans": [ { "bbox": [ 106, 627, 325, 640 ], "score": 1.0, "content": "ferent graph structures, which can be formulated as", "type": "text" }, { "bbox": [ 326, 627, 393, 639 ], "score": 0.91, "content": "\\mathbf { A } ^ { \\prime } = \\mathcal { F } ( \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 393, 627, 426, 640 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 426, 628, 446, 639 ], "score": 0.89, "content": "\\mathcal F ( \\cdot )", "type": "inline_equation" }, { "bbox": [ 447, 627, 505, 640 ], "score": 1.0, "content": "is a structure", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 638, 504, 652 ], "spans": [ { "bbox": [ 105, 638, 418, 652 ], "score": 1.0, "content": "perturbation function. For example, DropEdge (Rong et al., 2020) considers", "type": "text" }, { "bbox": [ 419, 639, 504, 650 ], "score": 0.91, "content": "\\mathcal { F } ( \\mathbf { A } , \\mathbf { X } ) = \\mathbf { A } - \\mathbf { A _ { s } }", "type": "inline_equation" } ], "index": 43 }, { "bbox": [ 106, 650, 506, 662 ], "spans": [ { "bbox": [ 106, 650, 204, 662 ], "score": 1.0, "content": "which is independent of", "type": "text" }, { "bbox": [ 204, 650, 213, 660 ], "score": 0.64, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 214, 650, 244, 662 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 244, 650, 258, 660 ], "score": 0.88, "content": "\\mathbf { A _ { s } }", "type": "inline_equation" }, { "bbox": [ 259, 650, 494, 662 ], "score": 1.0, "content": "is a sparse matrix consists of a subset of the original edges", "type": "text" }, { "bbox": [ 494, 650, 503, 659 ], "score": 0.8, "content": "E", "type": "inline_equation" }, { "bbox": [ 503, 650, 506, 662 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 659, 506, 675 ], "spans": [ { "bbox": [ 105, 659, 506, 675 ], "score": 1.0, "content": "GAUG-O (Zhao et al., 2021) leverages their proposed neural edge predictors to produce a different", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 672, 506, 691 ], "spans": [ { "bbox": [ 105, 672, 145, 690 ], "score": 1.0, "content": "structure", "type": "text" }, { "bbox": [ 145, 675, 158, 686 ], "score": 0.82, "content": "\\mathbf { A } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 158, 672, 187, 690 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 187, 672, 315, 691 ], "score": 0.87, "content": "\\begin{array} { r } { \\mathbf { A } _ { i j } ^ { \\prime } = \\left\\lfloor \\frac { 1 } { 1 + e ^ { - \\left( \\log \\mathbf { P } _ { i j } + G \\right) / \\tau } } + \\frac { 1 } { 2 } \\right\\rfloor } \\end{array}", "type": "inline_equation" }, { "bbox": [ 315, 674, 319, 689 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 320, 673, 435, 690 ], "score": 0.66, "content": "\\mathbf { P } _ { i j } = \\alpha \\mathbf { M } _ { i j } + ( 1 - \\alpha ) \\mathbf { A } _ { i j }", "type": "inline_equation" }, { "bbox": [ 435, 674, 438, 689 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 439, 673, 502, 688 ], "score": 0.91, "content": "\\mathbf { M } = { \\boldsymbol { \\sigma } } \\left( \\mathbf { Z } \\mathbf { Z } ^ { T } \\right)", "type": "inline_equation" }, { "bbox": [ 502, 674, 506, 689 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 46 }, { "bbox": [ 106, 689, 506, 703 ], "spans": [ { "bbox": [ 106, 690, 191, 703 ], "score": 0.88, "content": "\\mathbf { Z } = f \\left( \\mathbf { A } , f ( \\mathbf { A } , \\mathbf { X } ) \\right)", "type": "inline_equation" }, { "bbox": [ 191, 689, 195, 703 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 195, 693, 203, 701 ], "score": 0.72, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 203, 689, 409, 703 ], "score": 1.0, "content": "is the temperature of Gumbel-Softmax distribution,", "type": "text" }, { "bbox": [ 409, 690, 488, 703 ], "score": 0.88, "content": "G \\sim { \\mathrm { G u m b e l } } ( 0 , 1 )", "type": "inline_equation" }, { "bbox": [ 488, 689, 506, 703 ], "score": 1.0, "content": "is a", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 700, 506, 715 ], "spans": [ { "bbox": [ 105, 700, 222, 715 ], "score": 1.0, "content": "Gumbel random variate, and", "type": "text" }, { "bbox": [ 222, 703, 230, 711 ], "score": 0.81, "content": "\\alpha", "type": "inline_equation" }, { "bbox": [ 231, 700, 506, 715 ], "score": 1.0, "content": "is a hyperparameter mediating the influence of edge predictor on the", "type": "text" } ], "index": 48 }, { "bbox": [ 105, 712, 167, 725 ], "spans": [ { "bbox": [ 105, 712, 167, 725 ], "score": 1.0, "content": "original graph.", "type": "text" } ], "index": 49 } ], "index": 45, "bbox_fs": [ 105, 617, 506, 725 ] } ] }, { "preproc_blocks": [ { "type": "title", "bbox": [ 106, 83, 250, 94 ], "lines": [ { "bbox": [ 106, 82, 252, 95 ], "spans": [ { "bbox": [ 106, 82, 164, 95 ], "score": 1.0, "content": "Feature-level", "type": "text" }, { "bbox": [ 185, 82, 252, 95 ], "score": 1.0, "content": "Augmentation.", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 106, 95, 250, 170 ], "lines": [ { "bbox": [ 105, 92, 251, 105 ], "spans": [ { "bbox": [ 105, 92, 251, 105 ], "score": 1.0, "content": "Besides, feature-level augmenta-", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 104, 250, 116 ], "spans": [ { "bbox": [ 105, 104, 250, 116 ], "score": 1.0, "content": "tion function can be defines as", "type": "text" } ], "index": 2 }, { "bbox": [ 106, 114, 250, 128 ], "spans": [ { "bbox": [ 106, 115, 179, 127 ], "score": 0.92, "content": "\\mathbf { X } ^ { \\prime } \\ = \\ \\mathcal { H } ( \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 180, 114, 216, 128 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 216, 115, 236, 127 ], "score": 0.89, "content": "\\mathcal { H } ( \\cdot )", "type": "inline_equation" }, { "bbox": [ 237, 114, 250, 128 ], "score": 1.0, "content": "is", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 126, 251, 138 ], "spans": [ { "bbox": [ 105, 126, 251, 138 ], "score": 1.0, "content": "a feature perturbation function.", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 136, 251, 150 ], "spans": [ { "bbox": [ 105, 136, 251, 150 ], "score": 1.0, "content": "FLAG (Kong et al., 2020) de-", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 148, 250, 160 ], "spans": [ { "bbox": [ 106, 148, 250, 160 ], "score": 1.0, "content": "fines the perturbation function", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 158, 250, 171 ], "spans": [ { "bbox": [ 105, 158, 120, 171 ], "score": 1.0, "content": "as", "type": "text" }, { "bbox": [ 121, 159, 218, 171 ], "score": 0.9, "content": "\\begin{array} { r } { \\mathcal { H } ( \\mathbf { A } , \\mathbf { X } ) = \\textbf { X } + \\boldsymbol { \\delta } } \\end{array}", "type": "inline_equation" }, { "bbox": [ 218, 158, 250, 171 ], "score": 1.0, "content": "where", "type": "text" } ], "index": 7 } ], "index": 4 }, { "type": "table", "bbox": [ 260, 97, 500, 157 ], "blocks": [ { "type": "table_caption", "bbox": [ 263, 82, 497, 94 ], "group_id": 0, "lines": [ { "bbox": [ 263, 81, 497, 96 ], "spans": [ { "bbox": [ 263, 81, 497, 96 ], "score": 1.0, "content": "Table 1: Comparison of existing graph data augmentation.", "type": "text" } ], "index": 8 } ], "index": 8 }, { "type": "table_body", "bbox": [ 260, 97, 500, 157 ], "group_id": 0, "lines": [ { "bbox": [ 260, 97, 500, 157 ], "spans": [ { "bbox": [ 260, 97, 500, 157 ], "score": 0.976, "html": "
GraphData Augmentation
MethodConsideredPartTypePerturbed Part
DropEdgeASamplingA
GAUG-OA&XReconstruction
FLAGXNoise Injection
G-GCNA&XReconstructionAXX
Local AugmentationA&XGenerationX
", "type": "table", "image_path": "5d6da21b94eb34cdd0c21f3825cbb171febdf0012edef9ac16f22ab5a0c47b02.jpg" } ] } ], "index": 10.5, "virtual_lines": [ { "bbox": [ 260, 97, 500, 112.0 ], "spans": [], "index": 9 }, { "bbox": [ 260, 112.0, 500, 127.0 ], "spans": [], "index": 10 }, { "bbox": [ 260, 127.0, 500, 142.0 ], "spans": [], "index": 11 }, { "bbox": [ 260, 142.0, 500, 157.0 ], "spans": [], "index": 12 } ] } ], "index": 9.25 }, { "type": "text", "bbox": [ 106, 170, 505, 263 ], "lines": [ { "bbox": [ 105, 169, 505, 183 ], "spans": [ { "bbox": [ 105, 169, 159, 183 ], "score": 1.0, "content": "perturbation", "type": "text" }, { "bbox": [ 159, 171, 166, 180 ], "score": 0.74, "content": "\\pmb { \\delta }", "type": "inline_equation" }, { "bbox": [ 167, 169, 505, 183 ], "score": 1.0, "content": "is updated iteratively during the adversarial training phase. G-GCN (plain) (Zhu", "type": "text" } ], "index": 13 }, { "bbox": [ 104, 180, 506, 196 ], "spans": [ { "bbox": [ 104, 180, 336, 196 ], "score": 1.0, "content": "et al., 2020) obtains the global attribute feature matrix", "type": "text" }, { "bbox": [ 336, 181, 402, 192 ], "score": 0.92, "content": "\\mathbf { X } ^ { ( a ) } \\in \\bar { \\mathbb { R } ^ { N \\times d _ { a } } }", "type": "inline_equation" }, { "bbox": [ 402, 180, 506, 196 ], "score": 1.0, "content": "through minimizing the", "type": "text" } ], "index": 14 }, { "bbox": [ 104, 197, 505, 220 ], "spans": [ { "bbox": [ 104, 197, 299, 220 ], "score": 1.0, "content": "objective Qv∈V Qa∈CA(v) v a Pk∈U exp\u0010X(a)v ·Vk\u0011", "type": "text" }, { "bbox": [ 299, 198, 327, 211 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 328, 199, 337, 208 ], "score": 0.82, "content": "U", "type": "inline_equation" }, { "bbox": [ 338, 198, 448, 211 ], "score": 1.0, "content": "is the set of all attributes,", "type": "text" }, { "bbox": [ 448, 198, 478, 210 ], "score": 0.91, "content": "C A ( v )", "type": "inline_equation" }, { "bbox": [ 478, 198, 505, 211 ], "score": 1.0, "content": "is the", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 215, 506, 232 ], "spans": [ { "bbox": [ 105, 215, 222, 232 ], "score": 1.0, "content": "sampled context attributes of", "type": "text" }, { "bbox": [ 222, 221, 228, 228 ], "score": 0.75, "content": "v", "type": "inline_equation" }, { "bbox": [ 228, 215, 248, 232 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 248, 218, 299, 229 ], "score": 0.87, "content": "\\mathbf { V } \\in \\mathbb { R } ^ { d _ { a } \\times F }", "type": "inline_equation" }, { "bbox": [ 299, 215, 506, 232 ], "score": 1.0, "content": "denotes the parameters. Obviously, the perturbation", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 229, 505, 242 ], "spans": [ { "bbox": [ 106, 229, 505, 242 ], "score": 1.0, "content": "function of G-GCN has no close-form solution. In this work, we propose a novel feature-level", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 241, 504, 252 ], "spans": [ { "bbox": [ 106, 241, 504, 252 ], "score": 1.0, "content": "augmentation method, named local augmentation. And the comparison of the details of various graph", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 251, 326, 263 ], "spans": [ { "bbox": [ 106, 251, 326, 263 ], "score": 1.0, "content": "data augmentation techniques can be found in Table 1.", "type": "text" } ], "index": 19 } ], "index": 16 }, { "type": "title", "bbox": [ 108, 282, 249, 294 ], "lines": [ { "bbox": [ 105, 280, 251, 297 ], "spans": [ { "bbox": [ 105, 280, 251, 297 ], "score": 1.0, "content": "3 LOCAL AUGMENTATION", "type": "text" } ], "index": 20 } ], "index": 20 }, { "type": "text", "bbox": [ 106, 308, 506, 419 ], "lines": [ { "bbox": [ 105, 308, 506, 321 ], "spans": [ { "bbox": [ 105, 308, 506, 321 ], "score": 1.0, "content": "In this section, we describe details of the proposed method. The local augmentation framework", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 320, 505, 332 ], "spans": [ { "bbox": [ 106, 320, 505, 332 ], "score": 1.0, "content": "consists of three modules: learning the conditional distribution via a generative model, the active", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 330, 506, 343 ], "spans": [ { "bbox": [ 105, 330, 506, 343 ], "score": 1.0, "content": "learning trick, and the downstream GNN models, as illustrated in Figure 1. Note that the proposed", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 343, 506, 354 ], "spans": [ { "bbox": [ 106, 343, 506, 354 ], "score": 1.0, "content": "algorithm enhances the locality of node representations through augmenting 1-hop neighbors in a", "type": "text" } ], "index": 24 }, { "bbox": [ 104, 353, 506, 365 ], "spans": [ { "bbox": [ 104, 353, 506, 365 ], "score": 1.0, "content": "generative way. Specifically, we exploit a generative model to learn the conditional distribution of", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 363, 506, 376 ], "spans": [ { "bbox": [ 105, 363, 506, 376 ], "score": 1.0, "content": "the connected neighbors’ representations given the representation of a node. We describe the details", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 374, 506, 387 ], "spans": [ { "bbox": [ 105, 374, 506, 387 ], "score": 1.0, "content": "of learning the conditional distribution and the motivation for why local augmentation is able to", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 385, 506, 398 ], "spans": [ { "bbox": [ 105, 385, 506, 398 ], "score": 1.0, "content": "improve the performance in a probabilistic view in Sec. 3.1, detail the architecture of downstream", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 396, 506, 409 ], "spans": [ { "bbox": [ 106, 396, 506, 409 ], "score": 1.0, "content": "GNN models in Sec. 3.2. We finally elaborate the training procedure of both the generative model", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 407, 409, 419 ], "spans": [ { "bbox": [ 105, 407, 409, 419 ], "score": 1.0, "content": "and the downstream GNN models with the active learning trick in Sec. 3.3.", "type": "text" } ], "index": 30 } ], "index": 25.5 }, { "type": "image", "bbox": [ 111, 433, 497, 552 ], "blocks": [ { "type": "image_body", "bbox": [ 111, 433, 497, 552 ], "group_id": 0, "lines": [ { "bbox": [ 111, 433, 497, 552 ], "spans": [ { "bbox": [ 111, 433, 497, 552 ], "score": 0.97, "type": "image", "image_path": "a25e0a452d09cb122f2cc05b960b1e984bdab4b6769823194b1ac823b6b03d23.jpg" } ] } ], "index": 32, "virtual_lines": [ { "bbox": [ 111, 433, 497, 472.6666666666667 ], "spans": [], "index": 31 }, { "bbox": [ 111, 472.6666666666667, 497, 512.3333333333334 ], "spans": [], "index": 32 }, { "bbox": [ 111, 512.3333333333334, 497, 552.0 ], "spans": [], "index": 33 } ] }, { "type": "image_caption", "bbox": [ 106, 564, 506, 599 ], "group_id": 0, "lines": [ { "bbox": [ 106, 564, 506, 578 ], "spans": [ { "bbox": [ 106, 564, 506, 578 ], "score": 1.0, "content": "Figure 1: A schematic depiction of our local augmentation. The purple and yellow circles on the", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 576, 505, 588 ], "spans": [ { "bbox": [ 106, 576, 505, 588 ], "score": 1.0, "content": "graph correspond to the central node and its augmented neighbors respectively. After augmenting the", "type": "text" } ], "index": 35 }, { "bbox": [ 106, 587, 506, 599 ], "spans": [ { "bbox": [ 106, 587, 506, 599 ], "score": 1.0, "content": "neighborhood, we exploit the initial and the generated feature matrix as input for downstream GNNs.", "type": "text" } ], "index": 36 } ], "index": 35 } ], "index": 33.5 }, { "type": "title", "bbox": [ 107, 609, 328, 621 ], "lines": [ { "bbox": [ 106, 609, 329, 622 ], "spans": [ { "bbox": [ 106, 609, 329, 622 ], "score": 1.0, "content": "3.1 LEARNING THE CONDITIONAL DISTRIBUTION", "type": "text" } ], "index": 37 } ], "index": 37 }, { "type": "text", "bbox": [ 106, 631, 505, 708 ], "lines": [ { "bbox": [ 105, 630, 506, 645 ], "spans": [ { "bbox": [ 105, 630, 506, 645 ], "score": 1.0, "content": "We start by reviewing the semi-supervised learning of GNNs in a probabilistic view. Most existing", "type": "text" } ], "index": 38 }, { "bbox": [ 106, 642, 506, 655 ], "spans": [ { "bbox": [ 106, 642, 506, 655 ], "score": 1.0, "content": "GNN models (Kipf & Welling, 2017; Velickovi ˇ c et al., 2018) are viewed as a classification function ´", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 653, 506, 666 ], "spans": [ { "bbox": [ 105, 653, 506, 666 ], "score": 1.0, "content": "to predict the class labels of the graph nodes. In this work, we use a GNN classification estimator", "type": "text" } ], "index": 40 }, { "bbox": [ 107, 664, 505, 677 ], "spans": [ { "bbox": [ 107, 664, 160, 676 ], "score": 0.91, "content": "P _ { \\theta } ( \\mathbf { Y } | \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 160, 664, 164, 677 ], "score": 0.0, "content": "", "type": "text" }, { "bbox": [ 165, 665, 171, 675 ], "score": 0.69, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 171, 664, 418, 677 ], "score": 1.0, "content": "is the parameter) to model the conditional distribution of label", "type": "text" }, { "bbox": [ 419, 664, 429, 674 ], "score": 0.49, "content": "\\mathbf { Y }", "type": "inline_equation" }, { "bbox": [ 429, 664, 505, 677 ], "score": 1.0, "content": "with respect to the", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 675, 506, 687 ], "spans": [ { "bbox": [ 105, 675, 363, 687 ], "score": 1.0, "content": "graph structure A and feature matrix X. Given training samples", "type": "text" }, { "bbox": [ 363, 675, 409, 687 ], "score": 0.92, "content": "\\{ \\mathbf { A } , \\mathbf { X } , \\mathbf { Y } \\}", "type": "inline_equation" }, { "bbox": [ 409, 675, 469, 687 ], "score": 1.0, "content": ", the parameter", "type": "text" }, { "bbox": [ 470, 676, 476, 685 ], "score": 0.8, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 476, 675, 506, 687 ], "score": 1.0, "content": "can be", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 686, 506, 699 ], "spans": [ { "bbox": [ 105, 686, 506, 699 ], "score": 1.0, "content": "estimated using Maximum Likelihood Estimation (MLE), by optimizing the following likelihood", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 696, 145, 709 ], "spans": [ { "bbox": [ 105, 696, 145, 709 ], "score": 1.0, "content": "function:", "type": "text" } ], "index": 44 } ], "index": 41 }, { "type": "interline_equation", "bbox": [ 253, 708, 357, 735 ], "lines": [ { "bbox": [ 253, 708, 357, 735 ], "spans": [ { "bbox": [ 253, 708, 357, 735 ], "score": 0.94, "content": "\\operatorname* { m a x } \\prod _ { k \\in \\mathbf { K } } P _ { \\theta } \\left( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } \\right) ,", "type": "interline_equation", "image_path": "86a941f44b7532046443800c354539300c31a30f35ec36c9839d937e4f3f402b.jpg" } ] } ], "index": 45.5, "virtual_lines": [ { "bbox": [ 253, 708, 357, 721.5 ], "spans": [], "index": 45 }, { "bbox": [ 253, 721.5, 357, 735.0 ], "spans": [], "index": 46 } ] } ], "page_idx": 2, "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 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 751, 309, 760 ], "lines": [ { "bbox": [ 301, 750, 310, 762 ], "spans": [ { "bbox": [ 301, 750, 310, 762 ], "score": 1.0, "content": "3", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "title", "bbox": [ 106, 83, 250, 94 ], "lines": [ { "bbox": [ 106, 82, 252, 95 ], "spans": [ { "bbox": [ 106, 82, 164, 95 ], "score": 1.0, "content": "Feature-level", "type": "text" }, { "bbox": [ 185, 82, 252, 95 ], "score": 1.0, "content": "Augmentation.", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 106, 95, 250, 170 ], "lines": [ { "bbox": [ 105, 92, 251, 105 ], "spans": [ { "bbox": [ 105, 92, 251, 105 ], "score": 1.0, "content": "Besides, feature-level augmenta-", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 104, 250, 116 ], "spans": [ { "bbox": [ 105, 104, 250, 116 ], "score": 1.0, "content": "tion function can be defines as", "type": "text" } ], "index": 2 }, { "bbox": [ 106, 114, 250, 128 ], "spans": [ { "bbox": [ 106, 115, 179, 127 ], "score": 0.92, "content": "\\mathbf { X } ^ { \\prime } \\ = \\ \\mathcal { H } ( \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 180, 114, 216, 128 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 216, 115, 236, 127 ], "score": 0.89, "content": "\\mathcal { H } ( \\cdot )", "type": "inline_equation" }, { "bbox": [ 237, 114, 250, 128 ], "score": 1.0, "content": "is", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 126, 251, 138 ], "spans": [ { "bbox": [ 105, 126, 251, 138 ], "score": 1.0, "content": "a feature perturbation function.", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 136, 251, 150 ], "spans": [ { "bbox": [ 105, 136, 251, 150 ], "score": 1.0, "content": "FLAG (Kong et al., 2020) de-", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 148, 250, 160 ], "spans": [ { "bbox": [ 106, 148, 250, 160 ], "score": 1.0, "content": "fines the perturbation function", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 158, 250, 171 ], "spans": [ { "bbox": [ 105, 158, 120, 171 ], "score": 1.0, "content": "as", "type": "text" }, { "bbox": [ 121, 159, 218, 171 ], "score": 0.9, "content": "\\begin{array} { r } { \\mathcal { H } ( \\mathbf { A } , \\mathbf { X } ) = \\textbf { X } + \\boldsymbol { \\delta } } \\end{array}", "type": "inline_equation" }, { "bbox": [ 218, 158, 250, 171 ], "score": 1.0, "content": "where", "type": "text" } ], "index": 7 } ], "index": 4, "bbox_fs": [ 105, 92, 251, 171 ] }, { "type": "table", "bbox": [ 260, 97, 500, 157 ], "blocks": [ { "type": "table_caption", "bbox": [ 263, 82, 497, 94 ], "group_id": 0, "lines": [ { "bbox": [ 263, 81, 497, 96 ], "spans": [ { "bbox": [ 263, 81, 497, 96 ], "score": 1.0, "content": "Table 1: Comparison of existing graph data augmentation.", "type": "text" } ], "index": 8 } ], "index": 8 }, { "type": "table_body", "bbox": [ 260, 97, 500, 157 ], "group_id": 0, "lines": [ { "bbox": [ 260, 97, 500, 157 ], "spans": [ { "bbox": [ 260, 97, 500, 157 ], "score": 0.976, "html": "
GraphData Augmentation
MethodConsideredPartTypePerturbed Part
DropEdgeASamplingA
GAUG-OA&XReconstruction
FLAGXNoise Injection
G-GCNA&XReconstructionAXX
Local AugmentationA&XGenerationX
", "type": "table", "image_path": "5d6da21b94eb34cdd0c21f3825cbb171febdf0012edef9ac16f22ab5a0c47b02.jpg" } ] } ], "index": 10.5, "virtual_lines": [ { "bbox": [ 260, 97, 500, 112.0 ], "spans": [], "index": 9 }, { "bbox": [ 260, 112.0, 500, 127.0 ], "spans": [], "index": 10 }, { "bbox": [ 260, 127.0, 500, 142.0 ], "spans": [], "index": 11 }, { "bbox": [ 260, 142.0, 500, 157.0 ], "spans": [], "index": 12 } ] } ], "index": 9.25 }, { "type": "text", "bbox": [ 106, 170, 505, 263 ], "lines": [ { "bbox": [ 105, 169, 505, 183 ], "spans": [ { "bbox": [ 105, 169, 159, 183 ], "score": 1.0, "content": "perturbation", "type": "text" }, { "bbox": [ 159, 171, 166, 180 ], "score": 0.74, "content": "\\pmb { \\delta }", "type": "inline_equation" }, { "bbox": [ 167, 169, 505, 183 ], "score": 1.0, "content": "is updated iteratively during the adversarial training phase. G-GCN (plain) (Zhu", "type": "text" } ], "index": 13 }, { "bbox": [ 104, 180, 506, 196 ], "spans": [ { "bbox": [ 104, 180, 336, 196 ], "score": 1.0, "content": "et al., 2020) obtains the global attribute feature matrix", "type": "text" }, { "bbox": [ 336, 181, 402, 192 ], "score": 0.92, "content": "\\mathbf { X } ^ { ( a ) } \\in \\bar { \\mathbb { R } ^ { N \\times d _ { a } } }", "type": "inline_equation" }, { "bbox": [ 402, 180, 506, 196 ], "score": 1.0, "content": "through minimizing the", "type": "text" } ], "index": 14 }, { "bbox": [ 104, 197, 505, 220 ], "spans": [ { "bbox": [ 104, 197, 299, 220 ], "score": 1.0, "content": "objective Qv∈V Qa∈CA(v) v a Pk∈U exp\u0010X(a)v ·Vk\u0011", "type": "text" }, { "bbox": [ 299, 198, 327, 211 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 328, 199, 337, 208 ], "score": 0.82, "content": "U", "type": "inline_equation" }, { "bbox": [ 338, 198, 448, 211 ], "score": 1.0, "content": "is the set of all attributes,", "type": "text" }, { "bbox": [ 448, 198, 478, 210 ], "score": 0.91, "content": "C A ( v )", "type": "inline_equation" }, { "bbox": [ 478, 198, 505, 211 ], "score": 1.0, "content": "is the", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 215, 506, 232 ], "spans": [ { "bbox": [ 105, 215, 222, 232 ], "score": 1.0, "content": "sampled context attributes of", "type": "text" }, { "bbox": [ 222, 221, 228, 228 ], "score": 0.75, "content": "v", "type": "inline_equation" }, { "bbox": [ 228, 215, 248, 232 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 248, 218, 299, 229 ], "score": 0.87, "content": "\\mathbf { V } \\in \\mathbb { R } ^ { d _ { a } \\times F }", "type": "inline_equation" }, { "bbox": [ 299, 215, 506, 232 ], "score": 1.0, "content": "denotes the parameters. Obviously, the perturbation", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 229, 505, 242 ], "spans": [ { "bbox": [ 106, 229, 505, 242 ], "score": 1.0, "content": "function of G-GCN has no close-form solution. In this work, we propose a novel feature-level", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 241, 504, 252 ], "spans": [ { "bbox": [ 106, 241, 504, 252 ], "score": 1.0, "content": "augmentation method, named local augmentation. And the comparison of the details of various graph", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 251, 326, 263 ], "spans": [ { "bbox": [ 106, 251, 326, 263 ], "score": 1.0, "content": "data augmentation techniques can be found in Table 1.", "type": "text" } ], "index": 19 } ], "index": 16, "bbox_fs": [ 104, 169, 506, 263 ] }, { "type": "title", "bbox": [ 108, 282, 249, 294 ], "lines": [ { "bbox": [ 105, 280, 251, 297 ], "spans": [ { "bbox": [ 105, 280, 251, 297 ], "score": 1.0, "content": "3 LOCAL AUGMENTATION", "type": "text" } ], "index": 20 } ], "index": 20 }, { "type": "text", "bbox": [ 106, 308, 506, 419 ], "lines": [ { "bbox": [ 105, 308, 506, 321 ], "spans": [ { "bbox": [ 105, 308, 506, 321 ], "score": 1.0, "content": "In this section, we describe details of the proposed method. The local augmentation framework", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 320, 505, 332 ], "spans": [ { "bbox": [ 106, 320, 505, 332 ], "score": 1.0, "content": "consists of three modules: learning the conditional distribution via a generative model, the active", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 330, 506, 343 ], "spans": [ { "bbox": [ 105, 330, 506, 343 ], "score": 1.0, "content": "learning trick, and the downstream GNN models, as illustrated in Figure 1. Note that the proposed", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 343, 506, 354 ], "spans": [ { "bbox": [ 106, 343, 506, 354 ], "score": 1.0, "content": "algorithm enhances the locality of node representations through augmenting 1-hop neighbors in a", "type": "text" } ], "index": 24 }, { "bbox": [ 104, 353, 506, 365 ], "spans": [ { "bbox": [ 104, 353, 506, 365 ], "score": 1.0, "content": "generative way. Specifically, we exploit a generative model to learn the conditional distribution of", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 363, 506, 376 ], "spans": [ { "bbox": [ 105, 363, 506, 376 ], "score": 1.0, "content": "the connected neighbors’ representations given the representation of a node. We describe the details", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 374, 506, 387 ], "spans": [ { "bbox": [ 105, 374, 506, 387 ], "score": 1.0, "content": "of learning the conditional distribution and the motivation for why local augmentation is able to", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 385, 506, 398 ], "spans": [ { "bbox": [ 105, 385, 506, 398 ], "score": 1.0, "content": "improve the performance in a probabilistic view in Sec. 3.1, detail the architecture of downstream", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 396, 506, 409 ], "spans": [ { "bbox": [ 106, 396, 506, 409 ], "score": 1.0, "content": "GNN models in Sec. 3.2. We finally elaborate the training procedure of both the generative model", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 407, 409, 419 ], "spans": [ { "bbox": [ 105, 407, 409, 419 ], "score": 1.0, "content": "and the downstream GNN models with the active learning trick in Sec. 3.3.", "type": "text" } ], "index": 30 } ], "index": 25.5, "bbox_fs": [ 104, 308, 506, 419 ] }, { "type": "image", "bbox": [ 111, 433, 497, 552 ], "blocks": [ { "type": "image_body", "bbox": [ 111, 433, 497, 552 ], "group_id": 0, "lines": [ { "bbox": [ 111, 433, 497, 552 ], "spans": [ { "bbox": [ 111, 433, 497, 552 ], "score": 0.97, "type": "image", "image_path": "a25e0a452d09cb122f2cc05b960b1e984bdab4b6769823194b1ac823b6b03d23.jpg" } ] } ], "index": 32, "virtual_lines": [ { "bbox": [ 111, 433, 497, 472.6666666666667 ], "spans": [], "index": 31 }, { "bbox": [ 111, 472.6666666666667, 497, 512.3333333333334 ], "spans": [], "index": 32 }, { "bbox": [ 111, 512.3333333333334, 497, 552.0 ], "spans": [], "index": 33 } ] }, { "type": "image_caption", "bbox": [ 106, 564, 506, 599 ], "group_id": 0, "lines": [ { "bbox": [ 106, 564, 506, 578 ], "spans": [ { "bbox": [ 106, 564, 506, 578 ], "score": 1.0, "content": "Figure 1: A schematic depiction of our local augmentation. The purple and yellow circles on the", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 576, 505, 588 ], "spans": [ { "bbox": [ 106, 576, 505, 588 ], "score": 1.0, "content": "graph correspond to the central node and its augmented neighbors respectively. After augmenting the", "type": "text" } ], "index": 35 }, { "bbox": [ 106, 587, 506, 599 ], "spans": [ { "bbox": [ 106, 587, 506, 599 ], "score": 1.0, "content": "neighborhood, we exploit the initial and the generated feature matrix as input for downstream GNNs.", "type": "text" } ], "index": 36 } ], "index": 35 } ], "index": 33.5 }, { "type": "title", "bbox": [ 107, 609, 328, 621 ], "lines": [ { "bbox": [ 106, 609, 329, 622 ], "spans": [ { "bbox": [ 106, 609, 329, 622 ], "score": 1.0, "content": "3.1 LEARNING THE CONDITIONAL DISTRIBUTION", "type": "text" } ], "index": 37 } ], "index": 37 }, { "type": "text", "bbox": [ 106, 631, 505, 708 ], "lines": [ { "bbox": [ 105, 630, 506, 645 ], "spans": [ { "bbox": [ 105, 630, 506, 645 ], "score": 1.0, "content": "We start by reviewing the semi-supervised learning of GNNs in a probabilistic view. Most existing", "type": "text" } ], "index": 38 }, { "bbox": [ 106, 642, 506, 655 ], "spans": [ { "bbox": [ 106, 642, 506, 655 ], "score": 1.0, "content": "GNN models (Kipf & Welling, 2017; Velickovi ˇ c et al., 2018) are viewed as a classification function ´", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 653, 506, 666 ], "spans": [ { "bbox": [ 105, 653, 506, 666 ], "score": 1.0, "content": "to predict the class labels of the graph nodes. In this work, we use a GNN classification estimator", "type": "text" } ], "index": 40 }, { "bbox": [ 107, 664, 505, 677 ], "spans": [ { "bbox": [ 107, 664, 160, 676 ], "score": 0.91, "content": "P _ { \\theta } ( \\mathbf { Y } | \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 160, 664, 164, 677 ], "score": 0.0, "content": "", "type": "text" }, { "bbox": [ 165, 665, 171, 675 ], "score": 0.69, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 171, 664, 418, 677 ], "score": 1.0, "content": "is the parameter) to model the conditional distribution of label", "type": "text" }, { "bbox": [ 419, 664, 429, 674 ], "score": 0.49, "content": "\\mathbf { Y }", "type": "inline_equation" }, { "bbox": [ 429, 664, 505, 677 ], "score": 1.0, "content": "with respect to the", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 675, 506, 687 ], "spans": [ { "bbox": [ 105, 675, 363, 687 ], "score": 1.0, "content": "graph structure A and feature matrix X. Given training samples", "type": "text" }, { "bbox": [ 363, 675, 409, 687 ], "score": 0.92, "content": "\\{ \\mathbf { A } , \\mathbf { X } , \\mathbf { Y } \\}", "type": "inline_equation" }, { "bbox": [ 409, 675, 469, 687 ], "score": 1.0, "content": ", the parameter", "type": "text" }, { "bbox": [ 470, 676, 476, 685 ], "score": 0.8, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 476, 675, 506, 687 ], "score": 1.0, "content": "can be", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 686, 506, 699 ], "spans": [ { "bbox": [ 105, 686, 506, 699 ], "score": 1.0, "content": "estimated using Maximum Likelihood Estimation (MLE), by optimizing the following likelihood", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 696, 145, 709 ], "spans": [ { "bbox": [ 105, 696, 145, 709 ], "score": 1.0, "content": "function:", "type": "text" } ], "index": 44 } ], "index": 41, "bbox_fs": [ 105, 630, 506, 709 ] }, { "type": "interline_equation", "bbox": [ 253, 708, 357, 735 ], "lines": [ { "bbox": [ 253, 708, 357, 735 ], "spans": [ { "bbox": [ 253, 708, 357, 735 ], "score": 0.94, "content": "\\operatorname* { m a x } \\prod _ { k \\in \\mathbf { K } } P _ { \\theta } \\left( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } \\right) ,", "type": "interline_equation", "image_path": "86a941f44b7532046443800c354539300c31a30f35ec36c9839d937e4f3f402b.jpg" } ] } ], "index": 45.5, "virtual_lines": [ { "bbox": [ 253, 708, 357, 721.5 ], "spans": [], "index": 45 }, { "bbox": [ 253, 721.5, 357, 735.0 ], "spans": [], "index": 46 } ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 106, 81, 505, 129 ], "lines": [ { "bbox": [ 106, 82, 505, 95 ], "spans": [ { "bbox": [ 106, 82, 135, 95 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 135, 83, 145, 93 ], "score": 0.64, "content": "\\mathbf { K }", "type": "inline_equation" }, { "bbox": [ 146, 82, 505, 95 ], "score": 1.0, "content": "is the set of node indices of the training dataset whose labels are visible during the", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 93, 505, 105 ], "spans": [ { "bbox": [ 105, 93, 505, 105 ], "score": 1.0, "content": "semi-supervised training. To further boost the performance of GNN, we introduce a new model", "type": "text" } ], "index": 1 }, { "bbox": [ 107, 105, 505, 119 ], "spans": [ { "bbox": [ 107, 105, 173, 118 ], "score": 0.91, "content": "P _ { \\theta } ( { \\bf Y } , \\overline { { { \\bf X } } } | { \\bf A } , { \\bf X } )", "type": "inline_equation" }, { "bbox": [ 173, 105, 204, 119 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 204, 105, 214, 116 ], "score": 0.83, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 214, 105, 505, 119 ], "score": 1.0, "content": "is generated features by feature-level augmentation. For this model, the", "type": "text" } ], "index": 2 }, { "bbox": [ 104, 116, 505, 131 ], "spans": [ { "bbox": [ 104, 116, 343, 131 ], "score": 1.0, "content": "MLE method needs to optimize a marginalized probability", "type": "text" }, { "bbox": [ 343, 118, 354, 129 ], "score": 0.89, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 355, 116, 491, 131 ], "score": 1.0, "content": "over the generated feature matrix", "type": "text" }, { "bbox": [ 491, 117, 500, 128 ], "score": 0.78, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 501, 116, 505, 131 ], "score": 1.0, "content": ":", "type": "text" } ], "index": 3 } ], "index": 1.5 }, { "type": "interline_equation", "bbox": [ 239, 135, 373, 165 ], "lines": [ { "bbox": [ 239, 135, 373, 165 ], "spans": [ { "bbox": [ 239, 135, 373, 165 ], "score": 0.94, "content": "\\operatorname* { m a x } \\prod _ { k \\in \\mathbf { K } } \\int _ { \\overline { { \\mathbf { X } } } } P _ { \\theta } \\left( \\mathbf { Y } _ { k } , \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } \\right) .", "type": "interline_equation", "image_path": "0b5072d13dff98ceb3f376b6d3e0034b60f5da232a7265602f7ff6924a32a9a8.jpg" } ] } ], "index": 4.5, "virtual_lines": [ { "bbox": [ 239, 135, 373, 150.0 ], "spans": [], "index": 4 }, { "bbox": [ 239, 150.0, 373, 165.0 ], "spans": [], "index": 5 } ] }, { "type": "text", "bbox": [ 107, 169, 493, 182 ], "lines": [ { "bbox": [ 105, 169, 494, 185 ], "spans": [ { "bbox": [ 105, 169, 270, 185 ], "score": 1.0, "content": "For Bayesian tractability, we decompose", "type": "text" }, { "bbox": [ 271, 171, 282, 181 ], "score": 0.88, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 283, 169, 494, 185 ], "score": 1.0, "content": "in Eq.(3) as a product of two posterior probabilities:", "type": "text" } ], "index": 6 } ], "index": 6 }, { "type": "interline_equation", "bbox": [ 194, 187, 416, 202 ], "lines": [ { "bbox": [ 194, 187, 416, 202 ], "spans": [ { "bbox": [ 194, 187, 416, 202 ], "score": 0.9, "content": "\\begin{array} { r } { P _ { \\theta , \\phi } ( \\mathbf { Y } _ { k } , \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } ) : = P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } , \\overline { { \\mathbf { X } } } ) Q _ { \\phi } ( \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } ) , } \\end{array}", "type": "interline_equation", "image_path": "3969838a7b935379ff9a61fd7d4acd02bfdf7dbee1d678d807fb38029ca9429a.jpg" } ] } ], "index": 7, "virtual_lines": [ { "bbox": [ 194, 187, 416, 202 ], "spans": [], "index": 7 } ] }, { "type": "text", "bbox": [ 106, 208, 505, 288 ], "lines": [ { "bbox": [ 105, 208, 506, 223 ], "spans": [ { "bbox": [ 105, 208, 134, 223 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 208, 205, 221 ], "score": 0.92, "content": "P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } , \\mathbf { \\overline { { X } } } )", "type": "inline_equation" }, { "bbox": [ 205, 208, 225, 223 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 225, 208, 279, 221 ], "score": 0.93, "content": "Q _ { \\phi } ( { \\overline { { \\mathbf { X } } } } | \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 280, 208, 506, 223 ], "score": 1.0, "content": "denote the probabilistic distributions approximated by", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 219, 506, 233 ], "spans": [ { "bbox": [ 105, 219, 506, 233 ], "score": 1.0, "content": "the downstream GNN and the (feature-level augmentation) generator respectively, parameterized", "type": "text" } ], "index": 9 }, { "bbox": [ 106, 231, 505, 244 ], "spans": [ { "bbox": [ 106, 231, 119, 244 ], "score": 1.0, "content": "by", "type": "text" }, { "bbox": [ 120, 231, 126, 241 ], "score": 0.77, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 127, 231, 145, 244 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 145, 232, 152, 243 ], "score": 0.84, "content": "\\phi", "type": "inline_equation" }, { "bbox": [ 153, 231, 505, 244 ], "score": 1.0, "content": ". There are two benefits in the decomposition above. First, it allows us to decouple", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 241, 505, 255 ], "spans": [ { "bbox": [ 105, 241, 272, 255 ], "score": 1.0, "content": "the training of the downstream predictor", "type": "text" }, { "bbox": [ 272, 243, 284, 253 ], "score": 0.89, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 284, 241, 358, 255 ], "score": 1.0, "content": "and the generator", "type": "text" }, { "bbox": [ 358, 243, 372, 254 ], "score": 0.9, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 372, 241, 505, 255 ], "score": 1.0, "content": ", enabling the generator to easily", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 253, 506, 266 ], "spans": [ { "bbox": [ 105, 253, 506, 266 ], "score": 1.0, "content": "generalize to other downstream tasks. Moreover, inspired by the successes of data augmentation via", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 263, 506, 277 ], "spans": [ { "bbox": [ 105, 263, 506, 277 ], "score": 1.0, "content": "deep-learning-based generative modeling (Antoniou et al., 2017), the representation power of Eq.(4)", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 275, 442, 288 ], "spans": [ { "bbox": [ 105, 275, 271, 288 ], "score": 1.0, "content": "is superior than that of a single predictor", "type": "text" }, { "bbox": [ 271, 275, 330, 287 ], "score": 0.93, "content": "P _ { \\theta } \\left( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } \\right)", "type": "inline_equation" }, { "bbox": [ 330, 275, 442, 288 ], "score": 1.0, "content": "without data augmentation.", "type": "text" } ], "index": 14 } ], "index": 11 }, { "type": "text", "bbox": [ 107, 291, 505, 327 ], "lines": [ { "bbox": [ 106, 291, 504, 305 ], "spans": [ { "bbox": [ 106, 291, 243, 305 ], "score": 1.0, "content": "Consequently, once a generator", "type": "text" }, { "bbox": [ 243, 292, 258, 304 ], "score": 0.89, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 258, 291, 504, 305 ], "score": 1.0, "content": "is trained very well, our training procedure can optimize", "type": "text" } ], "index": 15 }, { "bbox": [ 107, 303, 505, 317 ], "spans": [ { "bbox": [ 107, 303, 177, 317 ], "score": 0.92, "content": "P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } , \\mathbf { \\overline { { X } } } )", "type": "inline_equation" }, { "bbox": [ 178, 304, 238, 317 ], "score": 1.0, "content": "with samples", "type": "text" }, { "bbox": [ 238, 304, 248, 315 ], "score": 0.76, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 249, 304, 443, 317 ], "score": 1.0, "content": "drawn from the fixed conditional distribution", "type": "text" }, { "bbox": [ 443, 305, 457, 317 ], "score": 0.89, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 457, 304, 505, 317 ], "score": 1.0, "content": ". Now, we", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 316, 281, 328 ], "spans": [ { "bbox": [ 105, 316, 281, 328 ], "score": 1.0, "content": "show how to train the generator as follows.", "type": "text" } ], "index": 17 } ], "index": 16 }, { "type": "text", "bbox": [ 107, 339, 504, 372 ], "lines": [ { "bbox": [ 106, 338, 505, 352 ], "spans": [ { "bbox": [ 106, 338, 505, 352 ], "score": 1.0, "content": "Generator To learn a feature augmentation generator, a naive solution is to learn one single", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 350, 505, 362 ], "spans": [ { "bbox": [ 105, 350, 505, 362 ], "score": 1.0, "content": "distribution for all the neighbors using the MLE method, i.e., solving the following optimization", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 361, 144, 374 ], "spans": [ { "bbox": [ 105, 361, 144, 374 ], "score": 1.0, "content": "problem", "type": "text" } ], "index": 20 } ], "index": 19 }, { "type": "interline_equation", "bbox": [ 192, 371, 419, 399 ], "lines": [ { "bbox": [ 192, 371, 419, 399 ], "spans": [ { "bbox": [ 192, 371, 419, 399 ], "score": 0.93, "content": "\\operatorname* { m a x } _ { \\psi } \\sum _ { j \\in \\mathcal { N } _ { i } } \\log p _ { \\psi } \\left( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } \\right) = \\operatorname* { m a x } _ { \\psi } \\log \\prod _ { j \\in \\mathcal { N } _ { i } } p _ { \\psi } \\left( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } \\right) ,", "type": "interline_equation", "image_path": "c8cd49cda13ba563e1e64405644de1a1918d032610b692a84d3bf50a442af942.jpg" } ] } ], "index": 21, "virtual_lines": [ { "bbox": [ 192, 371, 419, 399 ], "spans": [], "index": 21 } ] }, { "type": "text", "bbox": [ 107, 402, 504, 425 ], "lines": [ { "bbox": [ 105, 401, 505, 415 ], "spans": [ { "bbox": [ 105, 401, 133, 415 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 402, 194, 415 ], "score": 0.93, "content": "\\{ \\mathbf { X } _ { j \\mid j \\in \\mathcal { N } _ { i } } , \\mathbf { X } _ { i } \\}", "type": "inline_equation" }, { "bbox": [ 195, 401, 221, 415 ], "score": 1.0, "content": ". Then", "type": "text" }, { "bbox": [ 221, 404, 233, 415 ], "score": 0.87, "content": "p _ { \\psi }", "type": "inline_equation" }, { "bbox": [ 234, 401, 505, 415 ], "score": 1.0, "content": "can be used to augment features for all the neighbors. However, this", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 413, 468, 426 ], "spans": [ { "bbox": [ 106, 413, 468, 426 ], "score": 1.0, "content": "method ignores the differences between all the neighbors, which may induce severe noise.", "type": "text" } ], "index": 23 } ], "index": 22.5 }, { "type": "text", "bbox": [ 106, 429, 506, 500 ], "lines": [ { "bbox": [ 106, 430, 506, 442 ], "spans": [ { "bbox": [ 106, 430, 506, 442 ], "score": 1.0, "content": "To overcome the limitation, we assume that each neighbor satisfies a different conditional distribution.", "type": "text" } ], "index": 24 }, { "bbox": [ 106, 441, 505, 454 ], "spans": [ { "bbox": [ 106, 441, 310, 454 ], "score": 1.0, "content": "Specifically, there exists a conditional distribution", "type": "text" }, { "bbox": [ 310, 441, 355, 453 ], "score": 0.93, "content": "p ( \\cdot | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 355, 441, 469, 454 ], "score": 1.0, "content": "with latent random variable", "type": "text" }, { "bbox": [ 469, 443, 480, 453 ], "score": 0.85, "content": "\\mathbf { z } _ { j }", "type": "inline_equation" }, { "bbox": [ 480, 441, 505, 454 ], "score": 1.0, "content": ", such", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 451, 506, 466 ], "spans": [ { "bbox": [ 105, 451, 162, 466 ], "score": 1.0, "content": "that we have", "type": "text" }, { "bbox": [ 162, 452, 241, 465 ], "score": 0.92, "content": "\\mathbf { X } _ { j } \\sim p ( \\mathbf { X } | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 242, 451, 258, 466 ], "score": 1.0, "content": "for", "type": "text" }, { "bbox": [ 259, 452, 293, 465 ], "score": 0.92, "content": "\\mathbf { X } _ { j \\mid j \\in \\mathcal { N } _ { i } }", "type": "inline_equation" }, { "bbox": [ 294, 451, 369, 466 ], "score": 1.0, "content": ". Once we obtain", "type": "text" }, { "bbox": [ 369, 452, 414, 465 ], "score": 0.92, "content": "p ( \\cdot | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 414, 451, 506, 466 ], "score": 1.0, "content": "in some way, we can", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 465, 505, 479 ], "spans": [ { "bbox": [ 105, 465, 226, 479 ], "score": 1.0, "content": "generate augmented features", "type": "text" }, { "bbox": [ 226, 465, 236, 475 ], "score": 0.81, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 236, 465, 331, 479 ], "score": 1.0, "content": ", and then we can train", "type": "text" }, { "bbox": [ 332, 465, 402, 478 ], "score": 0.92, "content": "P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } , \\mathbf { \\overline { { X } } } )", "type": "inline_equation" }, { "bbox": [ 403, 465, 447, 479 ], "score": 1.0, "content": "instead of", "type": "text" }, { "bbox": [ 447, 465, 505, 477 ], "score": 0.92, "content": "P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" } ], "index": 27 }, { "bbox": [ 105, 475, 506, 490 ], "spans": [ { "bbox": [ 105, 475, 252, 490 ], "score": 1.0, "content": "to improve the final performance of", "type": "text" }, { "bbox": [ 252, 477, 264, 487 ], "score": 0.89, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 264, 475, 411, 490 ], "score": 1.0, "content": ". Below, we will present how to find", "type": "text" }, { "bbox": [ 411, 477, 456, 489 ], "score": 0.93, "content": "p ( \\cdot | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 456, 475, 506, 490 ], "score": 1.0, "content": ", which will", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 488, 214, 501 ], "spans": [ { "bbox": [ 105, 488, 196, 501 ], "score": 1.0, "content": "produce the generator", "type": "text" }, { "bbox": [ 196, 488, 210, 500 ], "score": 0.9, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 210, 488, 214, 501 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 29 } ], "index": 26.5 }, { "type": "text", "bbox": [ 106, 504, 506, 574 ], "lines": [ { "bbox": [ 105, 504, 506, 517 ], "spans": [ { "bbox": [ 105, 504, 506, 517 ], "score": 1.0, "content": "To achieve our purpose, a suitable method is the conditional variational auto-encoder (CVAE) (Kingma", "type": "text" } ], "index": 30 }, { "bbox": [ 104, 514, 506, 530 ], "spans": [ { "bbox": [ 104, 514, 491, 530 ], "score": 1.0, "content": "& Welling, 2013; Sohn et al., 2015), which can help learn the distribution of the latent variable", "type": "text" }, { "bbox": [ 492, 517, 502, 528 ], "score": 0.85, "content": "\\mathbf { z } _ { j }", "type": "inline_equation" }, { "bbox": [ 502, 514, 506, 530 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 527, 506, 541 ], "spans": [ { "bbox": [ 105, 527, 238, 541 ], "score": 1.0, "content": "and the conditional distribution", "type": "text" }, { "bbox": [ 239, 528, 283, 541 ], "score": 0.92, "content": "p ( \\cdot | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 284, 527, 372, 541 ], "score": 1.0, "content": ". So, a CVAE model", "type": "text" }, { "bbox": [ 372, 527, 430, 541 ], "score": 0.91, "content": "Q _ { \\phi } \\left( \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } \\right)", "type": "inline_equation" }, { "bbox": [ 430, 527, 506, 541 ], "score": 1.0, "content": "is adopted as our", "type": "text" } ], "index": 32 }, { "bbox": [ 104, 540, 506, 553 ], "spans": [ { "bbox": [ 104, 540, 176, 553 ], "score": 1.0, "content": "generator, where", "type": "text" }, { "bbox": [ 176, 540, 224, 552 ], "score": 0.89, "content": "\\phi = \\{ \\varphi , \\psi \\}", "type": "inline_equation" }, { "bbox": [ 224, 540, 228, 553 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 228, 542, 236, 552 ], "score": 0.67, "content": "\\varphi", "type": "inline_equation" }, { "bbox": [ 236, 540, 394, 553 ], "score": 1.0, "content": "denotes the variational parameters and", "type": "text" }, { "bbox": [ 394, 541, 402, 551 ], "score": 0.85, "content": "\\psi", "type": "inline_equation" }, { "bbox": [ 402, 540, 506, 553 ], "score": 1.0, "content": "represents the generative", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 550, 506, 564 ], "spans": [ { "bbox": [ 105, 550, 339, 564 ], "score": 1.0, "content": "parameters. To derive the optimization problem for CVAE,", "type": "text" }, { "bbox": [ 339, 551, 403, 563 ], "score": 0.53, "content": "\\log p _ { \\psi } \\left( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } \\right)", "type": "inline_equation" }, { "bbox": [ 403, 550, 506, 564 ], "score": 1.0, "content": "can be written with latent", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 562, 489, 575 ], "spans": [ { "bbox": [ 106, 562, 144, 575 ], "score": 1.0, "content": "variables", "type": "text" }, { "bbox": [ 144, 564, 151, 572 ], "score": 0.63, "content": "\\mathbf { z }", "type": "inline_equation" }, { "bbox": [ 151, 562, 489, 575 ], "score": 1.0, "content": "as follows, following previous work (Pandey & Dukkipati, 2017; Sohn et al., 2015):", "type": "text" } ], "index": 35 } ], "index": 32.5 }, { "type": "interline_equation", "bbox": [ 114, 579, 496, 636 ], "lines": [ { "bbox": [ 114, 579, 496, 636 ], "spans": [ { "bbox": [ 114, 579, 496, 636 ], "score": 0.94, "content": "\\begin{array} { l } { \\log p _ { \\psi } ( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } ) = \\displaystyle \\int q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\log \\frac { p _ { \\psi } ( \\mathbf { X } _ { j } , \\mathbf { z } | \\mathbf { X } _ { i } ) } { q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) } \\mathrm { d } \\mathbf { z } + K L ( q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\| p _ { \\psi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) ) } \\\\ { \\displaystyle \\qquad \\geq \\int q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\log \\frac { p _ { \\psi } ( \\mathbf { X } _ { j } , \\mathbf { z } | \\mathbf { X } _ { i } ) } { q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) } \\mathrm { d } \\mathbf { z } , } \\end{array}", "type": "interline_equation", "image_path": "04a19d0377699e430b4f1574cb88bab3737e06b72fd8ffdc284a657b70d4f26f.jpg" } ] } ], "index": 37, "virtual_lines": [ { "bbox": [ 114, 579, 496, 598.0 ], "spans": [], "index": 36 }, { "bbox": [ 114, 598.0, 496, 617.0 ], "spans": [], "index": 37 }, { "bbox": [ 114, 617.0, 496, 636.0 ], "spans": [], "index": 38 } ] }, { "type": "text", "bbox": [ 107, 639, 335, 651 ], "lines": [ { "bbox": [ 106, 639, 335, 652 ], "spans": [ { "bbox": [ 106, 639, 335, 652 ], "score": 1.0, "content": "and the evidence lower bound (ELBO) can be written as:", "type": "text" } ], "index": 39 } ], "index": 39 }, { "type": "interline_equation", "bbox": [ 111, 655, 487, 681 ], "lines": [ { "bbox": [ 111, 655, 487, 681 ], "spans": [ { "bbox": [ 111, 655, 487, 681 ], "score": 0.93, "content": "\\mathcal { L } ( \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ; \\psi , \\varphi ) = - K L ( q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) | | p _ { \\psi } ( \\mathbf { z } | \\mathbf { X } _ { i } ) ) + \\int q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\log p _ { \\psi } ( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } , \\mathbf { z } ) \\mathrm { d } \\mathbf { z } ,", "type": "interline_equation", "image_path": "0a1fac39e36905a3a4546a8f12f4e8cd9c64dd90538a0a88ad47d0994d897420.jpg" } ] } ], "index": 40, "virtual_lines": [ { "bbox": [ 111, 655, 487, 681 ], "spans": [], "index": 40 } ] }, { "type": "text", "bbox": [ 107, 685, 505, 733 ], "lines": [ { "bbox": [ 105, 686, 504, 699 ], "spans": [ { "bbox": [ 105, 686, 189, 699 ], "score": 1.0, "content": "where the encoder", "type": "text" }, { "bbox": [ 189, 686, 373, 699 ], "score": 0.92, "content": "q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\ = \\ { \\mathcal { N } } ( f ( \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) , g ( \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) )", "type": "inline_equation" }, { "bbox": [ 373, 686, 432, 699 ], "score": 1.0, "content": "and decoder", "type": "text" }, { "bbox": [ 433, 686, 504, 699 ], "score": 0.89, "content": "p _ { \\psi } ( { \\bf X } _ { j } | { \\bf X } _ { i } , { \\bf z } ) =", "type": "inline_equation" } ], "index": 41 }, { "bbox": [ 107, 696, 506, 711 ], "spans": [ { "bbox": [ 107, 698, 174, 710 ], "score": 0.92, "content": "\\mathcal { N } ( h ( \\mathbf { X } _ { i } , \\mathbf { z } ) , c I )", "type": "inline_equation" }, { "bbox": [ 174, 696, 317, 711 ], "score": 1.0, "content": ". The encoder is a two-layer MLP.", "type": "text" }, { "bbox": [ 317, 699, 324, 709 ], "score": 0.86, "content": "f", "type": "inline_equation" }, { "bbox": [ 325, 696, 343, 711 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 344, 701, 350, 709 ], "score": 0.76, "content": "g", "type": "inline_equation" }, { "bbox": [ 350, 696, 506, 711 ], "score": 1.0, "content": "share the first layer, and their second", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 708, 507, 722 ], "spans": [ { "bbox": [ 105, 708, 302, 722 ], "score": 1.0, "content": "layers employ different parameters. The decoder", "type": "text" }, { "bbox": [ 302, 709, 309, 718 ], "score": 0.84, "content": "h", "type": "inline_equation" }, { "bbox": [ 309, 708, 507, 722 ], "score": 1.0, "content": "is two-layer MLP. For simplicity and tractability,", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 720, 473, 734 ], "spans": [ { "bbox": [ 105, 720, 216, 734 ], "score": 1.0, "content": "the implemented generator", "type": "text" }, { "bbox": [ 216, 720, 268, 733 ], "score": 0.91, "content": "Q \\left( \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } \\right)", "type": "inline_equation" }, { "bbox": [ 268, 720, 439, 734 ], "score": 1.0, "content": "uses the same parameters across all nodes", "type": "text" }, { "bbox": [ 439, 721, 469, 732 ], "score": 0.91, "content": "v _ { i } \\in V", "type": "inline_equation" }, { "bbox": [ 469, 720, 473, 734 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 44 } ], "index": 42.5 } ], "page_idx": 3, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 106, 26, 308, 38 ], "lines": [ { "bbox": [ 106, 25, 309, 39 ], "spans": [ { "bbox": [ 106, 25, 309, 39 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 751, 308, 759 ], "lines": [ { "bbox": [ 301, 750, 309, 762 ], "spans": [ { "bbox": [ 301, 750, 309, 762 ], "score": 1.0, "content": "", "type": "text", "height": 12, "width": 8 } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 106, 81, 505, 129 ], "lines": [ { "bbox": [ 106, 82, 505, 95 ], "spans": [ { "bbox": [ 106, 82, 135, 95 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 135, 83, 145, 93 ], "score": 0.64, "content": "\\mathbf { K }", "type": "inline_equation" }, { "bbox": [ 146, 82, 505, 95 ], "score": 1.0, "content": "is the set of node indices of the training dataset whose labels are visible during the", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 93, 505, 105 ], "spans": [ { "bbox": [ 105, 93, 505, 105 ], "score": 1.0, "content": "semi-supervised training. To further boost the performance of GNN, we introduce a new model", "type": "text" } ], "index": 1 }, { "bbox": [ 107, 105, 505, 119 ], "spans": [ { "bbox": [ 107, 105, 173, 118 ], "score": 0.91, "content": "P _ { \\theta } ( { \\bf Y } , \\overline { { { \\bf X } } } | { \\bf A } , { \\bf X } )", "type": "inline_equation" }, { "bbox": [ 173, 105, 204, 119 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 204, 105, 214, 116 ], "score": 0.83, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 214, 105, 505, 119 ], "score": 1.0, "content": "is generated features by feature-level augmentation. For this model, the", "type": "text" } ], "index": 2 }, { "bbox": [ 104, 116, 505, 131 ], "spans": [ { "bbox": [ 104, 116, 343, 131 ], "score": 1.0, "content": "MLE method needs to optimize a marginalized probability", "type": "text" }, { "bbox": [ 343, 118, 354, 129 ], "score": 0.89, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 355, 116, 491, 131 ], "score": 1.0, "content": "over the generated feature matrix", "type": "text" }, { "bbox": [ 491, 117, 500, 128 ], "score": 0.78, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 501, 116, 505, 131 ], "score": 1.0, "content": ":", "type": "text" } ], "index": 3 } ], "index": 1.5, "bbox_fs": [ 104, 82, 505, 131 ] }, { "type": "interline_equation", "bbox": [ 239, 135, 373, 165 ], "lines": [ { "bbox": [ 239, 135, 373, 165 ], "spans": [ { "bbox": [ 239, 135, 373, 165 ], "score": 0.94, "content": "\\operatorname* { m a x } \\prod _ { k \\in \\mathbf { K } } \\int _ { \\overline { { \\mathbf { X } } } } P _ { \\theta } \\left( \\mathbf { Y } _ { k } , \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } \\right) .", "type": "interline_equation", "image_path": "0b5072d13dff98ceb3f376b6d3e0034b60f5da232a7265602f7ff6924a32a9a8.jpg" } ] } ], "index": 4.5, "virtual_lines": [ { "bbox": [ 239, 135, 373, 150.0 ], "spans": [], "index": 4 }, { "bbox": [ 239, 150.0, 373, 165.0 ], "spans": [], "index": 5 } ] }, { "type": "text", "bbox": [ 107, 169, 493, 182 ], "lines": [ { "bbox": [ 105, 169, 494, 185 ], "spans": [ { "bbox": [ 105, 169, 270, 185 ], "score": 1.0, "content": "For Bayesian tractability, we decompose", "type": "text" }, { "bbox": [ 271, 171, 282, 181 ], "score": 0.88, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 283, 169, 494, 185 ], "score": 1.0, "content": "in Eq.(3) as a product of two posterior probabilities:", "type": "text" } ], "index": 6 } ], "index": 6, "bbox_fs": [ 105, 169, 494, 185 ] }, { "type": "interline_equation", "bbox": [ 194, 187, 416, 202 ], "lines": [ { "bbox": [ 194, 187, 416, 202 ], "spans": [ { "bbox": [ 194, 187, 416, 202 ], "score": 0.9, "content": "\\begin{array} { r } { P _ { \\theta , \\phi } ( \\mathbf { Y } _ { k } , \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } ) : = P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } , \\overline { { \\mathbf { X } } } ) Q _ { \\phi } ( \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } ) , } \\end{array}", "type": "interline_equation", "image_path": "3969838a7b935379ff9a61fd7d4acd02bfdf7dbee1d678d807fb38029ca9429a.jpg" } ] } ], "index": 7, "virtual_lines": [ { "bbox": [ 194, 187, 416, 202 ], "spans": [], "index": 7 } ] }, { "type": "text", "bbox": [ 106, 208, 505, 288 ], "lines": [ { "bbox": [ 105, 208, 506, 223 ], "spans": [ { "bbox": [ 105, 208, 134, 223 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 208, 205, 221 ], "score": 0.92, "content": "P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } , \\mathbf { \\overline { { X } } } )", "type": "inline_equation" }, { "bbox": [ 205, 208, 225, 223 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 225, 208, 279, 221 ], "score": 0.93, "content": "Q _ { \\phi } ( { \\overline { { \\mathbf { X } } } } | \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 280, 208, 506, 223 ], "score": 1.0, "content": "denote the probabilistic distributions approximated by", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 219, 506, 233 ], "spans": [ { "bbox": [ 105, 219, 506, 233 ], "score": 1.0, "content": "the downstream GNN and the (feature-level augmentation) generator respectively, parameterized", "type": "text" } ], "index": 9 }, { "bbox": [ 106, 231, 505, 244 ], "spans": [ { "bbox": [ 106, 231, 119, 244 ], "score": 1.0, "content": "by", "type": "text" }, { "bbox": [ 120, 231, 126, 241 ], "score": 0.77, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 127, 231, 145, 244 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 145, 232, 152, 243 ], "score": 0.84, "content": "\\phi", "type": "inline_equation" }, { "bbox": [ 153, 231, 505, 244 ], "score": 1.0, "content": ". There are two benefits in the decomposition above. First, it allows us to decouple", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 241, 505, 255 ], "spans": [ { "bbox": [ 105, 241, 272, 255 ], "score": 1.0, "content": "the training of the downstream predictor", "type": "text" }, { "bbox": [ 272, 243, 284, 253 ], "score": 0.89, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 284, 241, 358, 255 ], "score": 1.0, "content": "and the generator", "type": "text" }, { "bbox": [ 358, 243, 372, 254 ], "score": 0.9, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 372, 241, 505, 255 ], "score": 1.0, "content": ", enabling the generator to easily", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 253, 506, 266 ], "spans": [ { "bbox": [ 105, 253, 506, 266 ], "score": 1.0, "content": "generalize to other downstream tasks. Moreover, inspired by the successes of data augmentation via", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 263, 506, 277 ], "spans": [ { "bbox": [ 105, 263, 506, 277 ], "score": 1.0, "content": "deep-learning-based generative modeling (Antoniou et al., 2017), the representation power of Eq.(4)", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 275, 442, 288 ], "spans": [ { "bbox": [ 105, 275, 271, 288 ], "score": 1.0, "content": "is superior than that of a single predictor", "type": "text" }, { "bbox": [ 271, 275, 330, 287 ], "score": 0.93, "content": "P _ { \\theta } \\left( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } \\right)", "type": "inline_equation" }, { "bbox": [ 330, 275, 442, 288 ], "score": 1.0, "content": "without data augmentation.", "type": "text" } ], "index": 14 } ], "index": 11, "bbox_fs": [ 105, 208, 506, 288 ] }, { "type": "text", "bbox": [ 107, 291, 505, 327 ], "lines": [ { "bbox": [ 106, 291, 504, 305 ], "spans": [ { "bbox": [ 106, 291, 243, 305 ], "score": 1.0, "content": "Consequently, once a generator", "type": "text" }, { "bbox": [ 243, 292, 258, 304 ], "score": 0.89, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 258, 291, 504, 305 ], "score": 1.0, "content": "is trained very well, our training procedure can optimize", "type": "text" } ], "index": 15 }, { "bbox": [ 107, 303, 505, 317 ], "spans": [ { "bbox": [ 107, 303, 177, 317 ], "score": 0.92, "content": "P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } , \\mathbf { \\overline { { X } } } )", "type": "inline_equation" }, { "bbox": [ 178, 304, 238, 317 ], "score": 1.0, "content": "with samples", "type": "text" }, { "bbox": [ 238, 304, 248, 315 ], "score": 0.76, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 249, 304, 443, 317 ], "score": 1.0, "content": "drawn from the fixed conditional distribution", "type": "text" }, { "bbox": [ 443, 305, 457, 317 ], "score": 0.89, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 457, 304, 505, 317 ], "score": 1.0, "content": ". Now, we", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 316, 281, 328 ], "spans": [ { "bbox": [ 105, 316, 281, 328 ], "score": 1.0, "content": "show how to train the generator as follows.", "type": "text" } ], "index": 17 } ], "index": 16, "bbox_fs": [ 105, 291, 505, 328 ] }, { "type": "text", "bbox": [ 107, 339, 504, 372 ], "lines": [ { "bbox": [ 106, 338, 505, 352 ], "spans": [ { "bbox": [ 106, 338, 505, 352 ], "score": 1.0, "content": "Generator To learn a feature augmentation generator, a naive solution is to learn one single", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 350, 505, 362 ], "spans": [ { "bbox": [ 105, 350, 505, 362 ], "score": 1.0, "content": "distribution for all the neighbors using the MLE method, i.e., solving the following optimization", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 361, 144, 374 ], "spans": [ { "bbox": [ 105, 361, 144, 374 ], "score": 1.0, "content": "problem", "type": "text" } ], "index": 20 } ], "index": 19, "bbox_fs": [ 105, 338, 505, 374 ] }, { "type": "interline_equation", "bbox": [ 192, 371, 419, 399 ], "lines": [ { "bbox": [ 192, 371, 419, 399 ], "spans": [ { "bbox": [ 192, 371, 419, 399 ], "score": 0.93, "content": "\\operatorname* { m a x } _ { \\psi } \\sum _ { j \\in \\mathcal { N } _ { i } } \\log p _ { \\psi } \\left( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } \\right) = \\operatorname* { m a x } _ { \\psi } \\log \\prod _ { j \\in \\mathcal { N } _ { i } } p _ { \\psi } \\left( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } \\right) ,", "type": "interline_equation", "image_path": "c8cd49cda13ba563e1e64405644de1a1918d032610b692a84d3bf50a442af942.jpg" } ] } ], "index": 21, "virtual_lines": [ { "bbox": [ 192, 371, 419, 399 ], "spans": [], "index": 21 } ] }, { "type": "text", "bbox": [ 107, 402, 504, 425 ], "lines": [ { "bbox": [ 105, 401, 505, 415 ], "spans": [ { "bbox": [ 105, 401, 133, 415 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 402, 194, 415 ], "score": 0.93, "content": "\\{ \\mathbf { X } _ { j \\mid j \\in \\mathcal { N } _ { i } } , \\mathbf { X } _ { i } \\}", "type": "inline_equation" }, { "bbox": [ 195, 401, 221, 415 ], "score": 1.0, "content": ". Then", "type": "text" }, { "bbox": [ 221, 404, 233, 415 ], "score": 0.87, "content": "p _ { \\psi }", "type": "inline_equation" }, { "bbox": [ 234, 401, 505, 415 ], "score": 1.0, "content": "can be used to augment features for all the neighbors. However, this", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 413, 468, 426 ], "spans": [ { "bbox": [ 106, 413, 468, 426 ], "score": 1.0, "content": "method ignores the differences between all the neighbors, which may induce severe noise.", "type": "text" } ], "index": 23 } ], "index": 22.5, "bbox_fs": [ 105, 401, 505, 426 ] }, { "type": "text", "bbox": [ 106, 429, 506, 500 ], "lines": [ { "bbox": [ 106, 430, 506, 442 ], "spans": [ { "bbox": [ 106, 430, 506, 442 ], "score": 1.0, "content": "To overcome the limitation, we assume that each neighbor satisfies a different conditional distribution.", "type": "text" } ], "index": 24 }, { "bbox": [ 106, 441, 505, 454 ], "spans": [ { "bbox": [ 106, 441, 310, 454 ], "score": 1.0, "content": "Specifically, there exists a conditional distribution", "type": "text" }, { "bbox": [ 310, 441, 355, 453 ], "score": 0.93, "content": "p ( \\cdot | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 355, 441, 469, 454 ], "score": 1.0, "content": "with latent random variable", "type": "text" }, { "bbox": [ 469, 443, 480, 453 ], "score": 0.85, "content": "\\mathbf { z } _ { j }", "type": "inline_equation" }, { "bbox": [ 480, 441, 505, 454 ], "score": 1.0, "content": ", such", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 451, 506, 466 ], "spans": [ { "bbox": [ 105, 451, 162, 466 ], "score": 1.0, "content": "that we have", "type": "text" }, { "bbox": [ 162, 452, 241, 465 ], "score": 0.92, "content": "\\mathbf { X } _ { j } \\sim p ( \\mathbf { X } | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 242, 451, 258, 466 ], "score": 1.0, "content": "for", "type": "text" }, { "bbox": [ 259, 452, 293, 465 ], "score": 0.92, "content": "\\mathbf { X } _ { j \\mid j \\in \\mathcal { N } _ { i } }", "type": "inline_equation" }, { "bbox": [ 294, 451, 369, 466 ], "score": 1.0, "content": ". Once we obtain", "type": "text" }, { "bbox": [ 369, 452, 414, 465 ], "score": 0.92, "content": "p ( \\cdot | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 414, 451, 506, 466 ], "score": 1.0, "content": "in some way, we can", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 465, 505, 479 ], "spans": [ { "bbox": [ 105, 465, 226, 479 ], "score": 1.0, "content": "generate augmented features", "type": "text" }, { "bbox": [ 226, 465, 236, 475 ], "score": 0.81, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 236, 465, 331, 479 ], "score": 1.0, "content": ", and then we can train", "type": "text" }, { "bbox": [ 332, 465, 402, 478 ], "score": 0.92, "content": "P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } , \\mathbf { \\overline { { X } } } )", "type": "inline_equation" }, { "bbox": [ 403, 465, 447, 479 ], "score": 1.0, "content": "instead of", "type": "text" }, { "bbox": [ 447, 465, 505, 477 ], "score": 0.92, "content": "P _ { \\theta } ( \\mathbf { Y } _ { k } | \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" } ], "index": 27 }, { "bbox": [ 105, 475, 506, 490 ], "spans": [ { "bbox": [ 105, 475, 252, 490 ], "score": 1.0, "content": "to improve the final performance of", "type": "text" }, { "bbox": [ 252, 477, 264, 487 ], "score": 0.89, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 264, 475, 411, 490 ], "score": 1.0, "content": ". Below, we will present how to find", "type": "text" }, { "bbox": [ 411, 477, 456, 489 ], "score": 0.93, "content": "p ( \\cdot | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 456, 475, 506, 490 ], "score": 1.0, "content": ", which will", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 488, 214, 501 ], "spans": [ { "bbox": [ 105, 488, 196, 501 ], "score": 1.0, "content": "produce the generator", "type": "text" }, { "bbox": [ 196, 488, 210, 500 ], "score": 0.9, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 210, 488, 214, 501 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 29 } ], "index": 26.5, "bbox_fs": [ 105, 430, 506, 501 ] }, { "type": "text", "bbox": [ 106, 504, 506, 574 ], "lines": [ { "bbox": [ 105, 504, 506, 517 ], "spans": [ { "bbox": [ 105, 504, 506, 517 ], "score": 1.0, "content": "To achieve our purpose, a suitable method is the conditional variational auto-encoder (CVAE) (Kingma", "type": "text" } ], "index": 30 }, { "bbox": [ 104, 514, 506, 530 ], "spans": [ { "bbox": [ 104, 514, 491, 530 ], "score": 1.0, "content": "& Welling, 2013; Sohn et al., 2015), which can help learn the distribution of the latent variable", "type": "text" }, { "bbox": [ 492, 517, 502, 528 ], "score": 0.85, "content": "\\mathbf { z } _ { j }", "type": "inline_equation" }, { "bbox": [ 502, 514, 506, 530 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 527, 506, 541 ], "spans": [ { "bbox": [ 105, 527, 238, 541 ], "score": 1.0, "content": "and the conditional distribution", "type": "text" }, { "bbox": [ 239, 528, 283, 541 ], "score": 0.92, "content": "p ( \\cdot | \\mathbf { X } _ { i } , \\mathbf { z } _ { j } )", "type": "inline_equation" }, { "bbox": [ 284, 527, 372, 541 ], "score": 1.0, "content": ". So, a CVAE model", "type": "text" }, { "bbox": [ 372, 527, 430, 541 ], "score": 0.91, "content": "Q _ { \\phi } \\left( \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } \\right)", "type": "inline_equation" }, { "bbox": [ 430, 527, 506, 541 ], "score": 1.0, "content": "is adopted as our", "type": "text" } ], "index": 32 }, { "bbox": [ 104, 540, 506, 553 ], "spans": [ { "bbox": [ 104, 540, 176, 553 ], "score": 1.0, "content": "generator, where", "type": "text" }, { "bbox": [ 176, 540, 224, 552 ], "score": 0.89, "content": "\\phi = \\{ \\varphi , \\psi \\}", "type": "inline_equation" }, { "bbox": [ 224, 540, 228, 553 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 228, 542, 236, 552 ], "score": 0.67, "content": "\\varphi", "type": "inline_equation" }, { "bbox": [ 236, 540, 394, 553 ], "score": 1.0, "content": "denotes the variational parameters and", "type": "text" }, { "bbox": [ 394, 541, 402, 551 ], "score": 0.85, "content": "\\psi", "type": "inline_equation" }, { "bbox": [ 402, 540, 506, 553 ], "score": 1.0, "content": "represents the generative", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 550, 506, 564 ], "spans": [ { "bbox": [ 105, 550, 339, 564 ], "score": 1.0, "content": "parameters. To derive the optimization problem for CVAE,", "type": "text" }, { "bbox": [ 339, 551, 403, 563 ], "score": 0.53, "content": "\\log p _ { \\psi } \\left( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } \\right)", "type": "inline_equation" }, { "bbox": [ 403, 550, 506, 564 ], "score": 1.0, "content": "can be written with latent", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 562, 489, 575 ], "spans": [ { "bbox": [ 106, 562, 144, 575 ], "score": 1.0, "content": "variables", "type": "text" }, { "bbox": [ 144, 564, 151, 572 ], "score": 0.63, "content": "\\mathbf { z }", "type": "inline_equation" }, { "bbox": [ 151, 562, 489, 575 ], "score": 1.0, "content": "as follows, following previous work (Pandey & Dukkipati, 2017; Sohn et al., 2015):", "type": "text" } ], "index": 35 } ], "index": 32.5, "bbox_fs": [ 104, 504, 506, 575 ] }, { "type": "interline_equation", "bbox": [ 114, 579, 496, 636 ], "lines": [ { "bbox": [ 114, 579, 496, 636 ], "spans": [ { "bbox": [ 114, 579, 496, 636 ], "score": 0.94, "content": "\\begin{array} { l } { \\log p _ { \\psi } ( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } ) = \\displaystyle \\int q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\log \\frac { p _ { \\psi } ( \\mathbf { X } _ { j } , \\mathbf { z } | \\mathbf { X } _ { i } ) } { q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) } \\mathrm { d } \\mathbf { z } + K L ( q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\| p _ { \\psi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) ) } \\\\ { \\displaystyle \\qquad \\geq \\int q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\log \\frac { p _ { \\psi } ( \\mathbf { X } _ { j } , \\mathbf { z } | \\mathbf { X } _ { i } ) } { q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) } \\mathrm { d } \\mathbf { z } , } \\end{array}", "type": "interline_equation", "image_path": "04a19d0377699e430b4f1574cb88bab3737e06b72fd8ffdc284a657b70d4f26f.jpg" } ] } ], "index": 37, "virtual_lines": [ { "bbox": [ 114, 579, 496, 598.0 ], "spans": [], "index": 36 }, { "bbox": [ 114, 598.0, 496, 617.0 ], "spans": [], "index": 37 }, { "bbox": [ 114, 617.0, 496, 636.0 ], "spans": [], "index": 38 } ] }, { "type": "text", "bbox": [ 107, 639, 335, 651 ], "lines": [ { "bbox": [ 106, 639, 335, 652 ], "spans": [ { "bbox": [ 106, 639, 335, 652 ], "score": 1.0, "content": "and the evidence lower bound (ELBO) can be written as:", "type": "text" } ], "index": 39 } ], "index": 39, "bbox_fs": [ 106, 639, 335, 652 ] }, { "type": "interline_equation", "bbox": [ 111, 655, 487, 681 ], "lines": [ { "bbox": [ 111, 655, 487, 681 ], "spans": [ { "bbox": [ 111, 655, 487, 681 ], "score": 0.93, "content": "\\mathcal { L } ( \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ; \\psi , \\varphi ) = - K L ( q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) | | p _ { \\psi } ( \\mathbf { z } | \\mathbf { X } _ { i } ) ) + \\int q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\log p _ { \\psi } ( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } , \\mathbf { z } ) \\mathrm { d } \\mathbf { z } ,", "type": "interline_equation", "image_path": "0a1fac39e36905a3a4546a8f12f4e8cd9c64dd90538a0a88ad47d0994d897420.jpg" } ] } ], "index": 40, "virtual_lines": [ { "bbox": [ 111, 655, 487, 681 ], "spans": [], "index": 40 } ] }, { "type": "text", "bbox": [ 107, 685, 505, 733 ], "lines": [ { "bbox": [ 105, 686, 504, 699 ], "spans": [ { "bbox": [ 105, 686, 189, 699 ], "score": 1.0, "content": "where the encoder", "type": "text" }, { "bbox": [ 189, 686, 373, 699 ], "score": 0.92, "content": "q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\ = \\ { \\mathcal { N } } ( f ( \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) , g ( \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) )", "type": "inline_equation" }, { "bbox": [ 373, 686, 432, 699 ], "score": 1.0, "content": "and decoder", "type": "text" }, { "bbox": [ 433, 686, 504, 699 ], "score": 0.89, "content": "p _ { \\psi } ( { \\bf X } _ { j } | { \\bf X } _ { i } , { \\bf z } ) =", "type": "inline_equation" } ], "index": 41 }, { "bbox": [ 107, 696, 506, 711 ], "spans": [ { "bbox": [ 107, 698, 174, 710 ], "score": 0.92, "content": "\\mathcal { N } ( h ( \\mathbf { X } _ { i } , \\mathbf { z } ) , c I )", "type": "inline_equation" }, { "bbox": [ 174, 696, 317, 711 ], "score": 1.0, "content": ". The encoder is a two-layer MLP.", "type": "text" }, { "bbox": [ 317, 699, 324, 709 ], "score": 0.86, "content": "f", "type": "inline_equation" }, { "bbox": [ 325, 696, 343, 711 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 344, 701, 350, 709 ], "score": 0.76, "content": "g", "type": "inline_equation" }, { "bbox": [ 350, 696, 506, 711 ], "score": 1.0, "content": "share the first layer, and their second", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 708, 507, 722 ], "spans": [ { "bbox": [ 105, 708, 302, 722 ], "score": 1.0, "content": "layers employ different parameters. The decoder", "type": "text" }, { "bbox": [ 302, 709, 309, 718 ], "score": 0.84, "content": "h", "type": "inline_equation" }, { "bbox": [ 309, 708, 507, 722 ], "score": 1.0, "content": "is two-layer MLP. For simplicity and tractability,", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 720, 473, 734 ], "spans": [ { "bbox": [ 105, 720, 216, 734 ], "score": 1.0, "content": "the implemented generator", "type": "text" }, { "bbox": [ 216, 720, 268, 733 ], "score": 0.91, "content": "Q \\left( \\overline { { \\mathbf { X } } } | \\mathbf { A } , \\mathbf { X } \\right)", "type": "inline_equation" }, { "bbox": [ 268, 720, 439, 734 ], "score": 1.0, "content": "uses the same parameters across all nodes", "type": "text" }, { "bbox": [ 439, 721, 469, 732 ], "score": 0.91, "content": "v _ { i } \\in V", "type": "inline_equation" }, { "bbox": [ 469, 720, 473, 734 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 44 } ], "index": 42.5, "bbox_fs": [ 105, 686, 507, 734 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 106, 81, 506, 151 ], "lines": [ { "bbox": [ 106, 82, 506, 96 ], "spans": [ { "bbox": [ 106, 82, 506, 96 ], "score": 1.0, "content": "Optimization of the MLE Now, we present how to optimize the MLE Eq.(4) using the feature", "type": "text" } ], "index": 0 }, { "bbox": [ 106, 93, 506, 106 ], "spans": [ { "bbox": [ 106, 93, 506, 106 ], "score": 1.0, "content": "matrix produced from the generator. Once the augmented feature matrix can be sampled from the", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 104, 506, 118 ], "spans": [ { "bbox": [ 105, 104, 506, 118 ], "score": 1.0, "content": "generator, we can optimize the parameters of Eq.(4) in the following way. Firstly, the parameter", "type": "text" } ], "index": 2 }, { "bbox": [ 107, 115, 506, 128 ], "spans": [ { "bbox": [ 107, 115, 158, 127 ], "score": 0.92, "content": "\\bar { \\phi } = \\{ \\psi , \\varphi \\}", "type": "inline_equation" }, { "bbox": [ 159, 115, 506, 128 ], "score": 1.0, "content": "can be optimized by maximizing the ELBO of the generator (6), i.e., we train the", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 126, 506, 139 ], "spans": [ { "bbox": [ 105, 126, 244, 139 ], "score": 1.0, "content": "generator. Secondly, the parameter", "type": "text" }, { "bbox": [ 244, 127, 250, 136 ], "score": 0.81, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 251, 126, 446, 139 ], "score": 1.0, "content": "is optimized by maximizing the MLE Eq.(4) with", "type": "text" }, { "bbox": [ 446, 127, 454, 138 ], "score": 0.85, "content": "\\phi", "type": "inline_equation" }, { "bbox": [ 454, 126, 506, 139 ], "score": 1.0, "content": "fixed, which", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 137, 506, 151 ], "spans": [ { "bbox": [ 105, 138, 237, 151 ], "score": 1.0, "content": "is the conditional distribution of", "type": "text" }, { "bbox": [ 237, 138, 252, 150 ], "score": 0.9, "content": "{ \\bf Y } _ { k }", "type": "inline_equation" }, { "bbox": [ 252, 138, 290, 151 ], "score": 1.0, "content": "given A,", "type": "text" }, { "bbox": [ 290, 138, 300, 149 ], "score": 0.51, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 301, 138, 321, 151 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 321, 137, 331, 148 ], "score": 0.82, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 331, 138, 506, 151 ], "score": 1.0, "content": ", i.e., we train the downstream GNN model.", "type": "text" } ], "index": 5 } ], "index": 2.5 }, { "type": "text", "bbox": [ 106, 154, 422, 167 ], "lines": [ { "bbox": [ 105, 154, 423, 168 ], "spans": [ { "bbox": [ 105, 154, 423, 168 ], "score": 1.0, "content": "In this paper, the MLE is formulated by a downstream GNN model as follows:", "type": "text" } ], "index": 6 } ], "index": 6 }, { "type": "interline_equation", "bbox": [ 219, 172, 391, 189 ], "lines": [ { "bbox": [ 219, 172, 391, 189 ], "spans": [ { "bbox": [ 219, 172, 391, 189 ], "score": 0.78, "content": "P _ { \\theta } \\left( \\mathbf { Y } _ { k } \\mid \\mathbf { A } , \\mathbf { X } , { \\overline { { \\mathbf { X } } } } \\right) \\propto - { \\overline { { \\mathcal { L } } } } ( \\theta | \\mathbf { A } , \\mathbf { X } , { \\overline { { \\mathbf { X } } } } , \\phi ) ,", "type": "interline_equation", "image_path": "57f3086c808bc412791db206faf439c5e0fdcda03f805a35f6a8dd476808ecd3.jpg" } ] } ], "index": 7, "virtual_lines": [ { "bbox": [ 219, 172, 391, 189 ], "spans": [], "index": 7 } ] }, { "type": "interline_equation", "bbox": [ 133, 194, 446, 216 ], "lines": [ { "bbox": [ 133, 194, 446, 216 ], "spans": [ { "bbox": [ 133, 194, 446, 216 ], "score": 0.72, "content": "\\begin{array} { r } { \\overline { { \\mathcal { L } } } ( \\theta | \\mathbf { A } , \\mathbf { X } , \\overline { { \\mathbf { X } } } , \\phi ) = - \\sum _ { k \\in \\mathbf { T } } \\sum _ { f = 1 } ^ { C } \\mathbf { Y } _ { k f } \\ln \\Big ( \\mathrm { s o f t m a x } \\big ( \\mathrm { G N N } ( \\mathbf { A } , \\mathbf { X } , \\overline { { \\mathbf { X } } } ) \\big ) _ { k f } \\Big ) . } \\end{array}", "type": "interline_equation", "image_path": "4b4f7de55c1633f1e64d504d7c14ecb1f9d93ef379b8dba8051c2b7e0be66189.jpg" } ] } ], "index": 8, "virtual_lines": [ { "bbox": [ 133, 194, 446, 216 ], "spans": [], "index": 8 } ] }, { "type": "title", "bbox": [ 108, 228, 277, 240 ], "lines": [ { "bbox": [ 106, 228, 279, 241 ], "spans": [ { "bbox": [ 106, 228, 279, 241 ], "score": 1.0, "content": "3.2 THE ARCHITECTURE OF LA-GNN", "type": "text" } ], "index": 9 } ], "index": 9 }, { "type": "text", "bbox": [ 107, 249, 504, 283 ], "lines": [ { "bbox": [ 105, 248, 506, 263 ], "spans": [ { "bbox": [ 105, 248, 506, 263 ], "score": 1.0, "content": "We discuss the details of downstream GNN models. And we use GCN, GAT, GCNII, and GRAND as", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 261, 506, 273 ], "spans": [ { "bbox": [ 105, 261, 506, 273 ], "score": 1.0, "content": "the backbones and test them on semi-supervised node classification tasks. We name the modified", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 271, 385, 284 ], "spans": [ { "bbox": [ 105, 271, 385, 284 ], "score": 1.0, "content": "GNN architecture as LA-GNN, where LA means local augmentation.", "type": "text" } ], "index": 12 } ], "index": 11 }, { "type": "text", "bbox": [ 106, 295, 322, 308 ], "lines": [ { "bbox": [ 106, 295, 324, 310 ], "spans": [ { "bbox": [ 106, 295, 324, 310 ], "score": 1.0, "content": "LA-GCN A 2-layer LA-GCN is defined as follows:", "type": "text" } ], "index": 13 } ], "index": 13 }, { "type": "interline_equation", "bbox": [ 135, 313, 475, 342 ], "lines": [ { "bbox": [ 135, 313, 475, 342 ], "spans": [ { "bbox": [ 135, 313, 475, 342 ], "score": 0.94, "content": "\\mathbf { H } ^ { ( 2 ) } = \\sigma \\left( \\hat { \\mathbf { A } } \\left( \\sigma \\left( \\hat { \\mathbf { A } } \\mathbf { X } \\mathbf { W } _ { 1 } ^ { ( 1 ) } \\right) \\bigg | \\bigg | \\sigma \\left( \\hat { \\mathbf { A } } \\overline { { \\mathbf { X } } } _ { 1 } \\mathbf { W } _ { 2 } ^ { ( 1 ) } \\right) \\bigg | \\bigg | \\cdots \\bigg | \\bigg | \\sigma \\left( \\hat { \\mathbf { A } } \\overline { { \\mathbf { X } } } _ { n } \\mathbf { W } _ { n + 1 } ^ { ( 1 ) } \\right) \\right) \\mathbf { W } ^ { ( 2 ) } \\right) ,", "type": "interline_equation", "image_path": "f239d746dfe55f2b758980f17e6d4d65f2e06aec6bfd878c3b066cd22f9bd920.jpg" } ] } ], "index": 15, "virtual_lines": [ { "bbox": [ 135, 313, 475, 322.6666666666667 ], "spans": [], "index": 14 }, { "bbox": [ 135, 322.6666666666667, 475, 332.33333333333337 ], "spans": [], "index": 15 }, { "bbox": [ 135, 332.33333333333337, 475, 342.00000000000006 ], "spans": [], "index": 16 } ] }, { "type": "text", "bbox": [ 106, 349, 505, 388 ], "lines": [ { "bbox": [ 105, 347, 505, 363 ], "spans": [ { "bbox": [ 105, 347, 132, 363 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 348, 146, 361 ], "score": 0.46, "content": "\\overline { { \\mathbf { X } } } _ { i }", "type": "inline_equation" }, { "bbox": [ 139, 348, 216, 362 ], "score": 0.62, "content": "\\bar { \\mathsf { \\bar { c } } } _ { i } ( i = 1 , 2 , \\cdots , n )", "type": "inline_equation" }, { "bbox": [ 216, 347, 453, 363 ], "score": 1.0, "content": "is the augmented feature matrix produced by the generator,", "type": "text" }, { "bbox": [ 453, 350, 460, 362 ], "score": 0.85, "content": "\\parallel", "type": "inline_equation" }, { "bbox": [ 460, 347, 505, 363 ], "score": 1.0, "content": "denotes an", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 359, 506, 376 ], "spans": [ { "bbox": [ 105, 359, 269, 376 ], "score": 1.0, "content": "operator of column-wise concatenation,", "type": "text" }, { "bbox": [ 270, 361, 364, 376 ], "score": 0.8, "content": "\\mathbf { W } _ { i } ^ { ( 1 ) } \\left( i = 1 , 2 , \\cdots , n \\right)", "type": "inline_equation" }, { "bbox": [ 364, 359, 506, 376 ], "score": 1.0, "content": "denotes the parameters of the first", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 374, 426, 389 ], "spans": [ { "bbox": [ 105, 374, 188, 389 ], "score": 1.0, "content": "LA-GCN layer, and", "type": "text" }, { "bbox": [ 188, 375, 212, 386 ], "score": 0.87, "content": "\\mathbf { W } ^ { ( 2 ) }", "type": "inline_equation" }, { "bbox": [ 212, 374, 426, 389 ], "score": 1.0, "content": "denotes the parameters of the second LA-GCN layer.", "type": "text" } ], "index": 19 } ], "index": 18 }, { "type": "text", "bbox": [ 106, 400, 505, 437 ], "lines": [ { "bbox": [ 105, 401, 505, 413 ], "spans": [ { "bbox": [ 105, 401, 483, 413 ], "score": 1.0, "content": "LA-GCNII Since GCNII (Chen et al., 2020) applies a fully-connected neural network on", "type": "text" }, { "bbox": [ 483, 401, 493, 411 ], "score": 0.71, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 493, 401, 505, 413 ], "score": 1.0, "content": "to", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 411, 506, 426 ], "spans": [ { "bbox": [ 105, 411, 305, 426 ], "score": 1.0, "content": "obtain a lower-dimensional initial representation", "type": "text" }, { "bbox": [ 306, 412, 326, 423 ], "score": 0.88, "content": "\\mathbf { H } ^ { ( 0 ) }", "type": "inline_equation" }, { "bbox": [ 326, 411, 506, 426 ], "score": 1.0, "content": "before the forward propagation, we apply a", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 423, 453, 437 ], "spans": [ { "bbox": [ 105, 423, 246, 437 ], "score": 1.0, "content": "fully-connected neural network on", "type": "text" }, { "bbox": [ 246, 425, 256, 435 ], "score": 0.67, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 257, 423, 275, 437 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 275, 424, 284, 435 ], "score": 0.86, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 285, 423, 323, 437 ], "score": 1.0, "content": "to obtain", "type": "text" }, { "bbox": [ 323, 424, 344, 435 ], "score": 0.9, "content": "\\mathbf { H } ^ { ( 0 ) }", "type": "inline_equation" }, { "bbox": [ 344, 423, 453, 437 ], "score": 1.0, "content": "for LA-GCNII as follows:", "type": "text" } ], "index": 22 } ], "index": 21 }, { "type": "interline_equation", "bbox": [ 184, 442, 427, 464 ], "lines": [ { "bbox": [ 184, 442, 427, 464 ], "spans": [ { "bbox": [ 184, 442, 427, 464 ], "score": 0.91, "content": "\\mathbf { H } ^ { ( 0 ) } = \\sigma ( \\mathbf { X } \\mathbf { W } _ { 1 } ^ { ( 0 ) } ) \\| \\sigma ( \\overline { { \\mathbf { X } } } _ { 1 } \\mathbf { W } _ { 2 } ^ { ( 0 ) } ) \\| \\cdots \\| \\sigma ( \\overline { { \\mathbf { X } } } _ { n } \\mathbf { W } _ { n + 1 } ^ { ( 0 ) } ) .", "type": "interline_equation", "image_path": "05fa145f5cff98d6991c19b9092629fc2b252f77d6342710b829821bf26747c2.jpg" } ] } ], "index": 23, "virtual_lines": [ { "bbox": [ 184, 442, 427, 464 ], "spans": [], "index": 23 } ] }, { "type": "text", "bbox": [ 106, 471, 504, 495 ], "lines": [ { "bbox": [ 107, 470, 506, 485 ], "spans": [ { "bbox": [ 107, 471, 127, 482 ], "score": 0.86, "content": "\\mathbf { H } ^ { ( 0 ) }", "type": "inline_equation" }, { "bbox": [ 127, 470, 506, 485 ], "score": 1.0, "content": "is fed into the next forward propagation layer. Besides, we do not modify the architecture of", "type": "text" } ], "index": 24 }, { "bbox": [ 106, 483, 402, 496 ], "spans": [ { "bbox": [ 106, 483, 402, 496 ], "score": 1.0, "content": "GAT and GRAND, and just add our generated feature matrix to the input.", "type": "text" } ], "index": 25 } ], "index": 24.5 }, { "type": "title", "bbox": [ 107, 509, 214, 520 ], "lines": [ { "bbox": [ 106, 509, 214, 521 ], "spans": [ { "bbox": [ 106, 509, 214, 521 ], "score": 1.0, "content": "3.3 ACTIVE LEARNING", "type": "text" } ], "index": 26 } ], "index": 26 }, { "type": "text", "bbox": [ 106, 529, 506, 642 ], "lines": [ { "bbox": [ 105, 529, 505, 542 ], "spans": [ { "bbox": [ 105, 529, 505, 542 ], "score": 1.0, "content": "In this section, we introduce a trick for the overall training framework. After the training of the", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 541, 504, 555 ], "spans": [ { "bbox": [ 105, 542, 305, 555 ], "score": 1.0, "content": "generator finishes, it contains an issue of using", "type": "text" }, { "bbox": [ 305, 541, 360, 555 ], "score": 0.93, "content": "Q _ { \\phi } ( { \\overline { { \\mathbf { X } } } } | \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 360, 542, 494, 555 ], "score": 1.0, "content": "of Eq.(4) for inference because", "type": "text" }, { "bbox": [ 495, 542, 504, 554 ], "score": 0.83, "content": "Q", "type": "inline_equation" } ], "index": 28 }, { "bbox": [ 105, 553, 506, 566 ], "spans": [ { "bbox": [ 105, 553, 506, 566 ], "score": 1.0, "content": "may generate some samples from the side part of the distribution. This critical question makes the", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 565, 505, 576 ], "spans": [ { "bbox": [ 106, 565, 505, 576 ], "score": 1.0, "content": "inferences inefficient. Inspired by Nielsen & Okoniewski (2019), we introduce active learning to", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 575, 506, 588 ], "spans": [ { "bbox": [ 105, 575, 506, 588 ], "score": 1.0, "content": "capture the suitable generated feature matrix and the corresponding generator, which improves the", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 585, 505, 599 ], "spans": [ { "bbox": [ 105, 585, 505, 599 ], "score": 1.0, "content": "inference efficiency and helps the optimization of the MLE. During active learning, the probability", "type": "text" } ], "index": 32 }, { "bbox": [ 106, 596, 506, 609 ], "spans": [ { "bbox": [ 106, 596, 506, 609 ], "score": 1.0, "content": "of each feature is proportional to its uncertainty evaluated by an acquisition function. We adopt the", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 608, 505, 621 ], "spans": [ { "bbox": [ 106, 608, 505, 621 ], "score": 1.0, "content": "Bayesian Active Learning by Disagreement (BALD) acquisition function (Houlsby et al., 2011) to", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 619, 506, 632 ], "spans": [ { "bbox": [ 106, 619, 506, 632 ], "score": 1.0, "content": "sample the most important inferences with the approximation from the Monte Carlo (MC) dropout", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 630, 153, 643 ], "spans": [ { "bbox": [ 105, 630, 153, 643 ], "score": 1.0, "content": "samples as", "type": "text" } ], "index": 36 } ], "index": 31.5 }, { "type": "interline_equation", "bbox": [ 165, 647, 444, 682 ], "lines": [ { "bbox": [ 165, 647, 444, 682 ], "spans": [ { "bbox": [ 165, 647, 444, 682 ], "score": 0.94, "content": "{ \\cal U } ( \\overline { { \\mathbf { X } } } ) \\approx H \\left[ \\frac { 1 } { N } \\sum _ { n = 1 } ^ { N } P \\left( \\mathbf { Y } _ { k } | \\overline { { \\mathbf { X } } } , \\omega _ { n } \\right) \\right] - \\frac { 1 } { N } \\sum _ { n = 1 } ^ { N } H \\left[ P \\left( \\mathbf { Y } _ { k } | \\overline { { \\mathbf { X } } } , \\omega _ { n } \\right) \\right] ,", "type": "interline_equation", "image_path": "044f1a58776aef8f5591f62fd4befd55bb068565b2de2e9bd55b68ba18b06999.jpg" } ] } ], "index": 38, "virtual_lines": [ { "bbox": [ 165, 647, 444, 658.6666666666666 ], "spans": [], "index": 37 }, { "bbox": [ 165, 658.6666666666666, 444, 670.3333333333333 ], "spans": [], "index": 38 }, { "bbox": [ 165, 670.3333333333333, 444, 681.9999999999999 ], "spans": [], "index": 39 } ] }, { "type": "text", "bbox": [ 107, 687, 505, 732 ], "lines": [ { "bbox": [ 105, 687, 505, 700 ], "spans": [ { "bbox": [ 105, 687, 133, 700 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 688, 144, 698 ], "score": 0.82, "content": "N", "type": "inline_equation" }, { "bbox": [ 144, 687, 285, 700 ], "score": 1.0, "content": "is the number of MC samples and", "type": "text" }, { "bbox": [ 285, 689, 299, 699 ], "score": 0.8, "content": "\\omega _ { n }", "type": "inline_equation" }, { "bbox": [ 299, 687, 505, 700 ], "score": 1.0, "content": "are the parameters of the network sampled for the", "type": "text" } ], "index": 40 }, { "bbox": [ 107, 699, 505, 711 ], "spans": [ { "bbox": [ 107, 701, 114, 709 ], "score": 0.73, "content": "n", "type": "inline_equation" }, { "bbox": [ 114, 699, 505, 711 ], "score": 1.0, "content": "-th MC dropout sample. A high BLAD score indicates a network with high uncertainty about the", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 710, 505, 722 ], "spans": [ { "bbox": [ 105, 710, 505, 722 ], "score": 1.0, "content": "generated feature matrix. So it tends to be selected to improve the GNN model. Finally, the overall", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 720, 481, 734 ], "spans": [ { "bbox": [ 105, 720, 481, 734 ], "score": 1.0, "content": "algorithm framework is summarized in Algorithm 1, which shows the optimization of Eq.(4).", "type": "text" } ], "index": 43 } ], "index": 41.5 } ], "page_idx": 4, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 106, 26, 308, 37 ], "lines": [ { "bbox": [ 106, 25, 309, 38 ], "spans": [ { "bbox": [ 106, 25, 309, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 751, 309, 760 ], "lines": [ { "bbox": [ 302, 750, 309, 762 ], "spans": [ { "bbox": [ 302, 750, 309, 762 ], "score": 1.0, "content": "5", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 106, 81, 506, 151 ], "lines": [ { "bbox": [ 106, 82, 506, 96 ], "spans": [ { "bbox": [ 106, 82, 506, 96 ], "score": 1.0, "content": "Optimization of the MLE Now, we present how to optimize the MLE Eq.(4) using the feature", "type": "text" } ], "index": 0 }, { "bbox": [ 106, 93, 506, 106 ], "spans": [ { "bbox": [ 106, 93, 506, 106 ], "score": 1.0, "content": "matrix produced from the generator. Once the augmented feature matrix can be sampled from the", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 104, 506, 118 ], "spans": [ { "bbox": [ 105, 104, 506, 118 ], "score": 1.0, "content": "generator, we can optimize the parameters of Eq.(4) in the following way. Firstly, the parameter", "type": "text" } ], "index": 2 }, { "bbox": [ 107, 115, 506, 128 ], "spans": [ { "bbox": [ 107, 115, 158, 127 ], "score": 0.92, "content": "\\bar { \\phi } = \\{ \\psi , \\varphi \\}", "type": "inline_equation" }, { "bbox": [ 159, 115, 506, 128 ], "score": 1.0, "content": "can be optimized by maximizing the ELBO of the generator (6), i.e., we train the", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 126, 506, 139 ], "spans": [ { "bbox": [ 105, 126, 244, 139 ], "score": 1.0, "content": "generator. Secondly, the parameter", "type": "text" }, { "bbox": [ 244, 127, 250, 136 ], "score": 0.81, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 251, 126, 446, 139 ], "score": 1.0, "content": "is optimized by maximizing the MLE Eq.(4) with", "type": "text" }, { "bbox": [ 446, 127, 454, 138 ], "score": 0.85, "content": "\\phi", "type": "inline_equation" }, { "bbox": [ 454, 126, 506, 139 ], "score": 1.0, "content": "fixed, which", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 137, 506, 151 ], "spans": [ { "bbox": [ 105, 138, 237, 151 ], "score": 1.0, "content": "is the conditional distribution of", "type": "text" }, { "bbox": [ 237, 138, 252, 150 ], "score": 0.9, "content": "{ \\bf Y } _ { k }", "type": "inline_equation" }, { "bbox": [ 252, 138, 290, 151 ], "score": 1.0, "content": "given A,", "type": "text" }, { "bbox": [ 290, 138, 300, 149 ], "score": 0.51, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 301, 138, 321, 151 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 321, 137, 331, 148 ], "score": 0.82, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 331, 138, 506, 151 ], "score": 1.0, "content": ", i.e., we train the downstream GNN model.", "type": "text" } ], "index": 5 } ], "index": 2.5, "bbox_fs": [ 105, 82, 506, 151 ] }, { "type": "text", "bbox": [ 106, 154, 422, 167 ], "lines": [ { "bbox": [ 105, 154, 423, 168 ], "spans": [ { "bbox": [ 105, 154, 423, 168 ], "score": 1.0, "content": "In this paper, the MLE is formulated by a downstream GNN model as follows:", "type": "text" } ], "index": 6 } ], "index": 6, "bbox_fs": [ 105, 154, 423, 168 ] }, { "type": "interline_equation", "bbox": [ 219, 172, 391, 189 ], "lines": [ { "bbox": [ 219, 172, 391, 189 ], "spans": [ { "bbox": [ 219, 172, 391, 189 ], "score": 0.78, "content": "P _ { \\theta } \\left( \\mathbf { Y } _ { k } \\mid \\mathbf { A } , \\mathbf { X } , { \\overline { { \\mathbf { X } } } } \\right) \\propto - { \\overline { { \\mathcal { L } } } } ( \\theta | \\mathbf { A } , \\mathbf { X } , { \\overline { { \\mathbf { X } } } } , \\phi ) ,", "type": "interline_equation", "image_path": "57f3086c808bc412791db206faf439c5e0fdcda03f805a35f6a8dd476808ecd3.jpg" } ] } ], "index": 7, "virtual_lines": [ { "bbox": [ 219, 172, 391, 189 ], "spans": [], "index": 7 } ] }, { "type": "interline_equation", "bbox": [ 133, 194, 446, 216 ], "lines": [ { "bbox": [ 133, 194, 446, 216 ], "spans": [ { "bbox": [ 133, 194, 446, 216 ], "score": 0.72, "content": "\\begin{array} { r } { \\overline { { \\mathcal { L } } } ( \\theta | \\mathbf { A } , \\mathbf { X } , \\overline { { \\mathbf { X } } } , \\phi ) = - \\sum _ { k \\in \\mathbf { T } } \\sum _ { f = 1 } ^ { C } \\mathbf { Y } _ { k f } \\ln \\Big ( \\mathrm { s o f t m a x } \\big ( \\mathrm { G N N } ( \\mathbf { A } , \\mathbf { X } , \\overline { { \\mathbf { X } } } ) \\big ) _ { k f } \\Big ) . } \\end{array}", "type": "interline_equation", "image_path": "4b4f7de55c1633f1e64d504d7c14ecb1f9d93ef379b8dba8051c2b7e0be66189.jpg" } ] } ], "index": 8, "virtual_lines": [ { "bbox": [ 133, 194, 446, 216 ], "spans": [], "index": 8 } ] }, { "type": "title", "bbox": [ 108, 228, 277, 240 ], "lines": [ { "bbox": [ 106, 228, 279, 241 ], "spans": [ { "bbox": [ 106, 228, 279, 241 ], "score": 1.0, "content": "3.2 THE ARCHITECTURE OF LA-GNN", "type": "text" } ], "index": 9 } ], "index": 9 }, { "type": "text", "bbox": [ 107, 249, 504, 283 ], "lines": [ { "bbox": [ 105, 248, 506, 263 ], "spans": [ { "bbox": [ 105, 248, 506, 263 ], "score": 1.0, "content": "We discuss the details of downstream GNN models. And we use GCN, GAT, GCNII, and GRAND as", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 261, 506, 273 ], "spans": [ { "bbox": [ 105, 261, 506, 273 ], "score": 1.0, "content": "the backbones and test them on semi-supervised node classification tasks. We name the modified", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 271, 385, 284 ], "spans": [ { "bbox": [ 105, 271, 385, 284 ], "score": 1.0, "content": "GNN architecture as LA-GNN, where LA means local augmentation.", "type": "text" } ], "index": 12 } ], "index": 11, "bbox_fs": [ 105, 248, 506, 284 ] }, { "type": "text", "bbox": [ 106, 295, 322, 308 ], "lines": [ { "bbox": [ 106, 295, 324, 310 ], "spans": [ { "bbox": [ 106, 295, 324, 310 ], "score": 1.0, "content": "LA-GCN A 2-layer LA-GCN is defined as follows:", "type": "text" } ], "index": 13 } ], "index": 13, "bbox_fs": [ 106, 295, 324, 310 ] }, { "type": "interline_equation", "bbox": [ 135, 313, 475, 342 ], "lines": [ { "bbox": [ 135, 313, 475, 342 ], "spans": [ { "bbox": [ 135, 313, 475, 342 ], "score": 0.94, "content": "\\mathbf { H } ^ { ( 2 ) } = \\sigma \\left( \\hat { \\mathbf { A } } \\left( \\sigma \\left( \\hat { \\mathbf { A } } \\mathbf { X } \\mathbf { W } _ { 1 } ^ { ( 1 ) } \\right) \\bigg | \\bigg | \\sigma \\left( \\hat { \\mathbf { A } } \\overline { { \\mathbf { X } } } _ { 1 } \\mathbf { W } _ { 2 } ^ { ( 1 ) } \\right) \\bigg | \\bigg | \\cdots \\bigg | \\bigg | \\sigma \\left( \\hat { \\mathbf { A } } \\overline { { \\mathbf { X } } } _ { n } \\mathbf { W } _ { n + 1 } ^ { ( 1 ) } \\right) \\right) \\mathbf { W } ^ { ( 2 ) } \\right) ,", "type": "interline_equation", "image_path": "f239d746dfe55f2b758980f17e6d4d65f2e06aec6bfd878c3b066cd22f9bd920.jpg" } ] } ], "index": 15, "virtual_lines": [ { "bbox": [ 135, 313, 475, 322.6666666666667 ], "spans": [], "index": 14 }, { "bbox": [ 135, 322.6666666666667, 475, 332.33333333333337 ], "spans": [], "index": 15 }, { "bbox": [ 135, 332.33333333333337, 475, 342.00000000000006 ], "spans": [], "index": 16 } ] }, { "type": "text", "bbox": [ 106, 349, 505, 388 ], "lines": [ { "bbox": [ 105, 347, 505, 363 ], "spans": [ { "bbox": [ 105, 347, 132, 363 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 348, 146, 361 ], "score": 0.46, "content": "\\overline { { \\mathbf { X } } } _ { i }", "type": "inline_equation" }, { "bbox": [ 139, 348, 216, 362 ], "score": 0.62, "content": "\\bar { \\mathsf { \\bar { c } } } _ { i } ( i = 1 , 2 , \\cdots , n )", "type": "inline_equation" }, { "bbox": [ 216, 347, 453, 363 ], "score": 1.0, "content": "is the augmented feature matrix produced by the generator,", "type": "text" }, { "bbox": [ 453, 350, 460, 362 ], "score": 0.85, "content": "\\parallel", "type": "inline_equation" }, { "bbox": [ 460, 347, 505, 363 ], "score": 1.0, "content": "denotes an", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 359, 506, 376 ], "spans": [ { "bbox": [ 105, 359, 269, 376 ], "score": 1.0, "content": "operator of column-wise concatenation,", "type": "text" }, { "bbox": [ 270, 361, 364, 376 ], "score": 0.8, "content": "\\mathbf { W } _ { i } ^ { ( 1 ) } \\left( i = 1 , 2 , \\cdots , n \\right)", "type": "inline_equation" }, { "bbox": [ 364, 359, 506, 376 ], "score": 1.0, "content": "denotes the parameters of the first", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 374, 426, 389 ], "spans": [ { "bbox": [ 105, 374, 188, 389 ], "score": 1.0, "content": "LA-GCN layer, and", "type": "text" }, { "bbox": [ 188, 375, 212, 386 ], "score": 0.87, "content": "\\mathbf { W } ^ { ( 2 ) }", "type": "inline_equation" }, { "bbox": [ 212, 374, 426, 389 ], "score": 1.0, "content": "denotes the parameters of the second LA-GCN layer.", "type": "text" } ], "index": 19 } ], "index": 18, "bbox_fs": [ 105, 347, 506, 389 ] }, { "type": "text", "bbox": [ 106, 400, 505, 437 ], "lines": [ { "bbox": [ 105, 401, 505, 413 ], "spans": [ { "bbox": [ 105, 401, 483, 413 ], "score": 1.0, "content": "LA-GCNII Since GCNII (Chen et al., 2020) applies a fully-connected neural network on", "type": "text" }, { "bbox": [ 483, 401, 493, 411 ], "score": 0.71, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 493, 401, 505, 413 ], "score": 1.0, "content": "to", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 411, 506, 426 ], "spans": [ { "bbox": [ 105, 411, 305, 426 ], "score": 1.0, "content": "obtain a lower-dimensional initial representation", "type": "text" }, { "bbox": [ 306, 412, 326, 423 ], "score": 0.88, "content": "\\mathbf { H } ^ { ( 0 ) }", "type": "inline_equation" }, { "bbox": [ 326, 411, 506, 426 ], "score": 1.0, "content": "before the forward propagation, we apply a", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 423, 453, 437 ], "spans": [ { "bbox": [ 105, 423, 246, 437 ], "score": 1.0, "content": "fully-connected neural network on", "type": "text" }, { "bbox": [ 246, 425, 256, 435 ], "score": 0.67, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 257, 423, 275, 437 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 275, 424, 284, 435 ], "score": 0.86, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 285, 423, 323, 437 ], "score": 1.0, "content": "to obtain", "type": "text" }, { "bbox": [ 323, 424, 344, 435 ], "score": 0.9, "content": "\\mathbf { H } ^ { ( 0 ) }", "type": "inline_equation" }, { "bbox": [ 344, 423, 453, 437 ], "score": 1.0, "content": "for LA-GCNII as follows:", "type": "text" } ], "index": 22 } ], "index": 21, "bbox_fs": [ 105, 401, 506, 437 ] }, { "type": "interline_equation", "bbox": [ 184, 442, 427, 464 ], "lines": [ { "bbox": [ 184, 442, 427, 464 ], "spans": [ { "bbox": [ 184, 442, 427, 464 ], "score": 0.91, "content": "\\mathbf { H } ^ { ( 0 ) } = \\sigma ( \\mathbf { X } \\mathbf { W } _ { 1 } ^ { ( 0 ) } ) \\| \\sigma ( \\overline { { \\mathbf { X } } } _ { 1 } \\mathbf { W } _ { 2 } ^ { ( 0 ) } ) \\| \\cdots \\| \\sigma ( \\overline { { \\mathbf { X } } } _ { n } \\mathbf { W } _ { n + 1 } ^ { ( 0 ) } ) .", "type": "interline_equation", "image_path": "05fa145f5cff98d6991c19b9092629fc2b252f77d6342710b829821bf26747c2.jpg" } ] } ], "index": 23, "virtual_lines": [ { "bbox": [ 184, 442, 427, 464 ], "spans": [], "index": 23 } ] }, { "type": "text", "bbox": [ 106, 471, 504, 495 ], "lines": [ { "bbox": [ 107, 470, 506, 485 ], "spans": [ { "bbox": [ 107, 471, 127, 482 ], "score": 0.86, "content": "\\mathbf { H } ^ { ( 0 ) }", "type": "inline_equation" }, { "bbox": [ 127, 470, 506, 485 ], "score": 1.0, "content": "is fed into the next forward propagation layer. Besides, we do not modify the architecture of", "type": "text" } ], "index": 24 }, { "bbox": [ 106, 483, 402, 496 ], "spans": [ { "bbox": [ 106, 483, 402, 496 ], "score": 1.0, "content": "GAT and GRAND, and just add our generated feature matrix to the input.", "type": "text" } ], "index": 25 } ], "index": 24.5, "bbox_fs": [ 106, 470, 506, 496 ] }, { "type": "title", "bbox": [ 107, 509, 214, 520 ], "lines": [ { "bbox": [ 106, 509, 214, 521 ], "spans": [ { "bbox": [ 106, 509, 214, 521 ], "score": 1.0, "content": "3.3 ACTIVE LEARNING", "type": "text" } ], "index": 26 } ], "index": 26 }, { "type": "text", "bbox": [ 106, 529, 506, 642 ], "lines": [ { "bbox": [ 105, 529, 505, 542 ], "spans": [ { "bbox": [ 105, 529, 505, 542 ], "score": 1.0, "content": "In this section, we introduce a trick for the overall training framework. After the training of the", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 541, 504, 555 ], "spans": [ { "bbox": [ 105, 542, 305, 555 ], "score": 1.0, "content": "generator finishes, it contains an issue of using", "type": "text" }, { "bbox": [ 305, 541, 360, 555 ], "score": 0.93, "content": "Q _ { \\phi } ( { \\overline { { \\mathbf { X } } } } | \\mathbf { A } , \\mathbf { X } )", "type": "inline_equation" }, { "bbox": [ 360, 542, 494, 555 ], "score": 1.0, "content": "of Eq.(4) for inference because", "type": "text" }, { "bbox": [ 495, 542, 504, 554 ], "score": 0.83, "content": "Q", "type": "inline_equation" } ], "index": 28 }, { "bbox": [ 105, 553, 506, 566 ], "spans": [ { "bbox": [ 105, 553, 506, 566 ], "score": 1.0, "content": "may generate some samples from the side part of the distribution. This critical question makes the", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 565, 505, 576 ], "spans": [ { "bbox": [ 106, 565, 505, 576 ], "score": 1.0, "content": "inferences inefficient. Inspired by Nielsen & Okoniewski (2019), we introduce active learning to", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 575, 506, 588 ], "spans": [ { "bbox": [ 105, 575, 506, 588 ], "score": 1.0, "content": "capture the suitable generated feature matrix and the corresponding generator, which improves the", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 585, 505, 599 ], "spans": [ { "bbox": [ 105, 585, 505, 599 ], "score": 1.0, "content": "inference efficiency and helps the optimization of the MLE. During active learning, the probability", "type": "text" } ], "index": 32 }, { "bbox": [ 106, 596, 506, 609 ], "spans": [ { "bbox": [ 106, 596, 506, 609 ], "score": 1.0, "content": "of each feature is proportional to its uncertainty evaluated by an acquisition function. We adopt the", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 608, 505, 621 ], "spans": [ { "bbox": [ 106, 608, 505, 621 ], "score": 1.0, "content": "Bayesian Active Learning by Disagreement (BALD) acquisition function (Houlsby et al., 2011) to", "type": "text" } ], "index": 34 }, { "bbox": [ 106, 619, 506, 632 ], "spans": [ { "bbox": [ 106, 619, 506, 632 ], "score": 1.0, "content": "sample the most important inferences with the approximation from the Monte Carlo (MC) dropout", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 630, 153, 643 ], "spans": [ { "bbox": [ 105, 630, 153, 643 ], "score": 1.0, "content": "samples as", "type": "text" } ], "index": 36 } ], "index": 31.5, "bbox_fs": [ 105, 529, 506, 643 ] }, { "type": "interline_equation", "bbox": [ 165, 647, 444, 682 ], "lines": [ { "bbox": [ 165, 647, 444, 682 ], "spans": [ { "bbox": [ 165, 647, 444, 682 ], "score": 0.94, "content": "{ \\cal U } ( \\overline { { \\mathbf { X } } } ) \\approx H \\left[ \\frac { 1 } { N } \\sum _ { n = 1 } ^ { N } P \\left( \\mathbf { Y } _ { k } | \\overline { { \\mathbf { X } } } , \\omega _ { n } \\right) \\right] - \\frac { 1 } { N } \\sum _ { n = 1 } ^ { N } H \\left[ P \\left( \\mathbf { Y } _ { k } | \\overline { { \\mathbf { X } } } , \\omega _ { n } \\right) \\right] ,", "type": "interline_equation", "image_path": "044f1a58776aef8f5591f62fd4befd55bb068565b2de2e9bd55b68ba18b06999.jpg" } ] } ], "index": 38, "virtual_lines": [ { "bbox": [ 165, 647, 444, 658.6666666666666 ], "spans": [], "index": 37 }, { "bbox": [ 165, 658.6666666666666, 444, 670.3333333333333 ], "spans": [], "index": 38 }, { "bbox": [ 165, 670.3333333333333, 444, 681.9999999999999 ], "spans": [], "index": 39 } ] }, { "type": "text", "bbox": [ 107, 687, 505, 732 ], "lines": [ { "bbox": [ 105, 687, 505, 700 ], "spans": [ { "bbox": [ 105, 687, 133, 700 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 688, 144, 698 ], "score": 0.82, "content": "N", "type": "inline_equation" }, { "bbox": [ 144, 687, 285, 700 ], "score": 1.0, "content": "is the number of MC samples and", "type": "text" }, { "bbox": [ 285, 689, 299, 699 ], "score": 0.8, "content": "\\omega _ { n }", "type": "inline_equation" }, { "bbox": [ 299, 687, 505, 700 ], "score": 1.0, "content": "are the parameters of the network sampled for the", "type": "text" } ], "index": 40 }, { "bbox": [ 107, 699, 505, 711 ], "spans": [ { "bbox": [ 107, 701, 114, 709 ], "score": 0.73, "content": "n", "type": "inline_equation" }, { "bbox": [ 114, 699, 505, 711 ], "score": 1.0, "content": "-th MC dropout sample. A high BLAD score indicates a network with high uncertainty about the", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 710, 505, 722 ], "spans": [ { "bbox": [ 105, 710, 505, 722 ], "score": 1.0, "content": "generated feature matrix. So it tends to be selected to improve the GNN model. Finally, the overall", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 720, 481, 734 ], "spans": [ { "bbox": [ 105, 720, 481, 734 ], "score": 1.0, "content": "algorithm framework is summarized in Algorithm 1, which shows the optimization of Eq.(4).", "type": "text" } ], "index": 43 } ], "index": 41.5, "bbox_fs": [ 105, 687, 505, 734 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 104, 81, 505, 107 ], "lines": [ { "bbox": [ 105, 81, 505, 95 ], "spans": [ { "bbox": [ 105, 81, 309, 95 ], "score": 1.0, "content": "Algorithm 1 The framework to train the Generator", "type": "text" }, { "bbox": [ 309, 83, 323, 94 ], "score": 0.88, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 323, 81, 428, 95 ], "score": 1.0, "content": "and the downstream GNN", "type": "text" }, { "bbox": [ 429, 83, 441, 93 ], "score": 0.81, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 441, 81, 505, 95 ], "score": 1.0, "content": "using the initial", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 93, 463, 108 ], "spans": [ { "bbox": [ 105, 93, 165, 108 ], "score": 1.0, "content": "feature matrix", "type": "text" }, { "bbox": [ 165, 95, 175, 105 ], "score": 0.37, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 176, 93, 307, 108 ], "score": 1.0, "content": "and the generated feature matrix", "type": "text" }, { "bbox": [ 308, 94, 318, 105 ], "score": 0.63, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 318, 93, 463, 108 ], "score": 1.0, "content": "selected by the acquisition function", "type": "text" } ], "index": 1 } ], "index": 0.5 }, { "type": "text", "bbox": [ 109, 119, 478, 257 ], "lines": [ { "bbox": [ 108, 118, 258, 135 ], "spans": [ { "bbox": [ 108, 118, 156, 135 ], "score": 1.0, "content": "1: Initialize", "type": "text" }, { "bbox": [ 156, 122, 169, 131 ], "score": 0.66, "content": "U { = }", "type": "inline_equation" }, { "bbox": [ 170, 118, 185, 135 ], "score": 1.0, "content": "-inf,", "type": "text" }, { "bbox": [ 185, 120, 195, 132 ], "score": 0.55, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 195, 118, 198, 135 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 198, 120, 211, 133 ], "score": 0.77, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 212, 118, 214, 135 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 214, 120, 226, 132 ], "score": 0.67, "content": "\\overline { { \\mathbf { X } } } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 227, 118, 245, 135 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 245, 121, 258, 134 ], "score": 0.87, "content": "Q _ { \\phi } ^ { \\prime }", "type": "inline_equation" } ], "index": 2 }, { "bbox": [ 110, 132, 303, 142 ], "spans": [ { "bbox": [ 110, 132, 135, 142 ], "score": 1.0, "content": "2: for", "type": "text" }, { "bbox": [ 135, 132, 156, 141 ], "score": 0.89, "content": "i = 1", "type": "inline_equation" }, { "bbox": [ 157, 132, 303, 142 ], "score": 1.0, "content": "to the number of generator iterations do", "type": "text" } ], "index": 3 }, { "bbox": [ 109, 141, 277, 154 ], "spans": [ { "bbox": [ 109, 141, 120, 153 ], "score": 1.0, "content": "3:", "type": "text" }, { "bbox": [ 134, 141, 206, 154 ], "score": 1.0, "content": "Train the generator", "type": "text" }, { "bbox": [ 206, 142, 219, 153 ], "score": 0.89, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 219, 141, 242, 154 ], "score": 1.0, "content": "using", "type": "text" }, { "bbox": [ 242, 142, 251, 151 ], "score": 0.28, "content": "\\mathbf { A }", "type": "inline_equation" }, { "bbox": [ 252, 141, 267, 154 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 268, 142, 277, 151 ], "score": 0.48, "content": "\\mathbf { X }", "type": "inline_equation" } ], "index": 4 }, { "bbox": [ 109, 150, 268, 165 ], "spans": [ { "bbox": [ 109, 152, 120, 164 ], "score": 1.0, "content": "4:", "type": "text" }, { "bbox": [ 134, 150, 222, 165 ], "score": 1.0, "content": "Generate feature matrix", "type": "text" }, { "bbox": [ 223, 153, 232, 162 ], "score": 0.8, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 232, 150, 254, 165 ], "score": 1.0, "content": "using", "type": "text" }, { "bbox": [ 255, 153, 268, 164 ], "score": 0.86, "content": "Q _ { \\phi }", "type": "inline_equation" } ], "index": 5 }, { "bbox": [ 109, 163, 248, 176 ], "spans": [ { "bbox": [ 109, 163, 120, 176 ], "score": 1.0, "content": "5:", "type": "text" }, { "bbox": [ 135, 164, 170, 176 ], "score": 1.0, "content": "Compute", "type": "text" }, { "bbox": [ 171, 163, 194, 175 ], "score": 0.91, "content": "U ( { \\overline { { \\mathbf { X } } } } )", "type": "inline_equation" }, { "bbox": [ 194, 164, 248, 176 ], "score": 1.0, "content": "using Eq.(10).", "type": "text" } ], "index": 6 }, { "bbox": [ 109, 174, 205, 187 ], "spans": [ { "bbox": [ 109, 175, 120, 187 ], "score": 1.0, "content": "6:", "type": "text" }, { "bbox": [ 133, 174, 143, 187 ], "score": 1.0, "content": "if", "type": "text" }, { "bbox": [ 143, 175, 183, 186 ], "score": 0.88, "content": "U ( { \\overline { { \\mathbf { X } } } } ) > U", "type": "inline_equation" }, { "bbox": [ 183, 174, 205, 187 ], "score": 1.0, "content": "then", "type": "text" } ], "index": 7 }, { "bbox": [ 109, 186, 189, 198 ], "spans": [ { "bbox": [ 109, 186, 120, 198 ], "score": 1.0, "content": "7:", "type": "text" }, { "bbox": [ 148, 186, 189, 198 ], "score": 0.66, "content": "U = U ( { \\overline { { \\mathbf { X } } } } )", "type": "inline_equation" } ], "index": 8 }, { "bbox": [ 109, 194, 229, 210 ], "spans": [ { "bbox": [ 109, 196, 120, 208 ], "score": 1.0, "content": "8:", "type": "text" }, { "bbox": [ 146, 194, 156, 210 ], "score": 1.0, "content": "if", "type": "text" }, { "bbox": [ 156, 198, 206, 208 ], "score": 0.8, "content": "i > N _ { w a r m u p }", "type": "inline_equation" }, { "bbox": [ 207, 194, 229, 210 ], "score": 1.0, "content": "then", "type": "text" } ], "index": 9 }, { "bbox": [ 109, 206, 465, 220 ], "spans": [ { "bbox": [ 109, 207, 120, 219 ], "score": 1.0, "content": "9:", "type": "text" }, { "bbox": [ 160, 206, 205, 220 ], "score": 1.0, "content": "Train GNN", "type": "text" }, { "bbox": [ 205, 209, 216, 218 ], "score": 0.83, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 216, 206, 239, 220 ], "score": 1.0, "content": "using", "type": "text" }, { "bbox": [ 240, 208, 248, 217 ], "score": 0.25, "content": "\\mathbf { A }", "type": "inline_equation" }, { "bbox": [ 249, 206, 264, 220 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 265, 207, 274, 217 ], "score": 0.83, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 274, 206, 465, 220 ], "score": 1.0, "content": "for the number of continued GNN training iterations", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 216, 242, 234 ], "spans": [ { "bbox": [ 106, 219, 121, 231 ], "score": 1.0, "content": "10:", "type": "text" }, { "bbox": [ 160, 216, 242, 234 ], "score": 1.0, "content": "X 0 = X , Q 0φ = Q φ", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 228, 199, 246 ], "spans": [ { "bbox": [ 105, 228, 122, 246 ], "score": 1.0, "content": "11:", "type": "text" }, { "bbox": [ 122, 231, 151, 244 ], "score": 0.33, "content": "\\overline { { \\mathbf { X } } } = \\overline { { \\mathbf { X } } } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 152, 228, 163, 246 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 164, 232, 199, 245 ], "score": 0.28, "content": "Q _ { \\phi } = Q _ { \\phi } ^ { \\prime }", "type": "inline_equation" } ], "index": 12 }, { "bbox": [ 106, 242, 435, 258 ], "spans": [ { "bbox": [ 106, 242, 224, 258 ], "score": 1.0, "content": "12: Train the downstream GNN", "type": "text" }, { "bbox": [ 225, 245, 236, 255 ], "score": 0.83, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 236, 242, 358, 258 ], "score": 1.0, "content": "with the generated feature matrix", "type": "text" }, { "bbox": [ 358, 244, 367, 254 ], "score": 0.76, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 367, 242, 422, 258 ], "score": 1.0, "content": ", and generator", "type": "text" }, { "bbox": [ 422, 245, 435, 256 ], "score": 0.79, "content": "Q _ { \\phi }", "type": "inline_equation" } ], "index": 13 } ], "index": 7.5 }, { "type": "title", "bbox": [ 107, 277, 191, 290 ], "lines": [ { "bbox": [ 104, 276, 192, 293 ], "spans": [ { "bbox": [ 104, 276, 192, 293 ], "score": 1.0, "content": "4 DISCUSSION", "type": "text" } ], "index": 14 } ], "index": 14 }, { "type": "text", "bbox": [ 107, 301, 432, 313 ], "lines": [ { "bbox": [ 105, 300, 433, 315 ], "spans": [ { "bbox": [ 105, 300, 433, 315 ], "score": 1.0, "content": "In this section, we discuss the motivation of this work and provide some analysis.", "type": "text" } ], "index": 15 } ], "index": 15 }, { "type": "text", "bbox": [ 106, 324, 506, 534 ], "lines": [ { "bbox": [ 106, 325, 505, 338 ], "spans": [ { "bbox": [ 106, 325, 505, 338 ], "score": 1.0, "content": "Connection to EP-B and GraphSAGE We discuss how our proposed model distinguishes from", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 336, 505, 348 ], "spans": [ { "bbox": [ 106, 336, 505, 348 ], "score": 1.0, "content": "the classical representation learning models on graphs. Previous methods such as EP-B (García-", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 346, 505, 360 ], "spans": [ { "bbox": [ 105, 346, 505, 360 ], "score": 1.0, "content": "Durán & Niepert, 2017) and GraphSAGE (Hamilton et al., 2017) rely on reconstruction loss function", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 357, 505, 371 ], "spans": [ { "bbox": [ 105, 357, 505, 371 ], "score": 1.0, "content": "between the central node and its neighbors’ embeddings. EP-B aims to minimize the reconstruction", "type": "text" } ], "index": 19 }, { "bbox": [ 104, 369, 507, 389 ], "spans": [ { "bbox": [ 104, 371, 241, 388 ], "score": 1.0, "content": "error by optimizing the objective", "type": "text" }, { "bbox": [ 242, 369, 435, 389 ], "score": 0.91, "content": "\\begin{array} { r } { \\operatorname* { m i n } { \\sum _ { u \\in V \\backslash \\{ v \\} } } \\left[ \\gamma + d ( \\widetilde { \\mathbf { X } } _ { v } , \\mathbf { X } _ { v } ) - d ( \\widetilde { \\mathbf { X } } _ { v } , \\mathbf { X } _ { u } ) \\right] } \\end{array}", "type": "inline_equation" }, { "bbox": [ 435, 371, 464, 388 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 464, 372, 478, 384 ], "score": 0.87, "content": "\\mathbf { X } _ { v }", "type": "inline_equation" }, { "bbox": [ 479, 371, 507, 388 ], "score": 1.0, "content": "repre-", "type": "text" } ], "index": 20 }, { "bbox": [ 104, 388, 506, 403 ], "spans": [ { "bbox": [ 104, 388, 197, 403 ], "score": 1.0, "content": "sents the target node;", "type": "text" }, { "bbox": [ 198, 390, 213, 401 ], "score": 0.88, "content": "\\mathbf { X } _ { u }", "type": "inline_equation" }, { "bbox": [ 213, 388, 334, 403 ], "score": 1.0, "content": "denotes the neighbor nodes;", "type": "text" }, { "bbox": [ 335, 388, 448, 401 ], "score": 0.85, "content": "\\widetilde { \\mathbf { X } } _ { v } = \\mathrm { A G G } ( \\mathbf { X } _ { l } | l \\in \\mathcal { N } ( v ) )", "type": "inline_equation" }, { "bbox": [ 448, 388, 506, 403 ], "score": 1.0, "content": "indicates the", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 401, 505, 413 ], "spans": [ { "bbox": [ 105, 401, 249, 413 ], "score": 1.0, "content": "reconstruction from neighbors; and", "type": "text" }, { "bbox": [ 250, 402, 258, 412 ], "score": 0.82, "content": "\\gamma", "type": "inline_equation" }, { "bbox": [ 258, 401, 505, 413 ], "score": 1.0, "content": "refers to the bias. Besides, GraphSAGE exploits the negative", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 412, 505, 424 ], "spans": [ { "bbox": [ 106, 412, 505, 424 ], "score": 1.0, "content": "sampling to differentiate the representations of remote node-pairs. GraphSAGE enforce nearby", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 423, 505, 435 ], "spans": [ { "bbox": [ 106, 423, 505, 435 ], "score": 1.0, "content": "nodes to have similar representations and to enforce disparate nodes to be distinct by minimizing the", "type": "text" } ], "index": 24 }, { "bbox": [ 104, 431, 506, 448 ], "spans": [ { "bbox": [ 104, 431, 143, 448 ], "score": 1.0, "content": "objective", "type": "text" }, { "bbox": [ 143, 433, 429, 447 ], "score": 0.86, "content": "\\operatorname* { m i n } - E _ { u \\sim \\mathcal { N } ( v ) } \\overset { \\cdot } { \\log } \\left( \\left( \\sigma ( \\mathbf { X } _ { u } ^ { T } \\mathbf { X } _ { v } ) \\right) \\right) - \\lambda E _ { v _ { n } \\sim P _ { n } ( v ) } \\log \\left( \\left( \\sigma ( - \\mathbf { X } _ { v _ { n } } ^ { T } \\mathbf { X } _ { v } ) \\right) \\right)", "type": "inline_equation" }, { "bbox": [ 429, 431, 457, 448 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 457, 434, 471, 444 ], "score": 0.89, "content": "\\mathbf { X } _ { v }", "type": "inline_equation" }, { "bbox": [ 472, 431, 506, 448 ], "score": 1.0, "content": "denotes", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 446, 505, 458 ], "spans": [ { "bbox": [ 106, 446, 158, 458 ], "score": 1.0, "content": "target node;", "type": "text" }, { "bbox": [ 159, 446, 174, 457 ], "score": 0.86, "content": "\\mathbf { X } _ { u }", "type": "inline_equation" }, { "bbox": [ 174, 446, 300, 458 ], "score": 1.0, "content": "represents the neighbor node;", "type": "text" }, { "bbox": [ 300, 447, 320, 458 ], "score": 0.89, "content": "{ \\bf X } _ { v _ { n } }", "type": "inline_equation" }, { "bbox": [ 320, 446, 415, 458 ], "score": 1.0, "content": "is disparate node; and", "type": "text" }, { "bbox": [ 415, 446, 441, 458 ], "score": 0.92, "content": "P _ { n } ( v )", "type": "inline_equation" }, { "bbox": [ 442, 446, 505, 458 ], "score": 1.0, "content": "is the negative", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 456, 506, 469 ], "spans": [ { "bbox": [ 105, 456, 506, 469 ], "score": 1.0, "content": "sampling. These approaches build upon the assumption that adjacent nodes share similar attributes.", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 468, 505, 480 ], "spans": [ { "bbox": [ 105, 468, 505, 480 ], "score": 1.0, "content": "In contrast, our model does not rely on such assumption and instead generates the neighboring node", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 478, 506, 491 ], "spans": [ { "bbox": [ 105, 478, 488, 491 ], "score": 1.0, "content": "features from the conditional distribution of central node representations. Given the target node,", "type": "text" }, { "bbox": [ 488, 479, 502, 489 ], "score": 0.88, "content": "\\mathbf { X } _ { v }", "type": "inline_equation" }, { "bbox": [ 502, 478, 506, 491 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 489, 505, 502 ], "spans": [ { "bbox": [ 105, 489, 378, 502 ], "score": 1.0, "content": "our aim is to learn the conditional distribution of the neighbor nodes,", "type": "text" }, { "bbox": [ 379, 489, 393, 501 ], "score": 0.87, "content": "\\mathbf { X } _ { u }", "type": "inline_equation" }, { "bbox": [ 394, 489, 505, 502 ], "score": 1.0, "content": ". A comparison between the", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 500, 505, 513 ], "spans": [ { "bbox": [ 105, 500, 505, 513 ], "score": 1.0, "content": "reconstruction-based representation learning on graphs and our proposed framework is illustrated", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 511, 506, 524 ], "spans": [ { "bbox": [ 105, 511, 506, 524 ], "score": 1.0, "content": "in Figure 2. And our local augmentation method is the third paradigm to exploit neighbors in a", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 522, 171, 536 ], "spans": [ { "bbox": [ 105, 522, 171, 536 ], "score": 1.0, "content": "generative way.", "type": "text" } ], "index": 33 } ], "index": 24.5 }, { "type": "image", "bbox": [ 122, 550, 486, 624 ], "blocks": [ { "type": "image_body", "bbox": [ 122, 550, 486, 624 ], "group_id": 0, "lines": [ { "bbox": [ 122, 550, 486, 624 ], "spans": [ { "bbox": [ 122, 550, 486, 624 ], "score": 0.963, "type": "image", "image_path": "02db34de261ebadeed56e54daa7a15cd3eaa86f7795ea776ca63ea498b28e4a9.jpg" } ] } ], "index": 35, "virtual_lines": [ { "bbox": [ 122, 550, 486, 574.6666666666666 ], "spans": [], "index": 34 }, { "bbox": [ 122, 574.6666666666666, 486, 599.3333333333333 ], "spans": [], "index": 35 }, { "bbox": [ 122, 599.3333333333333, 486, 623.9999999999999 ], "spans": [], "index": 36 } ] }, { "type": "image_caption", "bbox": [ 106, 635, 506, 680 ], "group_id": 0, "lines": [ { "bbox": [ 105, 635, 506, 648 ], "spans": [ { "bbox": [ 105, 635, 506, 648 ], "score": 1.0, "content": "Figure 2: (a) The original graph. (b) EP-B exploits the neighbors to reconstruct the central node’s", "type": "text" } ], "index": 37 }, { "bbox": [ 106, 647, 505, 659 ], "spans": [ { "bbox": [ 106, 647, 505, 659 ], "score": 1.0, "content": "embedding. (c) GraphSAGE encourages nearby nodes to have similar embeddings. (d) Given the", "type": "text" } ], "index": 38 }, { "bbox": [ 104, 658, 506, 670 ], "spans": [ { "bbox": [ 104, 658, 506, 670 ], "score": 1.0, "content": "representation of the central node, our aim is to infer the representations of the connected distribution", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 667, 163, 682 ], "spans": [ { "bbox": [ 105, 667, 163, 682 ], "score": 1.0, "content": "of neighbors.", "type": "text" } ], "index": 40 } ], "index": 38.5 } ], "index": 36.75 }, { "type": "text", "bbox": [ 107, 687, 505, 732 ], "lines": [ { "bbox": [ 105, 687, 507, 700 ], "spans": [ { "bbox": [ 105, 687, 507, 700 ], "score": 1.0, "content": "Local Augmentation vs. General Augmentation General image augmentation algorithms in-", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 698, 505, 711 ], "spans": [ { "bbox": [ 105, 698, 505, 711 ], "score": 1.0, "content": "clude geometric transformations, feature space augmentation, adversarial training, and generative", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 710, 506, 723 ], "spans": [ { "bbox": [ 105, 710, 506, 723 ], "score": 1.0, "content": "adversarial networks (Shorten & Khoshgoftaar, 2019). It is impossible to apply geometric transfor-", "type": "text" } ], "index": 43 }, { "bbox": [ 106, 721, 505, 733 ], "spans": [ { "bbox": [ 106, 721, 505, 733 ], "score": 1.0, "content": "mations directly to graph data augmentation since graphs are sensitive to node permutation. General", "type": "text" } ], "index": 44 } ], "index": 42.5 } ], "page_idx": 5, "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 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 752, 309, 760 ], "lines": [ { "bbox": [ 302, 751, 310, 762 ], "spans": [ { "bbox": [ 302, 751, 310, 762 ], "score": 1.0, "content": "6", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 104, 81, 505, 107 ], "lines": [ { "bbox": [ 105, 81, 505, 95 ], "spans": [ { "bbox": [ 105, 81, 309, 95 ], "score": 1.0, "content": "Algorithm 1 The framework to train the Generator", "type": "text" }, { "bbox": [ 309, 83, 323, 94 ], "score": 0.88, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 323, 81, 428, 95 ], "score": 1.0, "content": "and the downstream GNN", "type": "text" }, { "bbox": [ 429, 83, 441, 93 ], "score": 0.81, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 441, 81, 505, 95 ], "score": 1.0, "content": "using the initial", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 93, 463, 108 ], "spans": [ { "bbox": [ 105, 93, 165, 108 ], "score": 1.0, "content": "feature matrix", "type": "text" }, { "bbox": [ 165, 95, 175, 105 ], "score": 0.37, "content": "\\mathbf { X }", "type": "inline_equation" }, { "bbox": [ 176, 93, 307, 108 ], "score": 1.0, "content": "and the generated feature matrix", "type": "text" }, { "bbox": [ 308, 94, 318, 105 ], "score": 0.63, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 318, 93, 463, 108 ], "score": 1.0, "content": "selected by the acquisition function", "type": "text" } ], "index": 1 } ], "index": 0.5, "bbox_fs": [ 105, 81, 505, 108 ] }, { "type": "index", "bbox": [ 109, 119, 478, 257 ], "lines": [ { "bbox": [ 108, 118, 258, 135 ], "spans": [ { "bbox": [ 108, 118, 156, 135 ], "score": 1.0, "content": "1: Initialize", "type": "text" }, { "bbox": [ 156, 122, 169, 131 ], "score": 0.66, "content": "U { = }", "type": "inline_equation" }, { "bbox": [ 170, 118, 185, 135 ], "score": 1.0, "content": "-inf,", "type": "text" }, { "bbox": [ 185, 120, 195, 132 ], "score": 0.55, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 195, 118, 198, 135 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 198, 120, 211, 133 ], "score": 0.77, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 212, 118, 214, 135 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 214, 120, 226, 132 ], "score": 0.67, "content": "\\overline { { \\mathbf { X } } } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 227, 118, 245, 135 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 245, 121, 258, 134 ], "score": 0.87, "content": "Q _ { \\phi } ^ { \\prime }", "type": "inline_equation" } ], "index": 2, "is_list_start_line": true }, { "bbox": [ 110, 132, 303, 142 ], "spans": [ { "bbox": [ 110, 132, 135, 142 ], "score": 1.0, "content": "2: for", "type": "text" }, { "bbox": [ 135, 132, 156, 141 ], "score": 0.89, "content": "i = 1", "type": "inline_equation" }, { "bbox": [ 157, 132, 303, 142 ], "score": 1.0, "content": "to the number of generator iterations do", "type": "text" } ], "index": 3, "is_list_start_line": true }, { "bbox": [ 109, 141, 277, 154 ], "spans": [ { "bbox": [ 109, 141, 120, 153 ], "score": 1.0, "content": "3:", "type": "text" }, { "bbox": [ 134, 141, 206, 154 ], "score": 1.0, "content": "Train the generator", "type": "text" }, { "bbox": [ 206, 142, 219, 153 ], "score": 0.89, "content": "Q _ { \\phi }", "type": "inline_equation" }, { "bbox": [ 219, 141, 242, 154 ], "score": 1.0, "content": "using", "type": "text" }, { "bbox": [ 242, 142, 251, 151 ], "score": 0.28, "content": "\\mathbf { A }", "type": "inline_equation" }, { "bbox": [ 252, 141, 267, 154 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 268, 142, 277, 151 ], "score": 0.48, "content": "\\mathbf { X }", "type": "inline_equation" } ], "index": 4, "is_list_start_line": true }, { "bbox": [ 109, 150, 268, 165 ], "spans": [ { "bbox": [ 109, 152, 120, 164 ], "score": 1.0, "content": "4:", "type": "text" }, { "bbox": [ 134, 150, 222, 165 ], "score": 1.0, "content": "Generate feature matrix", "type": "text" }, { "bbox": [ 223, 153, 232, 162 ], "score": 0.8, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 232, 150, 254, 165 ], "score": 1.0, "content": "using", "type": "text" }, { "bbox": [ 255, 153, 268, 164 ], "score": 0.86, "content": "Q _ { \\phi }", "type": "inline_equation" } ], "index": 5, "is_list_start_line": true }, { "bbox": [ 109, 163, 248, 176 ], "spans": [ { "bbox": [ 109, 163, 120, 176 ], "score": 1.0, "content": "5:", "type": "text" }, { "bbox": [ 135, 164, 170, 176 ], "score": 1.0, "content": "Compute", "type": "text" }, { "bbox": [ 171, 163, 194, 175 ], "score": 0.91, "content": "U ( { \\overline { { \\mathbf { X } } } } )", "type": "inline_equation" }, { "bbox": [ 194, 164, 248, 176 ], "score": 1.0, "content": "using Eq.(10).", "type": "text" } ], "index": 6, "is_list_start_line": true }, { "bbox": [ 109, 174, 205, 187 ], "spans": [ { "bbox": [ 109, 175, 120, 187 ], "score": 1.0, "content": "6:", "type": "text" }, { "bbox": [ 133, 174, 143, 187 ], "score": 1.0, "content": "if", "type": "text" }, { "bbox": [ 143, 175, 183, 186 ], "score": 0.88, "content": "U ( { \\overline { { \\mathbf { X } } } } ) > U", "type": "inline_equation" }, { "bbox": [ 183, 174, 205, 187 ], "score": 1.0, "content": "then", "type": "text" } ], "index": 7, "is_list_start_line": true }, { "bbox": [ 109, 186, 189, 198 ], "spans": [ { "bbox": [ 109, 186, 120, 198 ], "score": 1.0, "content": "7:", "type": "text" }, { "bbox": [ 148, 186, 189, 198 ], "score": 0.66, "content": "U = U ( { \\overline { { \\mathbf { X } } } } )", "type": "inline_equation" } ], "index": 8, "is_list_start_line": true }, { "bbox": [ 109, 194, 229, 210 ], "spans": [ { "bbox": [ 109, 196, 120, 208 ], "score": 1.0, "content": "8:", "type": "text" }, { "bbox": [ 146, 194, 156, 210 ], "score": 1.0, "content": "if", "type": "text" }, { "bbox": [ 156, 198, 206, 208 ], "score": 0.8, "content": "i > N _ { w a r m u p }", "type": "inline_equation" }, { "bbox": [ 207, 194, 229, 210 ], "score": 1.0, "content": "then", "type": "text" } ], "index": 9, "is_list_start_line": true }, { "bbox": [ 109, 206, 465, 220 ], "spans": [ { "bbox": [ 109, 207, 120, 219 ], "score": 1.0, "content": "9:", "type": "text" }, { "bbox": [ 160, 206, 205, 220 ], "score": 1.0, "content": "Train GNN", "type": "text" }, { "bbox": [ 205, 209, 216, 218 ], "score": 0.83, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 216, 206, 239, 220 ], "score": 1.0, "content": "using", "type": "text" }, { "bbox": [ 240, 208, 248, 217 ], "score": 0.25, "content": "\\mathbf { A }", "type": "inline_equation" }, { "bbox": [ 249, 206, 264, 220 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 265, 207, 274, 217 ], "score": 0.83, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 274, 206, 465, 220 ], "score": 1.0, "content": "for the number of continued GNN training iterations", "type": "text" } ], "index": 10, "is_list_start_line": true }, { "bbox": [ 106, 216, 242, 234 ], "spans": [ { "bbox": [ 106, 219, 121, 231 ], "score": 1.0, "content": "10:", "type": "text" }, { "bbox": [ 160, 216, 242, 234 ], "score": 1.0, "content": "X 0 = X , Q 0φ = Q φ", "type": "text" } ], "index": 11, "is_list_start_line": true }, { "bbox": [ 105, 228, 199, 246 ], "spans": [ { "bbox": [ 105, 228, 122, 246 ], "score": 1.0, "content": "11:", "type": "text" }, { "bbox": [ 122, 231, 151, 244 ], "score": 0.33, "content": "\\overline { { \\mathbf { X } } } = \\overline { { \\mathbf { X } } } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 152, 228, 163, 246 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 164, 232, 199, 245 ], "score": 0.28, "content": "Q _ { \\phi } = Q _ { \\phi } ^ { \\prime }", "type": "inline_equation" } ], "index": 12, "is_list_start_line": true }, { "bbox": [ 106, 242, 435, 258 ], "spans": [ { "bbox": [ 106, 242, 224, 258 ], "score": 1.0, "content": "12: Train the downstream GNN", "type": "text" }, { "bbox": [ 225, 245, 236, 255 ], "score": 0.83, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 236, 242, 358, 258 ], "score": 1.0, "content": "with the generated feature matrix", "type": "text" }, { "bbox": [ 358, 244, 367, 254 ], "score": 0.76, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 367, 242, 422, 258 ], "score": 1.0, "content": ", and generator", "type": "text" }, { "bbox": [ 422, 245, 435, 256 ], "score": 0.79, "content": "Q _ { \\phi }", "type": "inline_equation" } ], "index": 13, "is_list_start_line": true } ], "index": 7.5, "bbox_fs": [ 105, 118, 465, 258 ] }, { "type": "title", "bbox": [ 107, 277, 191, 290 ], "lines": [ { "bbox": [ 104, 276, 192, 293 ], "spans": [ { "bbox": [ 104, 276, 192, 293 ], "score": 1.0, "content": "4 DISCUSSION", "type": "text" } ], "index": 14 } ], "index": 14 }, { "type": "text", "bbox": [ 107, 301, 432, 313 ], "lines": [ { "bbox": [ 105, 300, 433, 315 ], "spans": [ { "bbox": [ 105, 300, 433, 315 ], "score": 1.0, "content": "In this section, we discuss the motivation of this work and provide some analysis.", "type": "text" } ], "index": 15 } ], "index": 15, "bbox_fs": [ 105, 300, 433, 315 ] }, { "type": "text", "bbox": [ 106, 324, 506, 534 ], "lines": [ { "bbox": [ 106, 325, 505, 338 ], "spans": [ { "bbox": [ 106, 325, 505, 338 ], "score": 1.0, "content": "Connection to EP-B and GraphSAGE We discuss how our proposed model distinguishes from", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 336, 505, 348 ], "spans": [ { "bbox": [ 106, 336, 505, 348 ], "score": 1.0, "content": "the classical representation learning models on graphs. Previous methods such as EP-B (García-", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 346, 505, 360 ], "spans": [ { "bbox": [ 105, 346, 505, 360 ], "score": 1.0, "content": "Durán & Niepert, 2017) and GraphSAGE (Hamilton et al., 2017) rely on reconstruction loss function", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 357, 505, 371 ], "spans": [ { "bbox": [ 105, 357, 505, 371 ], "score": 1.0, "content": "between the central node and its neighbors’ embeddings. EP-B aims to minimize the reconstruction", "type": "text" } ], "index": 19 }, { "bbox": [ 104, 369, 507, 389 ], "spans": [ { "bbox": [ 104, 371, 241, 388 ], "score": 1.0, "content": "error by optimizing the objective", "type": "text" }, { "bbox": [ 242, 369, 435, 389 ], "score": 0.91, "content": "\\begin{array} { r } { \\operatorname* { m i n } { \\sum _ { u \\in V \\backslash \\{ v \\} } } \\left[ \\gamma + d ( \\widetilde { \\mathbf { X } } _ { v } , \\mathbf { X } _ { v } ) - d ( \\widetilde { \\mathbf { X } } _ { v } , \\mathbf { X } _ { u } ) \\right] } \\end{array}", "type": "inline_equation" }, { "bbox": [ 435, 371, 464, 388 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 464, 372, 478, 384 ], "score": 0.87, "content": "\\mathbf { X } _ { v }", "type": "inline_equation" }, { "bbox": [ 479, 371, 507, 388 ], "score": 1.0, "content": "repre-", "type": "text" } ], "index": 20 }, { "bbox": [ 104, 388, 506, 403 ], "spans": [ { "bbox": [ 104, 388, 197, 403 ], "score": 1.0, "content": "sents the target node;", "type": "text" }, { "bbox": [ 198, 390, 213, 401 ], "score": 0.88, "content": "\\mathbf { X } _ { u }", "type": "inline_equation" }, { "bbox": [ 213, 388, 334, 403 ], "score": 1.0, "content": "denotes the neighbor nodes;", "type": "text" }, { "bbox": [ 335, 388, 448, 401 ], "score": 0.85, "content": "\\widetilde { \\mathbf { X } } _ { v } = \\mathrm { A G G } ( \\mathbf { X } _ { l } | l \\in \\mathcal { N } ( v ) )", "type": "inline_equation" }, { "bbox": [ 448, 388, 506, 403 ], "score": 1.0, "content": "indicates the", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 401, 505, 413 ], "spans": [ { "bbox": [ 105, 401, 249, 413 ], "score": 1.0, "content": "reconstruction from neighbors; and", "type": "text" }, { "bbox": [ 250, 402, 258, 412 ], "score": 0.82, "content": "\\gamma", "type": "inline_equation" }, { "bbox": [ 258, 401, 505, 413 ], "score": 1.0, "content": "refers to the bias. Besides, GraphSAGE exploits the negative", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 412, 505, 424 ], "spans": [ { "bbox": [ 106, 412, 505, 424 ], "score": 1.0, "content": "sampling to differentiate the representations of remote node-pairs. GraphSAGE enforce nearby", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 423, 505, 435 ], "spans": [ { "bbox": [ 106, 423, 505, 435 ], "score": 1.0, "content": "nodes to have similar representations and to enforce disparate nodes to be distinct by minimizing the", "type": "text" } ], "index": 24 }, { "bbox": [ 104, 431, 506, 448 ], "spans": [ { "bbox": [ 104, 431, 143, 448 ], "score": 1.0, "content": "objective", "type": "text" }, { "bbox": [ 143, 433, 429, 447 ], "score": 0.86, "content": "\\operatorname* { m i n } - E _ { u \\sim \\mathcal { N } ( v ) } \\overset { \\cdot } { \\log } \\left( \\left( \\sigma ( \\mathbf { X } _ { u } ^ { T } \\mathbf { X } _ { v } ) \\right) \\right) - \\lambda E _ { v _ { n } \\sim P _ { n } ( v ) } \\log \\left( \\left( \\sigma ( - \\mathbf { X } _ { v _ { n } } ^ { T } \\mathbf { X } _ { v } ) \\right) \\right)", "type": "inline_equation" }, { "bbox": [ 429, 431, 457, 448 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 457, 434, 471, 444 ], "score": 0.89, "content": "\\mathbf { X } _ { v }", "type": "inline_equation" }, { "bbox": [ 472, 431, 506, 448 ], "score": 1.0, "content": "denotes", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 446, 505, 458 ], "spans": [ { "bbox": [ 106, 446, 158, 458 ], "score": 1.0, "content": "target node;", "type": "text" }, { "bbox": [ 159, 446, 174, 457 ], "score": 0.86, "content": "\\mathbf { X } _ { u }", "type": "inline_equation" }, { "bbox": [ 174, 446, 300, 458 ], "score": 1.0, "content": "represents the neighbor node;", "type": "text" }, { "bbox": [ 300, 447, 320, 458 ], "score": 0.89, "content": "{ \\bf X } _ { v _ { n } }", "type": "inline_equation" }, { "bbox": [ 320, 446, 415, 458 ], "score": 1.0, "content": "is disparate node; and", "type": "text" }, { "bbox": [ 415, 446, 441, 458 ], "score": 0.92, "content": "P _ { n } ( v )", "type": "inline_equation" }, { "bbox": [ 442, 446, 505, 458 ], "score": 1.0, "content": "is the negative", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 456, 506, 469 ], "spans": [ { "bbox": [ 105, 456, 506, 469 ], "score": 1.0, "content": "sampling. These approaches build upon the assumption that adjacent nodes share similar attributes.", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 468, 505, 480 ], "spans": [ { "bbox": [ 105, 468, 505, 480 ], "score": 1.0, "content": "In contrast, our model does not rely on such assumption and instead generates the neighboring node", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 478, 506, 491 ], "spans": [ { "bbox": [ 105, 478, 488, 491 ], "score": 1.0, "content": "features from the conditional distribution of central node representations. Given the target node,", "type": "text" }, { "bbox": [ 488, 479, 502, 489 ], "score": 0.88, "content": "\\mathbf { X } _ { v }", "type": "inline_equation" }, { "bbox": [ 502, 478, 506, 491 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 489, 505, 502 ], "spans": [ { "bbox": [ 105, 489, 378, 502 ], "score": 1.0, "content": "our aim is to learn the conditional distribution of the neighbor nodes,", "type": "text" }, { "bbox": [ 379, 489, 393, 501 ], "score": 0.87, "content": "\\mathbf { X } _ { u }", "type": "inline_equation" }, { "bbox": [ 394, 489, 505, 502 ], "score": 1.0, "content": ". A comparison between the", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 500, 505, 513 ], "spans": [ { "bbox": [ 105, 500, 505, 513 ], "score": 1.0, "content": "reconstruction-based representation learning on graphs and our proposed framework is illustrated", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 511, 506, 524 ], "spans": [ { "bbox": [ 105, 511, 506, 524 ], "score": 1.0, "content": "in Figure 2. And our local augmentation method is the third paradigm to exploit neighbors in a", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 522, 171, 536 ], "spans": [ { "bbox": [ 105, 522, 171, 536 ], "score": 1.0, "content": "generative way.", "type": "text" } ], "index": 33 } ], "index": 24.5, "bbox_fs": [ 104, 325, 507, 536 ] }, { "type": "image", "bbox": [ 122, 550, 486, 624 ], "blocks": [ { "type": "image_body", "bbox": [ 122, 550, 486, 624 ], "group_id": 0, "lines": [ { "bbox": [ 122, 550, 486, 624 ], "spans": [ { "bbox": [ 122, 550, 486, 624 ], "score": 0.963, "type": "image", "image_path": "02db34de261ebadeed56e54daa7a15cd3eaa86f7795ea776ca63ea498b28e4a9.jpg" } ] } ], "index": 35, "virtual_lines": [ { "bbox": [ 122, 550, 486, 574.6666666666666 ], "spans": [], "index": 34 }, { "bbox": [ 122, 574.6666666666666, 486, 599.3333333333333 ], "spans": [], "index": 35 }, { "bbox": [ 122, 599.3333333333333, 486, 623.9999999999999 ], "spans": [], "index": 36 } ] }, { "type": "image_caption", "bbox": [ 106, 635, 506, 680 ], "group_id": 0, "lines": [ { "bbox": [ 105, 635, 506, 648 ], "spans": [ { "bbox": [ 105, 635, 506, 648 ], "score": 1.0, "content": "Figure 2: (a) The original graph. (b) EP-B exploits the neighbors to reconstruct the central node’s", "type": "text" } ], "index": 37 }, { "bbox": [ 106, 647, 505, 659 ], "spans": [ { "bbox": [ 106, 647, 505, 659 ], "score": 1.0, "content": "embedding. (c) GraphSAGE encourages nearby nodes to have similar embeddings. (d) Given the", "type": "text" } ], "index": 38 }, { "bbox": [ 104, 658, 506, 670 ], "spans": [ { "bbox": [ 104, 658, 506, 670 ], "score": 1.0, "content": "representation of the central node, our aim is to infer the representations of the connected distribution", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 667, 163, 682 ], "spans": [ { "bbox": [ 105, 667, 163, 682 ], "score": 1.0, "content": "of neighbors.", "type": "text" } ], "index": 40 } ], "index": 38.5 } ], "index": 36.75 }, { "type": "text", "bbox": [ 107, 687, 505, 732 ], "lines": [ { "bbox": [ 105, 687, 507, 700 ], "spans": [ { "bbox": [ 105, 687, 507, 700 ], "score": 1.0, "content": "Local Augmentation vs. General Augmentation General image augmentation algorithms in-", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 698, 505, 711 ], "spans": [ { "bbox": [ 105, 698, 505, 711 ], "score": 1.0, "content": "clude geometric transformations, feature space augmentation, adversarial training, and generative", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 710, 506, 723 ], "spans": [ { "bbox": [ 105, 710, 506, 723 ], "score": 1.0, "content": "adversarial networks (Shorten & Khoshgoftaar, 2019). It is impossible to apply geometric transfor-", "type": "text" } ], "index": 43 }, { "bbox": [ 106, 721, 505, 733 ], "spans": [ { "bbox": [ 106, 721, 505, 733 ], "score": 1.0, "content": "mations directly to graph data augmentation since graphs are sensitive to node permutation. General", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 82, 505, 95 ], "spans": [ { "bbox": [ 105, 82, 505, 95 ], "score": 1.0, "content": "adversarial training, feature space augmentation, and generative adversarial networks don’t take the", "type": "text", "cross_page": true } ], "index": 0 }, { "bbox": [ 105, 93, 505, 106 ], "spans": [ { "bbox": [ 105, 93, 505, 106 ], "score": 1.0, "content": "graph structure into account. Graphs consist of a set of identities with certain pairs of these identities", "type": "text", "cross_page": true } ], "index": 1 }, { "bbox": [ 105, 105, 504, 117 ], "spans": [ { "bbox": [ 105, 105, 504, 117 ], "score": 1.0, "content": "connected by edges. We need to consider node features and the graph structure when designing the", "type": "text", "cross_page": true } ], "index": 2 }, { "bbox": [ 105, 115, 505, 128 ], "spans": [ { "bbox": [ 105, 115, 505, 128 ], "score": 1.0, "content": "graph data augmentation framework. Our proposed method of local augmentation fully considers", "type": "text", "cross_page": true } ], "index": 3 }, { "bbox": [ 105, 125, 505, 140 ], "spans": [ { "bbox": [ 105, 125, 505, 140 ], "score": 1.0, "content": "these two points. By extracting the neighbors’ feature vectors, we have enough data points to learn the", "type": "text", "cross_page": true } ], "index": 4 }, { "bbox": [ 105, 136, 505, 150 ], "spans": [ { "bbox": [ 105, 136, 505, 150 ], "score": 1.0, "content": "distribution. There are two benefits to designing local augmentation. First, by taking the sub-graph", "type": "text", "cross_page": true } ], "index": 5 }, { "bbox": [ 105, 148, 505, 161 ], "spans": [ { "bbox": [ 105, 148, 505, 161 ], "score": 1.0, "content": "structure and feature representation associated with this sub-graph structure as input for the generative", "type": "text", "cross_page": true } ], "index": 6 }, { "bbox": [ 105, 158, 505, 172 ], "spans": [ { "bbox": [ 105, 158, 505, 172 ], "score": 1.0, "content": "model, we can learn the information of the sub-graph structure. Second, the number of data points", "type": "text", "cross_page": true } ], "index": 7 }, { "bbox": [ 105, 170, 505, 183 ], "spans": [ { "bbox": [ 105, 170, 505, 183 ], "score": 1.0, "content": "to learn the distribution depends on the node degree. This assures that we have enough data points", "type": "text", "cross_page": true } ], "index": 8 }, { "bbox": [ 105, 181, 454, 194 ], "spans": [ { "bbox": [ 105, 181, 454, 194 ], "score": 1.0, "content": "compared with the general feature augmentation and we can learn a better distribution.", "type": "text", "cross_page": true } ], "index": 9 } ], "index": 42.5, "bbox_fs": [ 105, 687, 507, 733 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 107, 82, 505, 192 ], "lines": [ { "bbox": [ 105, 82, 505, 95 ], "spans": [ { "bbox": [ 105, 82, 505, 95 ], "score": 1.0, "content": "adversarial training, feature space augmentation, and generative adversarial networks don’t take the", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 93, 505, 106 ], "spans": [ { "bbox": [ 105, 93, 505, 106 ], "score": 1.0, "content": "graph structure into account. Graphs consist of a set of identities with certain pairs of these identities", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 105, 504, 117 ], "spans": [ { "bbox": [ 105, 105, 504, 117 ], "score": 1.0, "content": "connected by edges. We need to consider node features and the graph structure when designing the", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 115, 505, 128 ], "spans": [ { "bbox": [ 105, 115, 505, 128 ], "score": 1.0, "content": "graph data augmentation framework. Our proposed method of local augmentation fully considers", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 125, 505, 140 ], "spans": [ { "bbox": [ 105, 125, 505, 140 ], "score": 1.0, "content": "these two points. By extracting the neighbors’ feature vectors, we have enough data points to learn the", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 136, 505, 150 ], "spans": [ { "bbox": [ 105, 136, 505, 150 ], "score": 1.0, "content": "distribution. There are two benefits to designing local augmentation. First, by taking the sub-graph", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 148, 505, 161 ], "spans": [ { "bbox": [ 105, 148, 505, 161 ], "score": 1.0, "content": "structure and feature representation associated with this sub-graph structure as input for the generative", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 158, 505, 172 ], "spans": [ { "bbox": [ 105, 158, 505, 172 ], "score": 1.0, "content": "model, we can learn the information of the sub-graph structure. Second, the number of data points", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 170, 505, 183 ], "spans": [ { "bbox": [ 105, 170, 505, 183 ], "score": 1.0, "content": "to learn the distribution depends on the node degree. This assures that we have enough data points", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 181, 454, 194 ], "spans": [ { "bbox": [ 105, 181, 454, 194 ], "score": 1.0, "content": "compared with the general feature augmentation and we can learn a better distribution.", "type": "text" } ], "index": 9 } ], "index": 4.5 }, { "type": "text", "bbox": [ 107, 205, 505, 282 ], "lines": [ { "bbox": [ 106, 204, 506, 218 ], "spans": [ { "bbox": [ 106, 204, 506, 218 ], "score": 1.0, "content": "Complementing missing information Jia & Benson (2020) points out that some attribute informa-", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 217, 505, 228 ], "spans": [ { "bbox": [ 106, 217, 505, 228 ], "score": 1.0, "content": "tion might be missing on a subset of vertices. By learning the distribution of node representations from", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 226, 506, 239 ], "spans": [ { "bbox": [ 105, 226, 506, 239 ], "score": 1.0, "content": "the observed data, we can utilize the produced node representations from the generative model to com-", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 239, 505, 249 ], "spans": [ { "bbox": [ 106, 239, 505, 249 ], "score": 1.0, "content": "plement the information missing in the nodes’ attributes, which boosts the robustness of downstream", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 248, 506, 261 ], "spans": [ { "bbox": [ 105, 248, 506, 261 ], "score": 1.0, "content": "tasks. And we show that our model still works in the scenario that nodes lose a certain percentage of", "type": "text" } ], "index": 14 }, { "bbox": [ 106, 259, 506, 272 ], "spans": [ { "bbox": [ 106, 259, 506, 272 ], "score": 1.0, "content": "attributes. In other words, we can exploit the well-learned distribution to complement the contextual", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 271, 466, 283 ], "spans": [ { "bbox": [ 106, 271, 466, 283 ], "score": 1.0, "content": "information of the local neighborhood to enhance the locality of the node representations.", "type": "text" } ], "index": 16 } ], "index": 13 }, { "type": "title", "bbox": [ 108, 298, 200, 310 ], "lines": [ { "bbox": [ 105, 297, 201, 312 ], "spans": [ { "bbox": [ 105, 297, 201, 312 ], "score": 1.0, "content": "5 EXPERIMENTS", "type": "text" } ], "index": 17 } ], "index": 17 }, { "type": "text", "bbox": [ 107, 323, 277, 421 ], "lines": [ { "bbox": [ 106, 323, 279, 335 ], "spans": [ { "bbox": [ 106, 323, 279, 335 ], "score": 1.0, "content": "In this section, we evaluate the perfor-", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 334, 279, 345 ], "spans": [ { "bbox": [ 106, 334, 279, 345 ], "score": 1.0, "content": "mance of our proposed model on semi-", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 344, 278, 356 ], "spans": [ { "bbox": [ 106, 344, 278, 356 ], "score": 1.0, "content": "supervised node classification tasks on a", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 356, 279, 368 ], "spans": [ { "bbox": [ 106, 356, 279, 368 ], "score": 1.0, "content": "variety of public graph datasets and com-", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 367, 278, 378 ], "spans": [ { "bbox": [ 105, 367, 278, 378 ], "score": 1.0, "content": "pare our model with the state-of-the-art", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 377, 278, 390 ], "spans": [ { "bbox": [ 105, 377, 278, 390 ], "score": 1.0, "content": "graph neural networks. We also carry out", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 388, 279, 400 ], "spans": [ { "bbox": [ 106, 388, 279, 400 ], "score": 1.0, "content": "additional experiments to showcase the ne-", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 399, 277, 411 ], "spans": [ { "bbox": [ 105, 399, 277, 411 ], "score": 1.0, "content": "cessity of our design and its robustness to", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 411, 192, 422 ], "spans": [ { "bbox": [ 106, 411, 192, 422 ], "score": 1.0, "content": "missing information.", "type": "text" } ], "index": 26 } ], "index": 22 }, { "type": "table", "bbox": [ 286, 339, 502, 517 ], "blocks": [ { "type": "table_caption", "bbox": [ 299, 323, 490, 335 ], "group_id": 0, "lines": [ { "bbox": [ 297, 322, 490, 336 ], "spans": [ { "bbox": [ 297, 322, 473, 336 ], "score": 1.0, "content": "Table 2: Classification results on fixed split", "type": "text" }, { "bbox": [ 474, 324, 490, 334 ], "score": 0.68, "content": "( \\% )", "type": "inline_equation" } ], "index": 27 } ], "index": 27 }, { "type": "table_body", "bbox": [ 286, 339, 502, 517 ], "group_id": 0, "lines": [ { "bbox": [ 286, 339, 502, 517 ], "spans": [ { "bbox": [ 286, 339, 502, 517 ], "score": 0.98, "html": "
MethodCoraCiteseerPubmed
Chebyshev (Defferrard et al.,2016)81.269.874.4
APPNP (Klicpera et al.,2019)83.871.679.7
MixHop (Abu-El-Haija et al.,2019)81.971.480.8
Graph U-net (Gao& Ji,2019)84.473.279.6
GSNN-M (Wang et al.,2020a)83.972.279.1
S²GC (Zhu & Koniusz,2021)83.573.680.2
GCN (Kipf & Welling,2017)81.670.378.9
G-GCN (Zhu et al.,2020)83.771.380.9
DropEdge-GCN (Rong et al.,2020)82.872.379.6
GAUG-O-GCN (Zhao et al.,2021)83.673.379.3
LA-GCN84.172.581.3
GAT (Velickovic et al., 2018)83.070.40OM
LA-GAT83.972.3OOM
GCNII (Chen et al.,2020) LA-GCNII85.273.180.0
85.273.781.6
GRAND (Feng et al.,2020)85.475.482.7
LA-GRAND85.875.883.3
", "type": "table", "image_path": "f9eb386ca814a6d8ef0669f5563fa2f445b3f29b93219e79bf46814890f79cf4.jpg" } ] } ], "index": 34, "virtual_lines": [ { "bbox": [ 286, 339, 502, 352.6923076923077 ], "spans": [], "index": 28 }, { "bbox": [ 286, 352.6923076923077, 502, 366.38461538461536 ], "spans": [], "index": 29 }, { "bbox": [ 286, 366.38461538461536, 502, 380.07692307692304 ], "spans": [], "index": 30 }, { "bbox": [ 286, 380.07692307692304, 502, 393.7692307692307 ], "spans": [], "index": 31 }, { "bbox": [ 286, 393.7692307692307, 502, 407.4615384615384 ], "spans": [], "index": 32 }, { "bbox": [ 286, 407.4615384615384, 502, 421.1538461538461 ], "spans": [], "index": 33 }, { "bbox": [ 286, 421.1538461538461, 502, 434.84615384615375 ], "spans": [], "index": 34 }, { "bbox": [ 286, 434.84615384615375, 502, 448.53846153846143 ], "spans": [], "index": 42 }, { "bbox": [ 286, 448.53846153846143, 502, 462.2307692307691 ], "spans": [], "index": 43 }, { "bbox": [ 286, 462.2307692307691, 502, 475.9230769230768 ], "spans": [], "index": 44 }, { "bbox": [ 286, 475.9230769230768, 502, 489.61538461538447 ], "spans": [], "index": 45 }, { "bbox": [ 286, 489.61538461538447, 502, 503.30769230769215 ], "spans": [], "index": 46 }, { "bbox": [ 286, 503.30769230769215, 502, 516.9999999999999 ], "spans": [], "index": 47 } ] } ], "index": 30.5 }, { "type": "title", "bbox": [ 107, 435, 175, 446 ], "lines": [ { "bbox": [ 105, 434, 177, 448 ], "spans": [ { "bbox": [ 105, 434, 177, 448 ], "score": 1.0, "content": "5.1 DATASETS", "type": "text" } ], "index": 35 } ], "index": 35 }, { "type": "text", "bbox": [ 107, 456, 277, 522 ], "lines": [ { "bbox": [ 106, 455, 277, 468 ], "spans": [ { "bbox": [ 106, 455, 277, 468 ], "score": 1.0, "content": "We utilize seven public graph datasets", "type": "text" } ], "index": 36 }, { "bbox": [ 106, 467, 279, 479 ], "spans": [ { "bbox": [ 106, 467, 279, 479 ], "score": 1.0, "content": "(Cora, Citeseer, Pubmed, Squirrel, Ac-", "type": "text" } ], "index": 37 }, { "bbox": [ 106, 477, 279, 489 ], "spans": [ { "bbox": [ 106, 477, 279, 489 ], "score": 1.0, "content": "tor, Chameleon, and Cornell) for semi-", "type": "text" } ], "index": 38 }, { "bbox": [ 106, 489, 277, 500 ], "spans": [ { "bbox": [ 106, 489, 277, 500 ], "score": 1.0, "content": "supervised node classification tasks. The", "type": "text" } ], "index": 39 }, { "bbox": [ 106, 499, 277, 511 ], "spans": [ { "bbox": [ 106, 499, 277, 511 ], "score": 1.0, "content": "details of these datasets can be found in the", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 511, 148, 522 ], "spans": [ { "bbox": [ 105, 511, 148, 522 ], "score": 1.0, "content": "appendix.", "type": "text" } ], "index": 41 } ], "index": 38.5 }, { "type": "title", "bbox": [ 107, 536, 312, 547 ], "lines": [ { "bbox": [ 105, 534, 314, 549 ], "spans": [ { "bbox": [ 105, 534, 314, 549 ], "score": 1.0, "content": "5.2 SEMI-SUPERVISED NODE CLASSIFICATION", "type": "text" } ], "index": 48 } ], "index": 48 }, { "type": "text", "bbox": [ 108, 557, 289, 698 ], "lines": [ { "bbox": [ 106, 556, 289, 569 ], "spans": [ { "bbox": [ 106, 556, 289, 569 ], "score": 1.0, "content": "Baselines and Experimental Setup. We", "type": "text" } ], "index": 49 }, { "bbox": [ 106, 567, 290, 580 ], "spans": [ { "bbox": [ 106, 567, 290, 580 ], "score": 1.0, "content": "apply the standard fixed splits (Yang et al.,", "type": "text" } ], "index": 50 }, { "bbox": [ 105, 577, 290, 591 ], "spans": [ { "bbox": [ 105, 577, 290, 591 ], "score": 1.0, "content": "2016) on three datasets Cora, Citeseer, and", "type": "text" } ], "index": 51 }, { "bbox": [ 105, 588, 290, 601 ], "spans": [ { "bbox": [ 105, 588, 290, 601 ], "score": 1.0, "content": "Pubmed, with 20 nodes per class for train-", "type": "text" } ], "index": 52 }, { "bbox": [ 105, 600, 290, 612 ], "spans": [ { "bbox": [ 105, 600, 290, 612 ], "score": 1.0, "content": "ing, 500 nodes for validation, and 1,000", "type": "text" } ], "index": 53 }, { "bbox": [ 106, 611, 290, 623 ], "spans": [ { "bbox": [ 106, 611, 290, 623 ], "score": 1.0, "content": "nodes for testing. And we consider four", "type": "text" } ], "index": 54 }, { "bbox": [ 105, 621, 290, 634 ], "spans": [ { "bbox": [ 105, 621, 290, 634 ], "score": 1.0, "content": "backbones: GCN (Kipf & Welling, 2017),", "type": "text" } ], "index": 55 }, { "bbox": [ 105, 632, 290, 645 ], "spans": [ { "bbox": [ 105, 632, 290, 645 ], "score": 1.0, "content": "GAT (Velickovi ˇ c et al., 2018), GCNII (Chen ´", "type": "text" } ], "index": 56 }, { "bbox": [ 105, 644, 290, 656 ], "spans": [ { "bbox": [ 105, 644, 290, 656 ], "score": 1.0, "content": "et al., 2020), and GRAND (Feng et al., 2020)", "type": "text" } ], "index": 57 }, { "bbox": [ 106, 655, 290, 667 ], "spans": [ { "bbox": [ 106, 655, 290, 667 ], "score": 1.0, "content": "to evaluate our proposed framework and com-", "type": "text" } ], "index": 58 }, { "bbox": [ 105, 666, 291, 677 ], "spans": [ { "bbox": [ 105, 666, 291, 677 ], "score": 1.0, "content": "pare our model against state-of-the-art mod-", "type": "text" } ], "index": 59 }, { "bbox": [ 106, 677, 291, 689 ], "spans": [ { "bbox": [ 106, 677, 291, 689 ], "score": 1.0, "content": "els including 1) backbone models: Cheby-", "type": "text" } ], "index": 60 }, { "bbox": [ 106, 687, 290, 700 ], "spans": [ { "bbox": [ 106, 687, 290, 700 ], "score": 1.0, "content": "shev (Defferrard et al., 2016), GCN, GAT,", "type": "text" } ], "index": 61 } ], "index": 55 }, { "type": "table", "bbox": [ 297, 572, 503, 681 ], "blocks": [ { "type": "table_caption", "bbox": [ 299, 556, 502, 568 ], "group_id": 1, "lines": [ { "bbox": [ 298, 554, 501, 570 ], "spans": [ { "bbox": [ 298, 554, 485, 570 ], "score": 1.0, "content": "Table 3: Classification results on random split", "type": "text" }, { "bbox": [ 485, 557, 501, 568 ], "score": 0.74, "content": "( \\% )", "type": "inline_equation" } ], "index": 62 } ], "index": 62 }, { "type": "table_body", "bbox": [ 297, 572, 503, 681 ], "group_id": 1, "lines": [ { "bbox": [ 297, 572, 503, 681 ], "spans": [ { "bbox": [ 297, 572, 503, 681 ], "score": 0.979, "html": "
MethodSquirrelActorChameleonCornell
APPNP21.632.133.058.7
S²GC21.327.830.257.2
GCN22.526.225.155.7
DropEdge-GCN21.926.525.053.6
LA-GCN23.227.028.956.1
GAT24.227.234.855.8
LA-GAT28.227.438.656.5
GCNII25.331.930.257.3
LA-GCNII28.632.732.556.6
", "type": "table", "image_path": "ea2bb2f57aceba67f29a39ce747fe9a7e2b3c9347d35c5041e73a0d4b8bc0e35.jpg" } ] } ], "index": 66.5, "virtual_lines": [ { "bbox": [ 297, 572, 503, 585.625 ], "spans": [], "index": 63 }, { "bbox": [ 297, 585.625, 503, 599.25 ], "spans": [], "index": 64 }, { "bbox": [ 297, 599.25, 503, 612.875 ], "spans": [], "index": 65 }, { "bbox": [ 297, 612.875, 503, 626.5 ], "spans": [], "index": 66 }, { "bbox": [ 297, 626.5, 503, 640.125 ], "spans": [], "index": 67 }, { "bbox": [ 297, 640.125, 503, 653.75 ], "spans": [], "index": 68 }, { "bbox": [ 297, 653.75, 503, 667.375 ], "spans": [], "index": 69 }, { "bbox": [ 297, 667.375, 503, 681.0 ], "spans": [], "index": 70 } ] }, { "type": "table_footnote", "bbox": [ 107, 699, 506, 732 ], "group_id": 1, "lines": [ { "bbox": [ 105, 698, 507, 712 ], "spans": [ { "bbox": [ 105, 698, 507, 712 ], "score": 1.0, "content": "APPNP (Klicpera et al., 2019), Graph U-net (Gao & Ji, 2019), MixHop (Abu-El-Haija et al., 2019),", "type": "text" } ], "index": 71 }, { "bbox": [ 106, 709, 507, 722 ], "spans": [ { "bbox": [ 106, 710, 266, 722 ], "score": 1.0, "content": "GCNII, GSNN-M (Wang et al., 2020a),", "type": "text" }, { "bbox": [ 266, 709, 292, 721 ], "score": 0.85, "content": "\\mathrm { { \\cal S } ^ { 2 } { \\cal G } { \\cal C } }", "type": "inline_equation" }, { "bbox": [ 293, 710, 507, 722 ], "score": 1.0, "content": "(Zhu & Koniusz, 2021), and GRAND and 2) feature-", "type": "text" } ], "index": 72 }, { "bbox": [ 106, 721, 506, 733 ], "spans": [ { "bbox": [ 106, 721, 506, 733 ], "score": 1.0, "content": "level and topology-level augmentation models: G-GNNs (Zhu et al., 2020), DropEdge (Rong et al.,", "type": "text" } ], "index": 73 } ], "index": 72 } ], "index": 66.5 } ], "page_idx": 6, "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 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 751, 308, 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": [ 107, 82, 505, 192 ], "lines": [], "index": 4.5, "bbox_fs": [ 105, 82, 505, 194 ], "lines_deleted": true }, { "type": "text", "bbox": [ 107, 205, 505, 282 ], "lines": [ { "bbox": [ 106, 204, 506, 218 ], "spans": [ { "bbox": [ 106, 204, 506, 218 ], "score": 1.0, "content": "Complementing missing information Jia & Benson (2020) points out that some attribute informa-", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 217, 505, 228 ], "spans": [ { "bbox": [ 106, 217, 505, 228 ], "score": 1.0, "content": "tion might be missing on a subset of vertices. By learning the distribution of node representations from", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 226, 506, 239 ], "spans": [ { "bbox": [ 105, 226, 506, 239 ], "score": 1.0, "content": "the observed data, we can utilize the produced node representations from the generative model to com-", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 239, 505, 249 ], "spans": [ { "bbox": [ 106, 239, 505, 249 ], "score": 1.0, "content": "plement the information missing in the nodes’ attributes, which boosts the robustness of downstream", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 248, 506, 261 ], "spans": [ { "bbox": [ 105, 248, 506, 261 ], "score": 1.0, "content": "tasks. And we show that our model still works in the scenario that nodes lose a certain percentage of", "type": "text" } ], "index": 14 }, { "bbox": [ 106, 259, 506, 272 ], "spans": [ { "bbox": [ 106, 259, 506, 272 ], "score": 1.0, "content": "attributes. In other words, we can exploit the well-learned distribution to complement the contextual", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 271, 466, 283 ], "spans": [ { "bbox": [ 106, 271, 466, 283 ], "score": 1.0, "content": "information of the local neighborhood to enhance the locality of the node representations.", "type": "text" } ], "index": 16 } ], "index": 13, "bbox_fs": [ 105, 204, 506, 283 ] }, { "type": "title", "bbox": [ 108, 298, 200, 310 ], "lines": [ { "bbox": [ 105, 297, 201, 312 ], "spans": [ { "bbox": [ 105, 297, 201, 312 ], "score": 1.0, "content": "5 EXPERIMENTS", "type": "text" } ], "index": 17 } ], "index": 17 }, { "type": "text", "bbox": [ 107, 323, 277, 421 ], "lines": [ { "bbox": [ 106, 323, 279, 335 ], "spans": [ { "bbox": [ 106, 323, 279, 335 ], "score": 1.0, "content": "In this section, we evaluate the perfor-", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 334, 279, 345 ], "spans": [ { "bbox": [ 106, 334, 279, 345 ], "score": 1.0, "content": "mance of our proposed model on semi-", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 344, 278, 356 ], "spans": [ { "bbox": [ 106, 344, 278, 356 ], "score": 1.0, "content": "supervised node classification tasks on a", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 356, 279, 368 ], "spans": [ { "bbox": [ 106, 356, 279, 368 ], "score": 1.0, "content": "variety of public graph datasets and com-", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 367, 278, 378 ], "spans": [ { "bbox": [ 105, 367, 278, 378 ], "score": 1.0, "content": "pare our model with the state-of-the-art", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 377, 278, 390 ], "spans": [ { "bbox": [ 105, 377, 278, 390 ], "score": 1.0, "content": "graph neural networks. We also carry out", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 388, 279, 400 ], "spans": [ { "bbox": [ 106, 388, 279, 400 ], "score": 1.0, "content": "additional experiments to showcase the ne-", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 399, 277, 411 ], "spans": [ { "bbox": [ 105, 399, 277, 411 ], "score": 1.0, "content": "cessity of our design and its robustness to", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 411, 192, 422 ], "spans": [ { "bbox": [ 106, 411, 192, 422 ], "score": 1.0, "content": "missing information.", "type": "text" } ], "index": 26 } ], "index": 22, "bbox_fs": [ 105, 323, 279, 422 ] }, { "type": "table", "bbox": [ 286, 339, 502, 517 ], "blocks": [ { "type": "table_caption", "bbox": [ 299, 323, 490, 335 ], "group_id": 0, "lines": [ { "bbox": [ 297, 322, 490, 336 ], "spans": [ { "bbox": [ 297, 322, 473, 336 ], "score": 1.0, "content": "Table 2: Classification results on fixed split", "type": "text" }, { "bbox": [ 474, 324, 490, 334 ], "score": 0.68, "content": "( \\% )", "type": "inline_equation" } ], "index": 27 } ], "index": 27 }, { "type": "table_body", "bbox": [ 286, 339, 502, 517 ], "group_id": 0, "lines": [ { "bbox": [ 286, 339, 502, 517 ], "spans": [ { "bbox": [ 286, 339, 502, 517 ], "score": 0.98, "html": "
MethodCoraCiteseerPubmed
Chebyshev (Defferrard et al.,2016)81.269.874.4
APPNP (Klicpera et al.,2019)83.871.679.7
MixHop (Abu-El-Haija et al.,2019)81.971.480.8
Graph U-net (Gao& Ji,2019)84.473.279.6
GSNN-M (Wang et al.,2020a)83.972.279.1
S²GC (Zhu & Koniusz,2021)83.573.680.2
GCN (Kipf & Welling,2017)81.670.378.9
G-GCN (Zhu et al.,2020)83.771.380.9
DropEdge-GCN (Rong et al.,2020)82.872.379.6
GAUG-O-GCN (Zhao et al.,2021)83.673.379.3
LA-GCN84.172.581.3
GAT (Velickovic et al., 2018)83.070.40OM
LA-GAT83.972.3OOM
GCNII (Chen et al.,2020) LA-GCNII85.273.180.0
85.273.781.6
GRAND (Feng et al.,2020)85.475.482.7
LA-GRAND85.875.883.3
", "type": "table", "image_path": "f9eb386ca814a6d8ef0669f5563fa2f445b3f29b93219e79bf46814890f79cf4.jpg" } ] } ], "index": 34, "virtual_lines": [ { "bbox": [ 286, 339, 502, 352.6923076923077 ], "spans": [], "index": 28 }, { "bbox": [ 286, 352.6923076923077, 502, 366.38461538461536 ], "spans": [], "index": 29 }, { "bbox": [ 286, 366.38461538461536, 502, 380.07692307692304 ], "spans": [], "index": 30 }, { "bbox": [ 286, 380.07692307692304, 502, 393.7692307692307 ], "spans": [], "index": 31 }, { "bbox": [ 286, 393.7692307692307, 502, 407.4615384615384 ], "spans": [], "index": 32 }, { "bbox": [ 286, 407.4615384615384, 502, 421.1538461538461 ], "spans": [], "index": 33 }, { "bbox": [ 286, 421.1538461538461, 502, 434.84615384615375 ], "spans": [], "index": 34 }, { "bbox": [ 286, 434.84615384615375, 502, 448.53846153846143 ], "spans": [], "index": 42 }, { "bbox": [ 286, 448.53846153846143, 502, 462.2307692307691 ], "spans": [], "index": 43 }, { "bbox": [ 286, 462.2307692307691, 502, 475.9230769230768 ], "spans": [], "index": 44 }, { "bbox": [ 286, 475.9230769230768, 502, 489.61538461538447 ], "spans": [], "index": 45 }, { "bbox": [ 286, 489.61538461538447, 502, 503.30769230769215 ], "spans": [], "index": 46 }, { "bbox": [ 286, 503.30769230769215, 502, 516.9999999999999 ], "spans": [], "index": 47 } ] } ], "index": 30.5 }, { "type": "title", "bbox": [ 107, 435, 175, 446 ], "lines": [ { "bbox": [ 105, 434, 177, 448 ], "spans": [ { "bbox": [ 105, 434, 177, 448 ], "score": 1.0, "content": "5.1 DATASETS", "type": "text" } ], "index": 35 } ], "index": 35 }, { "type": "text", "bbox": [ 107, 456, 277, 522 ], "lines": [ { "bbox": [ 106, 455, 277, 468 ], "spans": [ { "bbox": [ 106, 455, 277, 468 ], "score": 1.0, "content": "We utilize seven public graph datasets", "type": "text" } ], "index": 36 }, { "bbox": [ 106, 467, 279, 479 ], "spans": [ { "bbox": [ 106, 467, 279, 479 ], "score": 1.0, "content": "(Cora, Citeseer, Pubmed, Squirrel, Ac-", "type": "text" } ], "index": 37 }, { "bbox": [ 106, 477, 279, 489 ], "spans": [ { "bbox": [ 106, 477, 279, 489 ], "score": 1.0, "content": "tor, Chameleon, and Cornell) for semi-", "type": "text" } ], "index": 38 }, { "bbox": [ 106, 489, 277, 500 ], "spans": [ { "bbox": [ 106, 489, 277, 500 ], "score": 1.0, "content": "supervised node classification tasks. The", "type": "text" } ], "index": 39 }, { "bbox": [ 106, 499, 277, 511 ], "spans": [ { "bbox": [ 106, 499, 277, 511 ], "score": 1.0, "content": "details of these datasets can be found in the", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 511, 148, 522 ], "spans": [ { "bbox": [ 105, 511, 148, 522 ], "score": 1.0, "content": "appendix.", "type": "text" } ], "index": 41 } ], "index": 38.5, "bbox_fs": [ 105, 455, 279, 522 ] }, { "type": "title", "bbox": [ 107, 536, 312, 547 ], "lines": [ { "bbox": [ 105, 534, 314, 549 ], "spans": [ { "bbox": [ 105, 534, 314, 549 ], "score": 1.0, "content": "5.2 SEMI-SUPERVISED NODE CLASSIFICATION", "type": "text" } ], "index": 48 } ], "index": 48 }, { "type": "text", "bbox": [ 108, 557, 289, 698 ], "lines": [ { "bbox": [ 106, 556, 289, 569 ], "spans": [ { "bbox": [ 106, 556, 289, 569 ], "score": 1.0, "content": "Baselines and Experimental Setup. We", "type": "text" } ], "index": 49 }, { "bbox": [ 106, 567, 290, 580 ], "spans": [ { "bbox": [ 106, 567, 290, 580 ], "score": 1.0, "content": "apply the standard fixed splits (Yang et al.,", "type": "text" } ], "index": 50 }, { "bbox": [ 105, 577, 290, 591 ], "spans": [ { "bbox": [ 105, 577, 290, 591 ], "score": 1.0, "content": "2016) on three datasets Cora, Citeseer, and", "type": "text" } ], "index": 51 }, { "bbox": [ 105, 588, 290, 601 ], "spans": [ { "bbox": [ 105, 588, 290, 601 ], "score": 1.0, "content": "Pubmed, with 20 nodes per class for train-", "type": "text" } ], "index": 52 }, { "bbox": [ 105, 600, 290, 612 ], "spans": [ { "bbox": [ 105, 600, 290, 612 ], "score": 1.0, "content": "ing, 500 nodes for validation, and 1,000", "type": "text" } ], "index": 53 }, { "bbox": [ 106, 611, 290, 623 ], "spans": [ { "bbox": [ 106, 611, 290, 623 ], "score": 1.0, "content": "nodes for testing. And we consider four", "type": "text" } ], "index": 54 }, { "bbox": [ 105, 621, 290, 634 ], "spans": [ { "bbox": [ 105, 621, 290, 634 ], "score": 1.0, "content": "backbones: GCN (Kipf & Welling, 2017),", "type": "text" } ], "index": 55 }, { "bbox": [ 105, 632, 290, 645 ], "spans": [ { "bbox": [ 105, 632, 290, 645 ], "score": 1.0, "content": "GAT (Velickovi ˇ c et al., 2018), GCNII (Chen ´", "type": "text" } ], "index": 56 }, { "bbox": [ 105, 644, 290, 656 ], "spans": [ { "bbox": [ 105, 644, 290, 656 ], "score": 1.0, "content": "et al., 2020), and GRAND (Feng et al., 2020)", "type": "text" } ], "index": 57 }, { "bbox": [ 106, 655, 290, 667 ], "spans": [ { "bbox": [ 106, 655, 290, 667 ], "score": 1.0, "content": "to evaluate our proposed framework and com-", "type": "text" } ], "index": 58 }, { "bbox": [ 105, 666, 291, 677 ], "spans": [ { "bbox": [ 105, 666, 291, 677 ], "score": 1.0, "content": "pare our model against state-of-the-art mod-", "type": "text" } ], "index": 59 }, { "bbox": [ 106, 677, 291, 689 ], "spans": [ { "bbox": [ 106, 677, 291, 689 ], "score": 1.0, "content": "els including 1) backbone models: Cheby-", "type": "text" } ], "index": 60 }, { "bbox": [ 106, 687, 290, 700 ], "spans": [ { "bbox": [ 106, 687, 290, 700 ], "score": 1.0, "content": "shev (Defferrard et al., 2016), GCN, GAT,", "type": "text" } ], "index": 61 } ], "index": 55, "bbox_fs": [ 105, 556, 291, 700 ] }, { "type": "table", "bbox": [ 297, 572, 503, 681 ], "blocks": [ { "type": "table_caption", "bbox": [ 299, 556, 502, 568 ], "group_id": 1, "lines": [ { "bbox": [ 298, 554, 501, 570 ], "spans": [ { "bbox": [ 298, 554, 485, 570 ], "score": 1.0, "content": "Table 3: Classification results on random split", "type": "text" }, { "bbox": [ 485, 557, 501, 568 ], "score": 0.74, "content": "( \\% )", "type": "inline_equation" } ], "index": 62 } ], "index": 62 }, { "type": "table_body", "bbox": [ 297, 572, 503, 681 ], "group_id": 1, "lines": [ { "bbox": [ 297, 572, 503, 681 ], "spans": [ { "bbox": [ 297, 572, 503, 681 ], "score": 0.979, "html": "
MethodSquirrelActorChameleonCornell
APPNP21.632.133.058.7
S²GC21.327.830.257.2
GCN22.526.225.155.7
DropEdge-GCN21.926.525.053.6
LA-GCN23.227.028.956.1
GAT24.227.234.855.8
LA-GAT28.227.438.656.5
GCNII25.331.930.257.3
LA-GCNII28.632.732.556.6
", "type": "table", "image_path": "ea2bb2f57aceba67f29a39ce747fe9a7e2b3c9347d35c5041e73a0d4b8bc0e35.jpg" } ] } ], "index": 66.5, "virtual_lines": [ { "bbox": [ 297, 572, 503, 585.625 ], "spans": [], "index": 63 }, { "bbox": [ 297, 585.625, 503, 599.25 ], "spans": [], "index": 64 }, { "bbox": [ 297, 599.25, 503, 612.875 ], "spans": [], "index": 65 }, { "bbox": [ 297, 612.875, 503, 626.5 ], "spans": [], "index": 66 }, { "bbox": [ 297, 626.5, 503, 640.125 ], "spans": [], "index": 67 }, { "bbox": [ 297, 640.125, 503, 653.75 ], "spans": [], "index": 68 }, { "bbox": [ 297, 653.75, 503, 667.375 ], "spans": [], "index": 69 }, { "bbox": [ 297, 667.375, 503, 681.0 ], "spans": [], "index": 70 } ] }, { "type": "table_footnote", "bbox": [ 107, 699, 506, 732 ], "group_id": 1, "lines": [ { "bbox": [ 105, 698, 507, 712 ], "spans": [ { "bbox": [ 105, 698, 507, 712 ], "score": 1.0, "content": "APPNP (Klicpera et al., 2019), Graph U-net (Gao & Ji, 2019), MixHop (Abu-El-Haija et al., 2019),", "type": "text" } ], "index": 71 }, { "bbox": [ 106, 709, 507, 722 ], "spans": [ { "bbox": [ 106, 710, 266, 722 ], "score": 1.0, "content": "GCNII, GSNN-M (Wang et al., 2020a),", "type": "text" }, { "bbox": [ 266, 709, 292, 721 ], "score": 0.85, "content": "\\mathrm { { \\cal S } ^ { 2 } { \\cal G } { \\cal C } }", "type": "inline_equation" }, { "bbox": [ 293, 710, 507, 722 ], "score": 1.0, "content": "(Zhu & Koniusz, 2021), and GRAND and 2) feature-", "type": "text" } ], "index": 72 }, { "bbox": [ 106, 721, 506, 733 ], "spans": [ { "bbox": [ 106, 721, 506, 733 ], "score": 1.0, "content": "level and topology-level augmentation models: G-GNNs (Zhu et al., 2020), DropEdge (Rong et al.,", "type": "text" } ], "index": 73 } ], "index": 72 } ], "index": 66.5 } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 107, 82, 506, 126 ], "lines": [ { "bbox": [ 106, 82, 506, 95 ], "spans": [ { "bbox": [ 106, 82, 506, 95 ], "score": 1.0, "content": "2020) and GAUG-O (Zhao et al., 2021). For four datasets Squirrel, Actor, Chameleon, and Cornell,", "type": "text" } ], "index": 0 }, { "bbox": [ 104, 92, 506, 108 ], "spans": [ { "bbox": [ 104, 92, 324, 108 ], "score": 1.0, "content": "we take 10 random splits (Shchur et al., 2018) where", "type": "text" }, { "bbox": [ 324, 94, 343, 104 ], "score": 0.85, "content": "10 \\%", "type": "inline_equation" }, { "bbox": [ 344, 92, 347, 108 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 347, 94, 367, 104 ], "score": 0.85, "content": "30 \\%", "type": "inline_equation" }, { "bbox": [ 367, 92, 388, 108 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 388, 94, 408, 104 ], "score": 0.88, "content": "60 \\%", "type": "inline_equation" }, { "bbox": [ 409, 92, 506, 108 ], "score": 1.0, "content": "of the date for training,", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 105, 505, 117 ], "spans": [ { "bbox": [ 106, 105, 505, 117 ], "score": 1.0, "content": "validation, testing; measure the performance of GCN, GAT, GCNII, and corresponding modified", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 115, 141, 127 ], "spans": [ { "bbox": [ 105, 115, 141, 127 ], "score": 1.0, "content": "models.", "type": "text" } ], "index": 3 } ], "index": 1.5 }, { "type": "text", "bbox": [ 107, 141, 297, 382 ], "lines": [ { "bbox": [ 106, 141, 297, 153 ], "spans": [ { "bbox": [ 106, 141, 297, 153 ], "score": 1.0, "content": "Results For three datasets Cora, Citeseer, and", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 152, 298, 164 ], "spans": [ { "bbox": [ 106, 152, 298, 164 ], "score": 1.0, "content": "Pubmed, we report the mean classification accu-", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 163, 298, 174 ], "spans": [ { "bbox": [ 105, 163, 298, 174 ], "score": 1.0, "content": "racy on the test nodes of all our models after 100", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 173, 298, 186 ], "spans": [ { "bbox": [ 105, 173, 298, 186 ], "score": 1.0, "content": "runs and report the values after running the ex-", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 185, 298, 197 ], "spans": [ { "bbox": [ 105, 185, 298, 197 ], "score": 1.0, "content": "periments of their models with our server under", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 195, 298, 208 ], "spans": [ { "bbox": [ 105, 195, 298, 208 ], "score": 1.0, "content": "their setting hyperparameters in their original pa-", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 207, 298, 219 ], "spans": [ { "bbox": [ 105, 207, 298, 219 ], "score": 1.0, "content": "pers. The results of the evaluation experiments", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 217, 299, 230 ], "spans": [ { "bbox": [ 105, 217, 299, 230 ], "score": 1.0, "content": "are summarized in Tables 2, 3, and in the ap-", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 229, 297, 240 ], "spans": [ { "bbox": [ 105, 229, 297, 240 ], "score": 1.0, "content": "pendix, which demonstrate that the backbone", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 239, 297, 252 ], "spans": [ { "bbox": [ 105, 239, 297, 252 ], "score": 1.0, "content": "models equipped with our method achieve the", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 250, 297, 263 ], "spans": [ { "bbox": [ 105, 250, 297, 263 ], "score": 1.0, "content": "best performance across all the datasets except", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 261, 297, 274 ], "spans": [ { "bbox": [ 105, 261, 297, 274 ], "score": 1.0, "content": "the Cornell dataset. More specifically, we can", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 273, 298, 284 ], "spans": [ { "bbox": [ 105, 273, 247, 284 ], "score": 1.0, "content": "improve upon GCN by a margin of", "type": "text" }, { "bbox": [ 247, 273, 269, 283 ], "score": 0.86, "content": "2 . 5 \\%", "type": "inline_equation" }, { "bbox": [ 269, 273, 272, 284 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 272, 273, 294, 284 ], "score": 0.85, "content": "2 . 2 \\%", "type": "inline_equation" }, { "bbox": [ 295, 273, 298, 284 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 283, 298, 296 ], "spans": [ { "bbox": [ 105, 283, 123, 296 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 123, 284, 145, 294 ], "score": 0.86, "content": "2 . 4 \\%", "type": "inline_equation" }, { "bbox": [ 145, 283, 298, 296 ], "score": 1.0, "content": "on Cora, Citeseer, and Pubmed respec-", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 295, 297, 306 ], "spans": [ { "bbox": [ 106, 295, 297, 306 ], "score": 1.0, "content": "tively. Moreover, LA-GNN outperforms other", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 306, 297, 318 ], "spans": [ { "bbox": [ 105, 306, 297, 318 ], "score": 1.0, "content": "backbone models including GAT and GCNII as", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 317, 298, 328 ], "spans": [ { "bbox": [ 106, 317, 298, 328 ], "score": 1.0, "content": "well as data augmentation models (Zhu et al.,", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 327, 298, 340 ], "spans": [ { "bbox": [ 106, 327, 298, 340 ], "score": 1.0, "content": "2020; Rong et al., 2020; Zhao et al., 2021) on", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 339, 297, 350 ], "spans": [ { "bbox": [ 106, 339, 297, 350 ], "score": 1.0, "content": "these citation network datasets. Besids, we also", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 349, 298, 362 ], "spans": [ { "bbox": [ 105, 349, 298, 362 ], "score": 1.0, "content": "provide the analysis of the distribution of our", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 360, 297, 372 ], "spans": [ { "bbox": [ 105, 360, 297, 372 ], "score": 1.0, "content": "generated feature matrix. And Figure 3 shows", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 370, 297, 384 ], "spans": [ { "bbox": [ 105, 370, 297, 384 ], "score": 1.0, "content": "the distribution of the attributes of the original", "type": "text" } ], "index": 25 } ], "index": 14.5 }, { "type": "text", "bbox": [ 106, 383, 503, 404 ], "lines": [ { "bbox": [ 105, 382, 505, 394 ], "spans": [ { "bbox": [ 105, 382, 505, 394 ], "score": 1.0, "content": "and inference neighbors, which can demonstrate our inference feature matrix follow the distribution", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 393, 218, 404 ], "spans": [ { "bbox": [ 106, 393, 218, 404 ], "score": 1.0, "content": "of the initial feature matrix.", "type": "text" } ], "index": 27 } ], "index": 26.5 }, { "type": "image", "bbox": [ 309, 144, 495, 289 ], "blocks": [ { "type": "image_body", "bbox": [ 309, 144, 495, 289 ], "group_id": 0, "lines": [ { "bbox": [ 309, 144, 495, 289 ], "spans": [ { "bbox": [ 309, 144, 495, 289 ], "score": 0.968, "type": "image", "image_path": "410d67587b543d15cc65cba5cdc78b6ecc62b88dfffe4c1dfb7018aab80db729.jpg" } ] } ], "index": 33.5, "virtual_lines": [ { "bbox": [ 309, 144, 495, 156.08333333333334 ], "spans": [], "index": 28 }, { "bbox": [ 309, 156.08333333333334, 495, 168.16666666666669 ], "spans": [], "index": 29 }, { "bbox": [ 309, 168.16666666666669, 495, 180.25000000000003 ], "spans": [], "index": 30 }, { "bbox": [ 309, 180.25000000000003, 495, 192.33333333333337 ], "spans": [], "index": 31 }, { "bbox": [ 309, 192.33333333333337, 495, 204.4166666666667 ], "spans": [], "index": 32 }, { "bbox": [ 309, 204.4166666666667, 495, 216.50000000000006 ], "spans": [], "index": 33 }, { "bbox": [ 309, 216.50000000000006, 495, 228.5833333333334 ], "spans": [], "index": 34 }, { "bbox": [ 309, 228.5833333333334, 495, 240.66666666666674 ], "spans": [], "index": 35 }, { "bbox": [ 309, 240.66666666666674, 495, 252.75000000000009 ], "spans": [], "index": 36 }, { "bbox": [ 309, 252.75000000000009, 495, 264.8333333333334 ], "spans": [], "index": 37 }, { "bbox": [ 309, 264.8333333333334, 495, 276.91666666666674 ], "spans": [], "index": 38 }, { "bbox": [ 309, 276.91666666666674, 495, 289.00000000000006 ], "spans": [], "index": 39 } ] }, { "type": "image_caption", "bbox": [ 305, 291, 505, 369 ], "group_id": 0, "lines": [ { "bbox": [ 304, 291, 506, 303 ], "spans": [ { "bbox": [ 304, 291, 506, 303 ], "score": 1.0, "content": "Figure 3: The distribution of the attribute bin of", "type": "text" } ], "index": 40 }, { "bbox": [ 304, 302, 505, 313 ], "spans": [ { "bbox": [ 304, 302, 505, 313 ], "score": 1.0, "content": "the inference neighbors vs. the distribution of the", "type": "text" } ], "index": 41 }, { "bbox": [ 304, 313, 506, 325 ], "spans": [ { "bbox": [ 304, 313, 506, 325 ], "score": 1.0, "content": "attribute bin of the original neighbors, with KL", "type": "text" } ], "index": 42 }, { "bbox": [ 303, 324, 505, 335 ], "spans": [ { "bbox": [ 303, 324, 351, 335 ], "score": 1.0, "content": "divergence", "type": "text" }, { "bbox": [ 351, 324, 390, 335 ], "score": 0.82, "content": "= 0 . 0 0 2 6", "type": "inline_equation" }, { "bbox": [ 390, 324, 505, 335 ], "score": 1.0, "content": ". The value of each feature", "type": "text" } ], "index": 43 }, { "bbox": [ 303, 335, 506, 347 ], "spans": [ { "bbox": [ 303, 335, 506, 347 ], "score": 1.0, "content": "bin is the sum of the attribute values of multiple di-", "type": "text" } ], "index": 44 }, { "bbox": [ 303, 346, 505, 358 ], "spans": [ { "bbox": [ 303, 346, 505, 358 ], "score": 1.0, "content": "mensions of the feature vector. We split the feature", "type": "text" } ], "index": 45 }, { "bbox": [ 304, 357, 437, 369 ], "spans": [ { "bbox": [ 304, 357, 437, 369 ], "score": 1.0, "content": "vector into multiple feature bins.", "type": "text" } ], "index": 46 } ], "index": 43 } ], "index": 38.25 }, { "type": "title", "bbox": [ 107, 420, 208, 432 ], "lines": [ { "bbox": [ 106, 419, 210, 433 ], "spans": [ { "bbox": [ 106, 419, 210, 433 ], "score": 1.0, "content": "5.3 ABLATION STUDY", "type": "text" } ], "index": 47 } ], "index": 47 }, { "type": "text", "bbox": [ 107, 442, 297, 606 ], "lines": [ { "bbox": [ 106, 441, 297, 454 ], "spans": [ { "bbox": [ 106, 441, 297, 454 ], "score": 1.0, "content": "In this section, to demonstrate the effectiveness", "type": "text" } ], "index": 48 }, { "bbox": [ 106, 453, 298, 465 ], "spans": [ { "bbox": [ 106, 453, 298, 465 ], "score": 1.0, "content": "of our proposed generative framework, we con-", "type": "text" } ], "index": 49 }, { "bbox": [ 106, 464, 298, 475 ], "spans": [ { "bbox": [ 106, 464, 298, 475 ], "score": 1.0, "content": "duct experiments that compare LA-GNN to sev-", "type": "text" } ], "index": 50 }, { "bbox": [ 106, 475, 297, 487 ], "spans": [ { "bbox": [ 106, 475, 297, 487 ], "score": 1.0, "content": "eral of its ablated variants without generative", "type": "text" } ], "index": 51 }, { "bbox": [ 106, 486, 298, 497 ], "spans": [ { "bbox": [ 106, 486, 298, 497 ], "score": 1.0, "content": "modeling. The results are shown in Table 4.", "type": "text" } ], "index": 52 }, { "bbox": [ 106, 495, 298, 509 ], "spans": [ { "bbox": [ 106, 497, 142, 507 ], "score": 0.65, "content": "{ } \" \\mathrm { G C N } +", "type": "inline_equation" }, { "bbox": [ 142, 495, 298, 509 ], "score": 1.0, "content": "width\" only increases the first network", "type": "text" } ], "index": 53 }, { "bbox": [ 106, 508, 298, 518 ], "spans": [ { "bbox": [ 106, 508, 298, 518 ], "score": 1.0, "content": "layer width for GCN and GCNII to match LA-", "type": "text" } ], "index": 54 }, { "bbox": [ 105, 518, 299, 531 ], "spans": [ { "bbox": [ 105, 518, 299, 531 ], "score": 1.0, "content": "GNN without giving generated samples as input.", "type": "text" } ], "index": 55 }, { "bbox": [ 106, 529, 298, 542 ], "spans": [ { "bbox": [ 106, 530, 119, 540 ], "score": 0.79, "content": "\" +", "type": "inline_equation" }, { "bbox": [ 119, 529, 298, 542 ], "score": 1.0, "content": "concatenation\" only replaces the generated", "type": "text" } ], "index": 56 }, { "bbox": [ 106, 541, 298, 552 ], "spans": [ { "bbox": [ 106, 541, 298, 552 ], "score": 1.0, "content": "feature matrix of LA-GNN with the original fea-", "type": "text" } ], "index": 57 }, { "bbox": [ 106, 551, 298, 564 ], "spans": [ { "bbox": [ 106, 551, 234, 564 ], "score": 1.0, "content": "ture matrix of the central node.", "type": "text" }, { "bbox": [ 235, 552, 247, 562 ], "score": 0.68, "content": "\" +", "type": "inline_equation" }, { "bbox": [ 247, 551, 298, 564 ], "score": 1.0, "content": "plain neigh-", "type": "text" } ], "index": 58 }, { "bbox": [ 106, 563, 298, 574 ], "spans": [ { "bbox": [ 106, 563, 298, 574 ], "score": 1.0, "content": "borhood\" replaces the generated feature matrix", "type": "text" } ], "index": 59 }, { "bbox": [ 106, 573, 298, 585 ], "spans": [ { "bbox": [ 106, 573, 298, 585 ], "score": 1.0, "content": "of LA-GNN with a neighborhood feature ma-", "type": "text" } ], "index": 60 }, { "bbox": [ 106, 584, 297, 596 ], "spans": [ { "bbox": [ 106, 584, 297, 596 ], "score": 1.0, "content": "trix where each row corresponds to the feature", "type": "text" } ], "index": 61 }, { "bbox": [ 106, 595, 297, 607 ], "spans": [ { "bbox": [ 106, 595, 297, 607 ], "score": 1.0, "content": "vector of the randomly sampled neighbor. The", "type": "text" } ], "index": 62 } ], "index": 55 }, { "type": "table", "bbox": [ 306, 479, 502, 596 ], "blocks": [ { "type": "table_caption", "bbox": [ 304, 442, 504, 475 ], "group_id": 0, "lines": [ { "bbox": [ 303, 442, 506, 454 ], "spans": [ { "bbox": [ 303, 442, 506, 454 ], "score": 1.0, "content": "Table 4: Effects of different components of our", "type": "text" } ], "index": 63 }, { "bbox": [ 303, 452, 505, 465 ], "spans": [ { "bbox": [ 303, 452, 505, 465 ], "score": 1.0, "content": "framework evaluated on the standard split of the", "type": "text" } ], "index": 64 }, { "bbox": [ 304, 464, 448, 475 ], "spans": [ { "bbox": [ 304, 464, 448, 475 ], "score": 1.0, "content": "Cora, Citeseer and Pubmed dataset.", "type": "text" } ], "index": 65 } ], "index": 64 }, { "type": "table_body", "bbox": [ 306, 479, 502, 596 ], "group_id": 0, "lines": [ { "bbox": [ 306, 479, 502, 596 ], "spans": [ { "bbox": [ 306, 479, 502, 596 ], "score": 0.98, "html": "
MethodCoraCiteseerPubmed
GCN81.670.378.9
GCNII85.273.180.0
GCN + width82.071.479.5
GCN + concatenation81.871.678.8
GCN + plain neighborhood80.968.875.0
GCNII + width85.173.180.2
GCNII + concatenation85.273.380.2
GCNII + plain neighborhood83.371.978.1
LA-GCN84.172.581.3
LA-GCNII85.273.781.6
", "type": "table", "image_path": "1e622fbcf762f746fb35f524d6f052f3f1fd7930c093ae304997e6254e7022a0.jpg" } ] } ], "index": 70, "virtual_lines": [ { "bbox": [ 306, 479, 502, 492.0 ], "spans": [], "index": 66 }, { "bbox": [ 306, 492.0, 502, 505.0 ], "spans": [], "index": 67 }, { "bbox": [ 306, 505.0, 502, 518.0 ], "spans": [], "index": 68 }, { "bbox": [ 306, 518.0, 502, 531.0 ], "spans": [], "index": 69 }, { "bbox": [ 306, 531.0, 502, 544.0 ], "spans": [], "index": 70 }, { "bbox": [ 306, 544.0, 502, 557.0 ], "spans": [], "index": 71 }, { "bbox": [ 306, 557.0, 502, 570.0 ], "spans": [], "index": 72 }, { "bbox": [ 306, 570.0, 502, 583.0 ], "spans": [], "index": 73 }, { "bbox": [ 306, 583.0, 502, 596.0 ], "spans": [], "index": 74 } ] } ], "index": 67.0 }, { "type": "text", "bbox": [ 107, 606, 505, 650 ], "lines": [ { "bbox": [ 106, 606, 505, 618 ], "spans": [ { "bbox": [ 106, 606, 505, 618 ], "score": 1.0, "content": "results show that the first two variants provide no notable improvement for the backbone models, and", "type": "text" } ], "index": 75 }, { "bbox": [ 105, 616, 505, 630 ], "spans": [ { "bbox": [ 105, 616, 505, 630 ], "score": 1.0, "content": "the third variant even results in degradation. By eliminating the possibility that these confounding", "type": "text" } ], "index": 76 }, { "bbox": [ 105, 628, 505, 641 ], "spans": [ { "bbox": [ 105, 628, 505, 641 ], "score": 1.0, "content": "factors irrelevant to our core approach may contribute to the final performance, it’s evident that the", "type": "text" } ], "index": 77 }, { "bbox": [ 105, 639, 506, 651 ], "spans": [ { "bbox": [ 105, 639, 506, 651 ], "score": 1.0, "content": "performance gain in Table 2 and 3 are due to our proposed generative local augmentation framework.", "type": "text" } ], "index": 78 } ], "index": 76.5 }, { "type": "title", "bbox": [ 108, 666, 306, 677 ], "lines": [ { "bbox": [ 105, 666, 307, 679 ], "spans": [ { "bbox": [ 105, 666, 307, 679 ], "score": 1.0, "content": "5.4 ROBUSTNESS TO MISSING INFORMATION", "type": "text" } ], "index": 79 } ], "index": 79 }, { "type": "text", "bbox": [ 108, 687, 505, 731 ], "lines": [ { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "In this section, we conduct experiments to verify that our proposed framework can robustify down-", "type": "text" } ], "index": 80 }, { "bbox": [ 106, 699, 505, 710 ], "spans": [ { "bbox": [ 106, 699, 505, 710 ], "score": 1.0, "content": "stream tasks against missing information in the feature attributes. Specifically, we mask a certain", "type": "text" } ], "index": 81 }, { "bbox": [ 105, 710, 505, 722 ], "spans": [ { "bbox": [ 105, 710, 505, 722 ], "score": 1.0, "content": "percentage of the attributes of each feature vector and use the same pipeline to do augmentation", "type": "text" } ], "index": 82 }, { "bbox": [ 105, 720, 507, 733 ], "spans": [ { "bbox": [ 105, 720, 507, 733 ], "score": 1.0, "content": "for the masked feature matrix. As shown in Table 5, we can see that as the mask ratio increases,", "type": "text" } ], "index": 83 } ], "index": 81.5 } ], "page_idx": 7, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 302, 752, 308, 760 ], "lines": [ { "bbox": [ 302, 750, 309, 761 ], "spans": [ { "bbox": [ 302, 750, 309, 761 ], "score": 1.0, "content": "8", "type": "text" } ] } ] }, { "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 2022", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 107, 82, 506, 126 ], "lines": [ { "bbox": [ 106, 82, 506, 95 ], "spans": [ { "bbox": [ 106, 82, 506, 95 ], "score": 1.0, "content": "2020) and GAUG-O (Zhao et al., 2021). For four datasets Squirrel, Actor, Chameleon, and Cornell,", "type": "text" } ], "index": 0 }, { "bbox": [ 104, 92, 506, 108 ], "spans": [ { "bbox": [ 104, 92, 324, 108 ], "score": 1.0, "content": "we take 10 random splits (Shchur et al., 2018) where", "type": "text" }, { "bbox": [ 324, 94, 343, 104 ], "score": 0.85, "content": "10 \\%", "type": "inline_equation" }, { "bbox": [ 344, 92, 347, 108 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 347, 94, 367, 104 ], "score": 0.85, "content": "30 \\%", "type": "inline_equation" }, { "bbox": [ 367, 92, 388, 108 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 388, 94, 408, 104 ], "score": 0.88, "content": "60 \\%", "type": "inline_equation" }, { "bbox": [ 409, 92, 506, 108 ], "score": 1.0, "content": "of the date for training,", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 105, 505, 117 ], "spans": [ { "bbox": [ 106, 105, 505, 117 ], "score": 1.0, "content": "validation, testing; measure the performance of GCN, GAT, GCNII, and corresponding modified", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 115, 141, 127 ], "spans": [ { "bbox": [ 105, 115, 141, 127 ], "score": 1.0, "content": "models.", "type": "text" } ], "index": 3 } ], "index": 1.5, "bbox_fs": [ 104, 82, 506, 127 ] }, { "type": "text", "bbox": [ 107, 141, 297, 382 ], "lines": [ { "bbox": [ 106, 141, 297, 153 ], "spans": [ { "bbox": [ 106, 141, 297, 153 ], "score": 1.0, "content": "Results For three datasets Cora, Citeseer, and", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 152, 298, 164 ], "spans": [ { "bbox": [ 106, 152, 298, 164 ], "score": 1.0, "content": "Pubmed, we report the mean classification accu-", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 163, 298, 174 ], "spans": [ { "bbox": [ 105, 163, 298, 174 ], "score": 1.0, "content": "racy on the test nodes of all our models after 100", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 173, 298, 186 ], "spans": [ { "bbox": [ 105, 173, 298, 186 ], "score": 1.0, "content": "runs and report the values after running the ex-", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 185, 298, 197 ], "spans": [ { "bbox": [ 105, 185, 298, 197 ], "score": 1.0, "content": "periments of their models with our server under", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 195, 298, 208 ], "spans": [ { "bbox": [ 105, 195, 298, 208 ], "score": 1.0, "content": "their setting hyperparameters in their original pa-", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 207, 298, 219 ], "spans": [ { "bbox": [ 105, 207, 298, 219 ], "score": 1.0, "content": "pers. The results of the evaluation experiments", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 217, 299, 230 ], "spans": [ { "bbox": [ 105, 217, 299, 230 ], "score": 1.0, "content": "are summarized in Tables 2, 3, and in the ap-", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 229, 297, 240 ], "spans": [ { "bbox": [ 105, 229, 297, 240 ], "score": 1.0, "content": "pendix, which demonstrate that the backbone", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 239, 297, 252 ], "spans": [ { "bbox": [ 105, 239, 297, 252 ], "score": 1.0, "content": "models equipped with our method achieve the", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 250, 297, 263 ], "spans": [ { "bbox": [ 105, 250, 297, 263 ], "score": 1.0, "content": "best performance across all the datasets except", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 261, 297, 274 ], "spans": [ { "bbox": [ 105, 261, 297, 274 ], "score": 1.0, "content": "the Cornell dataset. More specifically, we can", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 273, 298, 284 ], "spans": [ { "bbox": [ 105, 273, 247, 284 ], "score": 1.0, "content": "improve upon GCN by a margin of", "type": "text" }, { "bbox": [ 247, 273, 269, 283 ], "score": 0.86, "content": "2 . 5 \\%", "type": "inline_equation" }, { "bbox": [ 269, 273, 272, 284 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 272, 273, 294, 284 ], "score": 0.85, "content": "2 . 2 \\%", "type": "inline_equation" }, { "bbox": [ 295, 273, 298, 284 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 283, 298, 296 ], "spans": [ { "bbox": [ 105, 283, 123, 296 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 123, 284, 145, 294 ], "score": 0.86, "content": "2 . 4 \\%", "type": "inline_equation" }, { "bbox": [ 145, 283, 298, 296 ], "score": 1.0, "content": "on Cora, Citeseer, and Pubmed respec-", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 295, 297, 306 ], "spans": [ { "bbox": [ 106, 295, 297, 306 ], "score": 1.0, "content": "tively. Moreover, LA-GNN outperforms other", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 306, 297, 318 ], "spans": [ { "bbox": [ 105, 306, 297, 318 ], "score": 1.0, "content": "backbone models including GAT and GCNII as", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 317, 298, 328 ], "spans": [ { "bbox": [ 106, 317, 298, 328 ], "score": 1.0, "content": "well as data augmentation models (Zhu et al.,", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 327, 298, 340 ], "spans": [ { "bbox": [ 106, 327, 298, 340 ], "score": 1.0, "content": "2020; Rong et al., 2020; Zhao et al., 2021) on", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 339, 297, 350 ], "spans": [ { "bbox": [ 106, 339, 297, 350 ], "score": 1.0, "content": "these citation network datasets. Besids, we also", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 349, 298, 362 ], "spans": [ { "bbox": [ 105, 349, 298, 362 ], "score": 1.0, "content": "provide the analysis of the distribution of our", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 360, 297, 372 ], "spans": [ { "bbox": [ 105, 360, 297, 372 ], "score": 1.0, "content": "generated feature matrix. And Figure 3 shows", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 370, 297, 384 ], "spans": [ { "bbox": [ 105, 370, 297, 384 ], "score": 1.0, "content": "the distribution of the attributes of the original", "type": "text" } ], "index": 25 } ], "index": 14.5, "bbox_fs": [ 105, 141, 299, 384 ] }, { "type": "text", "bbox": [ 106, 383, 503, 404 ], "lines": [ { "bbox": [ 105, 382, 505, 394 ], "spans": [ { "bbox": [ 105, 382, 505, 394 ], "score": 1.0, "content": "and inference neighbors, which can demonstrate our inference feature matrix follow the distribution", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 393, 218, 404 ], "spans": [ { "bbox": [ 106, 393, 218, 404 ], "score": 1.0, "content": "of the initial feature matrix.", "type": "text" } ], "index": 27 } ], "index": 26.5, "bbox_fs": [ 105, 382, 505, 404 ] }, { "type": "image", "bbox": [ 309, 144, 495, 289 ], "blocks": [ { "type": "image_body", "bbox": [ 309, 144, 495, 289 ], "group_id": 0, "lines": [ { "bbox": [ 309, 144, 495, 289 ], "spans": [ { "bbox": [ 309, 144, 495, 289 ], "score": 0.968, "type": "image", "image_path": "410d67587b543d15cc65cba5cdc78b6ecc62b88dfffe4c1dfb7018aab80db729.jpg" } ] } ], "index": 33.5, "virtual_lines": [ { "bbox": [ 309, 144, 495, 156.08333333333334 ], "spans": [], "index": 28 }, { "bbox": [ 309, 156.08333333333334, 495, 168.16666666666669 ], "spans": [], "index": 29 }, { "bbox": [ 309, 168.16666666666669, 495, 180.25000000000003 ], "spans": [], "index": 30 }, { "bbox": [ 309, 180.25000000000003, 495, 192.33333333333337 ], "spans": [], "index": 31 }, { "bbox": [ 309, 192.33333333333337, 495, 204.4166666666667 ], "spans": [], "index": 32 }, { "bbox": [ 309, 204.4166666666667, 495, 216.50000000000006 ], "spans": [], "index": 33 }, { "bbox": [ 309, 216.50000000000006, 495, 228.5833333333334 ], "spans": [], "index": 34 }, { "bbox": [ 309, 228.5833333333334, 495, 240.66666666666674 ], "spans": [], "index": 35 }, { "bbox": [ 309, 240.66666666666674, 495, 252.75000000000009 ], "spans": [], "index": 36 }, { "bbox": [ 309, 252.75000000000009, 495, 264.8333333333334 ], "spans": [], "index": 37 }, { "bbox": [ 309, 264.8333333333334, 495, 276.91666666666674 ], "spans": [], "index": 38 }, { "bbox": [ 309, 276.91666666666674, 495, 289.00000000000006 ], "spans": [], "index": 39 } ] }, { "type": "image_caption", "bbox": [ 305, 291, 505, 369 ], "group_id": 0, "lines": [ { "bbox": [ 304, 291, 506, 303 ], "spans": [ { "bbox": [ 304, 291, 506, 303 ], "score": 1.0, "content": "Figure 3: The distribution of the attribute bin of", "type": "text" } ], "index": 40 }, { "bbox": [ 304, 302, 505, 313 ], "spans": [ { "bbox": [ 304, 302, 505, 313 ], "score": 1.0, "content": "the inference neighbors vs. the distribution of the", "type": "text" } ], "index": 41 }, { "bbox": [ 304, 313, 506, 325 ], "spans": [ { "bbox": [ 304, 313, 506, 325 ], "score": 1.0, "content": "attribute bin of the original neighbors, with KL", "type": "text" } ], "index": 42 }, { "bbox": [ 303, 324, 505, 335 ], "spans": [ { "bbox": [ 303, 324, 351, 335 ], "score": 1.0, "content": "divergence", "type": "text" }, { "bbox": [ 351, 324, 390, 335 ], "score": 0.82, "content": "= 0 . 0 0 2 6", "type": "inline_equation" }, { "bbox": [ 390, 324, 505, 335 ], "score": 1.0, "content": ". The value of each feature", "type": "text" } ], "index": 43 }, { "bbox": [ 303, 335, 506, 347 ], "spans": [ { "bbox": [ 303, 335, 506, 347 ], "score": 1.0, "content": "bin is the sum of the attribute values of multiple di-", "type": "text" } ], "index": 44 }, { "bbox": [ 303, 346, 505, 358 ], "spans": [ { "bbox": [ 303, 346, 505, 358 ], "score": 1.0, "content": "mensions of the feature vector. We split the feature", "type": "text" } ], "index": 45 }, { "bbox": [ 304, 357, 437, 369 ], "spans": [ { "bbox": [ 304, 357, 437, 369 ], "score": 1.0, "content": "vector into multiple feature bins.", "type": "text" } ], "index": 46 } ], "index": 43 } ], "index": 38.25 }, { "type": "title", "bbox": [ 107, 420, 208, 432 ], "lines": [ { "bbox": [ 106, 419, 210, 433 ], "spans": [ { "bbox": [ 106, 419, 210, 433 ], "score": 1.0, "content": "5.3 ABLATION STUDY", "type": "text" } ], "index": 47 } ], "index": 47 }, { "type": "text", "bbox": [ 107, 442, 297, 606 ], "lines": [ { "bbox": [ 106, 441, 297, 454 ], "spans": [ { "bbox": [ 106, 441, 297, 454 ], "score": 1.0, "content": "In this section, to demonstrate the effectiveness", "type": "text" } ], "index": 48 }, { "bbox": [ 106, 453, 298, 465 ], "spans": [ { "bbox": [ 106, 453, 298, 465 ], "score": 1.0, "content": "of our proposed generative framework, we con-", "type": "text" } ], "index": 49 }, { "bbox": [ 106, 464, 298, 475 ], "spans": [ { "bbox": [ 106, 464, 298, 475 ], "score": 1.0, "content": "duct experiments that compare LA-GNN to sev-", "type": "text" } ], "index": 50 }, { "bbox": [ 106, 475, 297, 487 ], "spans": [ { "bbox": [ 106, 475, 297, 487 ], "score": 1.0, "content": "eral of its ablated variants without generative", "type": "text" } ], "index": 51 }, { "bbox": [ 106, 486, 298, 497 ], "spans": [ { "bbox": [ 106, 486, 298, 497 ], "score": 1.0, "content": "modeling. The results are shown in Table 4.", "type": "text" } ], "index": 52 }, { "bbox": [ 106, 495, 298, 509 ], "spans": [ { "bbox": [ 106, 497, 142, 507 ], "score": 0.65, "content": "{ } \" \\mathrm { G C N } +", "type": "inline_equation" }, { "bbox": [ 142, 495, 298, 509 ], "score": 1.0, "content": "width\" only increases the first network", "type": "text" } ], "index": 53 }, { "bbox": [ 106, 508, 298, 518 ], "spans": [ { "bbox": [ 106, 508, 298, 518 ], "score": 1.0, "content": "layer width for GCN and GCNII to match LA-", "type": "text" } ], "index": 54 }, { "bbox": [ 105, 518, 299, 531 ], "spans": [ { "bbox": [ 105, 518, 299, 531 ], "score": 1.0, "content": "GNN without giving generated samples as input.", "type": "text" } ], "index": 55 }, { "bbox": [ 106, 529, 298, 542 ], "spans": [ { "bbox": [ 106, 530, 119, 540 ], "score": 0.79, "content": "\" +", "type": "inline_equation" }, { "bbox": [ 119, 529, 298, 542 ], "score": 1.0, "content": "concatenation\" only replaces the generated", "type": "text" } ], "index": 56 }, { "bbox": [ 106, 541, 298, 552 ], "spans": [ { "bbox": [ 106, 541, 298, 552 ], "score": 1.0, "content": "feature matrix of LA-GNN with the original fea-", "type": "text" } ], "index": 57 }, { "bbox": [ 106, 551, 298, 564 ], "spans": [ { "bbox": [ 106, 551, 234, 564 ], "score": 1.0, "content": "ture matrix of the central node.", "type": "text" }, { "bbox": [ 235, 552, 247, 562 ], "score": 0.68, "content": "\" +", "type": "inline_equation" }, { "bbox": [ 247, 551, 298, 564 ], "score": 1.0, "content": "plain neigh-", "type": "text" } ], "index": 58 }, { "bbox": [ 106, 563, 298, 574 ], "spans": [ { "bbox": [ 106, 563, 298, 574 ], "score": 1.0, "content": "borhood\" replaces the generated feature matrix", "type": "text" } ], "index": 59 }, { "bbox": [ 106, 573, 298, 585 ], "spans": [ { "bbox": [ 106, 573, 298, 585 ], "score": 1.0, "content": "of LA-GNN with a neighborhood feature ma-", "type": "text" } ], "index": 60 }, { "bbox": [ 106, 584, 297, 596 ], "spans": [ { "bbox": [ 106, 584, 297, 596 ], "score": 1.0, "content": "trix where each row corresponds to the feature", "type": "text" } ], "index": 61 }, { "bbox": [ 106, 595, 297, 607 ], "spans": [ { "bbox": [ 106, 595, 297, 607 ], "score": 1.0, "content": "vector of the randomly sampled neighbor. The", "type": "text" } ], "index": 62 } ], "index": 55, "bbox_fs": [ 105, 441, 299, 607 ] }, { "type": "table", "bbox": [ 306, 479, 502, 596 ], "blocks": [ { "type": "table_caption", "bbox": [ 304, 442, 504, 475 ], "group_id": 0, "lines": [ { "bbox": [ 303, 442, 506, 454 ], "spans": [ { "bbox": [ 303, 442, 506, 454 ], "score": 1.0, "content": "Table 4: Effects of different components of our", "type": "text" } ], "index": 63 }, { "bbox": [ 303, 452, 505, 465 ], "spans": [ { "bbox": [ 303, 452, 505, 465 ], "score": 1.0, "content": "framework evaluated on the standard split of the", "type": "text" } ], "index": 64 }, { "bbox": [ 304, 464, 448, 475 ], "spans": [ { "bbox": [ 304, 464, 448, 475 ], "score": 1.0, "content": "Cora, Citeseer and Pubmed dataset.", "type": "text" } ], "index": 65 } ], "index": 64 }, { "type": "table_body", "bbox": [ 306, 479, 502, 596 ], "group_id": 0, "lines": [ { "bbox": [ 306, 479, 502, 596 ], "spans": [ { "bbox": [ 306, 479, 502, 596 ], "score": 0.98, "html": "
MethodCoraCiteseerPubmed
GCN81.670.378.9
GCNII85.273.180.0
GCN + width82.071.479.5
GCN + concatenation81.871.678.8
GCN + plain neighborhood80.968.875.0
GCNII + width85.173.180.2
GCNII + concatenation85.273.380.2
GCNII + plain neighborhood83.371.978.1
LA-GCN84.172.581.3
LA-GCNII85.273.781.6
", "type": "table", "image_path": "1e622fbcf762f746fb35f524d6f052f3f1fd7930c093ae304997e6254e7022a0.jpg" } ] } ], "index": 70, "virtual_lines": [ { "bbox": [ 306, 479, 502, 492.0 ], "spans": [], "index": 66 }, { "bbox": [ 306, 492.0, 502, 505.0 ], "spans": [], "index": 67 }, { "bbox": [ 306, 505.0, 502, 518.0 ], "spans": [], "index": 68 }, { "bbox": [ 306, 518.0, 502, 531.0 ], "spans": [], "index": 69 }, { "bbox": [ 306, 531.0, 502, 544.0 ], "spans": [], "index": 70 }, { "bbox": [ 306, 544.0, 502, 557.0 ], "spans": [], "index": 71 }, { "bbox": [ 306, 557.0, 502, 570.0 ], "spans": [], "index": 72 }, { "bbox": [ 306, 570.0, 502, 583.0 ], "spans": [], "index": 73 }, { "bbox": [ 306, 583.0, 502, 596.0 ], "spans": [], "index": 74 } ] } ], "index": 67.0 }, { "type": "text", "bbox": [ 107, 606, 505, 650 ], "lines": [ { "bbox": [ 106, 606, 505, 618 ], "spans": [ { "bbox": [ 106, 606, 505, 618 ], "score": 1.0, "content": "results show that the first two variants provide no notable improvement for the backbone models, and", "type": "text" } ], "index": 75 }, { "bbox": [ 105, 616, 505, 630 ], "spans": [ { "bbox": [ 105, 616, 505, 630 ], "score": 1.0, "content": "the third variant even results in degradation. By eliminating the possibility that these confounding", "type": "text" } ], "index": 76 }, { "bbox": [ 105, 628, 505, 641 ], "spans": [ { "bbox": [ 105, 628, 505, 641 ], "score": 1.0, "content": "factors irrelevant to our core approach may contribute to the final performance, it’s evident that the", "type": "text" } ], "index": 77 }, { "bbox": [ 105, 639, 506, 651 ], "spans": [ { "bbox": [ 105, 639, 506, 651 ], "score": 1.0, "content": "performance gain in Table 2 and 3 are due to our proposed generative local augmentation framework.", "type": "text" } ], "index": 78 } ], "index": 76.5, "bbox_fs": [ 105, 606, 506, 651 ] }, { "type": "title", "bbox": [ 108, 666, 306, 677 ], "lines": [ { "bbox": [ 105, 666, 307, 679 ], "spans": [ { "bbox": [ 105, 666, 307, 679 ], "score": 1.0, "content": "5.4 ROBUSTNESS TO MISSING INFORMATION", "type": "text" } ], "index": 79 } ], "index": 79 }, { "type": "text", "bbox": [ 108, 687, 505, 731 ], "lines": [ { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "In this section, we conduct experiments to verify that our proposed framework can robustify down-", "type": "text" } ], "index": 80 }, { "bbox": [ 106, 699, 505, 710 ], "spans": [ { "bbox": [ 106, 699, 505, 710 ], "score": 1.0, "content": "stream tasks against missing information in the feature attributes. Specifically, we mask a certain", "type": "text" } ], "index": 81 }, { "bbox": [ 105, 710, 505, 722 ], "spans": [ { "bbox": [ 105, 710, 505, 722 ], "score": 1.0, "content": "percentage of the attributes of each feature vector and use the same pipeline to do augmentation", "type": "text" } ], "index": 82 }, { "bbox": [ 105, 720, 507, 733 ], "spans": [ { "bbox": [ 105, 720, 507, 733 ], "score": 1.0, "content": "for the masked feature matrix. As shown in Table 5, we can see that as the mask ratio increases,", "type": "text" } ], "index": 83 }, { "bbox": [ 105, 82, 505, 95 ], "spans": [ { "bbox": [ 105, 82, 505, 95 ], "score": 1.0, "content": "the gap of the performance between the GCN and LA-GCN enlarges in most cases in Cora and", "type": "text", "cross_page": true } ], "index": 0 }, { "bbox": [ 105, 92, 505, 106 ], "spans": [ { "bbox": [ 105, 92, 505, 106 ], "score": 1.0, "content": "Citeseer, which corroborates our insight discussed in Section 4. Since there exists large redundancy", "type": "text", "cross_page": true } ], "index": 1 }, { "bbox": [ 105, 104, 505, 117 ], "spans": [ { "bbox": [ 105, 104, 505, 117 ], "score": 1.0, "content": "in the features of the Pubmed dataset, the performance of GCN and LA-GCN decreases little as the", "type": "text", "cross_page": true } ], "index": 2 }, { "bbox": [ 105, 115, 505, 128 ], "spans": [ { "bbox": [ 105, 115, 505, 128 ], "score": 1.0, "content": "mask ratio increases and the gap of the performance does not enlarge. To conclude, our model can", "type": "text", "cross_page": true } ], "index": 3 }, { "bbox": [ 106, 127, 505, 138 ], "spans": [ { "bbox": [ 106, 127, 505, 138 ], "score": 1.0, "content": "complement the contextual information of the local neighborhood to enhance the locality of the node", "type": "text", "cross_page": true } ], "index": 4 }, { "bbox": [ 106, 138, 172, 150 ], "spans": [ { "bbox": [ 106, 138, 172, 150 ], "score": 1.0, "content": "representations.", "type": "text", "cross_page": true } ], "index": 5 } ], "index": 81.5, "bbox_fs": [ 105, 687, 507, 733 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 107, 82, 505, 149 ], "lines": [ { "bbox": [ 105, 82, 505, 95 ], "spans": [ { "bbox": [ 105, 82, 505, 95 ], "score": 1.0, "content": "the gap of the performance between the GCN and LA-GCN enlarges in most cases in Cora and", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 92, 505, 106 ], "spans": [ { "bbox": [ 105, 92, 505, 106 ], "score": 1.0, "content": "Citeseer, which corroborates our insight discussed in Section 4. Since there exists large redundancy", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 104, 505, 117 ], "spans": [ { "bbox": [ 105, 104, 505, 117 ], "score": 1.0, "content": "in the features of the Pubmed dataset, the performance of GCN and LA-GCN decreases little as the", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 115, 505, 128 ], "spans": [ { "bbox": [ 105, 115, 505, 128 ], "score": 1.0, "content": "mask ratio increases and the gap of the performance does not enlarge. To conclude, our model can", "type": "text" } ], "index": 3 }, { "bbox": [ 106, 127, 505, 138 ], "spans": [ { "bbox": [ 106, 127, 505, 138 ], "score": 1.0, "content": "complement the contextual information of the local neighborhood to enhance the locality of the node", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 138, 172, 150 ], "spans": [ { "bbox": [ 106, 138, 172, 150 ], "score": 1.0, "content": "representations.", "type": "text" } ], "index": 5 } ], "index": 2.5 }, { "type": "table", "bbox": [ 106, 198, 505, 235 ], "blocks": [ { "type": "table_caption", "bbox": [ 107, 167, 503, 190 ], "group_id": 0, "lines": [ { "bbox": [ 105, 166, 505, 180 ], "spans": [ { "bbox": [ 105, 166, 442, 180 ], "score": 1.0, "content": "Table 5: Summary of results on recovering study in terms of classification accuracy", "type": "text" }, { "bbox": [ 443, 168, 457, 178 ], "score": 0.51, "content": "( \\% )", "type": "inline_equation" }, { "bbox": [ 457, 166, 462, 180 ], "score": 1.0, "content": ".", "type": "text" }, { "bbox": [ 462, 168, 470, 178 ], "score": 0.45, "content": "\\downarrow", "type": "inline_equation" }, { "bbox": [ 470, 166, 505, 180 ], "score": 1.0, "content": "means a", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 178, 365, 190 ], "spans": [ { "bbox": [ 105, 178, 365, 190 ], "score": 1.0, "content": "decrease compared with the accuracy if features are not masked.", "type": "text" } ], "index": 7 } ], "index": 6.5 }, { "type": "table_body", "bbox": [ 106, 198, 505, 235 ], "group_id": 0, "lines": [ { "bbox": [ 106, 198, 505, 235 ], "spans": [ { "bbox": [ 106, 198, 505, 235 ], "score": 0.973, "html": "
DatasetCoraCiteseerPubmed
Mask Ratio0.10.20.40.80.10.20.40.80.10.20.40.8
GCN81.0(↓0.6)80.6(↓1.0)80.1(↓1.5)76.0 (↓5.6)70.1(↓0.2)69.3 (↓1.0)67.2 (↓3.1)61.0(↓9.3)78.5(↓0.4)78.5(↓0.4)77.5 (↓1.4)76.9 (↓2.0)
LA-GCN83.5 (↓0.6)83.1(↓1.0)81.6(↓2.5)81.1 (↓3.0)72.2(↓0.3)71.7 (↓0.8)69.3 (↓3.2)65.9 (↓6.6)81.4(↓0.1)80.9 (↓0.6)80.5 (↓1.0)79.4 (↓2.1)
", "type": "table", "image_path": "c260c3b41045601cf923d862867eee20614ad3ddba36580ac902a15d0586885c.jpg" } ] } ], "index": 9, "virtual_lines": [ { "bbox": [ 106, 198, 505, 210.33333333333334 ], "spans": [], "index": 8 }, { "bbox": [ 106, 210.33333333333334, 505, 222.66666666666669 ], "spans": [], "index": 9 }, { "bbox": [ 106, 222.66666666666669, 505, 235.00000000000003 ], "spans": [], "index": 10 } ] } ], "index": 7.75 }, { "type": "title", "bbox": [ 108, 259, 211, 272 ], "lines": [ { "bbox": [ 105, 258, 213, 275 ], "spans": [ { "bbox": [ 105, 258, 213, 275 ], "score": 1.0, "content": "6 RELATED WORK", "type": "text" } ], "index": 11 } ], "index": 11 }, { "type": "text", "bbox": [ 106, 284, 505, 394 ], "lines": [ { "bbox": [ 106, 284, 506, 297 ], "spans": [ { "bbox": [ 106, 284, 506, 297 ], "score": 1.0, "content": "Graph Neural Networks In general, convolution in the graph domain involves non-spectral (spa-", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 295, 505, 308 ], "spans": [ { "bbox": [ 106, 295, 505, 308 ], "score": 1.0, "content": "tial) and spectral approaches. Non-spectral methods generalize convolutions operating on spatially", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 306, 506, 319 ], "spans": [ { "bbox": [ 105, 306, 506, 319 ], "score": 1.0, "content": "close neighbors to the graph domain, such as Duvenaud et al. (2015); Atwood & Towsley (2016);", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 317, 506, 330 ], "spans": [ { "bbox": [ 105, 317, 506, 330 ], "score": 1.0, "content": "Niepert et al. (2016); Monti et al. (2017). Spectral approaches define the convolution operations based", "type": "text" } ], "index": 15 }, { "bbox": [ 104, 327, 506, 342 ], "spans": [ { "bbox": [ 104, 327, 506, 342 ], "score": 1.0, "content": "on the spectral formulation, such as Bruna et al. (2014); Defferrard et al. (2016); Kipf & Welling", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 340, 505, 351 ], "spans": [ { "bbox": [ 106, 340, 505, 351 ], "score": 1.0, "content": "(2017). Recently, several methods (Abu-El-Haija et al., 2019; Liao et al., 2019) based on GCN", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 350, 505, 363 ], "spans": [ { "bbox": [ 105, 350, 505, 363 ], "score": 1.0, "content": "have been proposed to obtain the higher-order filters. Besides, GAT (Velickovi ˇ c et al., 2018), Graph ´", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 360, 506, 374 ], "spans": [ { "bbox": [ 105, 360, 506, 374 ], "score": 1.0, "content": "U-Nets (Gao & Ji, 2019) combine attention networks and pooling operation with GNN separately,", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 372, 506, 385 ], "spans": [ { "bbox": [ 106, 372, 506, 385 ], "score": 1.0, "content": "which achieve state-of-the-art performance on node and link classification tasks. In this work, local", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 382, 441, 396 ], "spans": [ { "bbox": [ 105, 382, 441, 396 ], "score": 1.0, "content": "augmentation can be applied on various backbone models to improve performance.", "type": "text" } ], "index": 21 } ], "index": 16.5 }, { "type": "text", "bbox": [ 107, 406, 505, 581 ], "lines": [ { "bbox": [ 106, 406, 506, 418 ], "spans": [ { "bbox": [ 106, 406, 506, 418 ], "score": 1.0, "content": "Graph Generative Models Generative models (Goodfellow et al., 2014; Kingma & Welling, 2013)", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 417, 506, 429 ], "spans": [ { "bbox": [ 106, 417, 506, 429 ], "score": 1.0, "content": "are powerful tools of learning data distribution through unsupervised learning, and they have achieved", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 427, 506, 442 ], "spans": [ { "bbox": [ 105, 427, 506, 442 ], "score": 1.0, "content": "tremendous success in various applications. Recently, researchers have proposed several interesting", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 439, 506, 452 ], "spans": [ { "bbox": [ 105, 439, 506, 452 ], "score": 1.0, "content": "generative models for graph data generation. Variational graph auto-encoder (VGAE) (Kipf &", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 449, 505, 461 ], "spans": [ { "bbox": [ 106, 449, 505, 461 ], "score": 1.0, "content": "Welling, 2016) makes use of latent variables and learns interpretable latent representations for", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 461, 505, 473 ], "spans": [ { "bbox": [ 106, 461, 505, 473 ], "score": 1.0, "content": "undirected graphs. Salha et al. (2019) replace the GCN encoder in VGAE with a simple linear model", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 471, 507, 485 ], "spans": [ { "bbox": [ 105, 471, 507, 485 ], "score": 1.0, "content": "and emphasize the effectiveness of a simple node encoding scheme. Xu et al. (2019) propose a", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 483, 506, 496 ], "spans": [ { "bbox": [ 105, 483, 506, 496 ], "score": 1.0, "content": "generative model framework to learn node representations, by sampling graph generation sequences", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 494, 505, 506 ], "spans": [ { "bbox": [ 106, 494, 505, 506 ], "score": 1.0, "content": "constructed from observed graph data. ConDgen (Yang et al., 2019) exploits the GCN encoder to", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 504, 505, 518 ], "spans": [ { "bbox": [ 105, 504, 505, 518 ], "score": 1.0, "content": "handle the inherent challenges of flexible context-structure conditioning and permutation-invariant", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 516, 506, 528 ], "spans": [ { "bbox": [ 105, 516, 506, 528 ], "score": 1.0, "content": "generation. Besides, some methods have been proposed to apply the graph generative models in", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 526, 506, 540 ], "spans": [ { "bbox": [ 105, 526, 506, 540 ], "score": 1.0, "content": "various applications such as graph matching (Simonovsky & Komodakis, 2018), molecule design (Liu", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 538, 506, 550 ], "spans": [ { "bbox": [ 105, 538, 506, 550 ], "score": 1.0, "content": "et al., 2018), retrosynthesis prediction (Shi et al., 2020) and chemical design (Samanta et al., 2018).", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 547, 506, 562 ], "spans": [ { "bbox": [ 105, 547, 506, 562 ], "score": 1.0, "content": "Compared with these approaches mainly focusing on structure generation, our model takes full use", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 559, 505, 572 ], "spans": [ { "bbox": [ 105, 559, 505, 572 ], "score": 1.0, "content": "of the power of the generative model for feature representation generation, which can serve as an", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 570, 342, 582 ], "spans": [ { "bbox": [ 105, 570, 342, 582 ], "score": 1.0, "content": "enhanced technique for the downstream backbone models.", "type": "text" } ], "index": 37 } ], "index": 29.5 }, { "type": "title", "bbox": [ 108, 597, 195, 610 ], "lines": [ { "bbox": [ 104, 595, 198, 613 ], "spans": [ { "bbox": [ 104, 595, 198, 613 ], "score": 1.0, "content": "7 CONCLUSION", "type": "text" } ], "index": 38 } ], "index": 38 }, { "type": "text", "bbox": [ 107, 622, 505, 732 ], "lines": [ { "bbox": [ 106, 622, 505, 634 ], "spans": [ { "bbox": [ 106, 622, 505, 634 ], "score": 1.0, "content": "We propose local augmentation, a brand-new technique that exploits the generative model to learn", "type": "text" } ], "index": 39 }, { "bbox": [ 106, 632, 506, 645 ], "spans": [ { "bbox": [ 106, 632, 506, 645 ], "score": 1.0, "content": "the conditional distribution of the central node’s neighbors’ feature representations given its represen-", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 644, 506, 656 ], "spans": [ { "bbox": [ 106, 644, 506, 656 ], "score": 1.0, "content": "tation. We can augment more 1-hop neighbors from a well-trained generative model to enhance the", "type": "text" } ], "index": 41 }, { "bbox": [ 106, 655, 506, 668 ], "spans": [ { "bbox": [ 106, 655, 506, 668 ], "score": 1.0, "content": "performance of backbone GNN models. Experiments show that our model can improve performance", "type": "text" } ], "index": 42 }, { "bbox": [ 106, 666, 506, 678 ], "spans": [ { "bbox": [ 106, 666, 506, 678 ], "score": 1.0, "content": "across various GNN architectures and benchmark datasets by enriching local information. Besides,", "type": "text" } ], "index": 43 }, { "bbox": [ 106, 677, 506, 689 ], "spans": [ { "bbox": [ 106, 677, 506, 689 ], "score": 1.0, "content": "our model achieves new state-of-the-art results on various semi-supervised node classification tasks.", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "One limitation of our proposed framework is that we do not exploit the 2-hop neighbors or use the", "type": "text" } ], "index": 45 }, { "bbox": [ 106, 699, 505, 711 ], "spans": [ { "bbox": [ 106, 699, 505, 711 ], "score": 1.0, "content": "random walk to find more related neighbors for the central node. And one future work is that we", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 709, 506, 722 ], "spans": [ { "bbox": [ 105, 709, 176, 722 ], "score": 1.0, "content": "can extract more", "type": "text" }, { "bbox": [ 177, 710, 191, 720 ], "score": 0.37, "content": "^ { 2 / 3 }", "type": "inline_equation" }, { "bbox": [ 191, 709, 506, 722 ], "score": 1.0, "content": "-hop neighbors if the central node’s degree is small and learn the conditional", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 718, 349, 734 ], "spans": [ { "bbox": [ 105, 718, 349, 734 ], "score": 1.0, "content": "distribution for random sampling nodes if the graph is large.", "type": "text" } ], "index": 48 } ], "index": 43.5 } ], "page_idx": 8, "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 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 751, 308, 759 ], "lines": [ { "bbox": [ 302, 751, 309, 762 ], "spans": [ { "bbox": [ 302, 751, 309, 762 ], "score": 1.0, "content": "9", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 107, 82, 505, 149 ], "lines": [], "index": 2.5, "bbox_fs": [ 105, 82, 505, 150 ], "lines_deleted": true }, { "type": "table", "bbox": [ 106, 198, 505, 235 ], "blocks": [ { "type": "table_caption", "bbox": [ 107, 167, 503, 190 ], "group_id": 0, "lines": [ { "bbox": [ 105, 166, 505, 180 ], "spans": [ { "bbox": [ 105, 166, 442, 180 ], "score": 1.0, "content": "Table 5: Summary of results on recovering study in terms of classification accuracy", "type": "text" }, { "bbox": [ 443, 168, 457, 178 ], "score": 0.51, "content": "( \\% )", "type": "inline_equation" }, { "bbox": [ 457, 166, 462, 180 ], "score": 1.0, "content": ".", "type": "text" }, { "bbox": [ 462, 168, 470, 178 ], "score": 0.45, "content": "\\downarrow", "type": "inline_equation" }, { "bbox": [ 470, 166, 505, 180 ], "score": 1.0, "content": "means a", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 178, 365, 190 ], "spans": [ { "bbox": [ 105, 178, 365, 190 ], "score": 1.0, "content": "decrease compared with the accuracy if features are not masked.", "type": "text" } ], "index": 7 } ], "index": 6.5 }, { "type": "table_body", "bbox": [ 106, 198, 505, 235 ], "group_id": 0, "lines": [ { "bbox": [ 106, 198, 505, 235 ], "spans": [ { "bbox": [ 106, 198, 505, 235 ], "score": 0.973, "html": "
DatasetCoraCiteseerPubmed
Mask Ratio0.10.20.40.80.10.20.40.80.10.20.40.8
GCN81.0(↓0.6)80.6(↓1.0)80.1(↓1.5)76.0 (↓5.6)70.1(↓0.2)69.3 (↓1.0)67.2 (↓3.1)61.0(↓9.3)78.5(↓0.4)78.5(↓0.4)77.5 (↓1.4)76.9 (↓2.0)
LA-GCN83.5 (↓0.6)83.1(↓1.0)81.6(↓2.5)81.1 (↓3.0)72.2(↓0.3)71.7 (↓0.8)69.3 (↓3.2)65.9 (↓6.6)81.4(↓0.1)80.9 (↓0.6)80.5 (↓1.0)79.4 (↓2.1)
", "type": "table", "image_path": "c260c3b41045601cf923d862867eee20614ad3ddba36580ac902a15d0586885c.jpg" } ] } ], "index": 9, "virtual_lines": [ { "bbox": [ 106, 198, 505, 210.33333333333334 ], "spans": [], "index": 8 }, { "bbox": [ 106, 210.33333333333334, 505, 222.66666666666669 ], "spans": [], "index": 9 }, { "bbox": [ 106, 222.66666666666669, 505, 235.00000000000003 ], "spans": [], "index": 10 } ] } ], "index": 7.75 }, { "type": "title", "bbox": [ 108, 259, 211, 272 ], "lines": [ { "bbox": [ 105, 258, 213, 275 ], "spans": [ { "bbox": [ 105, 258, 213, 275 ], "score": 1.0, "content": "6 RELATED WORK", "type": "text" } ], "index": 11 } ], "index": 11 }, { "type": "text", "bbox": [ 106, 284, 505, 394 ], "lines": [ { "bbox": [ 106, 284, 506, 297 ], "spans": [ { "bbox": [ 106, 284, 506, 297 ], "score": 1.0, "content": "Graph Neural Networks In general, convolution in the graph domain involves non-spectral (spa-", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 295, 505, 308 ], "spans": [ { "bbox": [ 106, 295, 505, 308 ], "score": 1.0, "content": "tial) and spectral approaches. Non-spectral methods generalize convolutions operating on spatially", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 306, 506, 319 ], "spans": [ { "bbox": [ 105, 306, 506, 319 ], "score": 1.0, "content": "close neighbors to the graph domain, such as Duvenaud et al. (2015); Atwood & Towsley (2016);", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 317, 506, 330 ], "spans": [ { "bbox": [ 105, 317, 506, 330 ], "score": 1.0, "content": "Niepert et al. (2016); Monti et al. (2017). Spectral approaches define the convolution operations based", "type": "text" } ], "index": 15 }, { "bbox": [ 104, 327, 506, 342 ], "spans": [ { "bbox": [ 104, 327, 506, 342 ], "score": 1.0, "content": "on the spectral formulation, such as Bruna et al. (2014); Defferrard et al. (2016); Kipf & Welling", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 340, 505, 351 ], "spans": [ { "bbox": [ 106, 340, 505, 351 ], "score": 1.0, "content": "(2017). Recently, several methods (Abu-El-Haija et al., 2019; Liao et al., 2019) based on GCN", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 350, 505, 363 ], "spans": [ { "bbox": [ 105, 350, 505, 363 ], "score": 1.0, "content": "have been proposed to obtain the higher-order filters. Besides, GAT (Velickovi ˇ c et al., 2018), Graph ´", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 360, 506, 374 ], "spans": [ { "bbox": [ 105, 360, 506, 374 ], "score": 1.0, "content": "U-Nets (Gao & Ji, 2019) combine attention networks and pooling operation with GNN separately,", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 372, 506, 385 ], "spans": [ { "bbox": [ 106, 372, 506, 385 ], "score": 1.0, "content": "which achieve state-of-the-art performance on node and link classification tasks. In this work, local", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 382, 441, 396 ], "spans": [ { "bbox": [ 105, 382, 441, 396 ], "score": 1.0, "content": "augmentation can be applied on various backbone models to improve performance.", "type": "text" } ], "index": 21 } ], "index": 16.5, "bbox_fs": [ 104, 284, 506, 396 ] }, { "type": "text", "bbox": [ 107, 406, 505, 581 ], "lines": [ { "bbox": [ 106, 406, 506, 418 ], "spans": [ { "bbox": [ 106, 406, 506, 418 ], "score": 1.0, "content": "Graph Generative Models Generative models (Goodfellow et al., 2014; Kingma & Welling, 2013)", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 417, 506, 429 ], "spans": [ { "bbox": [ 106, 417, 506, 429 ], "score": 1.0, "content": "are powerful tools of learning data distribution through unsupervised learning, and they have achieved", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 427, 506, 442 ], "spans": [ { "bbox": [ 105, 427, 506, 442 ], "score": 1.0, "content": "tremendous success in various applications. Recently, researchers have proposed several interesting", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 439, 506, 452 ], "spans": [ { "bbox": [ 105, 439, 506, 452 ], "score": 1.0, "content": "generative models for graph data generation. Variational graph auto-encoder (VGAE) (Kipf &", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 449, 505, 461 ], "spans": [ { "bbox": [ 106, 449, 505, 461 ], "score": 1.0, "content": "Welling, 2016) makes use of latent variables and learns interpretable latent representations for", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 461, 505, 473 ], "spans": [ { "bbox": [ 106, 461, 505, 473 ], "score": 1.0, "content": "undirected graphs. Salha et al. (2019) replace the GCN encoder in VGAE with a simple linear model", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 471, 507, 485 ], "spans": [ { "bbox": [ 105, 471, 507, 485 ], "score": 1.0, "content": "and emphasize the effectiveness of a simple node encoding scheme. Xu et al. (2019) propose a", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 483, 506, 496 ], "spans": [ { "bbox": [ 105, 483, 506, 496 ], "score": 1.0, "content": "generative model framework to learn node representations, by sampling graph generation sequences", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 494, 505, 506 ], "spans": [ { "bbox": [ 106, 494, 505, 506 ], "score": 1.0, "content": "constructed from observed graph data. ConDgen (Yang et al., 2019) exploits the GCN encoder to", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 504, 505, 518 ], "spans": [ { "bbox": [ 105, 504, 505, 518 ], "score": 1.0, "content": "handle the inherent challenges of flexible context-structure conditioning and permutation-invariant", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 516, 506, 528 ], "spans": [ { "bbox": [ 105, 516, 506, 528 ], "score": 1.0, "content": "generation. Besides, some methods have been proposed to apply the graph generative models in", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 526, 506, 540 ], "spans": [ { "bbox": [ 105, 526, 506, 540 ], "score": 1.0, "content": "various applications such as graph matching (Simonovsky & Komodakis, 2018), molecule design (Liu", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 538, 506, 550 ], "spans": [ { "bbox": [ 105, 538, 506, 550 ], "score": 1.0, "content": "et al., 2018), retrosynthesis prediction (Shi et al., 2020) and chemical design (Samanta et al., 2018).", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 547, 506, 562 ], "spans": [ { "bbox": [ 105, 547, 506, 562 ], "score": 1.0, "content": "Compared with these approaches mainly focusing on structure generation, our model takes full use", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 559, 505, 572 ], "spans": [ { "bbox": [ 105, 559, 505, 572 ], "score": 1.0, "content": "of the power of the generative model for feature representation generation, which can serve as an", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 570, 342, 582 ], "spans": [ { "bbox": [ 105, 570, 342, 582 ], "score": 1.0, "content": "enhanced technique for the downstream backbone models.", "type": "text" } ], "index": 37 } ], "index": 29.5, "bbox_fs": [ 105, 406, 507, 582 ] }, { "type": "title", "bbox": [ 108, 597, 195, 610 ], "lines": [ { "bbox": [ 104, 595, 198, 613 ], "spans": [ { "bbox": [ 104, 595, 198, 613 ], "score": 1.0, "content": "7 CONCLUSION", "type": "text" } ], "index": 38 } ], "index": 38 }, { "type": "text", "bbox": [ 107, 622, 505, 732 ], "lines": [ { "bbox": [ 106, 622, 505, 634 ], "spans": [ { "bbox": [ 106, 622, 505, 634 ], "score": 1.0, "content": "We propose local augmentation, a brand-new technique that exploits the generative model to learn", "type": "text" } ], "index": 39 }, { "bbox": [ 106, 632, 506, 645 ], "spans": [ { "bbox": [ 106, 632, 506, 645 ], "score": 1.0, "content": "the conditional distribution of the central node’s neighbors’ feature representations given its represen-", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 644, 506, 656 ], "spans": [ { "bbox": [ 106, 644, 506, 656 ], "score": 1.0, "content": "tation. We can augment more 1-hop neighbors from a well-trained generative model to enhance the", "type": "text" } ], "index": 41 }, { "bbox": [ 106, 655, 506, 668 ], "spans": [ { "bbox": [ 106, 655, 506, 668 ], "score": 1.0, "content": "performance of backbone GNN models. Experiments show that our model can improve performance", "type": "text" } ], "index": 42 }, { "bbox": [ 106, 666, 506, 678 ], "spans": [ { "bbox": [ 106, 666, 506, 678 ], "score": 1.0, "content": "across various GNN architectures and benchmark datasets by enriching local information. Besides,", "type": "text" } ], "index": 43 }, { "bbox": [ 106, 677, 506, 689 ], "spans": [ { "bbox": [ 106, 677, 506, 689 ], "score": 1.0, "content": "our model achieves new state-of-the-art results on various semi-supervised node classification tasks.", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "One limitation of our proposed framework is that we do not exploit the 2-hop neighbors or use the", "type": "text" } ], "index": 45 }, { "bbox": [ 106, 699, 505, 711 ], "spans": [ { "bbox": [ 106, 699, 505, 711 ], "score": 1.0, "content": "random walk to find more related neighbors for the central node. And one future work is that we", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 709, 506, 722 ], "spans": [ { "bbox": [ 105, 709, 176, 722 ], "score": 1.0, "content": "can extract more", "type": "text" }, { "bbox": [ 177, 710, 191, 720 ], "score": 0.37, "content": "^ { 2 / 3 }", "type": "inline_equation" }, { "bbox": [ 191, 709, 506, 722 ], "score": 1.0, "content": "-hop neighbors if the central node’s degree is small and learn the conditional", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 718, 349, 734 ], "spans": [ { "bbox": [ 105, 718, 349, 734 ], "score": 1.0, "content": "distribution for random sampling nodes if the graph is large.", "type": "text" } ], "index": 48 } ], "index": 43.5, "bbox_fs": [ 105, 622, 506, 734 ] } ] }, { "preproc_blocks": [ { "type": "title", "bbox": [ 108, 82, 175, 93 ], "lines": [ { "bbox": [ 106, 81, 176, 95 ], "spans": [ { "bbox": [ 106, 81, 176, 95 ], "score": 1.0, "content": "REFERENCES", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 107, 100, 505, 145 ], "lines": [ { "bbox": [ 105, 99, 507, 113 ], "spans": [ { "bbox": [ 105, 99, 507, 113 ], "score": 1.0, "content": "Martín Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin,", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 111, 505, 124 ], "spans": [ { "bbox": [ 115, 111, 505, 124 ], "score": 1.0, "content": "Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. Tensorflow: A system for large-scale", "type": "text" } ], "index": 2 }, { "bbox": [ 115, 122, 505, 136 ], "spans": [ { "bbox": [ 115, 122, 505, 136 ], "score": 1.0, "content": "machine learning. In 12th {USENIX} symposium on operating systems design and implementation", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 133, 252, 146 ], "spans": [ { "bbox": [ 115, 133, 252, 146 ], "score": 1.0, "content": "({OSDI} 16), pp. 265–283, 2016.", "type": "text" } ], "index": 4 } ], "index": 2.5 }, { "type": "text", "bbox": [ 106, 153, 506, 197 ], "lines": [ { "bbox": [ 106, 153, 506, 165 ], "spans": [ { "bbox": [ 106, 153, 506, 165 ], "score": 1.0, "content": "Sami Abu-El-Haija, Bryan Perozzi, Amol Kapoor, Nazanin Alipourfard, Kristina Lerman, Hrayr", "type": "text" } ], "index": 5 }, { "bbox": [ 115, 163, 506, 176 ], "spans": [ { "bbox": [ 115, 163, 506, 176 ], "score": 1.0, "content": "Harutyunyan, Greg Ver Steeg, and Aram Galstyan. Mixhop: Higher-order graph convolutional", "type": "text" } ], "index": 6 }, { "bbox": [ 115, 174, 507, 188 ], "spans": [ { "bbox": [ 115, 174, 507, 188 ], "score": 1.0, "content": "architectures via sparsified neighborhood mixing. In international conference on machine learning,", "type": "text" } ], "index": 7 }, { "bbox": [ 115, 186, 218, 197 ], "spans": [ { "bbox": [ 115, 186, 218, 197 ], "score": 1.0, "content": "pp. 21–29. PMLR, 2019.", "type": "text" } ], "index": 8 } ], "index": 6.5 }, { "type": "text", "bbox": [ 106, 205, 503, 228 ], "lines": [ { "bbox": [ 106, 205, 505, 218 ], "spans": [ { "bbox": [ 106, 205, 505, 218 ], "score": 1.0, "content": "Antreas Antoniou, Amos Storkey, and Harrison Edwards. Data augmentation generative adversarial", "type": "text" } ], "index": 9 }, { "bbox": [ 115, 217, 321, 228 ], "spans": [ { "bbox": [ 115, 217, 321, 228 ], "score": 1.0, "content": "networks. arXiv preprint arXiv:1711.04340, 2017.", "type": "text" } ], "index": 10 } ], "index": 9.5 }, { "type": "text", "bbox": [ 106, 235, 504, 259 ], "lines": [ { "bbox": [ 106, 235, 506, 248 ], "spans": [ { "bbox": [ 106, 235, 506, 248 ], "score": 1.0, "content": "James Atwood and Don Towsley. Diffusion-convolutional neural networks. In Advances in neural", "type": "text" } ], "index": 11 }, { "bbox": [ 115, 247, 336, 259 ], "spans": [ { "bbox": [ 115, 247, 336, 259 ], "score": 1.0, "content": "information processing systems, pp. 1993–2001, 2016.", "type": "text" } ], "index": 12 } ], "index": 11.5 }, { "type": "text", "bbox": [ 106, 266, 504, 289 ], "lines": [ { "bbox": [ 105, 266, 505, 279 ], "spans": [ { "bbox": [ 105, 266, 505, 279 ], "score": 1.0, "content": "Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun. Spectral networks and locally", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 277, 503, 289 ], "spans": [ { "bbox": [ 115, 277, 503, 289 ], "score": 1.0, "content": "connected networks on graphs. In International Conference on Learning Representations, 2014.", "type": "text" } ], "index": 14 } ], "index": 13.5 }, { "type": "text", "bbox": [ 106, 296, 506, 330 ], "lines": [ { "bbox": [ 105, 296, 505, 310 ], "spans": [ { "bbox": [ 105, 296, 505, 310 ], "score": 1.0, "content": "Ming Chen, Zhewei Wei, Zengfeng Huang, Bolin Ding, and Yaliang Li. Simple and deep graph", "type": "text" } ], "index": 15 }, { "bbox": [ 115, 307, 507, 321 ], "spans": [ { "bbox": [ 115, 307, 507, 321 ], "score": 1.0, "content": "convolutional networks. In International Conference on Machine Learning, pp. 1725–1735. PMLR,", "type": "text" } ], "index": 16 }, { "bbox": [ 115, 317, 143, 332 ], "spans": [ { "bbox": [ 115, 317, 143, 332 ], "score": 1.0, "content": "2020.", "type": "text" } ], "index": 17 } ], "index": 16 }, { "type": "text", "bbox": [ 107, 338, 504, 371 ], "lines": [ { "bbox": [ 106, 338, 505, 351 ], "spans": [ { "bbox": [ 106, 338, 505, 351 ], "score": 1.0, "content": "Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on", "type": "text" } ], "index": 18 }, { "bbox": [ 115, 349, 507, 362 ], "spans": [ { "bbox": [ 115, 349, 507, 362 ], "score": 1.0, "content": "graphs with fast localized spectral filtering. In Advances in Neural Information Processing Systems,", "type": "text" } ], "index": 19 }, { "bbox": [ 115, 360, 142, 372 ], "spans": [ { "bbox": [ 115, 360, 142, 372 ], "score": 1.0, "content": "2016.", "type": "text" } ], "index": 20 } ], "index": 19 }, { "type": "text", "bbox": [ 105, 379, 504, 403 ], "lines": [ { "bbox": [ 106, 379, 505, 392 ], "spans": [ { "bbox": [ 106, 379, 505, 392 ], "score": 1.0, "content": "Zhijie Deng, Yinpeng Dong, and Jun Zhu. Batch virtual adversarial training for graph convolutional", "type": "text" } ], "index": 21 }, { "bbox": [ 115, 391, 321, 403 ], "spans": [ { "bbox": [ 115, 391, 321, 403 ], "score": 1.0, "content": "networks. arXiv preprint arXiv:1902.09192, 2019.", "type": "text" } ], "index": 22 } ], "index": 21.5 }, { "type": "text", "bbox": [ 108, 410, 504, 444 ], "lines": [ { "bbox": [ 106, 409, 506, 423 ], "spans": [ { "bbox": [ 106, 409, 506, 423 ], "score": 1.0, "content": "David Duvenaud, Dougal Maclaurin, Jorge Aguilera-Iparraguirre, Rafael Gómez-Bombarelli, Timo-", "type": "text" } ], "index": 23 }, { "bbox": [ 115, 420, 506, 435 ], "spans": [ { "bbox": [ 115, 420, 506, 435 ], "score": 1.0, "content": "thy Hirzel, Alán Aspuru-Guzik, and Ryan P Adams. Convolutional networks on graphs for learning", "type": "text" } ], "index": 24 }, { "bbox": [ 115, 432, 461, 445 ], "spans": [ { "bbox": [ 115, 432, 461, 445 ], "score": 1.0, "content": "molecular fingerprints. In Advances in Neural Information Processing Systems, 2015.", "type": "text" } ], "index": 25 } ], "index": 24 }, { "type": "text", "bbox": [ 107, 451, 506, 485 ], "lines": [ { "bbox": [ 105, 451, 505, 465 ], "spans": [ { "bbox": [ 105, 451, 505, 465 ], "score": 1.0, "content": "Fuli Feng, Xiangnan He, Jie Tang, and Tat-Seng Chua. Graph adversarial training: Dynamically", "type": "text" } ], "index": 26 }, { "bbox": [ 114, 462, 507, 477 ], "spans": [ { "bbox": [ 114, 462, 507, 477 ], "score": 1.0, "content": "regularizing based on graph structure. IEEE Transactions on Knowledge and Data Engineering,", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 471, 143, 486 ], "spans": [ { "bbox": [ 115, 471, 143, 486 ], "score": 1.0, "content": "2019.", "type": "text" } ], "index": 28 } ], "index": 27 }, { "type": "text", "bbox": [ 107, 493, 506, 527 ], "lines": [ { "bbox": [ 105, 491, 505, 507 ], "spans": [ { "bbox": [ 105, 491, 505, 507 ], "score": 1.0, "content": "Wenzheng Feng, Jie Zhang, Yuxiao Dong, Yu Han, Huanbo Luan, Qian Xu, Qiang Yang, Evgeny", "type": "text" } ], "index": 29 }, { "bbox": [ 115, 503, 506, 518 ], "spans": [ { "bbox": [ 115, 503, 506, 518 ], "score": 1.0, "content": "Kharlamov, and Jie Tang. Graph random neural network for semi-supervised learning on graphs.", "type": "text" } ], "index": 30 }, { "bbox": [ 115, 515, 205, 527 ], "spans": [ { "bbox": [ 115, 515, 205, 527 ], "score": 1.0, "content": "In NeurIPS’20, 2020.", "type": "text" } ], "index": 31 } ], "index": 30 }, { "type": "text", "bbox": [ 105, 534, 504, 557 ], "lines": [ { "bbox": [ 104, 532, 507, 550 ], "spans": [ { "bbox": [ 104, 532, 507, 550 ], "score": 1.0, "content": "Hongyang Gao and Shuiwang Ji. Graph u-nets. In international conference on machine learning, pp.", "type": "text" } ], "index": 32 }, { "bbox": [ 116, 545, 224, 557 ], "spans": [ { "bbox": [ 116, 545, 224, 557 ], "score": 1.0, "content": "2083–2092. PMLR, 2019.", "type": "text" } ], "index": 33 } ], "index": 32.5 }, { "type": "text", "bbox": [ 105, 565, 505, 588 ], "lines": [ { "bbox": [ 105, 563, 507, 580 ], "spans": [ { "bbox": [ 105, 563, 507, 580 ], "score": 1.0, "content": "Alberto García-Durán and Mathias Niepert. Learning graph representations with embedding propaga-", "type": "text" } ], "index": 34 }, { "bbox": [ 115, 575, 388, 589 ], "spans": [ { "bbox": [ 115, 575, 388, 589 ], "score": 1.0, "content": "tion. In Advances in Neural Information Processing Systems, 2017.", "type": "text" } ], "index": 35 } ], "index": 34.5 }, { "type": "text", "bbox": [ 107, 595, 505, 630 ], "lines": [ { "bbox": [ 105, 595, 506, 609 ], "spans": [ { "bbox": [ 105, 595, 506, 609 ], "score": 1.0, "content": "Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair,", "type": "text" } ], "index": 36 }, { "bbox": [ 116, 608, 505, 619 ], "spans": [ { "bbox": [ 116, 608, 505, 619 ], "score": 1.0, "content": "Aaron Courville, and Yoshua Bengio. Generative adversarial networks. In Advances in Neural", "type": "text" } ], "index": 37 }, { "bbox": [ 115, 617, 275, 631 ], "spans": [ { "bbox": [ 115, 617, 275, 631 ], "score": 1.0, "content": "Information Processing Systems, 2014.", "type": "text" } ], "index": 38 } ], "index": 37 }, { "type": "text", "bbox": [ 107, 637, 505, 671 ], "lines": [ { "bbox": [ 106, 637, 506, 651 ], "spans": [ { "bbox": [ 106, 637, 506, 651 ], "score": 1.0, "content": "Shengnan Guo, Youfang Lin, Ning Feng, Chao Song, and Huaiyu Wan. Attention based spatial-", "type": "text" } ], "index": 39 }, { "bbox": [ 115, 648, 505, 661 ], "spans": [ { "bbox": [ 115, 648, 505, 661 ], "score": 1.0, "content": "temporal graph convolutional networks for traffic flow forecasting. In Proceedings of the AAAI", "type": "text" } ], "index": 40 }, { "bbox": [ 116, 659, 347, 673 ], "spans": [ { "bbox": [ 116, 659, 347, 673 ], "score": 1.0, "content": "Conference on Artificial Intelligence, pp. 922–929, 2019.", "type": "text" } ], "index": 41 } ], "index": 40 }, { "type": "text", "bbox": [ 107, 678, 504, 702 ], "lines": [ { "bbox": [ 106, 678, 505, 692 ], "spans": [ { "bbox": [ 106, 678, 505, 692 ], "score": 1.0, "content": "William L Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large graphs.", "type": "text" } ], "index": 42 }, { "bbox": [ 115, 689, 366, 703 ], "spans": [ { "bbox": [ 115, 689, 366, 703 ], "score": 1.0, "content": "In Advances in Neural Information Processing Systems, 2017.", "type": "text" } ], "index": 43 } ], "index": 42.5 }, { "type": "text", "bbox": [ 107, 709, 503, 732 ], "lines": [ { "bbox": [ 105, 708, 505, 723 ], "spans": [ { "bbox": [ 105, 708, 505, 723 ], "score": 1.0, "content": "Neil Houlsby, Ferenc Huszár, Zoubin Ghahramani, and Máté Lengyel. Bayesian active learning for", "type": "text" } ], "index": 44 }, { "bbox": [ 116, 720, 429, 732 ], "spans": [ { "bbox": [ 116, 720, 429, 732 ], "score": 1.0, "content": "classification and preference learning. arXiv preprint arXiv:1112.5745, 2011.", "type": "text" } ], "index": 45 } ], "index": 44.5 } ], "page_idx": 9, "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 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 300, 751, 311, 760 ], "lines": [ { "bbox": [ 299, 750, 312, 764 ], "spans": [ { "bbox": [ 299, 750, 312, 764 ], "score": 1.0, "content": "10", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "title", "bbox": [ 108, 82, 175, 93 ], "lines": [ { "bbox": [ 106, 81, 176, 95 ], "spans": [ { "bbox": [ 106, 81, 176, 95 ], "score": 1.0, "content": "REFERENCES", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 107, 100, 505, 145 ], "lines": [ { "bbox": [ 105, 99, 507, 113 ], "spans": [ { "bbox": [ 105, 99, 507, 113 ], "score": 1.0, "content": "Martín Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin,", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 111, 505, 124 ], "spans": [ { "bbox": [ 115, 111, 505, 124 ], "score": 1.0, "content": "Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. Tensorflow: A system for large-scale", "type": "text" } ], "index": 2 }, { "bbox": [ 115, 122, 505, 136 ], "spans": [ { "bbox": [ 115, 122, 505, 136 ], "score": 1.0, "content": "machine learning. In 12th {USENIX} symposium on operating systems design and implementation", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 133, 252, 146 ], "spans": [ { "bbox": [ 115, 133, 252, 146 ], "score": 1.0, "content": "({OSDI} 16), pp. 265–283, 2016.", "type": "text" } ], "index": 4 } ], "index": 2.5, "bbox_fs": [ 105, 99, 507, 146 ] }, { "type": "text", "bbox": [ 106, 153, 506, 197 ], "lines": [ { "bbox": [ 106, 153, 506, 165 ], "spans": [ { "bbox": [ 106, 153, 506, 165 ], "score": 1.0, "content": "Sami Abu-El-Haija, Bryan Perozzi, Amol Kapoor, Nazanin Alipourfard, Kristina Lerman, Hrayr", "type": "text" } ], "index": 5 }, { "bbox": [ 115, 163, 506, 176 ], "spans": [ { "bbox": [ 115, 163, 506, 176 ], "score": 1.0, "content": "Harutyunyan, Greg Ver Steeg, and Aram Galstyan. Mixhop: Higher-order graph convolutional", "type": "text" } ], "index": 6 }, { "bbox": [ 115, 174, 507, 188 ], "spans": [ { "bbox": [ 115, 174, 507, 188 ], "score": 1.0, "content": "architectures via sparsified neighborhood mixing. In international conference on machine learning,", "type": "text" } ], "index": 7 }, { "bbox": [ 115, 186, 218, 197 ], "spans": [ { "bbox": [ 115, 186, 218, 197 ], "score": 1.0, "content": "pp. 21–29. PMLR, 2019.", "type": "text" } ], "index": 8 } ], "index": 6.5, "bbox_fs": [ 106, 153, 507, 197 ] }, { "type": "text", "bbox": [ 106, 205, 503, 228 ], "lines": [ { "bbox": [ 106, 205, 505, 218 ], "spans": [ { "bbox": [ 106, 205, 505, 218 ], "score": 1.0, "content": "Antreas Antoniou, Amos Storkey, and Harrison Edwards. Data augmentation generative adversarial", "type": "text" } ], "index": 9 }, { "bbox": [ 115, 217, 321, 228 ], "spans": [ { "bbox": [ 115, 217, 321, 228 ], "score": 1.0, "content": "networks. arXiv preprint arXiv:1711.04340, 2017.", "type": "text" } ], "index": 10 } ], "index": 9.5, "bbox_fs": [ 106, 205, 505, 228 ] }, { "type": "text", "bbox": [ 106, 235, 504, 259 ], "lines": [ { "bbox": [ 106, 235, 506, 248 ], "spans": [ { "bbox": [ 106, 235, 506, 248 ], "score": 1.0, "content": "James Atwood and Don Towsley. Diffusion-convolutional neural networks. In Advances in neural", "type": "text" } ], "index": 11 }, { "bbox": [ 115, 247, 336, 259 ], "spans": [ { "bbox": [ 115, 247, 336, 259 ], "score": 1.0, "content": "information processing systems, pp. 1993–2001, 2016.", "type": "text" } ], "index": 12 } ], "index": 11.5, "bbox_fs": [ 106, 235, 506, 259 ] }, { "type": "text", "bbox": [ 106, 266, 504, 289 ], "lines": [ { "bbox": [ 105, 266, 505, 279 ], "spans": [ { "bbox": [ 105, 266, 505, 279 ], "score": 1.0, "content": "Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun. Spectral networks and locally", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 277, 503, 289 ], "spans": [ { "bbox": [ 115, 277, 503, 289 ], "score": 1.0, "content": "connected networks on graphs. In International Conference on Learning Representations, 2014.", "type": "text" } ], "index": 14 } ], "index": 13.5, "bbox_fs": [ 105, 266, 505, 289 ] }, { "type": "text", "bbox": [ 106, 296, 506, 330 ], "lines": [ { "bbox": [ 105, 296, 505, 310 ], "spans": [ { "bbox": [ 105, 296, 505, 310 ], "score": 1.0, "content": "Ming Chen, Zhewei Wei, Zengfeng Huang, Bolin Ding, and Yaliang Li. Simple and deep graph", "type": "text" } ], "index": 15 }, { "bbox": [ 115, 307, 507, 321 ], "spans": [ { "bbox": [ 115, 307, 507, 321 ], "score": 1.0, "content": "convolutional networks. In International Conference on Machine Learning, pp. 1725–1735. PMLR,", "type": "text" } ], "index": 16 }, { "bbox": [ 115, 317, 143, 332 ], "spans": [ { "bbox": [ 115, 317, 143, 332 ], "score": 1.0, "content": "2020.", "type": "text" } ], "index": 17 } ], "index": 16, "bbox_fs": [ 105, 296, 507, 332 ] }, { "type": "text", "bbox": [ 107, 338, 504, 371 ], "lines": [ { "bbox": [ 106, 338, 505, 351 ], "spans": [ { "bbox": [ 106, 338, 505, 351 ], "score": 1.0, "content": "Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on", "type": "text" } ], "index": 18 }, { "bbox": [ 115, 349, 507, 362 ], "spans": [ { "bbox": [ 115, 349, 507, 362 ], "score": 1.0, "content": "graphs with fast localized spectral filtering. In Advances in Neural Information Processing Systems,", "type": "text" } ], "index": 19 }, { "bbox": [ 115, 360, 142, 372 ], "spans": [ { "bbox": [ 115, 360, 142, 372 ], "score": 1.0, "content": "2016.", "type": "text" } ], "index": 20 } ], "index": 19, "bbox_fs": [ 106, 338, 507, 372 ] }, { "type": "text", "bbox": [ 105, 379, 504, 403 ], "lines": [ { "bbox": [ 106, 379, 505, 392 ], "spans": [ { "bbox": [ 106, 379, 505, 392 ], "score": 1.0, "content": "Zhijie Deng, Yinpeng Dong, and Jun Zhu. Batch virtual adversarial training for graph convolutional", "type": "text" } ], "index": 21 }, { "bbox": [ 115, 391, 321, 403 ], "spans": [ { "bbox": [ 115, 391, 321, 403 ], "score": 1.0, "content": "networks. arXiv preprint arXiv:1902.09192, 2019.", "type": "text" } ], "index": 22 } ], "index": 21.5, "bbox_fs": [ 106, 379, 505, 403 ] }, { "type": "text", "bbox": [ 108, 410, 504, 444 ], "lines": [ { "bbox": [ 106, 409, 506, 423 ], "spans": [ { "bbox": [ 106, 409, 506, 423 ], "score": 1.0, "content": "David Duvenaud, Dougal Maclaurin, Jorge Aguilera-Iparraguirre, Rafael Gómez-Bombarelli, Timo-", "type": "text" } ], "index": 23 }, { "bbox": [ 115, 420, 506, 435 ], "spans": [ { "bbox": [ 115, 420, 506, 435 ], "score": 1.0, "content": "thy Hirzel, Alán Aspuru-Guzik, and Ryan P Adams. Convolutional networks on graphs for learning", "type": "text" } ], "index": 24 }, { "bbox": [ 115, 432, 461, 445 ], "spans": [ { "bbox": [ 115, 432, 461, 445 ], "score": 1.0, "content": "molecular fingerprints. In Advances in Neural Information Processing Systems, 2015.", "type": "text" } ], "index": 25 } ], "index": 24, "bbox_fs": [ 106, 409, 506, 445 ] }, { "type": "text", "bbox": [ 107, 451, 506, 485 ], "lines": [ { "bbox": [ 105, 451, 505, 465 ], "spans": [ { "bbox": [ 105, 451, 505, 465 ], "score": 1.0, "content": "Fuli Feng, Xiangnan He, Jie Tang, and Tat-Seng Chua. Graph adversarial training: Dynamically", "type": "text" } ], "index": 26 }, { "bbox": [ 114, 462, 507, 477 ], "spans": [ { "bbox": [ 114, 462, 507, 477 ], "score": 1.0, "content": "regularizing based on graph structure. IEEE Transactions on Knowledge and Data Engineering,", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 471, 143, 486 ], "spans": [ { "bbox": [ 115, 471, 143, 486 ], "score": 1.0, "content": "2019.", "type": "text" } ], "index": 28 } ], "index": 27, "bbox_fs": [ 105, 451, 507, 486 ] }, { "type": "text", "bbox": [ 107, 493, 506, 527 ], "lines": [ { "bbox": [ 105, 491, 505, 507 ], "spans": [ { "bbox": [ 105, 491, 505, 507 ], "score": 1.0, "content": "Wenzheng Feng, Jie Zhang, Yuxiao Dong, Yu Han, Huanbo Luan, Qian Xu, Qiang Yang, Evgeny", "type": "text" } ], "index": 29 }, { "bbox": [ 115, 503, 506, 518 ], "spans": [ { "bbox": [ 115, 503, 506, 518 ], "score": 1.0, "content": "Kharlamov, and Jie Tang. Graph random neural network for semi-supervised learning on graphs.", "type": "text" } ], "index": 30 }, { "bbox": [ 115, 515, 205, 527 ], "spans": [ { "bbox": [ 115, 515, 205, 527 ], "score": 1.0, "content": "In NeurIPS’20, 2020.", "type": "text" } ], "index": 31 } ], "index": 30, "bbox_fs": [ 105, 491, 506, 527 ] }, { "type": "text", "bbox": [ 105, 534, 504, 557 ], "lines": [ { "bbox": [ 104, 532, 507, 550 ], "spans": [ { "bbox": [ 104, 532, 507, 550 ], "score": 1.0, "content": "Hongyang Gao and Shuiwang Ji. Graph u-nets. In international conference on machine learning, pp.", "type": "text" } ], "index": 32 }, { "bbox": [ 116, 545, 224, 557 ], "spans": [ { "bbox": [ 116, 545, 224, 557 ], "score": 1.0, "content": "2083–2092. PMLR, 2019.", "type": "text" } ], "index": 33 } ], "index": 32.5, "bbox_fs": [ 104, 532, 507, 557 ] }, { "type": "text", "bbox": [ 105, 565, 505, 588 ], "lines": [ { "bbox": [ 105, 563, 507, 580 ], "spans": [ { "bbox": [ 105, 563, 507, 580 ], "score": 1.0, "content": "Alberto García-Durán and Mathias Niepert. Learning graph representations with embedding propaga-", "type": "text" } ], "index": 34 }, { "bbox": [ 115, 575, 388, 589 ], "spans": [ { "bbox": [ 115, 575, 388, 589 ], "score": 1.0, "content": "tion. In Advances in Neural Information Processing Systems, 2017.", "type": "text" } ], "index": 35 } ], "index": 34.5, "bbox_fs": [ 105, 563, 507, 589 ] }, { "type": "text", "bbox": [ 107, 595, 505, 630 ], "lines": [ { "bbox": [ 105, 595, 506, 609 ], "spans": [ { "bbox": [ 105, 595, 506, 609 ], "score": 1.0, "content": "Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair,", "type": "text" } ], "index": 36 }, { "bbox": [ 116, 608, 505, 619 ], "spans": [ { "bbox": [ 116, 608, 505, 619 ], "score": 1.0, "content": "Aaron Courville, and Yoshua Bengio. Generative adversarial networks. In Advances in Neural", "type": "text" } ], "index": 37 }, { "bbox": [ 115, 617, 275, 631 ], "spans": [ { "bbox": [ 115, 617, 275, 631 ], "score": 1.0, "content": "Information Processing Systems, 2014.", "type": "text" } ], "index": 38 } ], "index": 37, "bbox_fs": [ 105, 595, 506, 631 ] }, { "type": "text", "bbox": [ 107, 637, 505, 671 ], "lines": [ { "bbox": [ 106, 637, 506, 651 ], "spans": [ { "bbox": [ 106, 637, 506, 651 ], "score": 1.0, "content": "Shengnan Guo, Youfang Lin, Ning Feng, Chao Song, and Huaiyu Wan. Attention based spatial-", "type": "text" } ], "index": 39 }, { "bbox": [ 115, 648, 505, 661 ], "spans": [ { "bbox": [ 115, 648, 505, 661 ], "score": 1.0, "content": "temporal graph convolutional networks for traffic flow forecasting. In Proceedings of the AAAI", "type": "text" } ], "index": 40 }, { "bbox": [ 116, 659, 347, 673 ], "spans": [ { "bbox": [ 116, 659, 347, 673 ], "score": 1.0, "content": "Conference on Artificial Intelligence, pp. 922–929, 2019.", "type": "text" } ], "index": 41 } ], "index": 40, "bbox_fs": [ 106, 637, 506, 673 ] }, { "type": "text", "bbox": [ 107, 678, 504, 702 ], "lines": [ { "bbox": [ 106, 678, 505, 692 ], "spans": [ { "bbox": [ 106, 678, 505, 692 ], "score": 1.0, "content": "William L Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large graphs.", "type": "text" } ], "index": 42 }, { "bbox": [ 115, 689, 366, 703 ], "spans": [ { "bbox": [ 115, 689, 366, 703 ], "score": 1.0, "content": "In Advances in Neural Information Processing Systems, 2017.", "type": "text" } ], "index": 43 } ], "index": 42.5, "bbox_fs": [ 106, 678, 505, 703 ] }, { "type": "text", "bbox": [ 107, 709, 503, 732 ], "lines": [ { "bbox": [ 105, 708, 505, 723 ], "spans": [ { "bbox": [ 105, 708, 505, 723 ], "score": 1.0, "content": "Neil Houlsby, Ferenc Huszár, Zoubin Ghahramani, and Máté Lengyel. Bayesian active learning for", "type": "text" } ], "index": 44 }, { "bbox": [ 116, 720, 429, 732 ], "spans": [ { "bbox": [ 116, 720, 429, 732 ], "score": 1.0, "content": "classification and preference learning. arXiv preprint arXiv:1112.5745, 2011.", "type": "text" } ], "index": 45 } ], "index": 44.5, "bbox_fs": [ 105, 708, 505, 732 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 108, 82, 505, 116 ], "lines": [ { "bbox": [ 106, 82, 505, 95 ], "spans": [ { "bbox": [ 106, 82, 505, 95 ], "score": 1.0, "content": "Gao Huang, Zhuang Liu, Laurens Van Der Maaten, and Kilian Q Weinberger. Densely connected", "type": "text" } ], "index": 0 }, { "bbox": [ 116, 94, 505, 106 ], "spans": [ { "bbox": [ 116, 94, 505, 106 ], "score": 1.0, "content": "convolutional networks. In Proceedings of the IEEE conference on computer vision and pattern", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 105, 257, 116 ], "spans": [ { "bbox": [ 115, 105, 257, 116 ], "score": 1.0, "content": "recognition, pp. 4700–4708, 2017.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "text", "bbox": [ 108, 122, 504, 156 ], "lines": [ { "bbox": [ 105, 121, 505, 135 ], "spans": [ { "bbox": [ 105, 121, 505, 135 ], "score": 1.0, "content": "Junteng Jia and Austion R Benson. Residual correlation in graph neural network regression. In", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 133, 505, 146 ], "spans": [ { "bbox": [ 115, 133, 505, 146 ], "score": 1.0, "content": "Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data", "type": "text" } ], "index": 4 }, { "bbox": [ 115, 144, 230, 157 ], "spans": [ { "bbox": [ 115, 144, 230, 157 ], "score": 1.0, "content": "Mining, pp. 588–598, 2020.", "type": "text" } ], "index": 5 } ], "index": 4 }, { "type": "text", "bbox": [ 106, 162, 505, 185 ], "lines": [ { "bbox": [ 105, 160, 505, 176 ], "spans": [ { "bbox": [ 105, 160, 505, 176 ], "score": 1.0, "content": "Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint", "type": "text" } ], "index": 6 }, { "bbox": [ 116, 173, 214, 185 ], "spans": [ { "bbox": [ 116, 173, 214, 185 ], "score": 1.0, "content": "arXiv:1312.6114, 2013.", "type": "text" } ], "index": 7 } ], "index": 6.5 }, { "type": "text", "bbox": [ 106, 191, 505, 214 ], "lines": [ { "bbox": [ 105, 190, 505, 205 ], "spans": [ { "bbox": [ 105, 190, 505, 205 ], "score": 1.0, "content": "Thomas N Kipf and Max Welling. Variational graph auto-encoders. NIPS Workshop on Bayesian", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 202, 207, 216 ], "spans": [ { "bbox": [ 115, 202, 207, 216 ], "score": 1.0, "content": "Deep Learning, 2016.", "type": "text" } ], "index": 9 } ], "index": 8.5 }, { "type": "text", "bbox": [ 105, 220, 505, 244 ], "lines": [ { "bbox": [ 106, 220, 506, 234 ], "spans": [ { "bbox": [ 106, 220, 506, 234 ], "score": 1.0, "content": "Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks.", "type": "text" } ], "index": 10 }, { "bbox": [ 115, 231, 372, 244 ], "spans": [ { "bbox": [ 115, 231, 372, 244 ], "score": 1.0, "content": "In International Conference on Learning Representation, 2017.", "type": "text" } ], "index": 11 } ], "index": 10.5 }, { "type": "text", "bbox": [ 106, 249, 505, 284 ], "lines": [ { "bbox": [ 106, 249, 506, 263 ], "spans": [ { "bbox": [ 106, 249, 506, 263 ], "score": 1.0, "content": "Johannes Klicpera, Aleksandar Bojchevski, and Stephan Günnemann. Predict then propagate:", "type": "text" } ], "index": 12 }, { "bbox": [ 115, 259, 505, 275 ], "spans": [ { "bbox": [ 115, 259, 505, 275 ], "score": 1.0, "content": "Graph neural networks meet personalized pagerank. In International Conference on Learning", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 272, 207, 284 ], "spans": [ { "bbox": [ 115, 272, 207, 284 ], "score": 1.0, "content": "Representation, 2019.", "type": "text" } ], "index": 14 } ], "index": 13 }, { "type": "text", "bbox": [ 108, 289, 505, 324 ], "lines": [ { "bbox": [ 106, 289, 505, 303 ], "spans": [ { "bbox": [ 106, 289, 505, 303 ], "score": 1.0, "content": "Kezhi Kong, Guohao Li, Mucong Ding, Zuxuan Wu, Chen Zhu, Bernard Ghanem, Gavin Taylor, and", "type": "text" } ], "index": 15 }, { "bbox": [ 115, 301, 505, 314 ], "spans": [ { "bbox": [ 115, 301, 505, 314 ], "score": 1.0, "content": "Tom Goldstein. Flag: Adversarial data augmentation for graph neural networks. arXiv preprint", "type": "text" } ], "index": 16 }, { "bbox": [ 115, 312, 219, 324 ], "spans": [ { "bbox": [ 115, 312, 219, 324 ], "score": 1.0, "content": "arXiv:2010.09891, 2020.", "type": "text" } ], "index": 17 } ], "index": 16 }, { "type": "text", "bbox": [ 106, 330, 505, 353 ], "lines": [ { "bbox": [ 107, 331, 505, 343 ], "spans": [ { "bbox": [ 107, 331, 505, 343 ], "score": 1.0, "content": "Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper insights into graph convolutional networks for", "type": "text" } ], "index": 18 }, { "bbox": [ 116, 340, 506, 354 ], "spans": [ { "bbox": [ 116, 340, 506, 354 ], "score": 1.0, "content": "semi-supervised learning. In Proceedings of the AAAI Conference on Artificial Intelligence, 2018.", "type": "text" } ], "index": 19 } ], "index": 18.5 }, { "type": "text", "bbox": [ 105, 359, 504, 383 ], "lines": [ { "bbox": [ 105, 358, 506, 374 ], "spans": [ { "bbox": [ 105, 358, 506, 374 ], "score": 1.0, "content": "Renjie Liao, Zhizhen Zhao, Raquel Urtasun, and Richard S Zemel. Lanczosnet: Multi-scale deep", "type": "text" } ], "index": 20 }, { "bbox": [ 115, 370, 501, 383 ], "spans": [ { "bbox": [ 115, 370, 501, 383 ], "score": 1.0, "content": "graph convolutional networks. In International Conference on Learning Representations, 2019.", "type": "text" } ], "index": 21 } ], "index": 20.5 }, { "type": "text", "bbox": [ 106, 388, 505, 422 ], "lines": [ { "bbox": [ 106, 388, 505, 401 ], "spans": [ { "bbox": [ 106, 388, 505, 401 ], "score": 1.0, "content": "Qi Liu, Miltiadis Allamanis, Marc Brockschmidt, and Alexander L Gaunt. Constrained graph", "type": "text" } ], "index": 22 }, { "bbox": [ 115, 398, 505, 413 ], "spans": [ { "bbox": [ 115, 398, 505, 413 ], "score": 1.0, "content": "variational autoencoders for molecule design. In Advances in Neural Information Processing", "type": "text" } ], "index": 23 }, { "bbox": [ 114, 410, 179, 423 ], "spans": [ { "bbox": [ 114, 410, 179, 423 ], "score": 1.0, "content": "Systems, 2018.", "type": "text" } ], "index": 24 } ], "index": 23 }, { "type": "text", "bbox": [ 107, 428, 504, 462 ], "lines": [ { "bbox": [ 105, 427, 506, 442 ], "spans": [ { "bbox": [ 105, 427, 506, 442 ], "score": 1.0, "content": "Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg Corrado, and Jeffrey Dean. Distributed repre-", "type": "text" } ], "index": 25 }, { "bbox": [ 116, 440, 505, 452 ], "spans": [ { "bbox": [ 116, 440, 505, 452 ], "score": 1.0, "content": "sentations of words and phrases and their compositionality. In Advances in Neural Information", "type": "text" } ], "index": 26 }, { "bbox": [ 117, 451, 224, 463 ], "spans": [ { "bbox": [ 117, 451, 224, 463 ], "score": 1.0, "content": "Processing Systems, 2013.", "type": "text" } ], "index": 27 } ], "index": 26 }, { "type": "text", "bbox": [ 106, 468, 506, 513 ], "lines": [ { "bbox": [ 106, 469, 506, 480 ], "spans": [ { "bbox": [ 106, 469, 506, 480 ], "score": 1.0, "content": "Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodola, Jan Svoboda, and Michael M", "type": "text" } ], "index": 28 }, { "bbox": [ 115, 480, 506, 493 ], "spans": [ { "bbox": [ 115, 480, 506, 493 ], "score": 1.0, "content": "Bronstein. Geometric deep learning on graphs and manifolds using mixture model cnns. In", "type": "text" } ], "index": 29 }, { "bbox": [ 115, 491, 507, 504 ], "spans": [ { "bbox": [ 115, 491, 507, 504 ], "score": 1.0, "content": "Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 5115–5124,", "type": "text" } ], "index": 30 }, { "bbox": [ 114, 501, 143, 514 ], "spans": [ { "bbox": [ 114, 501, 143, 514 ], "score": 1.0, "content": "2017.", "type": "text" } ], "index": 31 } ], "index": 29.5 }, { "type": "text", "bbox": [ 105, 519, 505, 543 ], "lines": [ { "bbox": [ 105, 517, 505, 534 ], "spans": [ { "bbox": [ 105, 517, 505, 534 ], "score": 1.0, "content": "Christopher Nielsen and Michal M Okoniewski. Gan data augmentation through active learning", "type": "text" } ], "index": 32 }, { "bbox": [ 115, 531, 398, 543 ], "spans": [ { "bbox": [ 115, 531, 398, 543 ], "score": 1.0, "content": "inspired sample acquisition. In CVPR Workshops, pp. 109–112, 2019.", "type": "text" } ], "index": 33 } ], "index": 32.5 }, { "type": "text", "bbox": [ 106, 548, 505, 572 ], "lines": [ { "bbox": [ 106, 549, 505, 561 ], "spans": [ { "bbox": [ 106, 549, 505, 561 ], "score": 1.0, "content": "Mathias Niepert, Mohamed Ahmed, and Konstantin Kutzkov. Learning convolutional neural networks", "type": "text" } ], "index": 34 }, { "bbox": [ 115, 560, 484, 572 ], "spans": [ { "bbox": [ 115, 560, 484, 572 ], "score": 1.0, "content": "for graphs. In International conference on machine learning, pp. 2014–2023. PMLR, 2016.", "type": "text" } ], "index": 35 } ], "index": 34.5 }, { "type": "text", "bbox": [ 108, 577, 505, 612 ], "lines": [ { "bbox": [ 105, 576, 505, 592 ], "spans": [ { "bbox": [ 105, 576, 505, 592 ], "score": 1.0, "content": "Gaurav Pandey and Ambedkar Dukkipati. Variational methods for conditional multimodal deep", "type": "text" } ], "index": 36 }, { "bbox": [ 115, 589, 506, 601 ], "spans": [ { "bbox": [ 115, 589, 506, 601 ], "score": 1.0, "content": "learning. In 2017 International Joint Conference on Neural Networks (IJCNN), pp. 308–315. IEEE,", "type": "text" } ], "index": 37 }, { "bbox": [ 115, 598, 144, 613 ], "spans": [ { "bbox": [ 115, 598, 144, 613 ], "score": 1.0, "content": "2017.", "type": "text" } ], "index": 38 } ], "index": 37 }, { "type": "text", "bbox": [ 107, 618, 506, 662 ], "lines": [ { "bbox": [ 105, 617, 506, 631 ], "spans": [ { "bbox": [ 105, 617, 506, 631 ], "score": 1.0, "content": "Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor", "type": "text" } ], "index": 39 }, { "bbox": [ 115, 628, 506, 642 ], "spans": [ { "bbox": [ 115, 628, 506, 642 ], "score": 1.0, "content": "Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style,", "type": "text" } ], "index": 40 }, { "bbox": [ 115, 640, 507, 653 ], "spans": [ { "bbox": [ 115, 640, 507, 653 ], "score": 1.0, "content": "high-performance deep learning library. In Advances in Neural Information Processing Systems,", "type": "text" } ], "index": 41 }, { "bbox": [ 114, 650, 143, 663 ], "spans": [ { "bbox": [ 114, 650, 143, 663 ], "score": 1.0, "content": "2019.", "type": "text" } ], "index": 42 } ], "index": 40.5 }, { "type": "text", "bbox": [ 106, 669, 504, 692 ], "lines": [ { "bbox": [ 106, 669, 504, 682 ], "spans": [ { "bbox": [ 106, 669, 504, 682 ], "score": 1.0, "content": "Hongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei, and Bo Yang. Geom-gcn: Geometric", "type": "text" } ], "index": 43 }, { "bbox": [ 115, 680, 500, 694 ], "spans": [ { "bbox": [ 115, 680, 500, 694 ], "score": 1.0, "content": "graph convolutional networks. In International Conference on Learning Representations, 2020.", "type": "text" } ], "index": 44 } ], "index": 43.5 }, { "type": "text", "bbox": [ 108, 698, 505, 732 ], "lines": [ { "bbox": [ 106, 698, 506, 711 ], "spans": [ { "bbox": [ 106, 698, 506, 711 ], "score": 1.0, "content": "Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. Deepwalk: Online learning of social representa-", "type": "text" } ], "index": 45 }, { "bbox": [ 115, 709, 505, 723 ], "spans": [ { "bbox": [ 115, 709, 505, 723 ], "score": 1.0, "content": "tions. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery", "type": "text" } ], "index": 46 }, { "bbox": [ 116, 721, 267, 733 ], "spans": [ { "bbox": [ 116, 721, 267, 733 ], "score": 1.0, "content": "and data mining, pp. 701–710, 2014.", "type": "text" } ], "index": 47 } ], "index": 46 } ], "page_idx": 10, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 300, 751, 309, 760 ], "lines": [ { "bbox": [ 299, 750, 312, 765 ], "spans": [ { "bbox": [ 299, 750, 312, 765 ], "score": 1.0, "content": "", "type": "text", "height": 15, "width": 13 } ] } ] }, { "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 2022", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 108, 82, 505, 116 ], "lines": [ { "bbox": [ 106, 82, 505, 95 ], "spans": [ { "bbox": [ 106, 82, 505, 95 ], "score": 1.0, "content": "Gao Huang, Zhuang Liu, Laurens Van Der Maaten, and Kilian Q Weinberger. Densely connected", "type": "text" } ], "index": 0 }, { "bbox": [ 116, 94, 505, 106 ], "spans": [ { "bbox": [ 116, 94, 505, 106 ], "score": 1.0, "content": "convolutional networks. In Proceedings of the IEEE conference on computer vision and pattern", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 105, 257, 116 ], "spans": [ { "bbox": [ 115, 105, 257, 116 ], "score": 1.0, "content": "recognition, pp. 4700–4708, 2017.", "type": "text" } ], "index": 2 } ], "index": 1, "bbox_fs": [ 106, 82, 505, 116 ] }, { "type": "text", "bbox": [ 108, 122, 504, 156 ], "lines": [ { "bbox": [ 105, 121, 505, 135 ], "spans": [ { "bbox": [ 105, 121, 505, 135 ], "score": 1.0, "content": "Junteng Jia and Austion R Benson. Residual correlation in graph neural network regression. In", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 133, 505, 146 ], "spans": [ { "bbox": [ 115, 133, 505, 146 ], "score": 1.0, "content": "Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data", "type": "text" } ], "index": 4 }, { "bbox": [ 115, 144, 230, 157 ], "spans": [ { "bbox": [ 115, 144, 230, 157 ], "score": 1.0, "content": "Mining, pp. 588–598, 2020.", "type": "text" } ], "index": 5 } ], "index": 4, "bbox_fs": [ 105, 121, 505, 157 ] }, { "type": "text", "bbox": [ 106, 162, 505, 185 ], "lines": [ { "bbox": [ 105, 160, 505, 176 ], "spans": [ { "bbox": [ 105, 160, 505, 176 ], "score": 1.0, "content": "Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint", "type": "text" } ], "index": 6 }, { "bbox": [ 116, 173, 214, 185 ], "spans": [ { "bbox": [ 116, 173, 214, 185 ], "score": 1.0, "content": "arXiv:1312.6114, 2013.", "type": "text" } ], "index": 7 } ], "index": 6.5, "bbox_fs": [ 105, 160, 505, 185 ] }, { "type": "text", "bbox": [ 106, 191, 505, 214 ], "lines": [ { "bbox": [ 105, 190, 505, 205 ], "spans": [ { "bbox": [ 105, 190, 505, 205 ], "score": 1.0, "content": "Thomas N Kipf and Max Welling. Variational graph auto-encoders. NIPS Workshop on Bayesian", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 202, 207, 216 ], "spans": [ { "bbox": [ 115, 202, 207, 216 ], "score": 1.0, "content": "Deep Learning, 2016.", "type": "text" } ], "index": 9 } ], "index": 8.5, "bbox_fs": [ 105, 190, 505, 216 ] }, { "type": "text", "bbox": [ 105, 220, 505, 244 ], "lines": [ { "bbox": [ 106, 220, 506, 234 ], "spans": [ { "bbox": [ 106, 220, 506, 234 ], "score": 1.0, "content": "Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks.", "type": "text" } ], "index": 10 }, { "bbox": [ 115, 231, 372, 244 ], "spans": [ { "bbox": [ 115, 231, 372, 244 ], "score": 1.0, "content": "In International Conference on Learning Representation, 2017.", "type": "text" } ], "index": 11 } ], "index": 10.5, "bbox_fs": [ 106, 220, 506, 244 ] }, { "type": "text", "bbox": [ 106, 249, 505, 284 ], "lines": [ { "bbox": [ 106, 249, 506, 263 ], "spans": [ { "bbox": [ 106, 249, 506, 263 ], "score": 1.0, "content": "Johannes Klicpera, Aleksandar Bojchevski, and Stephan Günnemann. Predict then propagate:", "type": "text" } ], "index": 12 }, { "bbox": [ 115, 259, 505, 275 ], "spans": [ { "bbox": [ 115, 259, 505, 275 ], "score": 1.0, "content": "Graph neural networks meet personalized pagerank. In International Conference on Learning", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 272, 207, 284 ], "spans": [ { "bbox": [ 115, 272, 207, 284 ], "score": 1.0, "content": "Representation, 2019.", "type": "text" } ], "index": 14 } ], "index": 13, "bbox_fs": [ 106, 249, 506, 284 ] }, { "type": "text", "bbox": [ 108, 289, 505, 324 ], "lines": [ { "bbox": [ 106, 289, 505, 303 ], "spans": [ { "bbox": [ 106, 289, 505, 303 ], "score": 1.0, "content": "Kezhi Kong, Guohao Li, Mucong Ding, Zuxuan Wu, Chen Zhu, Bernard Ghanem, Gavin Taylor, and", "type": "text" } ], "index": 15 }, { "bbox": [ 115, 301, 505, 314 ], "spans": [ { "bbox": [ 115, 301, 505, 314 ], "score": 1.0, "content": "Tom Goldstein. Flag: Adversarial data augmentation for graph neural networks. arXiv preprint", "type": "text" } ], "index": 16 }, { "bbox": [ 115, 312, 219, 324 ], "spans": [ { "bbox": [ 115, 312, 219, 324 ], "score": 1.0, "content": "arXiv:2010.09891, 2020.", "type": "text" } ], "index": 17 } ], "index": 16, "bbox_fs": [ 106, 289, 505, 324 ] }, { "type": "text", "bbox": [ 106, 330, 505, 353 ], "lines": [ { "bbox": [ 107, 331, 505, 343 ], "spans": [ { "bbox": [ 107, 331, 505, 343 ], "score": 1.0, "content": "Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper insights into graph convolutional networks for", "type": "text" } ], "index": 18 }, { "bbox": [ 116, 340, 506, 354 ], "spans": [ { "bbox": [ 116, 340, 506, 354 ], "score": 1.0, "content": "semi-supervised learning. In Proceedings of the AAAI Conference on Artificial Intelligence, 2018.", "type": "text" } ], "index": 19 } ], "index": 18.5, "bbox_fs": [ 107, 331, 506, 354 ] }, { "type": "text", "bbox": [ 105, 359, 504, 383 ], "lines": [ { "bbox": [ 105, 358, 506, 374 ], "spans": [ { "bbox": [ 105, 358, 506, 374 ], "score": 1.0, "content": "Renjie Liao, Zhizhen Zhao, Raquel Urtasun, and Richard S Zemel. Lanczosnet: Multi-scale deep", "type": "text" } ], "index": 20 }, { "bbox": [ 115, 370, 501, 383 ], "spans": [ { "bbox": [ 115, 370, 501, 383 ], "score": 1.0, "content": "graph convolutional networks. In International Conference on Learning Representations, 2019.", "type": "text" } ], "index": 21 } ], "index": 20.5, "bbox_fs": [ 105, 358, 506, 383 ] }, { "type": "text", "bbox": [ 106, 388, 505, 422 ], "lines": [ { "bbox": [ 106, 388, 505, 401 ], "spans": [ { "bbox": [ 106, 388, 505, 401 ], "score": 1.0, "content": "Qi Liu, Miltiadis Allamanis, Marc Brockschmidt, and Alexander L Gaunt. Constrained graph", "type": "text" } ], "index": 22 }, { "bbox": [ 115, 398, 505, 413 ], "spans": [ { "bbox": [ 115, 398, 505, 413 ], "score": 1.0, "content": "variational autoencoders for molecule design. In Advances in Neural Information Processing", "type": "text" } ], "index": 23 }, { "bbox": [ 114, 410, 179, 423 ], "spans": [ { "bbox": [ 114, 410, 179, 423 ], "score": 1.0, "content": "Systems, 2018.", "type": "text" } ], "index": 24 } ], "index": 23, "bbox_fs": [ 106, 388, 505, 423 ] }, { "type": "text", "bbox": [ 107, 428, 504, 462 ], "lines": [ { "bbox": [ 105, 427, 506, 442 ], "spans": [ { "bbox": [ 105, 427, 506, 442 ], "score": 1.0, "content": "Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg Corrado, and Jeffrey Dean. Distributed repre-", "type": "text" } ], "index": 25 }, { "bbox": [ 116, 440, 505, 452 ], "spans": [ { "bbox": [ 116, 440, 505, 452 ], "score": 1.0, "content": "sentations of words and phrases and their compositionality. In Advances in Neural Information", "type": "text" } ], "index": 26 }, { "bbox": [ 117, 451, 224, 463 ], "spans": [ { "bbox": [ 117, 451, 224, 463 ], "score": 1.0, "content": "Processing Systems, 2013.", "type": "text" } ], "index": 27 } ], "index": 26, "bbox_fs": [ 105, 427, 506, 463 ] }, { "type": "text", "bbox": [ 106, 468, 506, 513 ], "lines": [ { "bbox": [ 106, 469, 506, 480 ], "spans": [ { "bbox": [ 106, 469, 506, 480 ], "score": 1.0, "content": "Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodola, Jan Svoboda, and Michael M", "type": "text" } ], "index": 28 }, { "bbox": [ 115, 480, 506, 493 ], "spans": [ { "bbox": [ 115, 480, 506, 493 ], "score": 1.0, "content": "Bronstein. Geometric deep learning on graphs and manifolds using mixture model cnns. In", "type": "text" } ], "index": 29 }, { "bbox": [ 115, 491, 507, 504 ], "spans": [ { "bbox": [ 115, 491, 507, 504 ], "score": 1.0, "content": "Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 5115–5124,", "type": "text" } ], "index": 30 }, { "bbox": [ 114, 501, 143, 514 ], "spans": [ { "bbox": [ 114, 501, 143, 514 ], "score": 1.0, "content": "2017.", "type": "text" } ], "index": 31 } ], "index": 29.5, "bbox_fs": [ 106, 469, 507, 514 ] }, { "type": "text", "bbox": [ 105, 519, 505, 543 ], "lines": [ { "bbox": [ 105, 517, 505, 534 ], "spans": [ { "bbox": [ 105, 517, 505, 534 ], "score": 1.0, "content": "Christopher Nielsen and Michal M Okoniewski. Gan data augmentation through active learning", "type": "text" } ], "index": 32 }, { "bbox": [ 115, 531, 398, 543 ], "spans": [ { "bbox": [ 115, 531, 398, 543 ], "score": 1.0, "content": "inspired sample acquisition. In CVPR Workshops, pp. 109–112, 2019.", "type": "text" } ], "index": 33 } ], "index": 32.5, "bbox_fs": [ 105, 517, 505, 543 ] }, { "type": "text", "bbox": [ 106, 548, 505, 572 ], "lines": [ { "bbox": [ 106, 549, 505, 561 ], "spans": [ { "bbox": [ 106, 549, 505, 561 ], "score": 1.0, "content": "Mathias Niepert, Mohamed Ahmed, and Konstantin Kutzkov. Learning convolutional neural networks", "type": "text" } ], "index": 34 }, { "bbox": [ 115, 560, 484, 572 ], "spans": [ { "bbox": [ 115, 560, 484, 572 ], "score": 1.0, "content": "for graphs. In International conference on machine learning, pp. 2014–2023. PMLR, 2016.", "type": "text" } ], "index": 35 } ], "index": 34.5, "bbox_fs": [ 106, 549, 505, 572 ] }, { "type": "text", "bbox": [ 108, 577, 505, 612 ], "lines": [ { "bbox": [ 105, 576, 505, 592 ], "spans": [ { "bbox": [ 105, 576, 505, 592 ], "score": 1.0, "content": "Gaurav Pandey and Ambedkar Dukkipati. Variational methods for conditional multimodal deep", "type": "text" } ], "index": 36 }, { "bbox": [ 115, 589, 506, 601 ], "spans": [ { "bbox": [ 115, 589, 506, 601 ], "score": 1.0, "content": "learning. In 2017 International Joint Conference on Neural Networks (IJCNN), pp. 308–315. IEEE,", "type": "text" } ], "index": 37 }, { "bbox": [ 115, 598, 144, 613 ], "spans": [ { "bbox": [ 115, 598, 144, 613 ], "score": 1.0, "content": "2017.", "type": "text" } ], "index": 38 } ], "index": 37, "bbox_fs": [ 105, 576, 506, 613 ] }, { "type": "text", "bbox": [ 107, 618, 506, 662 ], "lines": [ { "bbox": [ 105, 617, 506, 631 ], "spans": [ { "bbox": [ 105, 617, 506, 631 ], "score": 1.0, "content": "Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor", "type": "text" } ], "index": 39 }, { "bbox": [ 115, 628, 506, 642 ], "spans": [ { "bbox": [ 115, 628, 506, 642 ], "score": 1.0, "content": "Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style,", "type": "text" } ], "index": 40 }, { "bbox": [ 115, 640, 507, 653 ], "spans": [ { "bbox": [ 115, 640, 507, 653 ], "score": 1.0, "content": "high-performance deep learning library. In Advances in Neural Information Processing Systems,", "type": "text" } ], "index": 41 }, { "bbox": [ 114, 650, 143, 663 ], "spans": [ { "bbox": [ 114, 650, 143, 663 ], "score": 1.0, "content": "2019.", "type": "text" } ], "index": 42 } ], "index": 40.5, "bbox_fs": [ 105, 617, 507, 663 ] }, { "type": "text", "bbox": [ 106, 669, 504, 692 ], "lines": [ { "bbox": [ 106, 669, 504, 682 ], "spans": [ { "bbox": [ 106, 669, 504, 682 ], "score": 1.0, "content": "Hongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei, and Bo Yang. Geom-gcn: Geometric", "type": "text" } ], "index": 43 }, { "bbox": [ 115, 680, 500, 694 ], "spans": [ { "bbox": [ 115, 680, 500, 694 ], "score": 1.0, "content": "graph convolutional networks. In International Conference on Learning Representations, 2020.", "type": "text" } ], "index": 44 } ], "index": 43.5, "bbox_fs": [ 106, 669, 504, 694 ] }, { "type": "text", "bbox": [ 108, 698, 505, 732 ], "lines": [ { "bbox": [ 106, 698, 506, 711 ], "spans": [ { "bbox": [ 106, 698, 506, 711 ], "score": 1.0, "content": "Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. Deepwalk: Online learning of social representa-", "type": "text" } ], "index": 45 }, { "bbox": [ 115, 709, 505, 723 ], "spans": [ { "bbox": [ 115, 709, 505, 723 ], "score": 1.0, "content": "tions. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery", "type": "text" } ], "index": 46 }, { "bbox": [ 116, 721, 267, 733 ], "spans": [ { "bbox": [ 116, 721, 267, 733 ], "score": 1.0, "content": "and data mining, pp. 701–710, 2014.", "type": "text" } ], "index": 47 } ], "index": 46, "bbox_fs": [ 106, 698, 506, 733 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 107, 82, 505, 116 ], "lines": [ { "bbox": [ 105, 81, 506, 96 ], "spans": [ { "bbox": [ 105, 81, 506, 96 ], "score": 1.0, "content": "Yu Rong, Wenbing Huang, Tingyang Xu, and Junzhou Huang. Dropedge: Towards deep graph convo-", "type": "text" } ], "index": 0 }, { "bbox": [ 115, 93, 506, 106 ], "spans": [ { "bbox": [ 115, 93, 506, 106 ], "score": 1.0, "content": "lutional networks on node classification. In International Conference on Learning Representation,", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 104, 141, 116 ], "spans": [ { "bbox": [ 115, 104, 141, 116 ], "score": 1.0, "content": "2020.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "text", "bbox": [ 106, 123, 504, 145 ], "lines": [ { "bbox": [ 106, 123, 505, 135 ], "spans": [ { "bbox": [ 106, 123, 505, 135 ], "score": 1.0, "content": "Benedek Rozemberczki, Carl Allen, and Rik Sarkar. Multi-scale attributed node embedding. Journal", "type": "text" } ], "index": 3 }, { "bbox": [ 116, 134, 290, 146 ], "spans": [ { "bbox": [ 116, 134, 290, 146 ], "score": 1.0, "content": "of Complex Networks, 9(2):cnab014, 2021.", "type": "text" } ], "index": 4 } ], "index": 3.5 }, { "type": "text", "bbox": [ 107, 152, 504, 186 ], "lines": [ { "bbox": [ 106, 152, 506, 165 ], "spans": [ { "bbox": [ 106, 152, 506, 165 ], "score": 1.0, "content": "Guillaume Salha, Romain Hennequin, and Michalis Vazirgiannis. Keep it simple: Graph autoen-", "type": "text" } ], "index": 5 }, { "bbox": [ 116, 164, 505, 176 ], "spans": [ { "bbox": [ 116, 164, 505, 176 ], "score": 1.0, "content": "coders without graph convolutional networks. Workshop on Graph Representation Learning, 33rd", "type": "text" } ], "index": 6 }, { "bbox": [ 116, 174, 410, 187 ], "spans": [ { "bbox": [ 116, 174, 410, 187 ], "score": 1.0, "content": "Conference on Neural Information Processing Systems (NeurIPS), 2019.", "type": "text" } ], "index": 7 } ], "index": 6 }, { "type": "text", "bbox": [ 106, 192, 505, 227 ], "lines": [ { "bbox": [ 106, 192, 505, 206 ], "spans": [ { "bbox": [ 106, 192, 505, 206 ], "score": 1.0, "content": "Bidisha Samanta, Abir De, Niloy Ganguly, and Manuel Gomez-Rodriguez. Designing random", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 203, 506, 218 ], "spans": [ { "bbox": [ 115, 203, 506, 218 ], "score": 1.0, "content": "graph models using variational autoencoders with applications to chemical design. arXiv preprint", "type": "text" } ], "index": 9 }, { "bbox": [ 115, 215, 220, 227 ], "spans": [ { "bbox": [ 115, 215, 220, 227 ], "score": 1.0, "content": "arXiv:1802.05283, 2018.", "type": "text" } ], "index": 10 } ], "index": 9 }, { "type": "text", "bbox": [ 106, 233, 505, 257 ], "lines": [ { "bbox": [ 106, 233, 506, 246 ], "spans": [ { "bbox": [ 106, 233, 506, 246 ], "score": 1.0, "content": "Prithviraj Sen, Galileo Namata, Mustafa Bilgic, Lise Getoor, Brian Galligher, and Tina Eliassi-Rad.", "type": "text" } ], "index": 11 }, { "bbox": [ 116, 244, 416, 257 ], "spans": [ { "bbox": [ 116, 244, 416, 257 ], "score": 1.0, "content": "Collective classification in network data. AI magazine, 29(3):93–93, 2008.", "type": "text" } ], "index": 12 } ], "index": 11.5 }, { "type": "text", "bbox": [ 108, 263, 504, 286 ], "lines": [ { "bbox": [ 106, 264, 505, 275 ], "spans": [ { "bbox": [ 106, 264, 505, 275 ], "score": 1.0, "content": "Oleksandr Shchur, Maximilian Mumme, Aleksandar Bojchevski, and Stephan Günnemann. Pitfalls", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 275, 424, 286 ], "spans": [ { "bbox": [ 115, 275, 424, 286 ], "score": 1.0, "content": "of graph neural network evaluation. arXiv preprint arXiv:1811.05868, 2018.", "type": "text" } ], "index": 14 } ], "index": 13.5 }, { "type": "text", "bbox": [ 106, 292, 505, 326 ], "lines": [ { "bbox": [ 106, 293, 505, 305 ], "spans": [ { "bbox": [ 106, 293, 505, 305 ], "score": 1.0, "content": "Chence Shi, Minkai Xu, Hongyu Guo, Ming Zhang, and Jian Tang. A graph to graphs framework", "type": "text" } ], "index": 15 }, { "bbox": [ 116, 304, 506, 316 ], "spans": [ { "bbox": [ 116, 304, 506, 316 ], "score": 1.0, "content": "for retrosynthesis prediction. In International Conference on Machine Learning, pp. 8818–8827.", "type": "text" } ], "index": 16 }, { "bbox": [ 116, 315, 173, 326 ], "spans": [ { "bbox": [ 116, 315, 173, 326 ], "score": 1.0, "content": "PMLR, 2020.", "type": "text" } ], "index": 17 } ], "index": 16 }, { "type": "text", "bbox": [ 106, 333, 504, 356 ], "lines": [ { "bbox": [ 105, 332, 506, 347 ], "spans": [ { "bbox": [ 105, 332, 506, 347 ], "score": 1.0, "content": "Connor Shorten and Taghi M Khoshgoftaar. A survey on image data augmentation for deep learning.", "type": "text" } ], "index": 18 }, { "bbox": [ 115, 345, 270, 356 ], "spans": [ { "bbox": [ 115, 345, 270, 356 ], "score": 1.0, "content": "Journal of Big Data, 6(1):1–48, 2019.", "type": "text" } ], "index": 19 } ], "index": 18.5 }, { "type": "text", "bbox": [ 106, 362, 506, 397 ], "lines": [ { "bbox": [ 105, 361, 506, 377 ], "spans": [ { "bbox": [ 105, 361, 506, 377 ], "score": 1.0, "content": "Martin Simonovsky and Nikos Komodakis. Graphvae: Towards generation of small graphs using", "type": "text" } ], "index": 20 }, { "bbox": [ 116, 374, 507, 387 ], "spans": [ { "bbox": [ 116, 374, 507, 387 ], "score": 1.0, "content": "variational autoencoders. In International Conference on Artificial Neural Networks, pp. 412–422.", "type": "text" } ], "index": 21 }, { "bbox": [ 115, 385, 181, 398 ], "spans": [ { "bbox": [ 115, 385, 181, 398 ], "score": 1.0, "content": "Springer, 2018.", "type": "text" } ], "index": 22 } ], "index": 21 }, { "type": "text", "bbox": [ 107, 403, 506, 437 ], "lines": [ { "bbox": [ 105, 402, 505, 417 ], "spans": [ { "bbox": [ 105, 402, 505, 417 ], "score": 1.0, "content": "Kihyuk Sohn, Honglak Lee, and Xinchen Yan. Learning structured output representation using deep", "type": "text" } ], "index": 23 }, { "bbox": [ 115, 415, 506, 427 ], "spans": [ { "bbox": [ 115, 415, 506, 427 ], "score": 1.0, "content": "conditional generative models. Advances in neural information processing systems, 28:3483–3491,", "type": "text" } ], "index": 24 }, { "bbox": [ 115, 425, 142, 437 ], "spans": [ { "bbox": [ 115, 425, 142, 437 ], "score": 1.0, "content": "2015.", "type": "text" } ], "index": 25 } ], "index": 24 }, { "type": "text", "bbox": [ 107, 443, 506, 478 ], "lines": [ { "bbox": [ 106, 444, 504, 457 ], "spans": [ { "bbox": [ 106, 444, 504, 457 ], "score": 1.0, "content": "Jie Tang, Jimeng Sun, Chi Wang, and Zi Yang. Social influence analysis in large-scale networks. In", "type": "text" } ], "index": 26 }, { "bbox": [ 115, 454, 505, 468 ], "spans": [ { "bbox": [ 115, 454, 505, 468 ], "score": 1.0, "content": "Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 466, 230, 479 ], "spans": [ { "bbox": [ 115, 466, 230, 479 ], "score": 1.0, "content": "mining, pp. 807–816, 2009.", "type": "text" } ], "index": 28 } ], "index": 27 }, { "type": "text", "bbox": [ 106, 484, 506, 518 ], "lines": [ { "bbox": [ 105, 483, 505, 498 ], "spans": [ { "bbox": [ 105, 483, 505, 498 ], "score": 1.0, "content": "Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua ´", "type": "text" } ], "index": 29 }, { "bbox": [ 115, 496, 506, 509 ], "spans": [ { "bbox": [ 115, 496, 506, 509 ], "score": 1.0, "content": "Bengio. Graph attention networks. In International Conference on Learning Representations,", "type": "text" } ], "index": 30 }, { "bbox": [ 115, 506, 143, 519 ], "spans": [ { "bbox": [ 115, 506, 143, 519 ], "score": 1.0, "content": "2018.", "type": "text" } ], "index": 31 } ], "index": 30 }, { "type": "text", "bbox": [ 106, 524, 506, 559 ], "lines": [ { "bbox": [ 105, 524, 506, 538 ], "spans": [ { "bbox": [ 105, 524, 506, 538 ], "score": 1.0, "content": "Haibo Wang, Chuan Zhou, Xin Chen, Jia Wu, Shirui Pan, and Jilong Wang. Graph stochastic neural", "type": "text" } ], "index": 32 }, { "bbox": [ 115, 535, 506, 550 ], "spans": [ { "bbox": [ 115, 535, 506, 550 ], "score": 1.0, "content": "networks for semi-supervised learning. In Advances in Neural Information Processing Systems,", "type": "text" } ], "index": 33 }, { "bbox": [ 115, 545, 147, 560 ], "spans": [ { "bbox": [ 115, 545, 147, 560 ], "score": 1.0, "content": "2020a.", "type": "text" } ], "index": 34 } ], "index": 33 }, { "type": "text", "bbox": [ 107, 565, 506, 610 ], "lines": [ { "bbox": [ 105, 565, 506, 579 ], "spans": [ { "bbox": [ 105, 565, 506, 579 ], "score": 1.0, "content": "Minjie Wang, Da Zheng, Zihao Ye, Quan Gan, Mufei Li, Xiang Song, Jinjing Zhou, Chao Ma,", "type": "text" } ], "index": 35 }, { "bbox": [ 114, 576, 507, 590 ], "spans": [ { "bbox": [ 114, 576, 507, 590 ], "score": 1.0, "content": "Lingfan Yu, Yu Gai, Tianjun Xiao, Tong He, George Karypis, Jinyang Li, and Zheng Zhang.", "type": "text" } ], "index": 36 }, { "bbox": [ 115, 587, 506, 602 ], "spans": [ { "bbox": [ 115, 587, 506, 602 ], "score": 1.0, "content": "Deep graph library: A graph-centric, highly-performant package for graph neural networks. arXiv", "type": "text" } ], "index": 37 }, { "bbox": [ 114, 599, 254, 610 ], "spans": [ { "bbox": [ 114, 599, 254, 610 ], "score": 1.0, "content": "preprint arXiv:1909.01315, 2019.", "type": "text" } ], "index": 38 } ], "index": 36.5 }, { "type": "text", "bbox": [ 108, 617, 505, 651 ], "lines": [ { "bbox": [ 105, 615, 507, 632 ], "spans": [ { "bbox": [ 105, 615, 507, 632 ], "score": 1.0, "content": "Yiwei Wang, Wei Wang, Yuxuan Liang, Yujun Cai, Juncheng Liu, and Bryan Hooi. Nodeaug:", "type": "text" } ], "index": 39 }, { "bbox": [ 116, 629, 505, 641 ], "spans": [ { "bbox": [ 116, 629, 505, 641 ], "score": 1.0, "content": "Semi-supervised node classification with data augmentation. In Proceedings of the 26th ACM", "type": "text" } ], "index": 40 }, { "bbox": [ 115, 639, 507, 653 ], "spans": [ { "bbox": [ 115, 639, 507, 653 ], "score": 1.0, "content": "SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 207–217, 2020b.", "type": "text" } ], "index": 41 } ], "index": 40 }, { "type": "text", "bbox": [ 105, 657, 505, 681 ], "lines": [ { "bbox": [ 107, 658, 505, 670 ], "spans": [ { "bbox": [ 107, 658, 505, 670 ], "score": 1.0, "content": "Yu Wang and Tyler Derr. Tree decomposed graph neural network. In Proceedings of the 30th ACM", "type": "text" } ], "index": 42 }, { "bbox": [ 116, 669, 487, 682 ], "spans": [ { "bbox": [ 116, 669, 487, 682 ], "score": 1.0, "content": "International Conference on Information & Knowledge Management, pp. 2040–2049, 2021.", "type": "text" } ], "index": 43 } ], "index": 42.5 }, { "type": "text", "bbox": [ 107, 687, 506, 731 ], "lines": [ { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "Da Xu, Chuanwei Ruan, Kamiya Motwani, Evren Korpeoglu, Sushant Kumar, and Kannan Achan.", "type": "text" } ], "index": 44 }, { "bbox": [ 115, 698, 507, 711 ], "spans": [ { "bbox": [ 115, 698, 507, 711 ], "score": 1.0, "content": "Generative graph convolutional network for growing graphs. In ICASSP 2019-2019 IEEE Interna-", "type": "text" } ], "index": 45 }, { "bbox": [ 114, 709, 508, 723 ], "spans": [ { "bbox": [ 114, 709, 508, 723 ], "score": 1.0, "content": "tional Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3167–3171. IEEE,", "type": "text" } ], "index": 46 }, { "bbox": [ 115, 719, 143, 733 ], "spans": [ { "bbox": [ 115, 719, 143, 733 ], "score": 1.0, "content": "2019.", "type": "text" } ], "index": 47 } ], "index": 45.5 } ], "page_idx": 11, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 300, 751, 311, 760 ], "lines": [ { "bbox": [ 299, 750, 312, 764 ], "spans": [ { "bbox": [ 299, 750, 312, 764 ], "score": 1.0, "content": "12", "type": "text" } ] } ] }, { "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 2022", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 107, 82, 505, 116 ], "lines": [ { "bbox": [ 105, 81, 506, 96 ], "spans": [ { "bbox": [ 105, 81, 506, 96 ], "score": 1.0, "content": "Yu Rong, Wenbing Huang, Tingyang Xu, and Junzhou Huang. Dropedge: Towards deep graph convo-", "type": "text" } ], "index": 0 }, { "bbox": [ 115, 93, 506, 106 ], "spans": [ { "bbox": [ 115, 93, 506, 106 ], "score": 1.0, "content": "lutional networks on node classification. In International Conference on Learning Representation,", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 104, 141, 116 ], "spans": [ { "bbox": [ 115, 104, 141, 116 ], "score": 1.0, "content": "2020.", "type": "text" } ], "index": 2 } ], "index": 1, "bbox_fs": [ 105, 81, 506, 116 ] }, { "type": "text", "bbox": [ 106, 123, 504, 145 ], "lines": [ { "bbox": [ 106, 123, 505, 135 ], "spans": [ { "bbox": [ 106, 123, 505, 135 ], "score": 1.0, "content": "Benedek Rozemberczki, Carl Allen, and Rik Sarkar. Multi-scale attributed node embedding. Journal", "type": "text" } ], "index": 3 }, { "bbox": [ 116, 134, 290, 146 ], "spans": [ { "bbox": [ 116, 134, 290, 146 ], "score": 1.0, "content": "of Complex Networks, 9(2):cnab014, 2021.", "type": "text" } ], "index": 4 } ], "index": 3.5, "bbox_fs": [ 106, 123, 505, 146 ] }, { "type": "text", "bbox": [ 107, 152, 504, 186 ], "lines": [ { "bbox": [ 106, 152, 506, 165 ], "spans": [ { "bbox": [ 106, 152, 506, 165 ], "score": 1.0, "content": "Guillaume Salha, Romain Hennequin, and Michalis Vazirgiannis. Keep it simple: Graph autoen-", "type": "text" } ], "index": 5 }, { "bbox": [ 116, 164, 505, 176 ], "spans": [ { "bbox": [ 116, 164, 505, 176 ], "score": 1.0, "content": "coders without graph convolutional networks. Workshop on Graph Representation Learning, 33rd", "type": "text" } ], "index": 6 }, { "bbox": [ 116, 174, 410, 187 ], "spans": [ { "bbox": [ 116, 174, 410, 187 ], "score": 1.0, "content": "Conference on Neural Information Processing Systems (NeurIPS), 2019.", "type": "text" } ], "index": 7 } ], "index": 6, "bbox_fs": [ 106, 152, 506, 187 ] }, { "type": "text", "bbox": [ 106, 192, 505, 227 ], "lines": [ { "bbox": [ 106, 192, 505, 206 ], "spans": [ { "bbox": [ 106, 192, 505, 206 ], "score": 1.0, "content": "Bidisha Samanta, Abir De, Niloy Ganguly, and Manuel Gomez-Rodriguez. Designing random", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 203, 506, 218 ], "spans": [ { "bbox": [ 115, 203, 506, 218 ], "score": 1.0, "content": "graph models using variational autoencoders with applications to chemical design. arXiv preprint", "type": "text" } ], "index": 9 }, { "bbox": [ 115, 215, 220, 227 ], "spans": [ { "bbox": [ 115, 215, 220, 227 ], "score": 1.0, "content": "arXiv:1802.05283, 2018.", "type": "text" } ], "index": 10 } ], "index": 9, "bbox_fs": [ 106, 192, 506, 227 ] }, { "type": "text", "bbox": [ 106, 233, 505, 257 ], "lines": [ { "bbox": [ 106, 233, 506, 246 ], "spans": [ { "bbox": [ 106, 233, 506, 246 ], "score": 1.0, "content": "Prithviraj Sen, Galileo Namata, Mustafa Bilgic, Lise Getoor, Brian Galligher, and Tina Eliassi-Rad.", "type": "text" } ], "index": 11 }, { "bbox": [ 116, 244, 416, 257 ], "spans": [ { "bbox": [ 116, 244, 416, 257 ], "score": 1.0, "content": "Collective classification in network data. AI magazine, 29(3):93–93, 2008.", "type": "text" } ], "index": 12 } ], "index": 11.5, "bbox_fs": [ 106, 233, 506, 257 ] }, { "type": "text", "bbox": [ 108, 263, 504, 286 ], "lines": [ { "bbox": [ 106, 264, 505, 275 ], "spans": [ { "bbox": [ 106, 264, 505, 275 ], "score": 1.0, "content": "Oleksandr Shchur, Maximilian Mumme, Aleksandar Bojchevski, and Stephan Günnemann. Pitfalls", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 275, 424, 286 ], "spans": [ { "bbox": [ 115, 275, 424, 286 ], "score": 1.0, "content": "of graph neural network evaluation. arXiv preprint arXiv:1811.05868, 2018.", "type": "text" } ], "index": 14 } ], "index": 13.5, "bbox_fs": [ 106, 264, 505, 286 ] }, { "type": "text", "bbox": [ 106, 292, 505, 326 ], "lines": [ { "bbox": [ 106, 293, 505, 305 ], "spans": [ { "bbox": [ 106, 293, 505, 305 ], "score": 1.0, "content": "Chence Shi, Minkai Xu, Hongyu Guo, Ming Zhang, and Jian Tang. A graph to graphs framework", "type": "text" } ], "index": 15 }, { "bbox": [ 116, 304, 506, 316 ], "spans": [ { "bbox": [ 116, 304, 506, 316 ], "score": 1.0, "content": "for retrosynthesis prediction. In International Conference on Machine Learning, pp. 8818–8827.", "type": "text" } ], "index": 16 }, { "bbox": [ 116, 315, 173, 326 ], "spans": [ { "bbox": [ 116, 315, 173, 326 ], "score": 1.0, "content": "PMLR, 2020.", "type": "text" } ], "index": 17 } ], "index": 16, "bbox_fs": [ 106, 293, 506, 326 ] }, { "type": "text", "bbox": [ 106, 333, 504, 356 ], "lines": [ { "bbox": [ 105, 332, 506, 347 ], "spans": [ { "bbox": [ 105, 332, 506, 347 ], "score": 1.0, "content": "Connor Shorten and Taghi M Khoshgoftaar. A survey on image data augmentation for deep learning.", "type": "text" } ], "index": 18 }, { "bbox": [ 115, 345, 270, 356 ], "spans": [ { "bbox": [ 115, 345, 270, 356 ], "score": 1.0, "content": "Journal of Big Data, 6(1):1–48, 2019.", "type": "text" } ], "index": 19 } ], "index": 18.5, "bbox_fs": [ 105, 332, 506, 356 ] }, { "type": "text", "bbox": [ 106, 362, 506, 397 ], "lines": [ { "bbox": [ 105, 361, 506, 377 ], "spans": [ { "bbox": [ 105, 361, 506, 377 ], "score": 1.0, "content": "Martin Simonovsky and Nikos Komodakis. Graphvae: Towards generation of small graphs using", "type": "text" } ], "index": 20 }, { "bbox": [ 116, 374, 507, 387 ], "spans": [ { "bbox": [ 116, 374, 507, 387 ], "score": 1.0, "content": "variational autoencoders. In International Conference on Artificial Neural Networks, pp. 412–422.", "type": "text" } ], "index": 21 }, { "bbox": [ 115, 385, 181, 398 ], "spans": [ { "bbox": [ 115, 385, 181, 398 ], "score": 1.0, "content": "Springer, 2018.", "type": "text" } ], "index": 22 } ], "index": 21, "bbox_fs": [ 105, 361, 507, 398 ] }, { "type": "text", "bbox": [ 107, 403, 506, 437 ], "lines": [ { "bbox": [ 105, 402, 505, 417 ], "spans": [ { "bbox": [ 105, 402, 505, 417 ], "score": 1.0, "content": "Kihyuk Sohn, Honglak Lee, and Xinchen Yan. Learning structured output representation using deep", "type": "text" } ], "index": 23 }, { "bbox": [ 115, 415, 506, 427 ], "spans": [ { "bbox": [ 115, 415, 506, 427 ], "score": 1.0, "content": "conditional generative models. Advances in neural information processing systems, 28:3483–3491,", "type": "text" } ], "index": 24 }, { "bbox": [ 115, 425, 142, 437 ], "spans": [ { "bbox": [ 115, 425, 142, 437 ], "score": 1.0, "content": "2015.", "type": "text" } ], "index": 25 } ], "index": 24, "bbox_fs": [ 105, 402, 506, 437 ] }, { "type": "text", "bbox": [ 107, 443, 506, 478 ], "lines": [ { "bbox": [ 106, 444, 504, 457 ], "spans": [ { "bbox": [ 106, 444, 504, 457 ], "score": 1.0, "content": "Jie Tang, Jimeng Sun, Chi Wang, and Zi Yang. Social influence analysis in large-scale networks. In", "type": "text" } ], "index": 26 }, { "bbox": [ 115, 454, 505, 468 ], "spans": [ { "bbox": [ 115, 454, 505, 468 ], "score": 1.0, "content": "Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 466, 230, 479 ], "spans": [ { "bbox": [ 115, 466, 230, 479 ], "score": 1.0, "content": "mining, pp. 807–816, 2009.", "type": "text" } ], "index": 28 } ], "index": 27, "bbox_fs": [ 106, 444, 505, 479 ] }, { "type": "text", "bbox": [ 106, 484, 506, 518 ], "lines": [ { "bbox": [ 105, 483, 505, 498 ], "spans": [ { "bbox": [ 105, 483, 505, 498 ], "score": 1.0, "content": "Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua ´", "type": "text" } ], "index": 29 }, { "bbox": [ 115, 496, 506, 509 ], "spans": [ { "bbox": [ 115, 496, 506, 509 ], "score": 1.0, "content": "Bengio. Graph attention networks. In International Conference on Learning Representations,", "type": "text" } ], "index": 30 }, { "bbox": [ 115, 506, 143, 519 ], "spans": [ { "bbox": [ 115, 506, 143, 519 ], "score": 1.0, "content": "2018.", "type": "text" } ], "index": 31 } ], "index": 30, "bbox_fs": [ 105, 483, 506, 519 ] }, { "type": "text", "bbox": [ 106, 524, 506, 559 ], "lines": [ { "bbox": [ 105, 524, 506, 538 ], "spans": [ { "bbox": [ 105, 524, 506, 538 ], "score": 1.0, "content": "Haibo Wang, Chuan Zhou, Xin Chen, Jia Wu, Shirui Pan, and Jilong Wang. Graph stochastic neural", "type": "text" } ], "index": 32 }, { "bbox": [ 115, 535, 506, 550 ], "spans": [ { "bbox": [ 115, 535, 506, 550 ], "score": 1.0, "content": "networks for semi-supervised learning. In Advances in Neural Information Processing Systems,", "type": "text" } ], "index": 33 }, { "bbox": [ 115, 545, 147, 560 ], "spans": [ { "bbox": [ 115, 545, 147, 560 ], "score": 1.0, "content": "2020a.", "type": "text" } ], "index": 34 } ], "index": 33, "bbox_fs": [ 105, 524, 506, 560 ] }, { "type": "text", "bbox": [ 107, 565, 506, 610 ], "lines": [ { "bbox": [ 105, 565, 506, 579 ], "spans": [ { "bbox": [ 105, 565, 506, 579 ], "score": 1.0, "content": "Minjie Wang, Da Zheng, Zihao Ye, Quan Gan, Mufei Li, Xiang Song, Jinjing Zhou, Chao Ma,", "type": "text" } ], "index": 35 }, { "bbox": [ 114, 576, 507, 590 ], "spans": [ { "bbox": [ 114, 576, 507, 590 ], "score": 1.0, "content": "Lingfan Yu, Yu Gai, Tianjun Xiao, Tong He, George Karypis, Jinyang Li, and Zheng Zhang.", "type": "text" } ], "index": 36 }, { "bbox": [ 115, 587, 506, 602 ], "spans": [ { "bbox": [ 115, 587, 506, 602 ], "score": 1.0, "content": "Deep graph library: A graph-centric, highly-performant package for graph neural networks. arXiv", "type": "text" } ], "index": 37 }, { "bbox": [ 114, 599, 254, 610 ], "spans": [ { "bbox": [ 114, 599, 254, 610 ], "score": 1.0, "content": "preprint arXiv:1909.01315, 2019.", "type": "text" } ], "index": 38 } ], "index": 36.5, "bbox_fs": [ 105, 565, 507, 610 ] }, { "type": "text", "bbox": [ 108, 617, 505, 651 ], "lines": [ { "bbox": [ 105, 615, 507, 632 ], "spans": [ { "bbox": [ 105, 615, 507, 632 ], "score": 1.0, "content": "Yiwei Wang, Wei Wang, Yuxuan Liang, Yujun Cai, Juncheng Liu, and Bryan Hooi. Nodeaug:", "type": "text" } ], "index": 39 }, { "bbox": [ 116, 629, 505, 641 ], "spans": [ { "bbox": [ 116, 629, 505, 641 ], "score": 1.0, "content": "Semi-supervised node classification with data augmentation. In Proceedings of the 26th ACM", "type": "text" } ], "index": 40 }, { "bbox": [ 115, 639, 507, 653 ], "spans": [ { "bbox": [ 115, 639, 507, 653 ], "score": 1.0, "content": "SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 207–217, 2020b.", "type": "text" } ], "index": 41 } ], "index": 40, "bbox_fs": [ 105, 615, 507, 653 ] }, { "type": "text", "bbox": [ 105, 657, 505, 681 ], "lines": [ { "bbox": [ 107, 658, 505, 670 ], "spans": [ { "bbox": [ 107, 658, 505, 670 ], "score": 1.0, "content": "Yu Wang and Tyler Derr. Tree decomposed graph neural network. In Proceedings of the 30th ACM", "type": "text" } ], "index": 42 }, { "bbox": [ 116, 669, 487, 682 ], "spans": [ { "bbox": [ 116, 669, 487, 682 ], "score": 1.0, "content": "International Conference on Information & Knowledge Management, pp. 2040–2049, 2021.", "type": "text" } ], "index": 43 } ], "index": 42.5, "bbox_fs": [ 107, 658, 505, 682 ] }, { "type": "text", "bbox": [ 107, 687, 506, 731 ], "lines": [ { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "Da Xu, Chuanwei Ruan, Kamiya Motwani, Evren Korpeoglu, Sushant Kumar, and Kannan Achan.", "type": "text" } ], "index": 44 }, { "bbox": [ 115, 698, 507, 711 ], "spans": [ { "bbox": [ 115, 698, 507, 711 ], "score": 1.0, "content": "Generative graph convolutional network for growing graphs. In ICASSP 2019-2019 IEEE Interna-", "type": "text" } ], "index": 45 }, { "bbox": [ 114, 709, 508, 723 ], "spans": [ { "bbox": [ 114, 709, 508, 723 ], "score": 1.0, "content": "tional Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3167–3171. IEEE,", "type": "text" } ], "index": 46 }, { "bbox": [ 115, 719, 143, 733 ], "spans": [ { "bbox": [ 115, 719, 143, 733 ], "score": 1.0, "content": "2019.", "type": "text" } ], "index": 47 } ], "index": 45.5, "bbox_fs": [ 105, 687, 508, 733 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 108, 82, 504, 116 ], "lines": [ { "bbox": [ 106, 82, 506, 96 ], "spans": [ { "bbox": [ 106, 82, 506, 96 ], "score": 1.0, "content": "Keyulu Xu, Chengtao Li, Yonglong Tian, Tomohiro Sonobe, Ken-ichi Kawarabayashi, and Stefanie", "type": "text" } ], "index": 0 }, { "bbox": [ 115, 93, 505, 106 ], "spans": [ { "bbox": [ 115, 93, 505, 106 ], "score": 1.0, "content": "Jegelka. Representation learning on graphs with jumping knowledge networks. In International", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 104, 378, 118 ], "spans": [ { "bbox": [ 115, 104, 378, 118 ], "score": 1.0, "content": "Conference on Machine Learning, pp. 5453–5462. PMLR, 2018.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "text", "bbox": [ 106, 123, 504, 146 ], "lines": [ { "bbox": [ 106, 122, 505, 136 ], "spans": [ { "bbox": [ 106, 122, 505, 136 ], "score": 1.0, "content": "Carl Yang, Peiye Zhuang, Wenhan Shi, Alan Luu, and Pan Li. Conditional structure generation", "type": "text" } ], "index": 3 }, { "bbox": [ 116, 135, 471, 146 ], "spans": [ { "bbox": [ 116, 135, 471, 146 ], "score": 1.0, "content": "through graph variational generative adversarial nets. In NeurIPS, pp. 1338–1349, 2019.", "type": "text" } ], "index": 4 } ], "index": 3.5 }, { "type": "text", "bbox": [ 106, 153, 504, 176 ], "lines": [ { "bbox": [ 106, 153, 505, 166 ], "spans": [ { "bbox": [ 106, 153, 505, 166 ], "score": 1.0, "content": "Zhilin Yang, William Cohen, and Ruslan Salakhudinov. Revisiting semi-supervised learning with", "type": "text" } ], "index": 5 }, { "bbox": [ 115, 164, 471, 177 ], "spans": [ { "bbox": [ 115, 164, 471, 177 ], "score": 1.0, "content": "graph embeddings. In International Conference on Machine Learning, pp. 40–48, 2016.", "type": "text" } ], "index": 6 } ], "index": 5.5 }, { "type": "text", "bbox": [ 106, 182, 507, 227 ], "lines": [ { "bbox": [ 105, 183, 507, 196 ], "spans": [ { "bbox": [ 105, 183, 507, 196 ], "score": 1.0, "content": "Rex Ying, Ruining He, Kaifeng Chen, Pong Eksombatchai, William L Hamilton, and Jure Leskovec.", "type": "text" } ], "index": 7 }, { "bbox": [ 115, 193, 507, 207 ], "spans": [ { "bbox": [ 115, 193, 507, 207 ], "score": 1.0, "content": "Graph convolutional neural networks for web-scale recommender systems. In Proceedings of", "type": "text" } ], "index": 8 }, { "bbox": [ 114, 204, 507, 219 ], "spans": [ { "bbox": [ 114, 204, 507, 219 ], "score": 1.0, "content": "the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp.", "type": "text" } ], "index": 9 }, { "bbox": [ 116, 217, 181, 227 ], "spans": [ { "bbox": [ 116, 217, 181, 227 ], "score": 1.0, "content": "974–983, 2018.", "type": "text" } ], "index": 10 } ], "index": 8.5 }, { "type": "text", "bbox": [ 107, 234, 506, 268 ], "lines": [ { "bbox": [ 105, 234, 506, 248 ], "spans": [ { "bbox": [ 105, 234, 506, 248 ], "score": 1.0, "content": "Hanqing Zeng, Muhan Zhang, Yinglong Xia, Ajitesh Srivastava, Andrey Malevich, Rajgopal Kannan,", "type": "text" } ], "index": 11 }, { "bbox": [ 117, 245, 505, 258 ], "spans": [ { "bbox": [ 117, 245, 505, 258 ], "score": 1.0, "content": "Viktor Prasanna, Long Jin, and Ren Chen. Decoupling the depth and scope of graph neural", "type": "text" } ], "index": 12 }, { "bbox": [ 115, 257, 468, 269 ], "spans": [ { "bbox": [ 115, 257, 468, 269 ], "score": 1.0, "content": "networks. In Thirty-Fifth Conference on Neural Information Processing Systems, 2021.", "type": "text" } ], "index": 13 } ], "index": 12 }, { "type": "text", "bbox": [ 107, 275, 506, 309 ], "lines": [ { "bbox": [ 105, 275, 506, 289 ], "spans": [ { "bbox": [ 105, 275, 506, 289 ], "score": 1.0, "content": "Tong Zhao, Yozen Liu, Leonardo Neves, Oliver Woodford, Meng Jiang, and Neil Shah. Data", "type": "text" } ], "index": 14 }, { "bbox": [ 116, 286, 505, 299 ], "spans": [ { "bbox": [ 116, 286, 505, 299 ], "score": 1.0, "content": "augmentation for graph neural networks. In The Thirty-Fifth AAAI Conference on Artificial", "type": "text" } ], "index": 15 }, { "bbox": [ 116, 297, 194, 310 ], "spans": [ { "bbox": [ 116, 297, 194, 310 ], "score": 1.0, "content": "Intelligence, 2021.", "type": "text" } ], "index": 16 } ], "index": 15 }, { "type": "text", "bbox": [ 106, 316, 505, 339 ], "lines": [ { "bbox": [ 106, 316, 505, 329 ], "spans": [ { "bbox": [ 106, 316, 505, 329 ], "score": 1.0, "content": "Danhao Zhu, Xin-Yu Dai, and Jiajun Chen. Pre-train and learn: Preserve global information for", "type": "text" } ], "index": 17 }, { "bbox": [ 115, 327, 498, 341 ], "spans": [ { "bbox": [ 115, 327, 498, 341 ], "score": 1.0, "content": "graph neural networks. In Proceedings of the AAAI Conference on Artificial Intelligence, 2020.", "type": "text" } ], "index": 18 } ], "index": 17.5 }, { "type": "text", "bbox": [ 107, 346, 505, 369 ], "lines": [ { "bbox": [ 105, 345, 505, 360 ], "spans": [ { "bbox": [ 105, 345, 505, 360 ], "score": 1.0, "content": "Hao Zhu and Piotr Koniusz. Simple spectral graph convolution. In International Conference on", "type": "text" } ], "index": 19 }, { "bbox": [ 115, 357, 249, 370 ], "spans": [ { "bbox": [ 115, 357, 249, 370 ], "score": 1.0, "content": "Learning Representations, 2021.", "type": "text" } ], "index": 20 } ], "index": 19.5 } ], "page_idx": 12, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 300, 751, 310, 760 ], "lines": [ { "bbox": [ 299, 750, 312, 764 ], "spans": [ { "bbox": [ 299, 750, 312, 764 ], "score": 1.0, "content": "", "type": "text", "height": 14, "width": 13 } ] } ] }, { "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 2022", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 108, 82, 504, 116 ], "lines": [ { "bbox": [ 106, 82, 506, 96 ], "spans": [ { "bbox": [ 106, 82, 506, 96 ], "score": 1.0, "content": "Keyulu Xu, Chengtao Li, Yonglong Tian, Tomohiro Sonobe, Ken-ichi Kawarabayashi, and Stefanie", "type": "text" } ], "index": 0 }, { "bbox": [ 115, 93, 505, 106 ], "spans": [ { "bbox": [ 115, 93, 505, 106 ], "score": 1.0, "content": "Jegelka. Representation learning on graphs with jumping knowledge networks. In International", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 104, 378, 118 ], "spans": [ { "bbox": [ 115, 104, 378, 118 ], "score": 1.0, "content": "Conference on Machine Learning, pp. 5453–5462. PMLR, 2018.", "type": "text" } ], "index": 2 } ], "index": 1, "bbox_fs": [ 106, 82, 506, 118 ] }, { "type": "text", "bbox": [ 106, 123, 504, 146 ], "lines": [ { "bbox": [ 106, 122, 505, 136 ], "spans": [ { "bbox": [ 106, 122, 505, 136 ], "score": 1.0, "content": "Carl Yang, Peiye Zhuang, Wenhan Shi, Alan Luu, and Pan Li. Conditional structure generation", "type": "text" } ], "index": 3 }, { "bbox": [ 116, 135, 471, 146 ], "spans": [ { "bbox": [ 116, 135, 471, 146 ], "score": 1.0, "content": "through graph variational generative adversarial nets. In NeurIPS, pp. 1338–1349, 2019.", "type": "text" } ], "index": 4 } ], "index": 3.5, "bbox_fs": [ 106, 122, 505, 146 ] }, { "type": "text", "bbox": [ 106, 153, 504, 176 ], "lines": [ { "bbox": [ 106, 153, 505, 166 ], "spans": [ { "bbox": [ 106, 153, 505, 166 ], "score": 1.0, "content": "Zhilin Yang, William Cohen, and Ruslan Salakhudinov. Revisiting semi-supervised learning with", "type": "text" } ], "index": 5 }, { "bbox": [ 115, 164, 471, 177 ], "spans": [ { "bbox": [ 115, 164, 471, 177 ], "score": 1.0, "content": "graph embeddings. In International Conference on Machine Learning, pp. 40–48, 2016.", "type": "text" } ], "index": 6 } ], "index": 5.5, "bbox_fs": [ 106, 153, 505, 177 ] }, { "type": "text", "bbox": [ 106, 182, 507, 227 ], "lines": [ { "bbox": [ 105, 183, 507, 196 ], "spans": [ { "bbox": [ 105, 183, 507, 196 ], "score": 1.0, "content": "Rex Ying, Ruining He, Kaifeng Chen, Pong Eksombatchai, William L Hamilton, and Jure Leskovec.", "type": "text" } ], "index": 7 }, { "bbox": [ 115, 193, 507, 207 ], "spans": [ { "bbox": [ 115, 193, 507, 207 ], "score": 1.0, "content": "Graph convolutional neural networks for web-scale recommender systems. In Proceedings of", "type": "text" } ], "index": 8 }, { "bbox": [ 114, 204, 507, 219 ], "spans": [ { "bbox": [ 114, 204, 507, 219 ], "score": 1.0, "content": "the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp.", "type": "text" } ], "index": 9 }, { "bbox": [ 116, 217, 181, 227 ], "spans": [ { "bbox": [ 116, 217, 181, 227 ], "score": 1.0, "content": "974–983, 2018.", "type": "text" } ], "index": 10 } ], "index": 8.5, "bbox_fs": [ 105, 183, 507, 227 ] }, { "type": "text", "bbox": [ 107, 234, 506, 268 ], "lines": [ { "bbox": [ 105, 234, 506, 248 ], "spans": [ { "bbox": [ 105, 234, 506, 248 ], "score": 1.0, "content": "Hanqing Zeng, Muhan Zhang, Yinglong Xia, Ajitesh Srivastava, Andrey Malevich, Rajgopal Kannan,", "type": "text" } ], "index": 11 }, { "bbox": [ 117, 245, 505, 258 ], "spans": [ { "bbox": [ 117, 245, 505, 258 ], "score": 1.0, "content": "Viktor Prasanna, Long Jin, and Ren Chen. Decoupling the depth and scope of graph neural", "type": "text" } ], "index": 12 }, { "bbox": [ 115, 257, 468, 269 ], "spans": [ { "bbox": [ 115, 257, 468, 269 ], "score": 1.0, "content": "networks. In Thirty-Fifth Conference on Neural Information Processing Systems, 2021.", "type": "text" } ], "index": 13 } ], "index": 12, "bbox_fs": [ 105, 234, 506, 269 ] }, { "type": "text", "bbox": [ 107, 275, 506, 309 ], "lines": [ { "bbox": [ 105, 275, 506, 289 ], "spans": [ { "bbox": [ 105, 275, 506, 289 ], "score": 1.0, "content": "Tong Zhao, Yozen Liu, Leonardo Neves, Oliver Woodford, Meng Jiang, and Neil Shah. Data", "type": "text" } ], "index": 14 }, { "bbox": [ 116, 286, 505, 299 ], "spans": [ { "bbox": [ 116, 286, 505, 299 ], "score": 1.0, "content": "augmentation for graph neural networks. In The Thirty-Fifth AAAI Conference on Artificial", "type": "text" } ], "index": 15 }, { "bbox": [ 116, 297, 194, 310 ], "spans": [ { "bbox": [ 116, 297, 194, 310 ], "score": 1.0, "content": "Intelligence, 2021.", "type": "text" } ], "index": 16 } ], "index": 15, "bbox_fs": [ 105, 275, 506, 310 ] }, { "type": "text", "bbox": [ 106, 316, 505, 339 ], "lines": [ { "bbox": [ 106, 316, 505, 329 ], "spans": [ { "bbox": [ 106, 316, 505, 329 ], "score": 1.0, "content": "Danhao Zhu, Xin-Yu Dai, and Jiajun Chen. Pre-train and learn: Preserve global information for", "type": "text" } ], "index": 17 }, { "bbox": [ 115, 327, 498, 341 ], "spans": [ { "bbox": [ 115, 327, 498, 341 ], "score": 1.0, "content": "graph neural networks. In Proceedings of the AAAI Conference on Artificial Intelligence, 2020.", "type": "text" } ], "index": 18 } ], "index": 17.5, "bbox_fs": [ 106, 316, 505, 341 ] }, { "type": "text", "bbox": [ 107, 346, 505, 369 ], "lines": [ { "bbox": [ 105, 345, 505, 360 ], "spans": [ { "bbox": [ 105, 345, 505, 360 ], "score": 1.0, "content": "Hao Zhu and Piotr Koniusz. Simple spectral graph convolution. In International Conference on", "type": "text" } ], "index": 19 }, { "bbox": [ 115, 357, 249, 370 ], "spans": [ { "bbox": [ 115, 357, 249, 370 ], "score": 1.0, "content": "Learning Representations, 2021.", "type": "text" } ], "index": 20 } ], "index": 19.5, "bbox_fs": [ 105, 345, 505, 370 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 108, 81, 218, 94 ], "lines": [ { "bbox": [ 105, 78, 219, 97 ], "spans": [ { "bbox": [ 105, 78, 219, 97 ], "score": 1.0, "content": "A PROOF OF EQ.(6)", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 106, 105, 399, 118 ], "lines": [ { "bbox": [ 105, 106, 400, 119 ], "spans": [ { "bbox": [ 105, 106, 400, 119 ], "score": 1.0, "content": "We give more details of the derivation of the generator ELBO as follows:", "type": "text" } ], "index": 1 } ], "index": 1 }, { "type": "interline_equation", "bbox": [ 114, 128, 494, 380 ], "lines": [ { "bbox": [ 114, 128, 494, 380 ], "spans": [ { "bbox": [ 114, 128, 494, 380 ], "score": 0.9, "content": "\\begin{array} { r l } { \\log _ { \\rho } | \\mathbf { X } _ { i } | \\mathbb { X } _ { j } - j } & { \\neq \\langle z | \\mathbf { z } | \\mathbf { z } | \\mathbf { X } _ { j } , ~ \\mathbf { X } _ { i } \\rangle \\log _ { \\rho } \\langle ~ \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle \\mathrm { d } \\mathbf { z } } \\\\ & { = \\int \\langle z | \\mathbf { z } | \\mathbf { A } _ { \\mathbf { x } } \\mathbf { x } , ~ \\mathbf { X } _ { i } | \\log _ { \\rho } | \\mathbf { X } _ { i } \\mathbf { X } _ { j } | \\log _ { \\rho } \\langle ~ \\mathbf { X } _ { i } | \\mathbf { X } _ { j } , ~ \\mathbf { X } _ { i } \\rangle } \\\\ & { \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { z } | \\mathbf { X } _ { i } , ~ \\mathbf { X } _ { i } \\rangle \\log _ { \\rho } | \\langle ~ \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle \\mathrm { d } \\mathbf { z } | } \\\\ & { = \\int \\langle \\exp \\{ \\mathbf { X } _ { i } \\mathbf { X } _ { j } \\} | \\exp \\{ \\exp \\{ | \\mathbf { X } _ { i } \\mathbf { X } _ { j } | \\} \\} \\exp \\{ | \\langle \\mathbf { X } _ { i } \\mathbf { X } _ { j } , ~ \\mathbf { X } _ { i } , ~ \\mathbf { X } _ { j } | \\} \\mathrm { d } \\mathbf { z } } \\\\ & { \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { X } _ { i } \\rangle \\exp \\{ | \\langle \\mathbf { X } _ { j } | \\mathbf { X } _ { i } , ~ \\mathbf { X } _ { j } \\rangle | \\} } \\\\ & { \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { z } | \\mathrm { X } _ { i } \\rangle \\exp \\{ | \\langle \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle | \\} } \\\\ & { = \\int \\langle z | \\mathbf { z } | \\mathbf { X } _ { i } \\mathbf { X } _ { j } \\rangle \\log _ { \\rho } \\langle \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle \\exp \\{ | \\langle \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle | } \\\\ & { \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { Z } _ { j } \\rangle \\exp \\{ | \\langle \\mathbf { X } _ { j } | \\mathbf { X } _ { j } \\rangle | } \\\\ & \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { Z } _ { j } \\rangle \\exp \\{ \\end{array}", "type": "interline_equation", "image_path": "01504f03f7ada796d4cba0d38187f79fff717bd6ed61294a2986883682426937.jpg" } ] } ], "index": 3, "virtual_lines": [ { "bbox": [ 114, 128, 494, 212.0 ], "spans": [], "index": 2 }, { "bbox": [ 114, 212.0, 494, 296.0 ], "spans": [], "index": 3 }, { "bbox": [ 114, 296.0, 494, 380.0 ], "spans": [], "index": 4 } ] }, { "type": "interline_equation", "bbox": [ 126, 396, 486, 562 ], "lines": [ { "bbox": [ 126, 396, 486, 562 ], "spans": [ { "bbox": [ 126, 396, 486, 562 ], "score": 0.95, "content": "\\begin{array} { r l } { L _ { E L B O } = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\phi } ( { \\mathbf x } _ { j } , { \\mathbf X _ { i } } ) \\log } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) } } \\mathrm { d } { \\mathbf z } } \\\\ { } & { ~ = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\psi } ( { \\mathbf X _ { j } } , { \\mathbf X _ { i } } , { \\mathbf z } ) } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) p _ { \\psi } ( { \\mathbf X _ { i } } ) } } \\mathrm { d } { \\mathbf z } } \\\\ { } & { ~ = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\phi } ( { \\mathbf X _ { j } } | \\mathbf X _ { i } , { \\mathbf z } ) p _ { \\psi } ( { \\mathbf X _ { i } } , { \\mathbf z } ) } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) p _ { \\psi } ( { \\mathbf X _ { i } } ) } } \\mathrm { d } { \\mathbf z } } \\\\ { } & { ~ = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\phi } ( { \\mathbf X _ { j } } | \\mathbf X _ { i } , { \\mathbf z } ) p _ { \\psi } ( { \\mathbf z } | \\mathbf X _ { i } ) } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) } } \\mathrm { d } { \\mathbf z } } \\\\ { } & ~ = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\phi } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf z } ) p _ { \\phi } ( { \\mathbf Z } | \\mathbf X _ { i } ) } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) } } \\\\ { } & ~ = \\displaystyle { \\int } q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } \\end{array}", "type": "interline_equation", "image_path": "aa9a684ca0fb2a1ddb7fd7779680817f5be8a402f74f61f4ea0b13e88e8aae6e.jpg" } ] } ], "index": 6, "virtual_lines": [ { "bbox": [ 126, 396, 486, 451.3333333333333 ], "spans": [], "index": 5 }, { "bbox": [ 126, 451.3333333333333, 486, 506.66666666666663 ], "spans": [], "index": 6 }, { "bbox": [ 126, 506.66666666666663, 486, 562.0 ], "spans": [], "index": 7 } ] } ], "page_idx": 13, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 106, 26, 308, 38 ], "lines": [ { "bbox": [ 106, 25, 308, 39 ], "spans": [ { "bbox": [ 106, 25, 308, 39 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 300, 751, 311, 760 ], "lines": [ { "bbox": [ 299, 750, 312, 764 ], "spans": [ { "bbox": [ 299, 750, 312, 764 ], "score": 1.0, "content": "14", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 108, 81, 218, 94 ], "lines": [ { "bbox": [ 105, 78, 219, 97 ], "spans": [ { "bbox": [ 105, 78, 219, 97 ], "score": 1.0, "content": "A PROOF OF EQ.(6)", "type": "text" } ], "index": 0 } ], "index": 0, "bbox_fs": [ 105, 78, 219, 97 ] }, { "type": "text", "bbox": [ 106, 105, 399, 118 ], "lines": [ { "bbox": [ 105, 106, 400, 119 ], "spans": [ { "bbox": [ 105, 106, 400, 119 ], "score": 1.0, "content": "We give more details of the derivation of the generator ELBO as follows:", "type": "text" } ], "index": 1 } ], "index": 1, "bbox_fs": [ 105, 106, 400, 119 ] }, { "type": "interline_equation", "bbox": [ 114, 128, 494, 380 ], "lines": [ { "bbox": [ 114, 128, 494, 380 ], "spans": [ { "bbox": [ 114, 128, 494, 380 ], "score": 0.9, "content": "\\begin{array} { r l } { \\log _ { \\rho } | \\mathbf { X } _ { i } | \\mathbb { X } _ { j } - j } & { \\neq \\langle z | \\mathbf { z } | \\mathbf { z } | \\mathbf { X } _ { j } , ~ \\mathbf { X } _ { i } \\rangle \\log _ { \\rho } \\langle ~ \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle \\mathrm { d } \\mathbf { z } } \\\\ & { = \\int \\langle z | \\mathbf { z } | \\mathbf { A } _ { \\mathbf { x } } \\mathbf { x } , ~ \\mathbf { X } _ { i } | \\log _ { \\rho } | \\mathbf { X } _ { i } \\mathbf { X } _ { j } | \\log _ { \\rho } \\langle ~ \\mathbf { X } _ { i } | \\mathbf { X } _ { j } , ~ \\mathbf { X } _ { i } \\rangle } \\\\ & { \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { z } | \\mathbf { X } _ { i } , ~ \\mathbf { X } _ { i } \\rangle \\log _ { \\rho } | \\langle ~ \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle \\mathrm { d } \\mathbf { z } | } \\\\ & { = \\int \\langle \\exp \\{ \\mathbf { X } _ { i } \\mathbf { X } _ { j } \\} | \\exp \\{ \\exp \\{ | \\mathbf { X } _ { i } \\mathbf { X } _ { j } | \\} \\} \\exp \\{ | \\langle \\mathbf { X } _ { i } \\mathbf { X } _ { j } , ~ \\mathbf { X } _ { i } , ~ \\mathbf { X } _ { j } | \\} \\mathrm { d } \\mathbf { z } } \\\\ & { \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { X } _ { i } \\rangle \\exp \\{ | \\langle \\mathbf { X } _ { j } | \\mathbf { X } _ { i } , ~ \\mathbf { X } _ { j } \\rangle | \\} } \\\\ & { \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { z } | \\mathrm { X } _ { i } \\rangle \\exp \\{ | \\langle \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle | \\} } \\\\ & { = \\int \\langle z | \\mathbf { z } | \\mathbf { X } _ { i } \\mathbf { X } _ { j } \\rangle \\log _ { \\rho } \\langle \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle \\exp \\{ | \\langle \\mathbf { X } _ { i } | \\mathbf { X } _ { j } \\rangle | } \\\\ & { \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { Z } _ { j } \\rangle \\exp \\{ | \\langle \\mathbf { X } _ { j } | \\mathbf { X } _ { j } \\rangle | } \\\\ & \\quad - \\int \\langle z | \\mathbf { z } | \\mathbf { Z } _ { j } \\rangle \\exp \\{ \\end{array}", "type": "interline_equation", "image_path": "01504f03f7ada796d4cba0d38187f79fff717bd6ed61294a2986883682426937.jpg" } ] } ], "index": 3, "virtual_lines": [ { "bbox": [ 114, 128, 494, 212.0 ], "spans": [], "index": 2 }, { "bbox": [ 114, 212.0, 494, 296.0 ], "spans": [], "index": 3 }, { "bbox": [ 114, 296.0, 494, 380.0 ], "spans": [], "index": 4 } ] }, { "type": "interline_equation", "bbox": [ 126, 396, 486, 562 ], "lines": [ { "bbox": [ 126, 396, 486, 562 ], "spans": [ { "bbox": [ 126, 396, 486, 562 ], "score": 0.95, "content": "\\begin{array} { r l } { L _ { E L B O } = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\phi } ( { \\mathbf x } _ { j } , { \\mathbf X _ { i } } ) \\log } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) } } \\mathrm { d } { \\mathbf z } } \\\\ { } & { ~ = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\psi } ( { \\mathbf X _ { j } } , { \\mathbf X _ { i } } , { \\mathbf z } ) } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) p _ { \\psi } ( { \\mathbf X _ { i } } ) } } \\mathrm { d } { \\mathbf z } } \\\\ { } & { ~ = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\phi } ( { \\mathbf X _ { j } } | \\mathbf X _ { i } , { \\mathbf z } ) p _ { \\psi } ( { \\mathbf X _ { i } } , { \\mathbf z } ) } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) p _ { \\psi } ( { \\mathbf X _ { i } } ) } } \\mathrm { d } { \\mathbf z } } \\\\ { } & { ~ = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\phi } ( { \\mathbf X _ { j } } | \\mathbf X _ { i } , { \\mathbf z } ) p _ { \\psi } ( { \\mathbf z } | \\mathbf X _ { i } ) } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) } } \\mathrm { d } { \\mathbf z } } \\\\ { } & ~ = \\displaystyle { \\int } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } ) \\log \\frac { p _ { \\phi } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf z } ) p _ { \\phi } ( { \\mathbf Z } | \\mathbf X _ { i } ) } { q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , { \\mathbf X _ { i } } ) } } \\\\ { } & ~ = \\displaystyle { \\int } q _ { \\mathcal { G } } ( { \\mathbf z } | \\mathbf X _ { j } , \\mathbf X _ { i } \\end{array}", "type": "interline_equation", "image_path": "aa9a684ca0fb2a1ddb7fd7779680817f5be8a402f74f61f4ea0b13e88e8aae6e.jpg" } ] } ], "index": 6, "virtual_lines": [ { "bbox": [ 126, 396, 486, 451.3333333333333 ], "spans": [], "index": 5 }, { "bbox": [ 126, 451.3333333333333, 486, 506.66666666666663 ], "spans": [], "index": 6 }, { "bbox": [ 126, 506.66666666666663, 486, 562.0 ], "spans": [], "index": 7 } ] } ] }, { "preproc_blocks": [ { "type": "title", "bbox": [ 108, 81, 223, 94 ], "lines": [ { "bbox": [ 105, 80, 225, 96 ], "spans": [ { "bbox": [ 105, 80, 225, 96 ], "score": 1.0, "content": "B REPRODUCIBILITY", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "title", "bbox": [ 108, 109, 217, 121 ], "lines": [ { "bbox": [ 105, 109, 218, 122 ], "spans": [ { "bbox": [ 105, 109, 218, 122 ], "score": 1.0, "content": "B.1 DATASETS DETAILS", "type": "text" } ], "index": 1 } ], "index": 1 }, { "type": "text", "bbox": [ 107, 132, 505, 308 ], "lines": [ { "bbox": [ 106, 132, 505, 145 ], "spans": [ { "bbox": [ 106, 132, 505, 145 ], "score": 1.0, "content": "Cora, Citeseer, and Pubmed are standard citation network benchmark datasets Sen et al. (2008). In", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 143, 505, 156 ], "spans": [ { "bbox": [ 105, 143, 505, 156 ], "score": 1.0, "content": "these datasets, nodes represent documents, and edges denote citations; node feature corresponds to", "type": "text" } ], "index": 3 }, { "bbox": [ 106, 155, 505, 166 ], "spans": [ { "bbox": [ 106, 155, 505, 166 ], "score": 1.0, "content": "elements of a bag-of-words representation of a document, and node label corresponds to one of the", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 165, 505, 178 ], "spans": [ { "bbox": [ 105, 165, 505, 178 ], "score": 1.0, "content": "academic topics. Besides, we utilize four datasets used in Pei et al. (2020) for evaluation. Chameleon", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 177, 506, 188 ], "spans": [ { "bbox": [ 105, 177, 506, 188 ], "score": 1.0, "content": "and squirrel are two page-page networks on specific topics in Wikipedia Rozemberczki et al. (2021).", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 187, 506, 201 ], "spans": [ { "bbox": [ 105, 187, 506, 201 ], "score": 1.0, "content": "In these datasets, nodes represent web pages, and edges denote mutual links between pages; node", "type": "text" } ], "index": 7 }, { "bbox": [ 106, 199, 505, 211 ], "spans": [ { "bbox": [ 106, 199, 505, 211 ], "score": 1.0, "content": "features correspond to several informative nouns in the Wikipedia pages and labels correspond to", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 209, 506, 222 ], "spans": [ { "bbox": [ 105, 209, 506, 222 ], "score": 1.0, "content": "the number of the average monthly traffic of the web page. WebKB1 is a webpage dataset collected", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 220, 505, 233 ], "spans": [ { "bbox": [ 105, 220, 505, 233 ], "score": 1.0, "content": "from various universities. We use the one subdataset of it, Cornell. In this dataset, nodes represent", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 231, 505, 244 ], "spans": [ { "bbox": [ 106, 231, 505, 244 ], "score": 1.0, "content": "web pages, and edges are hyperlinks between them; node features correspond to the bag-of-words", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 242, 506, 255 ], "spans": [ { "bbox": [ 105, 242, 506, 255 ], "score": 1.0, "content": "representation of web pages and labels correspond to five categories, student, project, course, staff, and", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 252, 506, 267 ], "spans": [ { "bbox": [ 105, 252, 506, 267 ], "score": 1.0, "content": "faculty. Film dataset is the actor-only induced subgraph of the film-directoractor-writer network Tang", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 264, 506, 277 ], "spans": [ { "bbox": [ 105, 264, 506, 277 ], "score": 1.0, "content": "et al. (2009). In this dataset, Nodes represent actors, and edges denote co-occurrence on the same", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 273, 506, 289 ], "spans": [ { "bbox": [ 105, 273, 506, 289 ], "score": 1.0, "content": "Wikipedia page; node features correspond to some keywords in the Wikipedia pages and labels", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 287, 505, 298 ], "spans": [ { "bbox": [ 106, 287, 505, 298 ], "score": 1.0, "content": "correspond to five categories in terms of words of actor’s Wikipedia. All the dataset statistics are", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 298, 203, 309 ], "spans": [ { "bbox": [ 106, 298, 203, 309 ], "score": 1.0, "content": "summarized in Table 6.", "type": "text" } ], "index": 17 } ], "index": 9.5 }, { "type": "table", "bbox": [ 151, 345, 460, 413 ], "blocks": [ { "type": "table_caption", "bbox": [ 252, 331, 359, 343 ], "group_id": 0, "lines": [ { "bbox": [ 251, 330, 360, 343 ], "spans": [ { "bbox": [ 251, 330, 360, 343 ], "score": 1.0, "content": "Table 6: Datasets statistics", "type": "text" } ], "index": 18 } ], "index": 18 }, { "type": "table_body", "bbox": [ 151, 345, 460, 413 ], "group_id": 0, "lines": [ { "bbox": [ 151, 345, 460, 413 ], "spans": [ { "bbox": [ 151, 345, 460, 413 ], "score": 0.982, "html": "
DatasetCoraCite.Pubm.Cham.Squi.ActorCorn.
#Nodes2708332719717227752017600183
#Edges54294732443383610121707333544295
#Features14333703500232520899311703
# Classes7635555
", "type": "table", "image_path": "9189a83de3b4a0f4273adc81377846a9326d602d8a44f8ccfd0247d8b28f9990.jpg" } ] } ], "index": 20, "virtual_lines": [ { "bbox": [ 151, 345, 460, 367.6666666666667 ], "spans": [], "index": 19 }, { "bbox": [ 151, 367.6666666666667, 460, 390.33333333333337 ], "spans": [], "index": 20 }, { "bbox": [ 151, 390.33333333333337, 460, 413.00000000000006 ], "spans": [], "index": 21 } ] } ], "index": 19.0 }, { "type": "title", "bbox": [ 108, 450, 250, 462 ], "lines": [ { "bbox": [ 105, 450, 252, 464 ], "spans": [ { "bbox": [ 105, 450, 252, 464 ], "score": 1.0, "content": "B.2 IMPLEMENTATION DETAILS", "type": "text" } ], "index": 22 } ], "index": 22 }, { "type": "text", "bbox": [ 106, 473, 506, 605 ], "lines": [ { "bbox": [ 105, 472, 507, 487 ], "spans": [ { "bbox": [ 105, 472, 410, 487 ], "score": 1.0, "content": "We use Pytorch (Paszke et al., 2019) to implement LA-GNNs. The codes of", "type": "text" }, { "bbox": [ 410, 473, 436, 484 ], "score": 0.89, "content": "S ^ { 2 } G C", "type": "inline_equation" }, { "bbox": [ 436, 472, 507, 487 ], "score": 1.0, "content": "(Zhu & Koniusz,", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 484, 506, 497 ], "spans": [ { "bbox": [ 105, 484, 506, 497 ], "score": 1.0, "content": "2021), LA-GCN, LA-GAT, LA-GCNII, LA-GRAND, and DropEdge-GCN are implemented referring", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 494, 507, 509 ], "spans": [ { "bbox": [ 105, 494, 224, 509 ], "score": 1.0, "content": "to Pytorch implementation of", "type": "text" }, { "bbox": [ 225, 495, 253, 506 ], "score": 0.9, "content": "\\mathrm { S } ^ { 2 } \\mathrm { G } \\mathrm { C } ^ { 2 }", "type": "inline_equation" }, { "bbox": [ 253, 494, 257, 509 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 257, 495, 283, 506 ], "score": 0.81, "content": "\\mathrm { G C N } ^ { 3 }", "type": "inline_equation" }, { "bbox": [ 283, 494, 381, 509 ], "score": 1.0, "content": "(Kipf & Welling, 2017),", "type": "text" }, { "bbox": [ 381, 495, 406, 506 ], "score": 0.53, "content": "\\mathrm { G A T ^ { 4 } }", "type": "inline_equation" }, { "bbox": [ 406, 494, 507, 509 ], "score": 1.0, "content": "(Velickovi ˇ c et al., 2018), ´", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 506, 507, 519 ], "spans": [ { "bbox": [ 106, 506, 140, 517 ], "score": 0.56, "content": "\\mathrm { G C N I I } ^ { 5 }", "type": "inline_equation" }, { "bbox": [ 140, 506, 217, 519 ], "score": 1.0, "content": "(Chen et al., 2020)", "type": "text" }, { "bbox": [ 218, 506, 258, 517 ], "score": 0.43, "content": "\\mathrm { G R A N D } ^ { 6 }", "type": "inline_equation" }, { "bbox": [ 259, 506, 399, 519 ], "score": 1.0, "content": "(Feng et al., 2020), and DropEdge-", "type": "text" }, { "bbox": [ 399, 506, 425, 517 ], "score": 0.48, "content": "\\mathbf { \\Delta } G \\mathbf { C N } ^ { 7 }", "type": "inline_equation" }, { "bbox": [ 426, 506, 507, 519 ], "score": 1.0, "content": "(Rong et al., 2020).", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 516, 506, 530 ], "spans": [ { "bbox": [ 105, 516, 506, 530 ], "score": 1.0, "content": "Besides, we implement APPNP (Klicpera et al., 2019) with DGL (Wang et al., 2019) version of", "type": "text" } ], "index": 27 }, { "bbox": [ 104, 527, 506, 541 ], "spans": [ { "bbox": [ 104, 527, 506, 541 ], "score": 1.0, "content": "APPNP8. The datasets Cora, Citeseer, Pubmed are downloaded from TensorFlow (Abadi et al., 2016)", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 538, 506, 552 ], "spans": [ { "bbox": [ 105, 538, 181, 552 ], "score": 1.0, "content": "implementation of", "type": "text" }, { "bbox": [ 182, 539, 208, 550 ], "score": 0.87, "content": "\\mathrm { G C N ^ { 9 } }", "type": "inline_equation" }, { "bbox": [ 208, 538, 506, 552 ], "score": 1.0, "content": ", and the datasets Chameleon, Squirrel, Actor, and Cornell are downloaded", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 548, 506, 564 ], "spans": [ { "bbox": [ 105, 548, 250, 564 ], "score": 1.0, "content": "from the implementation of Geom-", "type": "text" }, { "bbox": [ 251, 550, 280, 561 ], "score": 0.77, "content": "\\mathrm { G C N ^ { 1 0 } }", "type": "inline_equation" }, { "bbox": [ 280, 548, 506, 564 ], "score": 1.0, "content": "(Pei et al., 2020). All the experiments in this work are", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 560, 506, 574 ], "spans": [ { "bbox": [ 105, 560, 506, 574 ], "score": 1.0, "content": "conducted on a single NVIDIA Tesla V100 with 32GB memory size. The operating system behind", "type": "text" } ], "index": 31 }, { "bbox": [ 106, 572, 506, 585 ], "spans": [ { "bbox": [ 106, 572, 506, 585 ], "score": 1.0, "content": "the Docker where the experiments are running is Red Hat 4.8.2-16. And the software that we use for", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 583, 507, 596 ], "spans": [ { "bbox": [ 105, 583, 507, 596 ], "score": 1.0, "content": "experiments are Python 3.6.8, numpy 1.19.2, sklearn 0.0, scipy 1.5.4, networkx 2.5.1, torch 1.6.0,", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 595, 324, 605 ], "spans": [ { "bbox": [ 106, 595, 324, 605 ], "score": 1.0, "content": "torchvision 0.7.0, CUDA 10.2.89, and CUDNN 8.0.2.", "type": "text" } ], "index": 34 } ], "index": 28.5 } ], "page_idx": 14, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 118, 622, 374, 732 ], "lines": [ { "bbox": [ 118, 622, 367, 636 ], "spans": [ { "bbox": [ 118, 622, 367, 636 ], "score": 1.0, "content": "1http://www.cs.cmu.edu/afs/cs.cmu.edu/project/theo-11/www/wwkb", "type": "text" } ] }, { "bbox": [ 118, 633, 262, 647 ], "spans": [ { "bbox": [ 118, 633, 262, 647 ], "score": 1.0, "content": "2https://github.com/allenhaozhu/SSGC", "type": "text" } ] }, { "bbox": [ 118, 644, 234, 658 ], "spans": [ { "bbox": [ 118, 644, 234, 658 ], "score": 1.0, "content": "3https://github.com/tkipf/pygcn", "type": "text" } ] }, { "bbox": [ 118, 654, 257, 669 ], "spans": [ { "bbox": [ 118, 654, 257, 669 ], "score": 1.0, "content": "4https://github.com/Diego999/pyGAT", "type": "text" } ] }, { "bbox": [ 118, 666, 255, 679 ], "spans": [ { "bbox": [ 118, 666, 255, 679 ], "score": 1.0, "content": "5https://github.com/chennnM/GCNII", "type": "text" } ] }, { "bbox": [ 118, 676, 260, 690 ], "spans": [ { "bbox": [ 118, 676, 260, 690 ], "score": 1.0, "content": "6https://github.com/THUDM/GRAND", "type": "text" } ] }, { "bbox": [ 118, 686, 270, 702 ], "spans": [ { "bbox": [ 118, 686, 270, 702 ], "score": 1.0, "content": "7https://github.com/DropEdge/DropEdge", "type": "text" } ] }, { "bbox": [ 117, 697, 358, 713 ], "spans": [ { "bbox": [ 117, 697, 358, 713 ], "score": 1.0, "content": "8https://github.com/dmlc/dgl/tree/master/examples/pytorch/appnp", "type": "text" } ] }, { "bbox": [ 117, 708, 302, 723 ], "spans": [ { "bbox": [ 117, 708, 302, 723 ], "score": 1.0, "content": "9https://github.com/tkipf/gcn/tree/master/gcn/data", "type": "text" } ] }, { "bbox": [ 114, 718, 376, 735 ], "spans": [ { "bbox": [ 114, 718, 376, 735 ], "score": 1.0, "content": "10https://github.com/graphdml-uiuc-jlu/geom-gcn/tree/master/new_data", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 300, 751, 310, 760 ], "lines": [ { "bbox": [ 299, 750, 312, 764 ], "spans": [ { "bbox": [ 299, 750, 312, 764 ], "score": 1.0, "content": "", "type": "text", "height": 14, "width": 13 } ] } ] }, { "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 2022", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "title", "bbox": [ 108, 81, 223, 94 ], "lines": [ { "bbox": [ 105, 80, 225, 96 ], "spans": [ { "bbox": [ 105, 80, 225, 96 ], "score": 1.0, "content": "B REPRODUCIBILITY", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "title", "bbox": [ 108, 109, 217, 121 ], "lines": [ { "bbox": [ 105, 109, 218, 122 ], "spans": [ { "bbox": [ 105, 109, 218, 122 ], "score": 1.0, "content": "B.1 DATASETS DETAILS", "type": "text" } ], "index": 1 } ], "index": 1 }, { "type": "text", "bbox": [ 107, 132, 505, 308 ], "lines": [ { "bbox": [ 106, 132, 505, 145 ], "spans": [ { "bbox": [ 106, 132, 505, 145 ], "score": 1.0, "content": "Cora, Citeseer, and Pubmed are standard citation network benchmark datasets Sen et al. (2008). In", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 143, 505, 156 ], "spans": [ { "bbox": [ 105, 143, 505, 156 ], "score": 1.0, "content": "these datasets, nodes represent documents, and edges denote citations; node feature corresponds to", "type": "text" } ], "index": 3 }, { "bbox": [ 106, 155, 505, 166 ], "spans": [ { "bbox": [ 106, 155, 505, 166 ], "score": 1.0, "content": "elements of a bag-of-words representation of a document, and node label corresponds to one of the", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 165, 505, 178 ], "spans": [ { "bbox": [ 105, 165, 505, 178 ], "score": 1.0, "content": "academic topics. Besides, we utilize four datasets used in Pei et al. (2020) for evaluation. Chameleon", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 177, 506, 188 ], "spans": [ { "bbox": [ 105, 177, 506, 188 ], "score": 1.0, "content": "and squirrel are two page-page networks on specific topics in Wikipedia Rozemberczki et al. (2021).", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 187, 506, 201 ], "spans": [ { "bbox": [ 105, 187, 506, 201 ], "score": 1.0, "content": "In these datasets, nodes represent web pages, and edges denote mutual links between pages; node", "type": "text" } ], "index": 7 }, { "bbox": [ 106, 199, 505, 211 ], "spans": [ { "bbox": [ 106, 199, 505, 211 ], "score": 1.0, "content": "features correspond to several informative nouns in the Wikipedia pages and labels correspond to", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 209, 506, 222 ], "spans": [ { "bbox": [ 105, 209, 506, 222 ], "score": 1.0, "content": "the number of the average monthly traffic of the web page. WebKB1 is a webpage dataset collected", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 220, 505, 233 ], "spans": [ { "bbox": [ 105, 220, 505, 233 ], "score": 1.0, "content": "from various universities. We use the one subdataset of it, Cornell. In this dataset, nodes represent", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 231, 505, 244 ], "spans": [ { "bbox": [ 106, 231, 505, 244 ], "score": 1.0, "content": "web pages, and edges are hyperlinks between them; node features correspond to the bag-of-words", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 242, 506, 255 ], "spans": [ { "bbox": [ 105, 242, 506, 255 ], "score": 1.0, "content": "representation of web pages and labels correspond to five categories, student, project, course, staff, and", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 252, 506, 267 ], "spans": [ { "bbox": [ 105, 252, 506, 267 ], "score": 1.0, "content": "faculty. Film dataset is the actor-only induced subgraph of the film-directoractor-writer network Tang", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 264, 506, 277 ], "spans": [ { "bbox": [ 105, 264, 506, 277 ], "score": 1.0, "content": "et al. (2009). In this dataset, Nodes represent actors, and edges denote co-occurrence on the same", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 273, 506, 289 ], "spans": [ { "bbox": [ 105, 273, 506, 289 ], "score": 1.0, "content": "Wikipedia page; node features correspond to some keywords in the Wikipedia pages and labels", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 287, 505, 298 ], "spans": [ { "bbox": [ 106, 287, 505, 298 ], "score": 1.0, "content": "correspond to five categories in terms of words of actor’s Wikipedia. All the dataset statistics are", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 298, 203, 309 ], "spans": [ { "bbox": [ 106, 298, 203, 309 ], "score": 1.0, "content": "summarized in Table 6.", "type": "text" } ], "index": 17 } ], "index": 9.5, "bbox_fs": [ 105, 132, 506, 309 ] }, { "type": "table", "bbox": [ 151, 345, 460, 413 ], "blocks": [ { "type": "table_caption", "bbox": [ 252, 331, 359, 343 ], "group_id": 0, "lines": [ { "bbox": [ 251, 330, 360, 343 ], "spans": [ { "bbox": [ 251, 330, 360, 343 ], "score": 1.0, "content": "Table 6: Datasets statistics", "type": "text" } ], "index": 18 } ], "index": 18 }, { "type": "table_body", "bbox": [ 151, 345, 460, 413 ], "group_id": 0, "lines": [ { "bbox": [ 151, 345, 460, 413 ], "spans": [ { "bbox": [ 151, 345, 460, 413 ], "score": 0.982, "html": "
DatasetCoraCite.Pubm.Cham.Squi.ActorCorn.
#Nodes2708332719717227752017600183
#Edges54294732443383610121707333544295
#Features14333703500232520899311703
# Classes7635555
", "type": "table", "image_path": "9189a83de3b4a0f4273adc81377846a9326d602d8a44f8ccfd0247d8b28f9990.jpg" } ] } ], "index": 20, "virtual_lines": [ { "bbox": [ 151, 345, 460, 367.6666666666667 ], "spans": [], "index": 19 }, { "bbox": [ 151, 367.6666666666667, 460, 390.33333333333337 ], "spans": [], "index": 20 }, { "bbox": [ 151, 390.33333333333337, 460, 413.00000000000006 ], "spans": [], "index": 21 } ] } ], "index": 19.0 }, { "type": "title", "bbox": [ 108, 450, 250, 462 ], "lines": [ { "bbox": [ 105, 450, 252, 464 ], "spans": [ { "bbox": [ 105, 450, 252, 464 ], "score": 1.0, "content": "B.2 IMPLEMENTATION DETAILS", "type": "text" } ], "index": 22 } ], "index": 22 }, { "type": "text", "bbox": [ 106, 473, 506, 605 ], "lines": [ { "bbox": [ 105, 472, 507, 487 ], "spans": [ { "bbox": [ 105, 472, 410, 487 ], "score": 1.0, "content": "We use Pytorch (Paszke et al., 2019) to implement LA-GNNs. The codes of", "type": "text" }, { "bbox": [ 410, 473, 436, 484 ], "score": 0.89, "content": "S ^ { 2 } G C", "type": "inline_equation" }, { "bbox": [ 436, 472, 507, 487 ], "score": 1.0, "content": "(Zhu & Koniusz,", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 484, 506, 497 ], "spans": [ { "bbox": [ 105, 484, 506, 497 ], "score": 1.0, "content": "2021), LA-GCN, LA-GAT, LA-GCNII, LA-GRAND, and DropEdge-GCN are implemented referring", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 494, 507, 509 ], "spans": [ { "bbox": [ 105, 494, 224, 509 ], "score": 1.0, "content": "to Pytorch implementation of", "type": "text" }, { "bbox": [ 225, 495, 253, 506 ], "score": 0.9, "content": "\\mathrm { S } ^ { 2 } \\mathrm { G } \\mathrm { C } ^ { 2 }", "type": "inline_equation" }, { "bbox": [ 253, 494, 257, 509 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 257, 495, 283, 506 ], "score": 0.81, "content": "\\mathrm { G C N } ^ { 3 }", "type": "inline_equation" }, { "bbox": [ 283, 494, 381, 509 ], "score": 1.0, "content": "(Kipf & Welling, 2017),", "type": "text" }, { "bbox": [ 381, 495, 406, 506 ], "score": 0.53, "content": "\\mathrm { G A T ^ { 4 } }", "type": "inline_equation" }, { "bbox": [ 406, 494, 507, 509 ], "score": 1.0, "content": "(Velickovi ˇ c et al., 2018), ´", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 506, 507, 519 ], "spans": [ { "bbox": [ 106, 506, 140, 517 ], "score": 0.56, "content": "\\mathrm { G C N I I } ^ { 5 }", "type": "inline_equation" }, { "bbox": [ 140, 506, 217, 519 ], "score": 1.0, "content": "(Chen et al., 2020)", "type": "text" }, { "bbox": [ 218, 506, 258, 517 ], "score": 0.43, "content": "\\mathrm { G R A N D } ^ { 6 }", "type": "inline_equation" }, { "bbox": [ 259, 506, 399, 519 ], "score": 1.0, "content": "(Feng et al., 2020), and DropEdge-", "type": "text" }, { "bbox": [ 399, 506, 425, 517 ], "score": 0.48, "content": "\\mathbf { \\Delta } G \\mathbf { C N } ^ { 7 }", "type": "inline_equation" }, { "bbox": [ 426, 506, 507, 519 ], "score": 1.0, "content": "(Rong et al., 2020).", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 516, 506, 530 ], "spans": [ { "bbox": [ 105, 516, 506, 530 ], "score": 1.0, "content": "Besides, we implement APPNP (Klicpera et al., 2019) with DGL (Wang et al., 2019) version of", "type": "text" } ], "index": 27 }, { "bbox": [ 104, 527, 506, 541 ], "spans": [ { "bbox": [ 104, 527, 506, 541 ], "score": 1.0, "content": "APPNP8. The datasets Cora, Citeseer, Pubmed are downloaded from TensorFlow (Abadi et al., 2016)", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 538, 506, 552 ], "spans": [ { "bbox": [ 105, 538, 181, 552 ], "score": 1.0, "content": "implementation of", "type": "text" }, { "bbox": [ 182, 539, 208, 550 ], "score": 0.87, "content": "\\mathrm { G C N ^ { 9 } }", "type": "inline_equation" }, { "bbox": [ 208, 538, 506, 552 ], "score": 1.0, "content": ", and the datasets Chameleon, Squirrel, Actor, and Cornell are downloaded", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 548, 506, 564 ], "spans": [ { "bbox": [ 105, 548, 250, 564 ], "score": 1.0, "content": "from the implementation of Geom-", "type": "text" }, { "bbox": [ 251, 550, 280, 561 ], "score": 0.77, "content": "\\mathrm { G C N ^ { 1 0 } }", "type": "inline_equation" }, { "bbox": [ 280, 548, 506, 564 ], "score": 1.0, "content": "(Pei et al., 2020). All the experiments in this work are", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 560, 506, 574 ], "spans": [ { "bbox": [ 105, 560, 506, 574 ], "score": 1.0, "content": "conducted on a single NVIDIA Tesla V100 with 32GB memory size. The operating system behind", "type": "text" } ], "index": 31 }, { "bbox": [ 106, 572, 506, 585 ], "spans": [ { "bbox": [ 106, 572, 506, 585 ], "score": 1.0, "content": "the Docker where the experiments are running is Red Hat 4.8.2-16. And the software that we use for", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 583, 507, 596 ], "spans": [ { "bbox": [ 105, 583, 507, 596 ], "score": 1.0, "content": "experiments are Python 3.6.8, numpy 1.19.2, sklearn 0.0, scipy 1.5.4, networkx 2.5.1, torch 1.6.0,", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 595, 324, 605 ], "spans": [ { "bbox": [ 106, 595, 324, 605 ], "score": 1.0, "content": "torchvision 0.7.0, CUDA 10.2.89, and CUDNN 8.0.2.", "type": "text" } ], "index": 34 } ], "index": 28.5, "bbox_fs": [ 104, 472, 507, 605 ] } ] }, { "preproc_blocks": [ { "type": "title", "bbox": [ 108, 82, 255, 93 ], "lines": [ { "bbox": [ 105, 81, 256, 95 ], "spans": [ { "bbox": [ 105, 81, 256, 95 ], "score": 1.0, "content": "B.3 HYPERPARAMETER DETAILS", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 107, 102, 505, 137 ], "lines": [ { "bbox": [ 104, 101, 505, 116 ], "spans": [ { "bbox": [ 104, 101, 493, 116 ], "score": 1.0, "content": "LA-GNNs introduce an additional parameter, that is the hidden layer for generated feature matrix", "type": "text" }, { "bbox": [ 494, 102, 505, 113 ], "score": 0.54, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" } ], "index": 1 }, { "bbox": [ 105, 114, 505, 126 ], "spans": [ { "bbox": [ 105, 114, 505, 126 ], "score": 1.0, "content": "before concatenation. The difference of architectures between GCN and LA-GCN can be found in", "type": "text" } ], "index": 2 }, { "bbox": [ 106, 125, 376, 137 ], "spans": [ { "bbox": [ 106, 125, 376, 137 ], "score": 1.0, "content": "Figure 4, and the LA-GCNII architecture can be found in Figure 5.", "type": "text" } ], "index": 3 } ], "index": 2 }, { "type": "image", "bbox": [ 127, 151, 485, 226 ], "blocks": [ { "type": "image_body", "bbox": [ 127, 151, 485, 226 ], "group_id": 0, "lines": [ { "bbox": [ 127, 151, 485, 226 ], "spans": [ { "bbox": [ 127, 151, 485, 226 ], "score": 0.961, "type": "image", "image_path": "d7816fad620dd0825bfeea46796303662cc8614bc99cb04d713507ea99f5f1a5.jpg" } ] } ], "index": 5, "virtual_lines": [ { "bbox": [ 127, 151, 485, 176.0 ], "spans": [], "index": 4 }, { "bbox": [ 127, 176.0, 485, 201.0 ], "spans": [], "index": 5 }, { "bbox": [ 127, 201.0, 485, 226.0 ], "spans": [], "index": 6 } ] }, { "type": "image_caption", "bbox": [ 105, 241, 506, 277 ], "group_id": 0, "lines": [ { "bbox": [ 106, 241, 505, 254 ], "spans": [ { "bbox": [ 106, 241, 505, 254 ], "score": 1.0, "content": "Figure 4: GCN and LA-GCN architectures. The difference between GCN and LA-GCN architectures", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 253, 505, 266 ], "spans": [ { "bbox": [ 105, 253, 347, 266 ], "score": 1.0, "content": "is that the LA-GCN has an additional convolutional layer for", "type": "text" }, { "bbox": [ 347, 253, 357, 263 ], "score": 0.8, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 357, 253, 505, 266 ], "score": 1.0, "content": "and it uses a concatenation operation", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 264, 245, 277 ], "spans": [ { "bbox": [ 106, 264, 245, 277 ], "score": 1.0, "content": "to mix the hidden representations.", "type": "text" } ], "index": 9 } ], "index": 8 } ], "index": 6.5 }, { "type": "image", "bbox": [ 107, 293, 505, 372 ], "blocks": [ { "type": "image_body", "bbox": [ 107, 293, 505, 372 ], "group_id": 1, "lines": [ { "bbox": [ 107, 293, 505, 372 ], "spans": [ { "bbox": [ 107, 293, 505, 372 ], "score": 0.951, "type": "image", "image_path": "5443477c1a5cf6f340de4b0323cbbb8400ffee35c029505e3e5d44d84aa3e826.jpg" } ] } ], "index": 11, "virtual_lines": [ { "bbox": [ 107, 293, 505, 319.3333333333333 ], "spans": [], "index": 10 }, { "bbox": [ 107, 319.3333333333333, 505, 345.66666666666663 ], "spans": [], "index": 11 }, { "bbox": [ 107, 345.66666666666663, 505, 371.99999999999994 ], "spans": [], "index": 12 } ] }, { "type": "image_caption", "bbox": [ 106, 394, 506, 429 ], "group_id": 1, "lines": [ { "bbox": [ 106, 395, 506, 407 ], "spans": [ { "bbox": [ 106, 395, 506, 407 ], "score": 1.0, "content": "Figure 5: LA-GCNII architecture. The difference between GCNII and LA-GCNII is that the LA-", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 406, 505, 419 ], "spans": [ { "bbox": [ 105, 406, 268, 419 ], "score": 1.0, "content": "GCNII has an additional MLP layer for", "type": "text" }, { "bbox": [ 268, 406, 279, 417 ], "score": 0.75, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 279, 406, 505, 419 ], "score": 1.0, "content": "and it uses a concatenation operation to mix the hidden", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 419, 172, 430 ], "spans": [ { "bbox": [ 105, 419, 172, 430 ], "score": 1.0, "content": "representations.", "type": "text" } ], "index": 15 } ], "index": 14 } ], "index": 12.5 }, { "type": "text", "bbox": [ 107, 440, 505, 474 ], "lines": [ { "bbox": [ 105, 439, 505, 454 ], "spans": [ { "bbox": [ 105, 439, 505, 454 ], "score": 1.0, "content": "The difference of hyperparameters between the GCN and LA-GCN is only the hidden layer size", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 451, 505, 465 ], "spans": [ { "bbox": [ 105, 451, 505, 465 ], "score": 1.0, "content": "before concatenation. For the LA-GCNII, LA-GAT, LA-GRAND, we tune the hyperparameters in", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 463, 385, 475 ], "spans": [ { "bbox": [ 106, 463, 385, 475 ], "score": 1.0, "content": "the same way as described in their original papers with validation set.", "type": "text" } ], "index": 18 } ], "index": 17 } ], "page_idx": 15, "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 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 300, 752, 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": [ 108, 82, 255, 93 ], "lines": [ { "bbox": [ 105, 81, 256, 95 ], "spans": [ { "bbox": [ 105, 81, 256, 95 ], "score": 1.0, "content": "B.3 HYPERPARAMETER DETAILS", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 107, 102, 505, 137 ], "lines": [ { "bbox": [ 104, 101, 505, 116 ], "spans": [ { "bbox": [ 104, 101, 493, 116 ], "score": 1.0, "content": "LA-GNNs introduce an additional parameter, that is the hidden layer for generated feature matrix", "type": "text" }, { "bbox": [ 494, 102, 505, 113 ], "score": 0.54, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" } ], "index": 1 }, { "bbox": [ 105, 114, 505, 126 ], "spans": [ { "bbox": [ 105, 114, 505, 126 ], "score": 1.0, "content": "before concatenation. The difference of architectures between GCN and LA-GCN can be found in", "type": "text" } ], "index": 2 }, { "bbox": [ 106, 125, 376, 137 ], "spans": [ { "bbox": [ 106, 125, 376, 137 ], "score": 1.0, "content": "Figure 4, and the LA-GCNII architecture can be found in Figure 5.", "type": "text" } ], "index": 3 } ], "index": 2, "bbox_fs": [ 104, 101, 505, 137 ] }, { "type": "image", "bbox": [ 127, 151, 485, 226 ], "blocks": [ { "type": "image_body", "bbox": [ 127, 151, 485, 226 ], "group_id": 0, "lines": [ { "bbox": [ 127, 151, 485, 226 ], "spans": [ { "bbox": [ 127, 151, 485, 226 ], "score": 0.961, "type": "image", "image_path": "d7816fad620dd0825bfeea46796303662cc8614bc99cb04d713507ea99f5f1a5.jpg" } ] } ], "index": 5, "virtual_lines": [ { "bbox": [ 127, 151, 485, 176.0 ], "spans": [], "index": 4 }, { "bbox": [ 127, 176.0, 485, 201.0 ], "spans": [], "index": 5 }, { "bbox": [ 127, 201.0, 485, 226.0 ], "spans": [], "index": 6 } ] }, { "type": "image_caption", "bbox": [ 105, 241, 506, 277 ], "group_id": 0, "lines": [ { "bbox": [ 106, 241, 505, 254 ], "spans": [ { "bbox": [ 106, 241, 505, 254 ], "score": 1.0, "content": "Figure 4: GCN and LA-GCN architectures. The difference between GCN and LA-GCN architectures", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 253, 505, 266 ], "spans": [ { "bbox": [ 105, 253, 347, 266 ], "score": 1.0, "content": "is that the LA-GCN has an additional convolutional layer for", "type": "text" }, { "bbox": [ 347, 253, 357, 263 ], "score": 0.8, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 357, 253, 505, 266 ], "score": 1.0, "content": "and it uses a concatenation operation", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 264, 245, 277 ], "spans": [ { "bbox": [ 106, 264, 245, 277 ], "score": 1.0, "content": "to mix the hidden representations.", "type": "text" } ], "index": 9 } ], "index": 8 } ], "index": 6.5 }, { "type": "image", "bbox": [ 107, 293, 505, 372 ], "blocks": [ { "type": "image_body", "bbox": [ 107, 293, 505, 372 ], "group_id": 1, "lines": [ { "bbox": [ 107, 293, 505, 372 ], "spans": [ { "bbox": [ 107, 293, 505, 372 ], "score": 0.951, "type": "image", "image_path": "5443477c1a5cf6f340de4b0323cbbb8400ffee35c029505e3e5d44d84aa3e826.jpg" } ] } ], "index": 11, "virtual_lines": [ { "bbox": [ 107, 293, 505, 319.3333333333333 ], "spans": [], "index": 10 }, { "bbox": [ 107, 319.3333333333333, 505, 345.66666666666663 ], "spans": [], "index": 11 }, { "bbox": [ 107, 345.66666666666663, 505, 371.99999999999994 ], "spans": [], "index": 12 } ] }, { "type": "image_caption", "bbox": [ 106, 394, 506, 429 ], "group_id": 1, "lines": [ { "bbox": [ 106, 395, 506, 407 ], "spans": [ { "bbox": [ 106, 395, 506, 407 ], "score": 1.0, "content": "Figure 5: LA-GCNII architecture. The difference between GCNII and LA-GCNII is that the LA-", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 406, 505, 419 ], "spans": [ { "bbox": [ 105, 406, 268, 419 ], "score": 1.0, "content": "GCNII has an additional MLP layer for", "type": "text" }, { "bbox": [ 268, 406, 279, 417 ], "score": 0.75, "content": "\\overline { { \\mathbf { X } } }", "type": "inline_equation" }, { "bbox": [ 279, 406, 505, 419 ], "score": 1.0, "content": "and it uses a concatenation operation to mix the hidden", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 419, 172, 430 ], "spans": [ { "bbox": [ 105, 419, 172, 430 ], "score": 1.0, "content": "representations.", "type": "text" } ], "index": 15 } ], "index": 14 } ], "index": 12.5 }, { "type": "text", "bbox": [ 107, 440, 505, 474 ], "lines": [ { "bbox": [ 105, 439, 505, 454 ], "spans": [ { "bbox": [ 105, 439, 505, 454 ], "score": 1.0, "content": "The difference of hyperparameters between the GCN and LA-GCN is only the hidden layer size", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 451, 505, 465 ], "spans": [ { "bbox": [ 105, 451, 505, 465 ], "score": 1.0, "content": "before concatenation. For the LA-GCNII, LA-GAT, LA-GRAND, we tune the hyperparameters in", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 463, 385, 475 ], "spans": [ { "bbox": [ 106, 463, 385, 475 ], "score": 1.0, "content": "the same way as described in their original papers with validation set.", "type": "text" } ], "index": 18 } ], "index": 17, "bbox_fs": [ 105, 439, 505, 475 ] } ] } ], "_backend": "pipeline", "_version_name": "2.2.2" }