diff --git "a/parse/train/Bkeeca4Kvr/Bkeeca4Kvr_middle.json" "b/parse/train/Bkeeca4Kvr/Bkeeca4Kvr_middle.json" new file mode 100644--- /dev/null +++ "b/parse/train/Bkeeca4Kvr/Bkeeca4Kvr_middle.json" @@ -0,0 +1,51311 @@ +{ + "pdf_info": [ + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 79, + 502, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 79, + 505, + 99 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 505, + 99 + ], + "score": 1.0, + "content": "FEW-SHOT LEARNING ON GRAPHS VIA SUPER-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 101, + 473, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 101, + 473, + 118 + ], + "score": 1.0, + "content": "CLASSES BASED ON GRAPH SPECTRAL MEASURES", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 113, + 135, + 320, + 147 + ], + "lines": [ + { + "bbox": [ + 111, + 135, + 321, + 148 + ], + "spans": [ + { + "bbox": [ + 111, + 135, + 321, + 148 + ], + "score": 1.0, + "content": "Jatin Chauhan, Deepak Nathani, Manohar Kaul", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 113, + 147, + 423, + 180 + ], + "lines": [ + { + "bbox": [ + 112, + 146, + 248, + 158 + ], + "spans": [ + { + "bbox": [ + 112, + 146, + 248, + 158 + ], + "score": 1.0, + "content": "Department of Computer Science", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 156, + 282, + 169 + ], + "spans": [ + { + "bbox": [ + 111, + 156, + 282, + 169 + ], + "score": 1.0, + "content": "Indian Institute of Technology Hyderabad", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 112, + 168, + 424, + 181 + ], + "spans": [ + { + "bbox": [ + 112, + 168, + 424, + 181 + ], + "score": 1.0, + "content": "{chauhanjatin100,deepakn1019,manohar.kaul}@gmail.com", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + }, + { + "type": "title", + "bbox": [ + 278, + 208, + 333, + 220 + ], + "lines": [ + { + "bbox": [ + 276, + 208, + 335, + 221 + ], + "spans": [ + { + "bbox": [ + 276, + 208, + 335, + 221 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 143, + 236, + 468, + 423 + ], + "lines": [ + { + "bbox": [ + 142, + 237, + 469, + 249 + ], + "spans": [ + { + "bbox": [ + 142, + 237, + 469, + 249 + ], + "score": 1.0, + "content": "We propose to study the problem of few-shot graph classification in graph neu-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 248, + 469, + 260 + ], + "spans": [ + { + "bbox": [ + 141, + 248, + 469, + 260 + ], + "score": 1.0, + "content": "ral networks (GNNs) to recognize unseen classes, given limited labeled graph", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 259, + 470, + 270 + ], + "spans": [ + { + "bbox": [ + 141, + 259, + 470, + 270 + ], + "score": 1.0, + "content": "examples. Despite several interesting GNN variants being proposed recently for", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 270, + 469, + 281 + ], + "spans": [ + { + "bbox": [ + 141, + 270, + 469, + 281 + ], + "score": 1.0, + "content": "node and graph classification tasks, when faced with scarce labeled examples in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 280, + 469, + 292 + ], + "spans": [ + { + "bbox": [ + 141, + 280, + 469, + 292 + ], + "score": 1.0, + "content": "the few-shot setting, these GNNs exhibit significant loss in classification perfor-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 291, + 470, + 303 + ], + "spans": [ + { + "bbox": [ + 141, + 291, + 470, + 303 + ], + "score": 1.0, + "content": "mance. Here, we present an approach where a probability measure is assigned", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 302, + 470, + 314 + ], + "spans": [ + { + "bbox": [ + 141, + 302, + 470, + 314 + ], + "score": 1.0, + "content": "to each graph based on the spectrum of the graph’s normalized Laplacian. This", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 312, + 469, + 326 + ], + "spans": [ + { + "bbox": [ + 141, + 312, + 469, + 326 + ], + "score": 1.0, + "content": "enables us to accordingly cluster the graph base-labels associated with each graph", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 324, + 469, + 337 + ], + "spans": [ + { + "bbox": [ + 141, + 324, + 257, + 337 + ], + "score": 1.0, + "content": "into super-classes, where the", + "type": "text" + }, + { + "bbox": [ + 257, + 324, + 270, + 334 + ], + "score": 0.84, + "content": "L ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 324, + 469, + 337 + ], + "score": 1.0, + "content": "Wasserstein distance serves as our underlying dis-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 335, + 470, + 348 + ], + "spans": [ + { + "bbox": [ + 141, + 335, + 470, + 348 + ], + "score": 1.0, + "content": "tance metric. Subsequently, a super-graph constructed based on the super-classes", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 346, + 469, + 358 + ], + "spans": [ + { + "bbox": [ + 141, + 346, + 469, + 358 + ], + "score": 1.0, + "content": "is then fed to our proposed GNN framework which exploits the latent inter-class", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 356, + 470, + 370 + ], + "spans": [ + { + "bbox": [ + 141, + 356, + 470, + 370 + ], + "score": 1.0, + "content": "relationships made explicit by the super-graph to achieve better class label sep-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 368, + 469, + 379 + ], + "spans": [ + { + "bbox": [ + 141, + 368, + 469, + 379 + ], + "score": 1.0, + "content": "aration among the graphs. We conduct exhaustive empirical evaluations of our", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 380, + 470, + 391 + ], + "spans": [ + { + "bbox": [ + 141, + 380, + 470, + 391 + ], + "score": 1.0, + "content": "proposed method and show that it outperforms both the adaptation of state-of-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 142, + 390, + 469, + 401 + ], + "spans": [ + { + "bbox": [ + 142, + 390, + 469, + 401 + ], + "score": 1.0, + "content": "the-art graph classification methods to few-shot scenario and our naive baseline", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 142, + 401, + 469, + 412 + ], + "spans": [ + { + "bbox": [ + 142, + 401, + 469, + 412 + ], + "score": 1.0, + "content": "GNNs. Additionally, we also extend and study the behavior of our method to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 412, + 329, + 424 + ], + "spans": [ + { + "bbox": [ + 141, + 412, + 329, + 424 + ], + "score": 1.0, + "content": "semi-supervised and active learning scenarios.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 15 + }, + { + "type": "title", + "bbox": [ + 108, + 451, + 205, + 463 + ], + "lines": [ + { + "bbox": [ + 105, + 450, + 208, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 208, + 466 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 478, + 505, + 599 + ], + "lines": [ + { + "bbox": [ + 105, + 477, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 506, + 492 + ], + "score": 1.0, + "content": "The need to analyze graph structured data coupled with the ubiquitous nature of graphs (Borgwardt", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 488, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 503 + ], + "score": 1.0, + "content": "et al., 2005; Duvenaud et al., 2015; Backstrom & Leskovec, 2010; Chau et al., 2011), has given", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "greater impetus to research interest in developing graph neural networks (GNNs) (Defferrard et al.,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "score": 1.0, + "content": "2016; Kipf & Welling, 2016; Hamilton et al., 2017; Velikovi et al., 2018) for learning tasks on such", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 521, + 506, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 537 + ], + "score": 1.0, + "content": "graphs. The overarching theme in GNNs is for each node’s feature vector to be generated by passing,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 533, + 506, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 419, + 547 + ], + "score": 1.0, + "content": "transforming, and recursively aggregating feature information from a given", + "type": "text" + }, + { + "bbox": [ + 420, + 534, + 426, + 543 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 533, + 506, + 547 + ], + "score": 1.0, + "content": "-hop neighborhood", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 543, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 506, + 558 + ], + "score": 1.0, + "content": "surrounding the node. However, GNNs still fall short in the ”few-shot” learning setting, where the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 554, + 505, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 569 + ], + "score": 1.0, + "content": "classifier must generalize well after seeing abundant base-class samples (while training) and very", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "few (or even zero) samples from a novel class (while testing). Given the scarcity and difficulty", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "score": 1.0, + "content": "involved with generation of labeled graph samples, it becomes all the more important to solve the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 588, + 326, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 326, + 601 + ], + "score": 1.0, + "content": "problem of graph classification in the few-shot setting.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 605, + 504, + 671 + ], + "lines": [ + { + "bbox": [ + 106, + 604, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 604, + 506, + 617 + ], + "score": 1.0, + "content": "Limitations and challenges: Recent work by Xu et. al. (Xu et al., 2019) indicated that most", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 615, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 630 + ], + "score": 1.0, + "content": "recently proposed GNNs were designed based on empirical intuition and heuristic approaches. They", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "studied the representational power of these GNNs and identified that most neighborhood aggregation", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 638, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 505, + 651 + ], + "score": 1.0, + "content": "and graph-pooling schemes had diminished discriminative power. They rectified this problem with", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 649, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 506, + 662 + ], + "score": 1.0, + "content": "the introduction of a novel injective neighborhood aggregation scheme, making it as strong as the", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 660, + 424, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 424, + 672 + ], + "score": 1.0, + "content": "Weisfeiler-Lehman (WL) graph isomorphism test (Weisfeiler & Leman, 1968).", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 107, + 677, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "Nevertheless, the problem posed by extremely scarce novel-class samples in the few-shot setting", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 688, + 504, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 504, + 699 + ], + "score": 1.0, + "content": "remains to persist as a formidable challenge, as it requires more rounds of aggregation to affect", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 698, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 713 + ], + "score": 1.0, + "content": "larger neighborhoods and hence necessitate greater depth in the GNN. However, when it comes to", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 708, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 505, + 723 + ], + "score": 1.0, + "content": "GNNs, experimental studies have shown that an increase in the number of layers results in dramatic", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 720, + 360, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 360, + 733 + ], + "score": 1.0, + "content": "performance drops in GNNs (Wu et al., 2019; Li et al., 2018b).", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 44 + } + ], + "page_idx": 0, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 294, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 303, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 308, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 308, + 761 + ], + "score": 1.0, + "content": "1", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 79, + 502, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 79, + 505, + 99 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 505, + 99 + ], + "score": 1.0, + "content": "FEW-SHOT LEARNING ON GRAPHS VIA SUPER-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 101, + 473, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 101, + 473, + 118 + ], + "score": 1.0, + "content": "CLASSES BASED ON GRAPH SPECTRAL MEASURES", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 113, + 135, + 320, + 147 + ], + "lines": [ + { + "bbox": [ + 111, + 135, + 321, + 148 + ], + "spans": [ + { + "bbox": [ + 111, + 135, + 321, + 148 + ], + "score": 1.0, + "content": "Jatin Chauhan, Deepak Nathani, Manohar Kaul", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 2, + "bbox_fs": [ + 111, + 135, + 321, + 148 + ] + }, + { + "type": "list", + "bbox": [ + 113, + 147, + 423, + 180 + ], + "lines": [ + { + "bbox": [ + 112, + 146, + 248, + 158 + ], + "spans": [ + { + "bbox": [ + 112, + 146, + 248, + 158 + ], + "score": 1.0, + "content": "Department of Computer Science", + "type": "text" + } + ], + "index": 3, + "is_list_start_line": true + }, + { + "bbox": [ + 111, + 156, + 282, + 169 + ], + "spans": [ + { + "bbox": [ + 111, + 156, + 282, + 169 + ], + "score": 1.0, + "content": "Indian Institute of Technology Hyderabad", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 112, + 168, + 424, + 181 + ], + "spans": [ + { + "bbox": [ + 112, + 168, + 424, + 181 + ], + "score": 1.0, + "content": "{chauhanjatin100,deepakn1019,manohar.kaul}@gmail.com", + "type": "text" + } + ], + "index": 5, + "is_list_start_line": true + } + ], + "index": 4, + "bbox_fs": [ + 111, + 146, + 424, + 181 + ] + }, + { + "type": "title", + "bbox": [ + 278, + 208, + 333, + 220 + ], + "lines": [ + { + "bbox": [ + 276, + 208, + 335, + 221 + ], + "spans": [ + { + "bbox": [ + 276, + 208, + 335, + 221 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 143, + 236, + 468, + 423 + ], + "lines": [ + { + "bbox": [ + 142, + 237, + 469, + 249 + ], + "spans": [ + { + "bbox": [ + 142, + 237, + 469, + 249 + ], + "score": 1.0, + "content": "We propose to study the problem of few-shot graph classification in graph neu-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 248, + 469, + 260 + ], + "spans": [ + { + "bbox": [ + 141, + 248, + 469, + 260 + ], + "score": 1.0, + "content": "ral networks (GNNs) to recognize unseen classes, given limited labeled graph", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 259, + 470, + 270 + ], + "spans": [ + { + "bbox": [ + 141, + 259, + 470, + 270 + ], + "score": 1.0, + "content": "examples. Despite several interesting GNN variants being proposed recently for", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 270, + 469, + 281 + ], + "spans": [ + { + "bbox": [ + 141, + 270, + 469, + 281 + ], + "score": 1.0, + "content": "node and graph classification tasks, when faced with scarce labeled examples in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 280, + 469, + 292 + ], + "spans": [ + { + "bbox": [ + 141, + 280, + 469, + 292 + ], + "score": 1.0, + "content": "the few-shot setting, these GNNs exhibit significant loss in classification perfor-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 291, + 470, + 303 + ], + "spans": [ + { + "bbox": [ + 141, + 291, + 470, + 303 + ], + "score": 1.0, + "content": "mance. Here, we present an approach where a probability measure is assigned", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 302, + 470, + 314 + ], + "spans": [ + { + "bbox": [ + 141, + 302, + 470, + 314 + ], + "score": 1.0, + "content": "to each graph based on the spectrum of the graph’s normalized Laplacian. This", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 312, + 469, + 326 + ], + "spans": [ + { + "bbox": [ + 141, + 312, + 469, + 326 + ], + "score": 1.0, + "content": "enables us to accordingly cluster the graph base-labels associated with each graph", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 324, + 469, + 337 + ], + "spans": [ + { + "bbox": [ + 141, + 324, + 257, + 337 + ], + "score": 1.0, + "content": "into super-classes, where the", + "type": "text" + }, + { + "bbox": [ + 257, + 324, + 270, + 334 + ], + "score": 0.84, + "content": "L ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 324, + 469, + 337 + ], + "score": 1.0, + "content": "Wasserstein distance serves as our underlying dis-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 335, + 470, + 348 + ], + "spans": [ + { + "bbox": [ + 141, + 335, + 470, + 348 + ], + "score": 1.0, + "content": "tance metric. Subsequently, a super-graph constructed based on the super-classes", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 346, + 469, + 358 + ], + "spans": [ + { + "bbox": [ + 141, + 346, + 469, + 358 + ], + "score": 1.0, + "content": "is then fed to our proposed GNN framework which exploits the latent inter-class", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 356, + 470, + 370 + ], + "spans": [ + { + "bbox": [ + 141, + 356, + 470, + 370 + ], + "score": 1.0, + "content": "relationships made explicit by the super-graph to achieve better class label sep-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 368, + 469, + 379 + ], + "spans": [ + { + "bbox": [ + 141, + 368, + 469, + 379 + ], + "score": 1.0, + "content": "aration among the graphs. We conduct exhaustive empirical evaluations of our", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 380, + 470, + 391 + ], + "spans": [ + { + "bbox": [ + 141, + 380, + 470, + 391 + ], + "score": 1.0, + "content": "proposed method and show that it outperforms both the adaptation of state-of-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 142, + 390, + 469, + 401 + ], + "spans": [ + { + "bbox": [ + 142, + 390, + 469, + 401 + ], + "score": 1.0, + "content": "the-art graph classification methods to few-shot scenario and our naive baseline", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 142, + 401, + 469, + 412 + ], + "spans": [ + { + "bbox": [ + 142, + 401, + 469, + 412 + ], + "score": 1.0, + "content": "GNNs. Additionally, we also extend and study the behavior of our method to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 412, + 329, + 424 + ], + "spans": [ + { + "bbox": [ + 141, + 412, + 329, + 424 + ], + "score": 1.0, + "content": "semi-supervised and active learning scenarios.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 15, + "bbox_fs": [ + 141, + 237, + 470, + 424 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 451, + 205, + 463 + ], + "lines": [ + { + "bbox": [ + 105, + 450, + 208, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 208, + 466 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 478, + 505, + 599 + ], + "lines": [ + { + "bbox": [ + 105, + 477, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 506, + 492 + ], + "score": 1.0, + "content": "The need to analyze graph structured data coupled with the ubiquitous nature of graphs (Borgwardt", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 488, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 503 + ], + "score": 1.0, + "content": "et al., 2005; Duvenaud et al., 2015; Backstrom & Leskovec, 2010; Chau et al., 2011), has given", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "greater impetus to research interest in developing graph neural networks (GNNs) (Defferrard et al.,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "score": 1.0, + "content": "2016; Kipf & Welling, 2016; Hamilton et al., 2017; Velikovi et al., 2018) for learning tasks on such", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 521, + 506, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 537 + ], + "score": 1.0, + "content": "graphs. The overarching theme in GNNs is for each node’s feature vector to be generated by passing,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 533, + 506, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 419, + 547 + ], + "score": 1.0, + "content": "transforming, and recursively aggregating feature information from a given", + "type": "text" + }, + { + "bbox": [ + 420, + 534, + 426, + 543 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 533, + 506, + 547 + ], + "score": 1.0, + "content": "-hop neighborhood", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 543, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 506, + 558 + ], + "score": 1.0, + "content": "surrounding the node. However, GNNs still fall short in the ”few-shot” learning setting, where the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 554, + 505, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 569 + ], + "score": 1.0, + "content": "classifier must generalize well after seeing abundant base-class samples (while training) and very", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "few (or even zero) samples from a novel class (while testing). Given the scarcity and difficulty", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "score": 1.0, + "content": "involved with generation of labeled graph samples, it becomes all the more important to solve the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 588, + 326, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 326, + 601 + ], + "score": 1.0, + "content": "problem of graph classification in the few-shot setting.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 477, + 506, + 601 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 605, + 504, + 671 + ], + "lines": [ + { + "bbox": [ + 106, + 604, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 604, + 506, + 617 + ], + "score": 1.0, + "content": "Limitations and challenges: Recent work by Xu et. al. (Xu et al., 2019) indicated that most", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 615, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 630 + ], + "score": 1.0, + "content": "recently proposed GNNs were designed based on empirical intuition and heuristic approaches. They", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "studied the representational power of these GNNs and identified that most neighborhood aggregation", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 638, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 505, + 651 + ], + "score": 1.0, + "content": "and graph-pooling schemes had diminished discriminative power. They rectified this problem with", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 649, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 506, + 662 + ], + "score": 1.0, + "content": "the introduction of a novel injective neighborhood aggregation scheme, making it as strong as the", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 660, + 424, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 424, + 672 + ], + "score": 1.0, + "content": "Weisfeiler-Lehman (WL) graph isomorphism test (Weisfeiler & Leman, 1968).", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 604, + 506, + 672 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 677, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "Nevertheless, the problem posed by extremely scarce novel-class samples in the few-shot setting", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 688, + 504, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 504, + 699 + ], + "score": 1.0, + "content": "remains to persist as a formidable challenge, as it requires more rounds of aggregation to affect", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 698, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 713 + ], + "score": 1.0, + "content": "larger neighborhoods and hence necessitate greater depth in the GNN. However, when it comes to", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 708, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 505, + 723 + ], + "score": 1.0, + "content": "GNNs, experimental studies have shown that an increase in the number of layers results in dramatic", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 720, + 360, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 360, + 733 + ], + "score": 1.0, + "content": "performance drops in GNNs (Wu et al., 2019; Li et al., 2018b).", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 44, + "bbox_fs": [ + 105, + 676, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 182 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Our work: Motivated by the aforementioned observations and challenges, our method does the", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "following. We begin with a once-off preprocessing step. We assign a probability measure to each", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "graph, which we refer to as a graph spectral measure (similar to (Gu et al., 2015)), based on the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "spectrum of the graph’s normalized Laplacian matrix representation. Given this metric space of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 349, + 139 + ], + "score": 1.0, + "content": "graph spectral measures and the underlying distance as the", + "type": "text" + }, + { + "bbox": [ + 349, + 127, + 362, + 137 + ], + "score": 0.84, + "content": "L ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "Wasserstein distance, we compute", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "Wasserstein barycenters (Agueh & Carlier, 2011) for each set of graphs specific to a base class and", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 162 + ], + "score": 1.0, + "content": "term these barycenters as prototype graphs. With this set of prototype graphs for each base class", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 505, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 505, + 172 + ], + "score": 1.0, + "content": "label, we cluster the spectral measures associated with each prototype graph in Wasserstein space to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 172, + 210, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 210, + 182 + ], + "score": 1.0, + "content": "create a super-class label.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 187, + 505, + 242 + ], + "lines": [ + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "score": 1.0, + "content": "Utilizing this super-class information, we then build a graph of graphs called a super-graph.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "score": 1.0, + "content": "The intuition behind this is to exploit the non-explicit and latent inter-class relationships between", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 208, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 104, + 208, + 506, + 222 + ], + "score": 1.0, + "content": "graphs via their spectral measures and use a GNN on this to also introduce a relational inductive", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 219, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 505, + 233 + ], + "score": 1.0, + "content": "bias (Battaglia et al., 2018), which in turn affords us an improved sample complexity and hence", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 402, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 402, + 243 + ], + "score": 1.0, + "content": "better combinatorial generalization given such few samples to begin with.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 106, + 248, + 505, + 357 + ], + "lines": [ + { + "bbox": [ + 105, + 247, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 506, + 261 + ], + "score": 1.0, + "content": "Given, the super-classes and the super-graph, we train our proposed GNN model for few-shot learn-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 258, + 507, + 272 + ], + "spans": [ + { + "bbox": [ + 104, + 258, + 507, + 272 + ], + "score": 1.0, + "content": "ing on graphs. Our GNN consists of a graph isomorphism network (GIN) Xu et al. (2019) as a", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 270, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 178, + 282 + ], + "score": 1.0, + "content": "feature extractor", + "type": "text" + }, + { + "bbox": [ + 178, + 270, + 201, + 282 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 270, + 505, + 282 + ], + "score": 1.0, + "content": "to generate graph embeddings; on which subsequently acts our classifier", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 107, + 279, + 507, + 294 + ], + "spans": [ + { + "bbox": [ + 107, + 281, + 126, + 293 + ], + "score": 0.89, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 279, + 270, + 294 + ], + "score": 1.0, + "content": "comprising of two components: (i)", + "type": "text" + }, + { + "bbox": [ + 270, + 281, + 291, + 291 + ], + "score": 0.88, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 279, + 507, + 294 + ], + "score": 1.0, + "content": ": a MLP layer to learn and predict the super class as-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 289, + 507, + 306 + ], + "spans": [ + { + "bbox": [ + 104, + 289, + 216, + 306 + ], + "score": 1.0, + "content": "sociated to a graph, and (ii)", + "type": "text" + }, + { + "bbox": [ + 217, + 291, + 244, + 302 + ], + "score": 0.9, + "content": "\\Dot { C } ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 289, + 507, + 306 + ], + "score": 1.0, + "content": ": a graph attention network (GAT) to predict the actual class label", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 302, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 104, + 302, + 464, + 316 + ], + "score": 1.0, + "content": "of a graph. The overall loss function is a sum of the cross-entropy losses associated with", + "type": "text" + }, + { + "bbox": [ + 465, + 303, + 487, + 313 + ], + "score": 0.88, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 302, + 506, + 316 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 107, + 310, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 107, + 313, + 134, + 324 + ], + "score": 0.88, + "content": "C ^ { G A \\breve { T } }", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 310, + 506, + 329 + ], + "score": 1.0, + "content": ". We follow initialization based strategy (Chen et al., 2019), with a training and fine-tuning", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 324, + 504, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 439, + 336 + ], + "score": 1.0, + "content": "phase, so that in the fine-tuning phase, the pre-trained parameters associated with", + "type": "text" + }, + { + "bbox": [ + 440, + 325, + 462, + 336 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 324, + 482, + 336 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 482, + 325, + 504, + 335 + ], + "score": 0.88, + "content": "C ^ { s u p }", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "are frozen, and the few novel labeled graph samples are used to update the weights and attention", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 344, + 182, + 359 + ], + "spans": [ + { + "bbox": [ + 104, + 344, + 182, + 359 + ], + "score": 1.0, + "content": "learned by CGAT .", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 107, + 363, + 505, + 441 + ], + "lines": [ + { + "bbox": [ + 105, + 362, + 505, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 377 + ], + "score": 1.0, + "content": "Our contributions: To the best of our knowledge, we are the first to introduce few shot learning", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "on graphs for graph classification. Next, we propose an architecture that makes use of the graph’s", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 386, + 506, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 506, + 398 + ], + "score": 1.0, + "content": "spectral measures to generate a set of super-classes and a super-graph to better model the latent", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 397, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 505, + 408 + ], + "score": 1.0, + "content": "relations between classes, followed by our GNN trained using an initialization method. Finally, we", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "conduct extensive experiments to gain insight into our method. For example, in the 20-shot setting", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 417, + 504, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 450, + 431 + ], + "score": 1.0, + "content": "on the TRIANGLES dataset, our method shows a substantial improvement of nearly", + "type": "text" + }, + { + "bbox": [ + 450, + 418, + 465, + 429 + ], + "score": 0.86, + "content": "7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 417, + 484, + 431 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 484, + 418, + 504, + 429 + ], + "score": 0.87, + "content": "2 0 \\%", + "type": "inline_equation" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 430, + 333, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 333, + 442 + ], + "score": 1.0, + "content": "over DL-based and unsupervised baselines, respectively.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27 + }, + { + "type": "title", + "bbox": [ + 108, + 471, + 210, + 484 + ], + "lines": [ + { + "bbox": [ + 104, + 470, + 213, + 487 + ], + "spans": [ + { + "bbox": [ + 104, + 470, + 213, + 487 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 506, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "Few-shot learning in the computer vision community was first introduced by (Fei-Fei et al., 2006)", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "with the intuition that learning the underlying properties of the base classes given abundant samples", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 527, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 505, + 542 + ], + "score": 1.0, + "content": "can help generalize better to unseen classes with few-labeled samples available. Various learning", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "algorithms have been proposed in the image domain, among which a broad category of initializa-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "score": 1.0, + "content": "tion based methods aim to learn transferable knowledge from training classes, so that the model", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 562, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 562, + 505, + 573 + ], + "score": 1.0, + "content": "can be adapted to unseen classes with limited labeled examples (Finn et al., 2017); (Rusu et al.,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "2018); (Nichol et al., 2018). Recently proposed and widely accepted Initialization based methods", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 595 + ], + "score": 1.0, + "content": "can broadly be classified into: (i) methods that learn good model parameters with limited labeled", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 594, + 504, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 504, + 606 + ], + "score": 1.0, + "content": "examples and a small number of gradient update steps (Finn et al., 2017) and (ii) methods that learn", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "an optimizer (Ravi & Larochelle, 2017). We refer the interested reader to Chen et. al. (Chen et al.,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 615, + 368, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 368, + 628 + ], + "score": 1.0, + "content": "2019) for more examples of few-shot learning methods in vision.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "Graph neural networks (GNNs) were first introduced in (Gori et al., 2005); (Scarselli et al., 2009)", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "score": 1.0, + "content": "as recurrent message passing algorithms. Subsequent work (Bruna et al., 2014); (Henaff et al.,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 655, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 668 + ], + "score": 1.0, + "content": "2015) proposed to learn smooth spectral multipliers of the graph Laplacian, but incurred higher", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "computational cost. This computational bottleneck was later resolved (Defferrard et al., 2016); (Kipf", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "& Welling, 2016) by learning polynomials of the graph Laplacian. GNNs are a natural extension to", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "Convolutional neural networks (CNNs) on non-Euclidean data. Recent work (Velikovi et al., 2018)", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "introduced the concept of self-attention in GNNs, which allows each node to provide attention to", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "the enclosing neighborhood resulting in improved learning. We refer the reader to (Bronstein et al.,", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 720, + 272, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 272, + 732 + ], + "score": 1.0, + "content": "2016) for detailed information on GNNs.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 47 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "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, + 182 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Our work: Motivated by the aforementioned observations and challenges, our method does the", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "following. We begin with a once-off preprocessing step. We assign a probability measure to each", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "graph, which we refer to as a graph spectral measure (similar to (Gu et al., 2015)), based on the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "spectrum of the graph’s normalized Laplacian matrix representation. Given this metric space of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 349, + 139 + ], + "score": 1.0, + "content": "graph spectral measures and the underlying distance as the", + "type": "text" + }, + { + "bbox": [ + 349, + 127, + 362, + 137 + ], + "score": 0.84, + "content": "L ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "Wasserstein distance, we compute", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "Wasserstein barycenters (Agueh & Carlier, 2011) for each set of graphs specific to a base class and", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 162 + ], + "score": 1.0, + "content": "term these barycenters as prototype graphs. With this set of prototype graphs for each base class", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 505, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 505, + 172 + ], + "score": 1.0, + "content": "label, we cluster the spectral measures associated with each prototype graph in Wasserstein space to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 172, + 210, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 210, + 182 + ], + "score": 1.0, + "content": "create a super-class label.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 4, + "bbox_fs": [ + 105, + 82, + 506, + 182 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 187, + 505, + 242 + ], + "lines": [ + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "score": 1.0, + "content": "Utilizing this super-class information, we then build a graph of graphs called a super-graph.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "score": 1.0, + "content": "The intuition behind this is to exploit the non-explicit and latent inter-class relationships between", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 208, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 104, + 208, + 506, + 222 + ], + "score": 1.0, + "content": "graphs via their spectral measures and use a GNN on this to also introduce a relational inductive", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 219, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 505, + 233 + ], + "score": 1.0, + "content": "bias (Battaglia et al., 2018), which in turn affords us an improved sample complexity and hence", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 402, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 402, + 243 + ], + "score": 1.0, + "content": "better combinatorial generalization given such few samples to begin with.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11, + "bbox_fs": [ + 104, + 186, + 506, + 243 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 248, + 505, + 357 + ], + "lines": [ + { + "bbox": [ + 105, + 247, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 506, + 261 + ], + "score": 1.0, + "content": "Given, the super-classes and the super-graph, we train our proposed GNN model for few-shot learn-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 258, + 507, + 272 + ], + "spans": [ + { + "bbox": [ + 104, + 258, + 507, + 272 + ], + "score": 1.0, + "content": "ing on graphs. Our GNN consists of a graph isomorphism network (GIN) Xu et al. (2019) as a", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 270, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 178, + 282 + ], + "score": 1.0, + "content": "feature extractor", + "type": "text" + }, + { + "bbox": [ + 178, + 270, + 201, + 282 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 270, + 505, + 282 + ], + "score": 1.0, + "content": "to generate graph embeddings; on which subsequently acts our classifier", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 107, + 279, + 507, + 294 + ], + "spans": [ + { + "bbox": [ + 107, + 281, + 126, + 293 + ], + "score": 0.89, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 279, + 270, + 294 + ], + "score": 1.0, + "content": "comprising of two components: (i)", + "type": "text" + }, + { + "bbox": [ + 270, + 281, + 291, + 291 + ], + "score": 0.88, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 279, + 507, + 294 + ], + "score": 1.0, + "content": ": a MLP layer to learn and predict the super class as-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 289, + 507, + 306 + ], + "spans": [ + { + "bbox": [ + 104, + 289, + 216, + 306 + ], + "score": 1.0, + "content": "sociated to a graph, and (ii)", + "type": "text" + }, + { + "bbox": [ + 217, + 291, + 244, + 302 + ], + "score": 0.9, + "content": "\\Dot { C } ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 289, + 507, + 306 + ], + "score": 1.0, + "content": ": a graph attention network (GAT) to predict the actual class label", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 302, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 104, + 302, + 464, + 316 + ], + "score": 1.0, + "content": "of a graph. The overall loss function is a sum of the cross-entropy losses associated with", + "type": "text" + }, + { + "bbox": [ + 465, + 303, + 487, + 313 + ], + "score": 0.88, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 302, + 506, + 316 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 107, + 310, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 107, + 313, + 134, + 324 + ], + "score": 0.88, + "content": "C ^ { G A \\breve { T } }", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 310, + 506, + 329 + ], + "score": 1.0, + "content": ". We follow initialization based strategy (Chen et al., 2019), with a training and fine-tuning", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 324, + 504, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 439, + 336 + ], + "score": 1.0, + "content": "phase, so that in the fine-tuning phase, the pre-trained parameters associated with", + "type": "text" + }, + { + "bbox": [ + 440, + 325, + 462, + 336 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 324, + 482, + 336 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 482, + 325, + 504, + 335 + ], + "score": 0.88, + "content": "C ^ { s u p }", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "are frozen, and the few novel labeled graph samples are used to update the weights and attention", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 344, + 182, + 359 + ], + "spans": [ + { + "bbox": [ + 104, + 344, + 182, + 359 + ], + "score": 1.0, + "content": "learned by CGAT .", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 18.5, + "bbox_fs": [ + 104, + 247, + 507, + 359 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 363, + 505, + 441 + ], + "lines": [ + { + "bbox": [ + 105, + 362, + 505, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 377 + ], + "score": 1.0, + "content": "Our contributions: To the best of our knowledge, we are the first to introduce few shot learning", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "on graphs for graph classification. Next, we propose an architecture that makes use of the graph’s", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 386, + 506, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 506, + 398 + ], + "score": 1.0, + "content": "spectral measures to generate a set of super-classes and a super-graph to better model the latent", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 397, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 505, + 408 + ], + "score": 1.0, + "content": "relations between classes, followed by our GNN trained using an initialization method. Finally, we", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "conduct extensive experiments to gain insight into our method. For example, in the 20-shot setting", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 417, + 504, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 450, + 431 + ], + "score": 1.0, + "content": "on the TRIANGLES dataset, our method shows a substantial improvement of nearly", + "type": "text" + }, + { + "bbox": [ + 450, + 418, + 465, + 429 + ], + "score": 0.86, + "content": "7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 417, + 484, + 431 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 484, + 418, + 504, + 429 + ], + "score": 0.87, + "content": "2 0 \\%", + "type": "inline_equation" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 430, + 333, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 333, + 442 + ], + "score": 1.0, + "content": "over DL-based and unsupervised baselines, respectively.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 362, + 506, + 442 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 471, + 210, + 484 + ], + "lines": [ + { + "bbox": [ + 104, + 470, + 213, + 487 + ], + "spans": [ + { + "bbox": [ + 104, + 470, + 213, + 487 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 506, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "Few-shot learning in the computer vision community was first introduced by (Fei-Fei et al., 2006)", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "with the intuition that learning the underlying properties of the base classes given abundant samples", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 527, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 505, + 542 + ], + "score": 1.0, + "content": "can help generalize better to unseen classes with few-labeled samples available. Various learning", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "algorithms have been proposed in the image domain, among which a broad category of initializa-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "score": 1.0, + "content": "tion based methods aim to learn transferable knowledge from training classes, so that the model", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 562, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 562, + 505, + 573 + ], + "score": 1.0, + "content": "can be adapted to unseen classes with limited labeled examples (Finn et al., 2017); (Rusu et al.,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "2018); (Nichol et al., 2018). Recently proposed and widely accepted Initialization based methods", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 595 + ], + "score": 1.0, + "content": "can broadly be classified into: (i) methods that learn good model parameters with limited labeled", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 594, + 504, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 504, + 606 + ], + "score": 1.0, + "content": "examples and a small number of gradient update steps (Finn et al., 2017) and (ii) methods that learn", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "an optimizer (Ravi & Larochelle, 2017). We refer the interested reader to Chen et. al. (Chen et al.,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 615, + 368, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 368, + 628 + ], + "score": 1.0, + "content": "2019) for more examples of few-shot learning methods in vision.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 506, + 506, + 628 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "Graph neural networks (GNNs) were first introduced in (Gori et al., 2005); (Scarselli et al., 2009)", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "score": 1.0, + "content": "as recurrent message passing algorithms. Subsequent work (Bruna et al., 2014); (Henaff et al.,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 655, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 668 + ], + "score": 1.0, + "content": "2015) proposed to learn smooth spectral multipliers of the graph Laplacian, but incurred higher", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "computational cost. This computational bottleneck was later resolved (Defferrard et al., 2016); (Kipf", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "& Welling, 2016) by learning polynomials of the graph Laplacian. GNNs are a natural extension to", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "Convolutional neural networks (CNNs) on non-Euclidean data. Recent work (Velikovi et al., 2018)", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "introduced the concept of self-attention in GNNs, which allows each node to provide attention to", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "the enclosing neighborhood resulting in improved learning. We refer the reader to (Bronstein et al.,", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 720, + 272, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 272, + 732 + ], + "score": 1.0, + "content": "2016) for detailed information on GNNs.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 47, + "bbox_fs": [ + 105, + 633, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 137 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 504, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 504, + 94 + ], + "score": 1.0, + "content": "Despite all the success of GNNs, few-shot classification remains an under-addressed problem. Some", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "recent attempts have focused on solving the few-shot learning on graph data where GNNs are either", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "score": 1.0, + "content": "trained via co-training and self-training (Li et al., 2018a), or extended by stacking transposed graph", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "convolutional layers imputing a structural regularizer (Zhang et al., 2019) - however, both these", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 301, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 301, + 138 + ], + "score": 1.0, + "content": "works focus only on the node classification task.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 106, + 143, + 504, + 165 + ], + "lines": [ + { + "bbox": [ + 106, + 142, + 504, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 142, + 504, + 156 + ], + "score": 1.0, + "content": "To the best of our knowledge, there does not exist any work pertaining few-shot learning on graphs", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 447, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 447, + 166 + ], + "score": 1.0, + "content": "focusing on the graph classification task, thus providing the motivation for this work.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 107, + 171, + 505, + 489 + ], + "lines": [ + { + "bbox": [ + 106, + 171, + 505, + 184 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 505, + 184 + ], + "score": 1.0, + "content": "Comparison to few-shot learning on images: Few shot learning (FSL) has gained wide-spread", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 181, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 505, + 195 + ], + "score": 1.0, + "content": "traction in the image domain in recent years. However the success of FSL in images is not eas-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 193, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 106, + 193, + 505, + 206 + ], + "score": 1.0, + "content": "ily translated to the graph domain for the following reasons: (a) Images are typically represented", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 205, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 205, + 505, + 216 + ], + "score": 1.0, + "content": "in Euclidean space and thus can easily be manipulated and handled using well-known metrics like", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 178, + 227 + ], + "score": 1.0, + "content": "cosine similarity,", + "type": "text" + }, + { + "bbox": [ + 178, + 215, + 191, + 227 + ], + "score": 0.92, + "content": "L _ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "norms etc. However, graphs come from non-Euclidean domains and exhibit", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 227, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 505, + 238 + ], + "score": 1.0, + "content": "much more complex relationships and interdependency between objects. Furthermore, the notion", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 237, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 505, + 249 + ], + "score": 1.0, + "content": "of a distance between graphs is also not straightforward and requires construction of graph kernels", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 248, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 505, + 261 + ], + "score": 1.0, + "content": "or the use of standard metrics on graph embeddings (Kriege et al., 2019). Additionally, such graph", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 258, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 506, + 272 + ], + "score": 1.0, + "content": "kernels dont capture higher order relations very well. (b) In the FSL setting on images, the number", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 270, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 505, + 283 + ], + "score": 1.0, + "content": "of training samples from various classes is also abundantly more than what is available for graph", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 281, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 505, + 294 + ], + "score": 1.0, + "content": "datasets. The image domain allows training generative models to learn the task distribution and can", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 291, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 505, + 305 + ], + "score": 1.0, + "content": "further be used to generate samples for data augmentation, which act as very good priors. In contrast,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 302, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 505, + 316 + ], + "score": 1.0, + "content": "graph generative models are still in their infancy and work in very restricted settings. Furthermore,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 104, + 313, + 506, + 327 + ], + "score": 1.0, + "content": "methods like cropping and rotation to improve the models can’t be used for graphs given the per-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 324, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 338 + ], + "score": 1.0, + "content": "mutation invariant nature of graphs. Additionally, removal of any component from the graph can", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 336, + 506, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 506, + 349 + ], + "score": 1.0, + "content": "adversely affect its structural properties, such as in biological datasets. (c) The image domain has", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 347, + 506, + 359 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 506, + 359 + ], + "score": 1.0, + "content": "very well-known regularization methods (e.g. Tikhonov, Lasso) that help generalize much better to", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "novel datasets. Although, they dont bring any extra supervised information and hence cannot fully", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "address the problem of FSL in the image domain. To the best of our knowledge, this is still an open", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "score": 1.0, + "content": "research problem in the image domain. On the other hand, in the graph domain, our work would", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "be a first step towards graph classification in an FSL setting, which would then hopefully pave the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 401, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 506, + 415 + ], + "score": 1.0, + "content": "path for better FSL graph regularizers. (d) Transfer learning has led to substantial improvements", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "on various image related tasks due to the high degree of transferability of feature extractors. Thus,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "downstream tasks like few-shot learning can be performed well with high quality feature extractor", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "score": 1.0, + "content": "models, such as Resnet variants trained on Imagenet. Transfer learning, or for that matter even good", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 445, + 506, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 506, + 458 + ], + "score": 1.0, + "content": "feature extractors, remains a daunting challenge in the graph domain. For graphs, there neither exists", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 456, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 469 + ], + "score": 1.0, + "content": "a dataset which can serve as a pivot for high quality feature learning, nor does there exist a Graph", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "score": 1.0, + "content": "NN which can capture the higher order relations between various categories of graphs, thus making", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 478, + 245, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 245, + 491 + ], + "score": 1.0, + "content": "this a highly challenging problem.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 21 + }, + { + "type": "title", + "bbox": [ + 108, + 507, + 207, + 519 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 209, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 209, + 522 + ], + "score": 1.0, + "content": "3 PRELIMINARIES", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 533, + 505, + 577 + ], + "lines": [ + { + "bbox": [ + 105, + 533, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 505, + 545 + ], + "score": 1.0, + "content": "In this section, we introduce our notation and provide the necessary background for our few-shot", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 544, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 505, + 556 + ], + "score": 1.0, + "content": "learning setup on graphs. We begin by describing the various data sample types, followed by our", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "score": 1.0, + "content": "learning procedure, in order to formally define few-shot learning on graphs. Finally, we define the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 566, + 306, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 306, + 579 + ], + "score": 1.0, + "content": "graph spectral distance between a pair of graphs.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 106, + 582, + 505, + 658 + ], + "lines": [ + { + "bbox": [ + 106, + 582, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 198, + 595 + ], + "score": 1.0, + "content": "Data sample sets: Let", + "type": "text" + }, + { + "bbox": [ + 198, + 583, + 206, + 594 + ], + "score": 0.81, + "content": "\\mathcal { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 582, + 403, + 595 + ], + "score": 1.0, + "content": "denote a set of undirected unweighted graphs and", + "type": "text" + }, + { + "bbox": [ + 403, + 583, + 412, + 594 + ], + "score": 0.81, + "content": "\\mathcal { V }", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 582, + 506, + 595 + ], + "score": 1.0, + "content": "be the set of associated", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "class labels. We consider two disjoint populations of labeled graphs consisting of i.i.d. graph sam-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 601, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 269, + 624 + ], + "score": 1.0, + "content": "ples, the set of base class labeled graphs", + "type": "text" + }, + { + "bbox": [ + 270, + 605, + 371, + 619 + ], + "score": 0.92, + "content": "\\mathbf { \\bar { { G } } } _ { B } = \\{ ( g _ { i } ^ { ( B ) } , y _ { i } ^ { ( B ) } ) \\bar \\} _ { i = 1 } ^ { n } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 607, + 506, + 619 + ], + "score": 1.0, + "content": "and the set of novel class labeled", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 104, + 615, + 507, + 642 + ], + "spans": [ + { + "bbox": [ + 104, + 617, + 136, + 638 + ], + "score": 1.0, + "content": "graphs", + "type": "text" + }, + { + "bbox": [ + 136, + 619, + 239, + 634 + ], + "score": 0.93, + "content": "G _ { N } = \\{ ( g _ { i } ^ { ( N ) } , y _ { i } ^ { ( N ) } ) \\} _ { i = 1 } ^ { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 615, + 284, + 642 + ], + "score": 1.0, + "content": "y(N )i )}mi=1, where g(Bi", + "type": "text" + }, + { + "bbox": [ + 270, + 619, + 387, + 634 + ], + "score": 0.78, + "content": "g _ { i } ^ { ( B ) } , g _ { i } ^ { ( N ) } \\in \\mathcal { G } , y _ { i } ^ { ( B ) } \\in \\mathcal { V } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 615, + 421, + 637 + ], + "score": 1.0, + "content": "y(B)i ∈ Y (B), and y(Ni", + "type": "text" + }, + { + "bbox": [ + 408, + 618, + 461, + 633 + ], + "score": 0.91, + "content": "y _ { i } ^ { ( N ) } \\in \\mathcal { y } ^ { ( N ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 618, + 507, + 635 + ], + "score": 1.0, + "content": ". Here, the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 104, + 631, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 104, + 631, + 299, + 648 + ], + "score": 1.0, + "content": "set of base and novel class labels are denoted by", + "type": "text" + }, + { + "bbox": [ + 299, + 634, + 379, + 646 + ], + "score": 0.91, + "content": "{ \\mathcal { V } } ^ { ( B ) } = \\{ 1 , \\ldots , K \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 380, + 631, + 397, + 648 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 398, + 633, + 501, + 646 + ], + "score": 0.91, + "content": "\\mathcal { V } ^ { ( N ) } = \\{ K + 1 , \\ldots , K ^ { \\prime } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 631, + 506, + 648 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 104, + 644, + 505, + 659 + ], + "spans": [ + { + "bbox": [ + 104, + 644, + 185, + 659 + ], + "score": 1.0, + "content": "respectively, where", + "type": "text" + }, + { + "bbox": [ + 186, + 646, + 221, + 657 + ], + "score": 0.91, + "content": "K ^ { \\prime } > K", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 644, + 247, + 659 + ], + "score": 1.0, + "content": ". Both", + "type": "text" + }, + { + "bbox": [ + 248, + 645, + 269, + 657 + ], + "score": 0.91, + "content": "\\mathcal { V } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 644, + 287, + 659 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 288, + 646, + 309, + 658 + ], + "score": 0.91, + "content": "\\mathcal { V } ^ { ( N ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 644, + 400, + 659 + ], + "score": 1.0, + "content": "are disjoint subsets of", + "type": "text" + }, + { + "bbox": [ + 401, + 647, + 409, + 657 + ], + "score": 0.75, + "content": "\\mathcal { V }", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 644, + 426, + 659 + ], + "score": 1.0, + "content": ", so,", + "type": "text" + }, + { + "bbox": [ + 427, + 646, + 499, + 658 + ], + "score": 0.91, + "content": "\\mathcal { V } ^ { ( B ) } \\cap \\mathcal { V } ^ { ( N ) } = \\emptyset", + "type": "inline_equation" + }, + { + "bbox": [ + 500, + 644, + 505, + 659 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 43.5 + }, + { + "type": "text", + "bbox": [ + 107, + 663, + 505, + 700 + ], + "lines": [ + { + "bbox": [ + 105, + 662, + 505, + 676 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 147, + 676 + ], + "score": 1.0, + "content": "Note that", + "type": "text" + }, + { + "bbox": [ + 147, + 665, + 182, + 674 + ], + "score": 0.87, + "content": "m \\ll n", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 662, + 505, + 676 + ], + "score": 1.0, + "content": ", i.e., there are far fewer novel class labeled graphs compared to the base class", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 673, + 505, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 673, + 204, + 687 + ], + "score": 1.0, + "content": "labeled ones. Besides", + "type": "text" + }, + { + "bbox": [ + 205, + 675, + 221, + 685 + ], + "score": 0.87, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 673, + 243, + 687 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 243, + 675, + 259, + 686 + ], + "score": 0.88, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 673, + 356, + 687 + ], + "score": 1.0, + "content": ", we consider a set of", + "type": "text" + }, + { + "bbox": [ + 357, + 676, + 362, + 685 + ], + "score": 0.77, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 673, + 471, + 687 + ], + "score": 1.0, + "content": "unlabeled unseen graphs", + "type": "text" + }, + { + "bbox": [ + 471, + 675, + 505, + 686 + ], + "score": 0.88, + "content": "\\begin{array} { l l } { G _ { U } } & { : = } \\end{array}", + "type": "inline_equation" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 685, + 344, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 685, + 292, + 700 + ], + "score": 0.89, + "content": "\\{ g _ { 1 } ^ { ( U ) } , \\ldots , g _ { t } ^ { ( U ) } \\mid g _ { i } ^ { ( U ) } \\in \\pi _ { 1 } ( G _ { N } ) , i = 1 \\ldots t \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 685, + 344, + 702 + ], + "score": 1.0, + "content": ", for testing1.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 105, + 711, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 708, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 118, + 708, + 197, + 724 + ], + "score": 1.0, + "content": "1We use the notation", + "type": "text" + }, + { + "bbox": [ + 198, + 712, + 219, + 722 + ], + "score": 0.91, + "content": "\\pi _ { 1 } ( p )", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 708, + 237, + 724 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 237, + 712, + 259, + 722 + ], + "score": 0.9, + "content": "\\pi _ { 2 } ( p )", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 708, + 467, + 724 + ], + "score": 1.0, + "content": "to denote the left and right projection of an ordered pair", + "type": "text" + }, + { + "bbox": [ + 467, + 714, + 473, + 722 + ], + "score": 0.79, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 473, + 708, + 506, + 724 + ], + "score": 1.0, + "content": ", respec-", + "type": "text" + } + ] + }, + { + "bbox": [ + 104, + 718, + 132, + 734 + ], + "spans": [ + { + "bbox": [ + 104, + 718, + 132, + 734 + ], + "score": 1.0, + "content": "tively.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "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": "text", + "bbox": [ + 107, + 82, + 505, + 137 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 504, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 504, + 94 + ], + "score": 1.0, + "content": "Despite all the success of GNNs, few-shot classification remains an under-addressed problem. Some", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "recent attempts have focused on solving the few-shot learning on graph data where GNNs are either", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "score": 1.0, + "content": "trained via co-training and self-training (Li et al., 2018a), or extended by stacking transposed graph", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "convolutional layers imputing a structural regularizer (Zhang et al., 2019) - however, both these", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 301, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 301, + 138 + ], + "score": 1.0, + "content": "works focus only on the node classification task.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2, + "bbox_fs": [ + 105, + 82, + 505, + 138 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 143, + 504, + 165 + ], + "lines": [ + { + "bbox": [ + 106, + 142, + 504, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 142, + 504, + 156 + ], + "score": 1.0, + "content": "To the best of our knowledge, there does not exist any work pertaining few-shot learning on graphs", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 447, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 447, + 166 + ], + "score": 1.0, + "content": "focusing on the graph classification task, thus providing the motivation for this work.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5, + "bbox_fs": [ + 106, + 142, + 504, + 166 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 171, + 505, + 489 + ], + "lines": [ + { + "bbox": [ + 106, + 171, + 505, + 184 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 505, + 184 + ], + "score": 1.0, + "content": "Comparison to few-shot learning on images: Few shot learning (FSL) has gained wide-spread", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 181, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 505, + 195 + ], + "score": 1.0, + "content": "traction in the image domain in recent years. However the success of FSL in images is not eas-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 193, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 106, + 193, + 505, + 206 + ], + "score": 1.0, + "content": "ily translated to the graph domain for the following reasons: (a) Images are typically represented", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 205, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 205, + 505, + 216 + ], + "score": 1.0, + "content": "in Euclidean space and thus can easily be manipulated and handled using well-known metrics like", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 178, + 227 + ], + "score": 1.0, + "content": "cosine similarity,", + "type": "text" + }, + { + "bbox": [ + 178, + 215, + 191, + 227 + ], + "score": 0.92, + "content": "L _ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "norms etc. However, graphs come from non-Euclidean domains and exhibit", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 227, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 505, + 238 + ], + "score": 1.0, + "content": "much more complex relationships and interdependency between objects. Furthermore, the notion", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 237, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 505, + 249 + ], + "score": 1.0, + "content": "of a distance between graphs is also not straightforward and requires construction of graph kernels", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 248, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 505, + 261 + ], + "score": 1.0, + "content": "or the use of standard metrics on graph embeddings (Kriege et al., 2019). Additionally, such graph", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 258, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 506, + 272 + ], + "score": 1.0, + "content": "kernels dont capture higher order relations very well. (b) In the FSL setting on images, the number", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 270, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 505, + 283 + ], + "score": 1.0, + "content": "of training samples from various classes is also abundantly more than what is available for graph", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 281, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 505, + 294 + ], + "score": 1.0, + "content": "datasets. The image domain allows training generative models to learn the task distribution and can", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 291, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 505, + 305 + ], + "score": 1.0, + "content": "further be used to generate samples for data augmentation, which act as very good priors. In contrast,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 302, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 505, + 316 + ], + "score": 1.0, + "content": "graph generative models are still in their infancy and work in very restricted settings. Furthermore,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 104, + 313, + 506, + 327 + ], + "score": 1.0, + "content": "methods like cropping and rotation to improve the models can’t be used for graphs given the per-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 324, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 338 + ], + "score": 1.0, + "content": "mutation invariant nature of graphs. Additionally, removal of any component from the graph can", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 336, + 506, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 506, + 349 + ], + "score": 1.0, + "content": "adversely affect its structural properties, such as in biological datasets. (c) The image domain has", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 347, + 506, + 359 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 506, + 359 + ], + "score": 1.0, + "content": "very well-known regularization methods (e.g. Tikhonov, Lasso) that help generalize much better to", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "novel datasets. Although, they dont bring any extra supervised information and hence cannot fully", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "address the problem of FSL in the image domain. To the best of our knowledge, this is still an open", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "score": 1.0, + "content": "research problem in the image domain. On the other hand, in the graph domain, our work would", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "be a first step towards graph classification in an FSL setting, which would then hopefully pave the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 401, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 506, + 415 + ], + "score": 1.0, + "content": "path for better FSL graph regularizers. (d) Transfer learning has led to substantial improvements", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "on various image related tasks due to the high degree of transferability of feature extractors. Thus,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "downstream tasks like few-shot learning can be performed well with high quality feature extractor", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "score": 1.0, + "content": "models, such as Resnet variants trained on Imagenet. Transfer learning, or for that matter even good", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 445, + 506, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 506, + 458 + ], + "score": 1.0, + "content": "feature extractors, remains a daunting challenge in the graph domain. For graphs, there neither exists", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 456, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 469 + ], + "score": 1.0, + "content": "a dataset which can serve as a pivot for high quality feature learning, nor does there exist a Graph", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "score": 1.0, + "content": "NN which can capture the higher order relations between various categories of graphs, thus making", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 478, + 245, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 245, + 491 + ], + "score": 1.0, + "content": "this a highly challenging problem.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 21, + "bbox_fs": [ + 104, + 171, + 506, + 491 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 507, + 207, + 519 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 209, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 209, + 522 + ], + "score": 1.0, + "content": "3 PRELIMINARIES", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 533, + 505, + 577 + ], + "lines": [ + { + "bbox": [ + 105, + 533, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 505, + 545 + ], + "score": 1.0, + "content": "In this section, we introduce our notation and provide the necessary background for our few-shot", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 544, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 505, + 556 + ], + "score": 1.0, + "content": "learning setup on graphs. We begin by describing the various data sample types, followed by our", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "score": 1.0, + "content": "learning procedure, in order to formally define few-shot learning on graphs. Finally, we define the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 566, + 306, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 306, + 579 + ], + "score": 1.0, + "content": "graph spectral distance between a pair of graphs.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 533, + 505, + 579 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 582, + 505, + 658 + ], + "lines": [ + { + "bbox": [ + 106, + 582, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 198, + 595 + ], + "score": 1.0, + "content": "Data sample sets: Let", + "type": "text" + }, + { + "bbox": [ + 198, + 583, + 206, + 594 + ], + "score": 0.81, + "content": "\\mathcal { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 582, + 403, + 595 + ], + "score": 1.0, + "content": "denote a set of undirected unweighted graphs and", + "type": "text" + }, + { + "bbox": [ + 403, + 583, + 412, + 594 + ], + "score": 0.81, + "content": "\\mathcal { V }", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 582, + 506, + 595 + ], + "score": 1.0, + "content": "be the set of associated", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "class labels. We consider two disjoint populations of labeled graphs consisting of i.i.d. graph sam-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 601, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 269, + 624 + ], + "score": 1.0, + "content": "ples, the set of base class labeled graphs", + "type": "text" + }, + { + "bbox": [ + 270, + 605, + 371, + 619 + ], + "score": 0.92, + "content": "\\mathbf { \\bar { { G } } } _ { B } = \\{ ( g _ { i } ^ { ( B ) } , y _ { i } ^ { ( B ) } ) \\bar \\} _ { i = 1 } ^ { n } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 607, + 506, + 619 + ], + "score": 1.0, + "content": "and the set of novel class labeled", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 104, + 615, + 507, + 642 + ], + "spans": [ + { + "bbox": [ + 104, + 617, + 136, + 638 + ], + "score": 1.0, + "content": "graphs", + "type": "text" + }, + { + "bbox": [ + 136, + 619, + 239, + 634 + ], + "score": 0.93, + "content": "G _ { N } = \\{ ( g _ { i } ^ { ( N ) } , y _ { i } ^ { ( N ) } ) \\} _ { i = 1 } ^ { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 615, + 284, + 642 + ], + "score": 1.0, + "content": "y(N )i )}mi=1, where g(Bi", + "type": "text" + }, + { + "bbox": [ + 270, + 619, + 387, + 634 + ], + "score": 0.78, + "content": "g _ { i } ^ { ( B ) } , g _ { i } ^ { ( N ) } \\in \\mathcal { G } , y _ { i } ^ { ( B ) } \\in \\mathcal { V } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 615, + 421, + 637 + ], + "score": 1.0, + "content": "y(B)i ∈ Y (B), and y(Ni", + "type": "text" + }, + { + "bbox": [ + 408, + 618, + 461, + 633 + ], + "score": 0.91, + "content": "y _ { i } ^ { ( N ) } \\in \\mathcal { y } ^ { ( N ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 618, + 507, + 635 + ], + "score": 1.0, + "content": ". Here, the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 104, + 631, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 104, + 631, + 299, + 648 + ], + "score": 1.0, + "content": "set of base and novel class labels are denoted by", + "type": "text" + }, + { + "bbox": [ + 299, + 634, + 379, + 646 + ], + "score": 0.91, + "content": "{ \\mathcal { V } } ^ { ( B ) } = \\{ 1 , \\ldots , K \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 380, + 631, + 397, + 648 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 398, + 633, + 501, + 646 + ], + "score": 0.91, + "content": "\\mathcal { V } ^ { ( N ) } = \\{ K + 1 , \\ldots , K ^ { \\prime } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 631, + 506, + 648 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 104, + 644, + 505, + 659 + ], + "spans": [ + { + "bbox": [ + 104, + 644, + 185, + 659 + ], + "score": 1.0, + "content": "respectively, where", + "type": "text" + }, + { + "bbox": [ + 186, + 646, + 221, + 657 + ], + "score": 0.91, + "content": "K ^ { \\prime } > K", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 644, + 247, + 659 + ], + "score": 1.0, + "content": ". Both", + "type": "text" + }, + { + "bbox": [ + 248, + 645, + 269, + 657 + ], + "score": 0.91, + "content": "\\mathcal { V } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 644, + 287, + 659 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 288, + 646, + 309, + 658 + ], + "score": 0.91, + "content": "\\mathcal { V } ^ { ( N ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 644, + 400, + 659 + ], + "score": 1.0, + "content": "are disjoint subsets of", + "type": "text" + }, + { + "bbox": [ + 401, + 647, + 409, + 657 + ], + "score": 0.75, + "content": "\\mathcal { V }", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 644, + 426, + 659 + ], + "score": 1.0, + "content": ", so,", + "type": "text" + }, + { + "bbox": [ + 427, + 646, + 499, + 658 + ], + "score": 0.91, + "content": "\\mathcal { V } ^ { ( B ) } \\cap \\mathcal { V } ^ { ( N ) } = \\emptyset", + "type": "inline_equation" + }, + { + "bbox": [ + 500, + 644, + 505, + 659 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 43.5, + "bbox_fs": [ + 104, + 582, + 507, + 659 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 663, + 505, + 700 + ], + "lines": [ + { + "bbox": [ + 105, + 662, + 505, + 676 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 147, + 676 + ], + "score": 1.0, + "content": "Note that", + "type": "text" + }, + { + "bbox": [ + 147, + 665, + 182, + 674 + ], + "score": 0.87, + "content": "m \\ll n", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 662, + 505, + 676 + ], + "score": 1.0, + "content": ", i.e., there are far fewer novel class labeled graphs compared to the base class", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 673, + 505, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 673, + 204, + 687 + ], + "score": 1.0, + "content": "labeled ones. Besides", + "type": "text" + }, + { + "bbox": [ + 205, + 675, + 221, + 685 + ], + "score": 0.87, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 673, + 243, + 687 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 243, + 675, + 259, + 686 + ], + "score": 0.88, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 673, + 356, + 687 + ], + "score": 1.0, + "content": ", we consider a set of", + "type": "text" + }, + { + "bbox": [ + 357, + 676, + 362, + 685 + ], + "score": 0.77, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 673, + 471, + 687 + ], + "score": 1.0, + "content": "unlabeled unseen graphs", + "type": "text" + }, + { + "bbox": [ + 471, + 675, + 505, + 686 + ], + "score": 0.88, + "content": "\\begin{array} { l l } { G _ { U } } & { : = } \\end{array}", + "type": "inline_equation" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 685, + 344, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 685, + 292, + 700 + ], + "score": 0.89, + "content": "\\{ g _ { 1 } ^ { ( U ) } , \\ldots , g _ { t } ^ { ( U ) } \\mid g _ { i } ^ { ( U ) } \\in \\pi _ { 1 } ( G _ { N } ) , i = 1 \\ldots t \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 685, + 344, + 702 + ], + "score": 1.0, + "content": ", for testing1.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48, + "bbox_fs": [ + 105, + 662, + 505, + 702 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 104, + 80, + 506, + 97 + ], + "spans": [ + { + "bbox": [ + 104, + 80, + 506, + 97 + ], + "score": 1.0, + "content": "Learning procedure: Inspired by the initialization based methods, we similarly follow a two-stage", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 290, + 108 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 290, + 108 + ], + "score": 1.0, + "content": "approach of training followed by fine-tuning.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 106, + 110, + 505, + 177 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 309, + 123 + ], + "score": 1.0, + "content": "During training, we train a graph feature extractor", + "type": "text" + }, + { + "bbox": [ + 309, + 110, + 344, + 122 + ], + "score": 0.94, + "content": "F _ { \\theta } ( G _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 110, + 447, + 123 + ], + "score": 1.0, + "content": "with network parameters", + "type": "text" + }, + { + "bbox": [ + 447, + 111, + 453, + 120 + ], + "score": 0.78, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "followed by", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 121, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 121, + 152, + 134 + ], + "score": 1.0, + "content": "a classifier", + "type": "text" + }, + { + "bbox": [ + 153, + 122, + 184, + 133 + ], + "score": 0.93, + "content": "C ( G _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 121, + 250, + 134 + ], + "score": 1.0, + "content": "on graphs from", + "type": "text" + }, + { + "bbox": [ + 251, + 122, + 266, + 132 + ], + "score": 0.9, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 121, + 505, + 134 + ], + "score": 1.0, + "content": ", where the loss function is the standard cross-entropy loss", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 132, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 118, + 144 + ], + "score": 0.87, + "content": "\\mathcal { L } _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 132, + 506, + 145 + ], + "score": 1.0, + "content": ". In order to better recognize and generalize well on samples from novel classes, in the fine-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 143, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 294, + 155 + ], + "score": 1.0, + "content": "tuning phase, the pre-trained feature extractor", + "type": "text" + }, + { + "bbox": [ + 295, + 143, + 317, + 155 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 143, + 505, + 155 + ], + "score": 1.0, + "content": "along with its trained parameters is fixed and", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 153, + 506, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 160, + 168 + ], + "score": 1.0, + "content": "the classifier", + "type": "text" + }, + { + "bbox": [ + 160, + 154, + 192, + 166 + ], + "score": 0.92, + "content": "C ( G _ { N } )", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 153, + 425, + 168 + ], + "score": 1.0, + "content": "is trained on the novel class labeled graph samples from", + "type": "text" + }, + { + "bbox": [ + 425, + 154, + 441, + 165 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 153, + 506, + 168 + ], + "score": 1.0, + "content": ", with the same", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 162, + 142, + 179 + ], + "spans": [ + { + "bbox": [ + 104, + 162, + 124, + 179 + ], + "score": 1.0, + "content": "loss", + "type": "text" + }, + { + "bbox": [ + 124, + 166, + 137, + 176 + ], + "score": 0.88, + "content": "\\mathcal { L } _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 162, + 142, + 179 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4.5 + }, + { + "type": "text", + "bbox": [ + 106, + 182, + 504, + 204 + ], + "lines": [ + { + "bbox": [ + 106, + 182, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 182, + 505, + 194 + ], + "score": 1.0, + "content": "Now, given the classification of data samples and the two-stage learning method, our problem of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 192, + 345, + 205 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 345, + 205 + ], + "score": 1.0, + "content": "few-shot classification on graphs can be defined as follows.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 106, + 209, + 505, + 266 + ], + "lines": [ + { + "bbox": [ + 105, + 209, + 504, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 220, + 223 + ], + "score": 1.0, + "content": "Problem definition: Given", + "type": "text" + }, + { + "bbox": [ + 220, + 212, + 227, + 220 + ], + "score": 0.65, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 209, + 355, + 223 + ], + "score": 1.0, + "content": "base-class labeled graphs from", + "type": "text" + }, + { + "bbox": [ + 356, + 210, + 371, + 221 + ], + "score": 0.88, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 209, + 494, + 223 + ], + "score": 1.0, + "content": "during the training phase and", + "type": "text" + }, + { + "bbox": [ + 494, + 212, + 504, + 220 + ], + "score": 0.66, + "content": "m", + "type": "inline_equation" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 221, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 221, + 240, + 234 + ], + "score": 1.0, + "content": "novel-class labeled graphs from", + "type": "text" + }, + { + "bbox": [ + 240, + 221, + 257, + 232 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 221, + 409, + 234 + ], + "score": 1.0, + "content": "during the fine-tuning phase, where", + "type": "text" + }, + { + "bbox": [ + 410, + 222, + 445, + 232 + ], + "score": 0.88, + "content": "m \\ll n", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 221, + 505, + 234 + ], + "score": 1.0, + "content": ", the objective", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 232, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 106, + 232, + 291, + 244 + ], + "score": 1.0, + "content": "of few-shot graph classification is to classify", + "type": "text" + }, + { + "bbox": [ + 291, + 233, + 297, + 242 + ], + "score": 0.74, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 232, + 429, + 244 + ], + "score": 1.0, + "content": "unseen test graph samples from", + "type": "text" + }, + { + "bbox": [ + 430, + 232, + 445, + 243 + ], + "score": 0.87, + "content": "G _ { U }", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 232, + 505, + 244 + ], + "score": 1.0, + "content": ". Moreover, if", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 107, + 242, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 107, + 243, + 142, + 254 + ], + "score": 0.91, + "content": "m = q T", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 242, + 173, + 256 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 174, + 243, + 230, + 254 + ], + "score": 0.92, + "content": "T = K ^ { \\prime } - K", + "type": "inline_equation" + }, + { + "bbox": [ + 230, + 242, + 405, + 256 + ], + "score": 1.0, + "content": ", i.e., each novel class label appears exactly", + "type": "text" + }, + { + "bbox": [ + 405, + 245, + 412, + 255 + ], + "score": 0.8, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 242, + 447, + 256 + ], + "score": 1.0, + "content": "times in", + "type": "text" + }, + { + "bbox": [ + 448, + 243, + 464, + 254 + ], + "score": 0.9, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 242, + 506, + 256 + ], + "score": 1.0, + "content": ", then this", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 253, + 311, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 214, + 268 + ], + "score": 1.0, + "content": "setting is referred to as the", + "type": "text" + }, + { + "bbox": [ + 214, + 255, + 221, + 265 + ], + "score": 0.8, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 253, + 244, + 268 + ], + "score": 1.0, + "content": "-shot,", + "type": "text" + }, + { + "bbox": [ + 244, + 254, + 253, + 264 + ], + "score": 0.81, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 253, + 311, + 268 + ], + "score": 1.0, + "content": "-way learning.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 106, + 270, + 505, + 365 + ], + "lines": [ + { + "bbox": [ + 106, + 270, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 338, + 284 + ], + "score": 1.0, + "content": "Graph spectral distance: Let us consider the graphs in", + "type": "text" + }, + { + "bbox": [ + 338, + 271, + 346, + 282 + ], + "score": 0.83, + "content": "\\mathcal { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 346, + 270, + 505, + 284 + ], + "score": 1.0, + "content": ". The normalized Laplacian of a graph", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 280, + 506, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 135, + 295 + ], + "score": 0.9, + "content": "g \\in { \\mathcal { G } }", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 280, + 191, + 297 + ], + "score": 1.0, + "content": "is defined as", + "type": "text" + }, + { + "bbox": [ + 191, + 281, + 295, + 295 + ], + "score": 0.92, + "content": "\\Delta _ { g } = I - D ^ { - 1 / 2 } A D ^ { 1 / 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 296, + 280, + 328, + 297 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 329, + 283, + 337, + 293 + ], + "score": 0.81, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 280, + 357, + 297 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 357, + 283, + 367, + 293 + ], + "score": 0.83, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 280, + 506, + 297 + ], + "score": 1.0, + "content": "are the adjacency and the degree", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 101, + 289, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 101, + 289, + 182, + 316 + ], + "score": 1.0, + "content": "matrices of graph", + "type": "text" + }, + { + "bbox": [ + 182, + 299, + 189, + 308 + ], + "score": 0.74, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 289, + 360, + 316 + ], + "score": 1.0, + "content": ", respectively. The set of eigenvalues of", + "type": "text" + }, + { + "bbox": [ + 360, + 297, + 374, + 309 + ], + "score": 0.91, + "content": "\\Delta _ { g }", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 289, + 416, + 316 + ], + "score": 1.0, + "content": "given by", + "type": "text" + }, + { + "bbox": [ + 416, + 294, + 449, + 309 + ], + "score": 0.92, + "content": "\\{ \\lambda _ { i } \\} _ { i = 1 } ^ { | V | }", + "type": "inline_equation" + }, + { + "bbox": [ + 450, + 289, + 505, + 316 + ], + "score": 1.0, + "content": "is called the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 307, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 104, + 307, + 157, + 321 + ], + "score": 1.0, + "content": "spectrum of", + "type": "text" + }, + { + "bbox": [ + 172, + 307, + 248, + 321 + ], + "score": 1.0, + "content": "and is denoted by", + "type": "text" + }, + { + "bbox": [ + 268, + 307, + 416, + 321 + ], + "score": 1.0, + "content": ". It is well known that the spectrum", + "type": "text" + }, + { + "bbox": [ + 417, + 309, + 437, + 320 + ], + "score": 0.88, + "content": "\\sigma ( g )", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 307, + 506, + 321 + ], + "score": 1.0, + "content": "of a normalized", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 319, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 274, + 331 + ], + "score": 1.0, + "content": "Laplacian matrix is contained in interval", + "type": "text" + }, + { + "bbox": [ + 274, + 319, + 295, + 331 + ], + "score": 0.47, + "content": "[ 0 , 2 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 319, + 401, + 331 + ], + "score": 1.0, + "content": ". We assign a Dirac mass", + "type": "text" + }, + { + "bbox": [ + 401, + 319, + 415, + 331 + ], + "score": 0.88, + "content": "\\delta _ { \\lambda _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 319, + 505, + 331 + ], + "score": 1.0, + "content": "concentrated on each", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 328, + 506, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 152, + 342 + ], + "score": 0.92, + "content": "\\lambda _ { i } \\ \\in \\ \\sigma ( g )", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 328, + 330, + 344 + ], + "score": 1.0, + "content": ", thus associating a probability measure to", + "type": "text" + }, + { + "bbox": [ + 330, + 330, + 350, + 342 + ], + "score": 0.92, + "content": "\\sigma ( g )", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 328, + 409, + 344 + ], + "score": 1.0, + "content": "supported on", + "type": "text" + }, + { + "bbox": [ + 410, + 330, + 430, + 342 + ], + "score": 0.82, + "content": "[ 0 , 2 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 328, + 506, + 344 + ], + "score": 1.0, + "content": ", called the graph", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 340, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 178, + 354 + ], + "score": 1.0, + "content": "spectral measure", + "type": "text" + }, + { + "bbox": [ + 179, + 343, + 201, + 354 + ], + "score": 0.89, + "content": "\\mu _ { \\sigma ( g ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 340, + 278, + 354 + ], + "score": 1.0, + "content": ". Furthermore, let", + "type": "text" + }, + { + "bbox": [ + 278, + 341, + 314, + 353 + ], + "score": 0.93, + "content": "P ( [ 0 , 2 ] )", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 340, + 505, + 354 + ], + "score": 1.0, + "content": "be the set of probability measures on interval", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 107, + 351, + 133, + 366 + ], + "spans": [ + { + "bbox": [ + 107, + 353, + 127, + 365 + ], + "score": 0.4, + "content": "[ 0 , 2 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 128, + 351, + 133, + 366 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 105, + 369, + 504, + 393 + ], + "lines": [ + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 185, + 383 + ], + "score": 1.0, + "content": "We now define the", + "type": "text" + }, + { + "bbox": [ + 185, + 371, + 191, + 381 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 369, + 505, + 383 + ], + "score": 1.0, + "content": "-th Wasserstein distance between probability measures, which we later use to", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 381, + 321, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 321, + 394 + ], + "score": 1.0, + "content": "define the spectral distance between a pair of graphs.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 106, + 402, + 505, + 436 + ], + "lines": [ + { + "bbox": [ + 105, + 402, + 505, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 176, + 415 + ], + "score": 1.0, + "content": "Definition 1 Let", + "type": "text" + }, + { + "bbox": [ + 177, + 403, + 222, + 415 + ], + "score": 0.91, + "content": "p \\in [ 1 , \\infty )", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 402, + 254, + 415 + ], + "score": 1.0, + "content": "and let", + "type": "text" + }, + { + "bbox": [ + 254, + 403, + 371, + 415 + ], + "score": 0.91, + "content": "c : [ 0 , 2 ] \\times [ 0 , 2 ] [ 0 , + \\infty ]", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 402, + 505, + 415 + ], + "score": 1.0, + "content": "be the cost function between the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 414, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 104, + 414, + 193, + 427 + ], + "score": 1.0, + "content": "probability measures", + "type": "text" + }, + { + "bbox": [ + 193, + 414, + 257, + 426 + ], + "score": 0.92, + "content": "\\mu , \\nu \\in P ( [ 0 , 2 ] )", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 414, + 299, + 427 + ], + "score": 1.0, + "content": ". Then the", + "type": "text" + }, + { + "bbox": [ + 300, + 416, + 306, + 426 + ], + "score": 0.72, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 414, + 479, + 427 + ], + "score": 1.0, + "content": "-th Wasserstein distance between measures", + "type": "text" + }, + { + "bbox": [ + 479, + 416, + 486, + 426 + ], + "score": 0.71, + "content": "\\mu", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 414, + 506, + 427 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 425, + 160, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 114, + 435 + ], + "score": 0.64, + "content": "\\nu", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 425, + 160, + 439 + ], + "score": 1.0, + "content": "is given by", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26 + }, + { + "type": "interline_equation", + "bbox": [ + 188, + 435, + 421, + 472 + ], + "lines": [ + { + "bbox": [ + 188, + 435, + 421, + 472 + ], + "spans": [ + { + "bbox": [ + 188, + 435, + 421, + 472 + ], + "score": 0.93, + "content": "W _ { p } ( \\mu , \\nu ) = \\left( \\operatorname* { i n f } _ { \\gamma } \\int _ { [ 0 , 2 ] \\times [ 0 , 2 ] } c ( x , y ) ^ { p } d \\gamma \\mid \\gamma \\in \\Pi ( \\mu , \\nu ) \\right) ^ { \\frac { 1 } { p } }", + "type": "interline_equation", + "image_path": "34613c1c0832df651fd54184395645c27fd1a9bf9f646499c259923761e9bd54.jpg" + } + ] + } + ], + "index": 28.5, + "virtual_lines": [ + { + "bbox": [ + 188, + 435, + 421, + 453.5 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 188, + 453.5, + 421, + 472.0 + ], + "spans": [], + "index": 29 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 474, + 505, + 497 + ], + "lines": [ + { + "bbox": [ + 106, + 473, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 133, + 487 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 474, + 165, + 487 + ], + "score": 0.93, + "content": "\\Pi ( \\mu , \\nu )", + "type": "inline_equation" + }, + { + "bbox": [ + 165, + 473, + 431, + 487 + ], + "score": 1.0, + "content": "is the set of transport plans, i.e., the collection of all measures on", + "type": "text" + }, + { + "bbox": [ + 431, + 474, + 484, + 487 + ], + "score": 0.91, + "content": "[ 0 , 2 ] \\times [ 0 , 2 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 473, + 505, + 487 + ], + "score": 1.0, + "content": "with", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 486, + 186, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 149, + 498 + ], + "score": 1.0, + "content": "marginals", + "type": "text" + }, + { + "bbox": [ + 149, + 488, + 156, + 497 + ], + "score": 0.79, + "content": "\\mu", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 486, + 175, + 498 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 175, + 488, + 181, + 495 + ], + "score": 0.73, + "content": "\\nu", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 486, + 186, + 498 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30.5 + }, + { + "type": "text", + "bbox": [ + 105, + 507, + 505, + 531 + ], + "lines": [ + { + "bbox": [ + 106, + 507, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 507, + 246, + 520 + ], + "score": 1.0, + "content": "Given the general definition of the", + "type": "text" + }, + { + "bbox": [ + 246, + 509, + 253, + 519 + ], + "score": 0.83, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 507, + 505, + 520 + ], + "score": 1.0, + "content": "-th Wasserstein distance between probability measures and the", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 518, + 487, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 476, + 531 + ], + "score": 1.0, + "content": "graph spectral measure, we can now define the spectral distance between a pair of graphs in", + "type": "text" + }, + { + "bbox": [ + 476, + 519, + 484, + 529 + ], + "score": 0.83, + "content": "\\mathcal { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 518, + 487, + 531 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5 + }, + { + "type": "text", + "bbox": [ + 103, + 538, + 469, + 552 + ], + "lines": [ + { + "bbox": [ + 105, + 538, + 469, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 234, + 553 + ], + "score": 1.0, + "content": "Definition 2 Given two graphs", + "type": "text" + }, + { + "bbox": [ + 234, + 540, + 271, + 551 + ], + "score": 0.92, + "content": "g , g ^ { \\prime } \\in \\mathcal { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 538, + 469, + 553 + ], + "score": 1.0, + "content": ", the spectral distance between them is defined as", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "interline_equation", + "bbox": [ + 238, + 556, + 372, + 572 + ], + "lines": [ + { + "bbox": [ + 238, + 556, + 372, + 572 + ], + "spans": [ + { + "bbox": [ + 238, + 556, + 372, + 572 + ], + "score": 0.92, + "content": "W ^ { p } ( g , g ^ { \\prime } ) : = W _ { p } \\left( \\mu _ { \\sigma ( g ) } , \\mu _ { \\sigma ( g ^ { \\prime } ) } \\right)", + "type": "interline_equation", + "image_path": "d89709e1a2a9eee3ee2245c73557bd920b69e751fe1e8e0d895a71cecea20d9f.jpg" + } + ] + } + ], + "index": 35, + "virtual_lines": [ + { + "bbox": [ + 238, + 556, + 372, + 572 + ], + "spans": [], + "index": 35 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 582, + 504, + 617 + ], + "lines": [ + { + "bbox": [ + 105, + 582, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 147, + 596 + ], + "score": 1.0, + "content": "In words,", + "type": "text" + }, + { + "bbox": [ + 148, + 583, + 189, + 595 + ], + "score": 0.92, + "content": "W ^ { p } ( g , g ^ { \\prime } )", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 582, + 506, + 596 + ], + "score": 1.0, + "content": "is the optimal cost of moving mass from the graph spectral measure of graph", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 107, + 594, + 506, + 606 + ], + "spans": [ + { + "bbox": [ + 107, + 597, + 113, + 606 + ], + "score": 0.75, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 113, + 594, + 181, + 606 + ], + "score": 1.0, + "content": "to that of graph", + "type": "text" + }, + { + "bbox": [ + 181, + 595, + 190, + 606 + ], + "score": 0.86, + "content": "g ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 594, + 432, + 606 + ], + "score": 1.0, + "content": ", where the cost of moving unit mass is proportional to the", + "type": "text" + }, + { + "bbox": [ + 432, + 596, + 438, + 606 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 594, + 506, + 606 + ], + "score": 1.0, + "content": "-th power of the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 604, + 300, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 270, + 618 + ], + "score": 1.0, + "content": "difference of real-eigenvalues in interval", + "type": "text" + }, + { + "bbox": [ + 271, + 605, + 295, + 617 + ], + "score": 0.92, + "content": "[ 0 , 2 ] ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 604, + 300, + 618 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37 + }, + { + "type": "title", + "bbox": [ + 107, + 632, + 200, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 630, + 201, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 201, + 648 + ], + "score": 1.0, + "content": "4 OUR METHOD", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 106, + 658, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 106, + 658, + 506, + 671 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 506, + 671 + ], + "score": 1.0, + "content": "We present our proposed approach here. First, given abundant base-class labels, we cluster them into", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 669, + 506, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 506, + 682 + ], + "score": 1.0, + "content": "super-classes by computing prototype graphs from each class, followed by clustering the prototype", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 681, + 506, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 506, + 693 + ], + "score": 1.0, + "content": "graphs based on their spectral properties. This clustering of prototype graphs induces a natural", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 691, + 505, + 704 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 505, + 704 + ], + "score": 1.0, + "content": "clustering on their corresponding class labels, resulting in super-classes (as outlined in Section 4.1).", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 711, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 119, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 119, + 710, + 281, + 723 + ], + "score": 1.0, + "content": "2In practice, extremely fast computation of", + "type": "text" + }, + { + "bbox": [ + 282, + 711, + 320, + 722 + ], + "score": 0.92, + "content": "W ^ { p } ( g , g ^ { \\prime } )", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "is achieved using a regularized optimal transport", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 720, + 371, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 371, + 732 + ], + "score": 1.0, + "content": "(OT) (Genevay et al., 2016), which makes use of the Sinkhorn algorithm.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "4", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 104, + 80, + 506, + 97 + ], + "spans": [ + { + "bbox": [ + 104, + 80, + 506, + 97 + ], + "score": 1.0, + "content": "Learning procedure: Inspired by the initialization based methods, we similarly follow a two-stage", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 290, + 108 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 290, + 108 + ], + "score": 1.0, + "content": "approach of training followed by fine-tuning.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5, + "bbox_fs": [ + 104, + 80, + 506, + 108 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 110, + 505, + 177 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 309, + 123 + ], + "score": 1.0, + "content": "During training, we train a graph feature extractor", + "type": "text" + }, + { + "bbox": [ + 309, + 110, + 344, + 122 + ], + "score": 0.94, + "content": "F _ { \\theta } ( G _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 110, + 447, + 123 + ], + "score": 1.0, + "content": "with network parameters", + "type": "text" + }, + { + "bbox": [ + 447, + 111, + 453, + 120 + ], + "score": 0.78, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "followed by", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 121, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 121, + 152, + 134 + ], + "score": 1.0, + "content": "a classifier", + "type": "text" + }, + { + "bbox": [ + 153, + 122, + 184, + 133 + ], + "score": 0.93, + "content": "C ( G _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 121, + 250, + 134 + ], + "score": 1.0, + "content": "on graphs from", + "type": "text" + }, + { + "bbox": [ + 251, + 122, + 266, + 132 + ], + "score": 0.9, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 121, + 505, + 134 + ], + "score": 1.0, + "content": ", where the loss function is the standard cross-entropy loss", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 132, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 118, + 144 + ], + "score": 0.87, + "content": "\\mathcal { L } _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 132, + 506, + 145 + ], + "score": 1.0, + "content": ". In order to better recognize and generalize well on samples from novel classes, in the fine-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 143, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 294, + 155 + ], + "score": 1.0, + "content": "tuning phase, the pre-trained feature extractor", + "type": "text" + }, + { + "bbox": [ + 295, + 143, + 317, + 155 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 143, + 505, + 155 + ], + "score": 1.0, + "content": "along with its trained parameters is fixed and", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 153, + 506, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 160, + 168 + ], + "score": 1.0, + "content": "the classifier", + "type": "text" + }, + { + "bbox": [ + 160, + 154, + 192, + 166 + ], + "score": 0.92, + "content": "C ( G _ { N } )", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 153, + 425, + 168 + ], + "score": 1.0, + "content": "is trained on the novel class labeled graph samples from", + "type": "text" + }, + { + "bbox": [ + 425, + 154, + 441, + 165 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 153, + 506, + 168 + ], + "score": 1.0, + "content": ", with the same", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 162, + 142, + 179 + ], + "spans": [ + { + "bbox": [ + 104, + 162, + 124, + 179 + ], + "score": 1.0, + "content": "loss", + "type": "text" + }, + { + "bbox": [ + 124, + 166, + 137, + 176 + ], + "score": 0.88, + "content": "\\mathcal { L } _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 162, + 142, + 179 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4.5, + "bbox_fs": [ + 104, + 110, + 506, + 179 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 182, + 504, + 204 + ], + "lines": [ + { + "bbox": [ + 106, + 182, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 182, + 505, + 194 + ], + "score": 1.0, + "content": "Now, given the classification of data samples and the two-stage learning method, our problem of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 192, + 345, + 205 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 345, + 205 + ], + "score": 1.0, + "content": "few-shot classification on graphs can be defined as follows.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5, + "bbox_fs": [ + 106, + 182, + 505, + 205 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 209, + 505, + 266 + ], + "lines": [ + { + "bbox": [ + 105, + 209, + 504, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 220, + 223 + ], + "score": 1.0, + "content": "Problem definition: Given", + "type": "text" + }, + { + "bbox": [ + 220, + 212, + 227, + 220 + ], + "score": 0.65, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 209, + 355, + 223 + ], + "score": 1.0, + "content": "base-class labeled graphs from", + "type": "text" + }, + { + "bbox": [ + 356, + 210, + 371, + 221 + ], + "score": 0.88, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 209, + 494, + 223 + ], + "score": 1.0, + "content": "during the training phase and", + "type": "text" + }, + { + "bbox": [ + 494, + 212, + 504, + 220 + ], + "score": 0.66, + "content": "m", + "type": "inline_equation" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 221, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 221, + 240, + 234 + ], + "score": 1.0, + "content": "novel-class labeled graphs from", + "type": "text" + }, + { + "bbox": [ + 240, + 221, + 257, + 232 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 221, + 409, + 234 + ], + "score": 1.0, + "content": "during the fine-tuning phase, where", + "type": "text" + }, + { + "bbox": [ + 410, + 222, + 445, + 232 + ], + "score": 0.88, + "content": "m \\ll n", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 221, + 505, + 234 + ], + "score": 1.0, + "content": ", the objective", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 232, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 106, + 232, + 291, + 244 + ], + "score": 1.0, + "content": "of few-shot graph classification is to classify", + "type": "text" + }, + { + "bbox": [ + 291, + 233, + 297, + 242 + ], + "score": 0.74, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 232, + 429, + 244 + ], + "score": 1.0, + "content": "unseen test graph samples from", + "type": "text" + }, + { + "bbox": [ + 430, + 232, + 445, + 243 + ], + "score": 0.87, + "content": "G _ { U }", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 232, + 505, + 244 + ], + "score": 1.0, + "content": ". Moreover, if", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 107, + 242, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 107, + 243, + 142, + 254 + ], + "score": 0.91, + "content": "m = q T", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 242, + 173, + 256 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 174, + 243, + 230, + 254 + ], + "score": 0.92, + "content": "T = K ^ { \\prime } - K", + "type": "inline_equation" + }, + { + "bbox": [ + 230, + 242, + 405, + 256 + ], + "score": 1.0, + "content": ", i.e., each novel class label appears exactly", + "type": "text" + }, + { + "bbox": [ + 405, + 245, + 412, + 255 + ], + "score": 0.8, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 242, + 447, + 256 + ], + "score": 1.0, + "content": "times in", + "type": "text" + }, + { + "bbox": [ + 448, + 243, + 464, + 254 + ], + "score": 0.9, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 242, + 506, + 256 + ], + "score": 1.0, + "content": ", then this", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 253, + 311, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 214, + 268 + ], + "score": 1.0, + "content": "setting is referred to as the", + "type": "text" + }, + { + "bbox": [ + 214, + 255, + 221, + 265 + ], + "score": 0.8, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 253, + 244, + 268 + ], + "score": 1.0, + "content": "-shot,", + "type": "text" + }, + { + "bbox": [ + 244, + 254, + 253, + 264 + ], + "score": 0.81, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 253, + 311, + 268 + ], + "score": 1.0, + "content": "-way learning.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 209, + 506, + 268 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 270, + 505, + 365 + ], + "lines": [ + { + "bbox": [ + 106, + 270, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 338, + 284 + ], + "score": 1.0, + "content": "Graph spectral distance: Let us consider the graphs in", + "type": "text" + }, + { + "bbox": [ + 338, + 271, + 346, + 282 + ], + "score": 0.83, + "content": "\\mathcal { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 346, + 270, + 505, + 284 + ], + "score": 1.0, + "content": ". The normalized Laplacian of a graph", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 280, + 506, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 282, + 135, + 295 + ], + "score": 0.9, + "content": "g \\in { \\mathcal { G } }", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 280, + 191, + 297 + ], + "score": 1.0, + "content": "is defined as", + "type": "text" + }, + { + "bbox": [ + 191, + 281, + 295, + 295 + ], + "score": 0.92, + "content": "\\Delta _ { g } = I - D ^ { - 1 / 2 } A D ^ { 1 / 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 296, + 280, + 328, + 297 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 329, + 283, + 337, + 293 + ], + "score": 0.81, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 280, + 357, + 297 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 357, + 283, + 367, + 293 + ], + "score": 0.83, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 280, + 506, + 297 + ], + "score": 1.0, + "content": "are the adjacency and the degree", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 101, + 289, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 101, + 289, + 182, + 316 + ], + "score": 1.0, + "content": "matrices of graph", + "type": "text" + }, + { + "bbox": [ + 182, + 299, + 189, + 308 + ], + "score": 0.74, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 289, + 360, + 316 + ], + "score": 1.0, + "content": ", respectively. The set of eigenvalues of", + "type": "text" + }, + { + "bbox": [ + 360, + 297, + 374, + 309 + ], + "score": 0.91, + "content": "\\Delta _ { g }", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 289, + 416, + 316 + ], + "score": 1.0, + "content": "given by", + "type": "text" + }, + { + "bbox": [ + 416, + 294, + 449, + 309 + ], + "score": 0.92, + "content": "\\{ \\lambda _ { i } \\} _ { i = 1 } ^ { | V | }", + "type": "inline_equation" + }, + { + "bbox": [ + 450, + 289, + 505, + 316 + ], + "score": 1.0, + "content": "is called the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 307, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 104, + 307, + 157, + 321 + ], + "score": 1.0, + "content": "spectrum of", + "type": "text" + }, + { + "bbox": [ + 172, + 307, + 248, + 321 + ], + "score": 1.0, + "content": "and is denoted by", + "type": "text" + }, + { + "bbox": [ + 268, + 307, + 416, + 321 + ], + "score": 1.0, + "content": ". It is well known that the spectrum", + "type": "text" + }, + { + "bbox": [ + 417, + 309, + 437, + 320 + ], + "score": 0.88, + "content": "\\sigma ( g )", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 307, + 506, + 321 + ], + "score": 1.0, + "content": "of a normalized", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 319, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 274, + 331 + ], + "score": 1.0, + "content": "Laplacian matrix is contained in interval", + "type": "text" + }, + { + "bbox": [ + 274, + 319, + 295, + 331 + ], + "score": 0.47, + "content": "[ 0 , 2 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 319, + 401, + 331 + ], + "score": 1.0, + "content": ". We assign a Dirac mass", + "type": "text" + }, + { + "bbox": [ + 401, + 319, + 415, + 331 + ], + "score": 0.88, + "content": "\\delta _ { \\lambda _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 319, + 505, + 331 + ], + "score": 1.0, + "content": "concentrated on each", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 328, + 506, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 152, + 342 + ], + "score": 0.92, + "content": "\\lambda _ { i } \\ \\in \\ \\sigma ( g )", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 328, + 330, + 344 + ], + "score": 1.0, + "content": ", thus associating a probability measure to", + "type": "text" + }, + { + "bbox": [ + 330, + 330, + 350, + 342 + ], + "score": 0.92, + "content": "\\sigma ( g )", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 328, + 409, + 344 + ], + "score": 1.0, + "content": "supported on", + "type": "text" + }, + { + "bbox": [ + 410, + 330, + 430, + 342 + ], + "score": 0.82, + "content": "[ 0 , 2 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 328, + 506, + 344 + ], + "score": 1.0, + "content": ", called the graph", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 340, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 178, + 354 + ], + "score": 1.0, + "content": "spectral measure", + "type": "text" + }, + { + "bbox": [ + 179, + 343, + 201, + 354 + ], + "score": 0.89, + "content": "\\mu _ { \\sigma ( g ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 340, + 278, + 354 + ], + "score": 1.0, + "content": ". Furthermore, let", + "type": "text" + }, + { + "bbox": [ + 278, + 341, + 314, + 353 + ], + "score": 0.93, + "content": "P ( [ 0 , 2 ] )", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 340, + 505, + 354 + ], + "score": 1.0, + "content": "be the set of probability measures on interval", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 107, + 351, + 133, + 366 + ], + "spans": [ + { + "bbox": [ + 107, + 353, + 127, + 365 + ], + "score": 0.4, + "content": "[ 0 , 2 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 128, + 351, + 133, + 366 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18.5, + "bbox_fs": [ + 101, + 270, + 506, + 366 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 369, + 504, + 393 + ], + "lines": [ + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 185, + 383 + ], + "score": 1.0, + "content": "We now define the", + "type": "text" + }, + { + "bbox": [ + 185, + 371, + 191, + 381 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 369, + 505, + 383 + ], + "score": 1.0, + "content": "-th Wasserstein distance between probability measures, which we later use to", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 381, + 321, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 321, + 394 + ], + "score": 1.0, + "content": "define the spectral distance between a pair of graphs.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 369, + 505, + 394 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 402, + 505, + 436 + ], + "lines": [ + { + "bbox": [ + 105, + 402, + 505, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 176, + 415 + ], + "score": 1.0, + "content": "Definition 1 Let", + "type": "text" + }, + { + "bbox": [ + 177, + 403, + 222, + 415 + ], + "score": 0.91, + "content": "p \\in [ 1 , \\infty )", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 402, + 254, + 415 + ], + "score": 1.0, + "content": "and let", + "type": "text" + }, + { + "bbox": [ + 254, + 403, + 371, + 415 + ], + "score": 0.91, + "content": "c : [ 0 , 2 ] \\times [ 0 , 2 ] [ 0 , + \\infty ]", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 402, + 505, + 415 + ], + "score": 1.0, + "content": "be the cost function between the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 414, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 104, + 414, + 193, + 427 + ], + "score": 1.0, + "content": "probability measures", + "type": "text" + }, + { + "bbox": [ + 193, + 414, + 257, + 426 + ], + "score": 0.92, + "content": "\\mu , \\nu \\in P ( [ 0 , 2 ] )", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 414, + 299, + 427 + ], + "score": 1.0, + "content": ". Then the", + "type": "text" + }, + { + "bbox": [ + 300, + 416, + 306, + 426 + ], + "score": 0.72, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 414, + 479, + 427 + ], + "score": 1.0, + "content": "-th Wasserstein distance between measures", + "type": "text" + }, + { + "bbox": [ + 479, + 416, + 486, + 426 + ], + "score": 0.71, + "content": "\\mu", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 414, + 506, + 427 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 425, + 160, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 114, + 435 + ], + "score": 0.64, + "content": "\\nu", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 425, + 160, + 439 + ], + "score": 1.0, + "content": "is given by", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26, + "bbox_fs": [ + 104, + 402, + 506, + 439 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 188, + 435, + 421, + 472 + ], + "lines": [ + { + "bbox": [ + 188, + 435, + 421, + 472 + ], + "spans": [ + { + "bbox": [ + 188, + 435, + 421, + 472 + ], + "score": 0.93, + "content": "W _ { p } ( \\mu , \\nu ) = \\left( \\operatorname* { i n f } _ { \\gamma } \\int _ { [ 0 , 2 ] \\times [ 0 , 2 ] } c ( x , y ) ^ { p } d \\gamma \\mid \\gamma \\in \\Pi ( \\mu , \\nu ) \\right) ^ { \\frac { 1 } { p } }", + "type": "interline_equation", + "image_path": "34613c1c0832df651fd54184395645c27fd1a9bf9f646499c259923761e9bd54.jpg" + } + ] + } + ], + "index": 28.5, + "virtual_lines": [ + { + "bbox": [ + 188, + 435, + 421, + 453.5 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 188, + 453.5, + 421, + 472.0 + ], + "spans": [], + "index": 29 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 474, + 505, + 497 + ], + "lines": [ + { + "bbox": [ + 106, + 473, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 133, + 487 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 474, + 165, + 487 + ], + "score": 0.93, + "content": "\\Pi ( \\mu , \\nu )", + "type": "inline_equation" + }, + { + "bbox": [ + 165, + 473, + 431, + 487 + ], + "score": 1.0, + "content": "is the set of transport plans, i.e., the collection of all measures on", + "type": "text" + }, + { + "bbox": [ + 431, + 474, + 484, + 487 + ], + "score": 0.91, + "content": "[ 0 , 2 ] \\times [ 0 , 2 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 473, + 505, + 487 + ], + "score": 1.0, + "content": "with", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 486, + 186, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 149, + 498 + ], + "score": 1.0, + "content": "marginals", + "type": "text" + }, + { + "bbox": [ + 149, + 488, + 156, + 497 + ], + "score": 0.79, + "content": "\\mu", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 486, + 175, + 498 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 175, + 488, + 181, + 495 + ], + "score": 0.73, + "content": "\\nu", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 486, + 186, + 498 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 473, + 505, + 498 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 507, + 505, + 531 + ], + "lines": [ + { + "bbox": [ + 106, + 507, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 507, + 246, + 520 + ], + "score": 1.0, + "content": "Given the general definition of the", + "type": "text" + }, + { + "bbox": [ + 246, + 509, + 253, + 519 + ], + "score": 0.83, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 507, + 505, + 520 + ], + "score": 1.0, + "content": "-th Wasserstein distance between probability measures and the", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 518, + 487, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 476, + 531 + ], + "score": 1.0, + "content": "graph spectral measure, we can now define the spectral distance between a pair of graphs in", + "type": "text" + }, + { + "bbox": [ + 476, + 519, + 484, + 529 + ], + "score": 0.83, + "content": "\\mathcal { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 518, + 487, + 531 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5, + "bbox_fs": [ + 105, + 507, + 505, + 531 + ] + }, + { + "type": "text", + "bbox": [ + 103, + 538, + 469, + 552 + ], + "lines": [ + { + "bbox": [ + 105, + 538, + 469, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 234, + 553 + ], + "score": 1.0, + "content": "Definition 2 Given two graphs", + "type": "text" + }, + { + "bbox": [ + 234, + 540, + 271, + 551 + ], + "score": 0.92, + "content": "g , g ^ { \\prime } \\in \\mathcal { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 538, + 469, + 553 + ], + "score": 1.0, + "content": ", the spectral distance between them is defined as", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 538, + 469, + 553 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 238, + 556, + 372, + 572 + ], + "lines": [ + { + "bbox": [ + 238, + 556, + 372, + 572 + ], + "spans": [ + { + "bbox": [ + 238, + 556, + 372, + 572 + ], + "score": 0.92, + "content": "W ^ { p } ( g , g ^ { \\prime } ) : = W _ { p } \\left( \\mu _ { \\sigma ( g ) } , \\mu _ { \\sigma ( g ^ { \\prime } ) } \\right)", + "type": "interline_equation", + "image_path": "d89709e1a2a9eee3ee2245c73557bd920b69e751fe1e8e0d895a71cecea20d9f.jpg" + } + ] + } + ], + "index": 35, + "virtual_lines": [ + { + "bbox": [ + 238, + 556, + 372, + 572 + ], + "spans": [], + "index": 35 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 582, + 504, + 617 + ], + "lines": [ + { + "bbox": [ + 105, + 582, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 147, + 596 + ], + "score": 1.0, + "content": "In words,", + "type": "text" + }, + { + "bbox": [ + 148, + 583, + 189, + 595 + ], + "score": 0.92, + "content": "W ^ { p } ( g , g ^ { \\prime } )", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 582, + 506, + 596 + ], + "score": 1.0, + "content": "is the optimal cost of moving mass from the graph spectral measure of graph", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 107, + 594, + 506, + 606 + ], + "spans": [ + { + "bbox": [ + 107, + 597, + 113, + 606 + ], + "score": 0.75, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 113, + 594, + 181, + 606 + ], + "score": 1.0, + "content": "to that of graph", + "type": "text" + }, + { + "bbox": [ + 181, + 595, + 190, + 606 + ], + "score": 0.86, + "content": "g ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 594, + 432, + 606 + ], + "score": 1.0, + "content": ", where the cost of moving unit mass is proportional to the", + "type": "text" + }, + { + "bbox": [ + 432, + 596, + 438, + 606 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 594, + 506, + 606 + ], + "score": 1.0, + "content": "-th power of the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 604, + 300, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 270, + 618 + ], + "score": 1.0, + "content": "difference of real-eigenvalues in interval", + "type": "text" + }, + { + "bbox": [ + 271, + 605, + 295, + 617 + ], + "score": 0.92, + "content": "[ 0 , 2 ] ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 604, + 300, + 618 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 582, + 506, + 618 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 632, + 200, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 630, + 201, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 201, + 648 + ], + "score": 1.0, + "content": "4 OUR METHOD", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 106, + 658, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 106, + 658, + 506, + 671 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 506, + 671 + ], + "score": 1.0, + "content": "We present our proposed approach here. First, given abundant base-class labels, we cluster them into", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 669, + 506, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 506, + 682 + ], + "score": 1.0, + "content": "super-classes by computing prototype graphs from each class, followed by clustering the prototype", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 681, + 506, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 506, + 693 + ], + "score": 1.0, + "content": "graphs based on their spectral properties. This clustering of prototype graphs induces a natural", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 691, + 505, + 704 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 505, + 704 + ], + "score": 1.0, + "content": "clustering on their corresponding class labels, resulting in super-classes (as outlined in Section 4.1).", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 658, + 506, + 704 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 83, + 503, + 194 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 83, + 503, + 194 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 83, + 503, + 194 + ], + "spans": [ + { + "bbox": [ + 109, + 83, + 503, + 194 + ], + "score": 0.968, + "type": "image", + "image_path": "393d3119a11d19636ddb73ae543b4196b5496b3b1defea32cbff310a102d2d91.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 83, + 503, + 120.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 120.0, + 503, + 157.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 157.0, + 503, + 194.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 163, + 203, + 447, + 216 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 163, + 203, + 447, + 217 + ], + "spans": [ + { + "bbox": [ + 163, + 203, + 447, + 217 + ], + "score": 1.0, + "content": "Figure 1: The training (left) and fine-tuning (right) stages of our GNN.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 106, + 236, + 505, + 281 + ], + "lines": [ + { + "bbox": [ + 105, + 236, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 505, + 249 + ], + "score": 1.0, + "content": "These super-classes are then used in the creation of a super-graph used further down by our GNN.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 247, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 505, + 261 + ], + "score": 1.0, + "content": "Note that the creation of super-classes, followed by building a super-graph are a once-off process.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 257, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 104, + 257, + 506, + 272 + ], + "score": 1.0, + "content": "The prototype graphs as well as the super-classes for the base classes can be stored in memory for", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 269, + 155, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 269, + 155, + 282 + ], + "score": 1.0, + "content": "further use.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 106, + 286, + 505, + 342 + ], + "lines": [ + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "Next, we explain our graph neural network’s architecture which comprises of a feature extractor", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 107, + 297, + 506, + 310 + ], + "spans": [ + { + "bbox": [ + 107, + 298, + 129, + 309 + ], + "score": 0.91, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 129, + 297, + 193, + 310 + ], + "score": 1.0, + "content": "and a classifier", + "type": "text" + }, + { + "bbox": [ + 193, + 298, + 213, + 309 + ], + "score": 0.91, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 297, + 374, + 310 + ], + "score": 1.0, + "content": ", described in Section 4.2. The classifier", + "type": "text" + }, + { + "bbox": [ + 375, + 298, + 394, + 309 + ], + "score": 0.92, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 297, + 506, + 310 + ], + "score": 1.0, + "content": "is further subdivided into a", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 307, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 145, + 321 + ], + "score": 1.0, + "content": "classifier", + "type": "text" + }, + { + "bbox": [ + 145, + 309, + 167, + 318 + ], + "score": 0.87, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 307, + 506, + 321 + ], + "score": 1.0, + "content": "that predicts the superclass of a graph feature vector and a graph attention network", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 316, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 104, + 316, + 136, + 335 + ], + "score": 1.0, + "content": "(GAT)", + "type": "text" + }, + { + "bbox": [ + 136, + 319, + 164, + 330 + ], + "score": 0.88, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 316, + 506, + 335 + ], + "score": 1.0, + "content": "to predict the graph’s class label. Figure 1 illustrates the training and fine-tuning", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 330, + 189, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 189, + 342 + ], + "score": 1.0, + "content": "phases of our GNN.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10 + }, + { + "type": "title", + "bbox": [ + 108, + 356, + 256, + 367 + ], + "lines": [ + { + "bbox": [ + 106, + 356, + 257, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 257, + 368 + ], + "score": 1.0, + "content": "4.1 COMPUTING SUPER CLASSES", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 376, + 505, + 414 + ], + "lines": [ + { + "bbox": [ + 105, + 376, + 504, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 504, + 389 + ], + "score": 1.0, + "content": "In order to exploit inter-class relationships between base-class labels, we cluster them in the follow-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 387, + 503, + 401 + ], + "spans": [ + { + "bbox": [ + 104, + 388, + 260, + 401 + ], + "score": 1.0, + "content": "ing manner. First, we partition the set", + "type": "text" + }, + { + "bbox": [ + 261, + 389, + 276, + 400 + ], + "score": 0.89, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 276, + 388, + 369, + 401 + ], + "score": 1.0, + "content": "into class-specific sets", + "type": "text" + }, + { + "bbox": [ + 370, + 387, + 388, + 399 + ], + "score": 0.9, + "content": "G ^ { ( i ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 388, + 406, + 401 + ], + "score": 1.0, + "content": ", for", + "type": "text" + }, + { + "bbox": [ + 406, + 389, + 454, + 399 + ], + "score": 0.88, + "content": "i = 1 \\dots K", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 388, + 485, + 401 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 486, + 388, + 503, + 399 + ], + "score": 0.91, + "content": "G ^ { ( i ) }", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 101, + 394, + 375, + 419 + ], + "spans": [ + { + "bbox": [ + 101, + 394, + 268, + 419 + ], + "score": 1.0, + "content": "is the set of graphs with base-class label", + "type": "text" + }, + { + "bbox": [ + 269, + 402, + 273, + 411 + ], + "score": 0.69, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 394, + 303, + 419 + ], + "score": 1.0, + "content": ". Thus,", + "type": "text" + }, + { + "bbox": [ + 303, + 400, + 372, + 415 + ], + "score": 0.93, + "content": "\\begin{array} { r } { G _ { B } = \\bigsqcup _ { i = 1 } ^ { K } G ^ { ( i ) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 373, + 394, + 375, + 419 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 418, + 504, + 442 + ], + "lines": [ + { + "bbox": [ + 106, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "Then, we compute class prototype graphs for each class-specific set. The class prototype graph for", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 429, + 252, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 128, + 443 + ], + "score": 1.0, + "content": "class", + "type": "text" + }, + { + "bbox": [ + 128, + 430, + 133, + 439 + ], + "score": 0.75, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 133, + 429, + 195, + 443 + ], + "score": 1.0, + "content": "represented by", + "type": "text" + }, + { + "bbox": [ + 195, + 431, + 205, + 441 + ], + "score": 0.84, + "content": "p _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 429, + 252, + 443 + ], + "score": 1.0, + "content": "is given by", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5 + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 447, + 386, + 485 + ], + "lines": [ + { + "bbox": [ + 225, + 447, + 386, + 485 + ], + "spans": [ + { + "bbox": [ + 225, + 447, + 386, + 485 + ], + "score": 0.95, + "content": "p _ { i } = \\operatorname * { a r g m i n } _ { g _ { i } \\in \\pi _ { 1 } ( G ^ { ( i ) } ) } \\frac { 1 } { | G ^ { ( i ) } | } \\sum _ { j = 1 } ^ { | G ^ { ( i ) } | } W ^ { p } ( g _ { i } , g _ { j } )", + "type": "interline_equation", + "image_path": "184a8c2a4d8c67644a73819913d2c42712d2ae5fc43d95dd4c9e69267eebce09.jpg" + } + ] + } + ], + "index": 19.5, + "virtual_lines": [ + { + "bbox": [ + 225, + 447, + 386, + 466.0 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 225, + 466.0, + 386, + 485.0 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 490, + 505, + 523 + ], + "lines": [ + { + "bbox": [ + 106, + 489, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 256, + 503 + ], + "score": 1.0, + "content": "Essentially, the class prototype graph", + "type": "text" + }, + { + "bbox": [ + 256, + 492, + 266, + 501 + ], + "score": 0.85, + "content": "p _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 266, + 489, + 295, + 503 + ], + "score": 1.0, + "content": "for the", + "type": "text" + }, + { + "bbox": [ + 296, + 491, + 300, + 500 + ], + "score": 0.77, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 489, + 505, + 503 + ], + "score": 1.0, + "content": "-th class is the graph with the least average spectral", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 501, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 357, + 514 + ], + "score": 1.0, + "content": "distance to the rest of the graphs in the same class. Given these", + "type": "text" + }, + { + "bbox": [ + 358, + 502, + 368, + 511 + ], + "score": 0.84, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 501, + 505, + 514 + ], + "score": 1.0, + "content": "prototypes, we cluster them using", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 512, + 280, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 234, + 523 + ], + "score": 1.0, + "content": "Lloyd’s method (also known as", + "type": "text" + }, + { + "bbox": [ + 234, + 513, + 240, + 522 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 512, + 280, + 523 + ], + "score": 1.0, + "content": "-means)3.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 106, + 528, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 266, + 542 + ], + "score": 1.0, + "content": "Clustering prototype graphs: Given", + "type": "text" + }, + { + "bbox": [ + 267, + 529, + 277, + 539 + ], + "score": 0.82, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 528, + 368, + 542 + ], + "score": 1.0, + "content": "unlabeled prototypes", + "type": "text" + }, + { + "bbox": [ + 368, + 529, + 464, + 541 + ], + "score": 0.9, + "content": "p _ { 1 } , \\dotsc , p _ { K } \\in \\pi _ { 1 } ( G _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 528, + 506, + 542 + ], + "score": 1.0, + "content": "and their", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 539, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 104, + 539, + 225, + 555 + ], + "score": 1.0, + "content": "associated spectral measures", + "type": "text" + }, + { + "bbox": [ + 225, + 540, + 351, + 553 + ], + "score": 0.91, + "content": " { \\mu } _ { \\sigma ( p _ { 1 } ) } , \\ldots , { \\mu } _ { \\sigma ( p _ { K } ) } \\in P ( [ 0 , 2 ] )", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 539, + 506, + 555 + ], + "score": 1.0, + "content": ". We rename the spectral measures as", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 107, + 551, + 504, + 563 + ], + "spans": [ + { + "bbox": [ + 107, + 553, + 151, + 562 + ], + "score": 0.9, + "content": "s _ { 1 } , \\ldots , s _ { K }", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 551, + 497, + 563 + ], + "score": 1.0, + "content": "to ease notation. Thus, our goal is to associate these spectral measures to at most", + "type": "text" + }, + { + "bbox": [ + 497, + 551, + 504, + 561 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 561, + 307, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 168, + 574 + ], + "score": 1.0, + "content": "clusters, where", + "type": "text" + }, + { + "bbox": [ + 169, + 562, + 194, + 573 + ], + "score": 0.91, + "content": "k \\geq 1", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 561, + 307, + 574 + ], + "score": 1.0, + "content": "is a user defined parameter.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25.5 + }, + { + "type": "text", + "bbox": [ + 106, + 578, + 504, + 602 + ], + "lines": [ + { + "bbox": [ + 105, + 577, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 124, + 592 + ], + "score": 1.0, + "content": "The", + "type": "text" + }, + { + "bbox": [ + 124, + 579, + 131, + 589 + ], + "score": 0.81, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 577, + 225, + 592 + ], + "score": 1.0, + "content": "-means problem finds a", + "type": "text" + }, + { + "bbox": [ + 226, + 579, + 232, + 589 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 577, + 271, + 592 + ], + "score": 1.0, + "content": "-partition", + "type": "text" + }, + { + "bbox": [ + 271, + 579, + 349, + 591 + ], + "score": 0.95, + "content": "C = \\{ C _ { 1 } , \\ldots , C _ { k } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 577, + 505, + 592 + ], + "score": 1.0, + "content": "that minimizes the following objective", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 588, + 342, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 342, + 603 + ], + "score": 1.0, + "content": "that represents the overall distortion error of the clustering", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 28.5 + }, + { + "type": "interline_equation", + "bbox": [ + 237, + 606, + 372, + 642 + ], + "lines": [ + { + "bbox": [ + 237, + 606, + 372, + 642 + ], + "spans": [ + { + "bbox": [ + 237, + 606, + 372, + 642 + ], + "score": 0.94, + "content": "\\underset { C } { \\operatorname { a r g m i n } } \\sum _ { i = 1 } ^ { k } \\sum _ { s _ { i } \\in C _ { i } } W _ { p } ( s _ { i } , B ( C _ { i } ) )", + "type": "interline_equation", + "image_path": "4073ea7dd99c2452de4f406f1a96a9e85bbfa50c9d7fcdccc4fe50e72615b66f.jpg" + } + ] + } + ], + "index": 30.5, + "virtual_lines": [ + { + "bbox": [ + 237, + 606, + 372, + 624.0 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 237, + 624.0, + 372, + 642.0 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 647, + 505, + 671 + ], + "lines": [ + { + "bbox": [ + 105, + 646, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 646, + 133, + 662 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 650, + 143, + 659 + ], + "score": 0.85, + "content": "s _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 646, + 269, + 662 + ], + "score": 1.0, + "content": "is a prototype graph in cluster", + "type": "text" + }, + { + "bbox": [ + 269, + 648, + 281, + 659 + ], + "score": 0.89, + "content": "C _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 646, + 300, + 662 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 300, + 648, + 327, + 660 + ], + "score": 0.93, + "content": "B ( C _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 646, + 506, + 662 + ], + "score": 1.0, + "content": "is the Wasserstein barycenter of the cluster", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 107, + 659, + 248, + 672 + ], + "spans": [ + { + "bbox": [ + 107, + 659, + 118, + 670 + ], + "score": 0.86, + "content": "C _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 118, + 659, + 248, + 672 + ], + "score": 1.0, + "content": ". The barycenter is computed as", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5 + }, + { + "type": "interline_equation", + "bbox": [ + 229, + 676, + 382, + 713 + ], + "lines": [ + { + "bbox": [ + 229, + 676, + 382, + 713 + ], + "spans": [ + { + "bbox": [ + 229, + 676, + 382, + 713 + ], + "score": 0.95, + "content": "B ( C _ { i } ) = \\operatorname * { a r g m i n } _ { p \\in P ( [ 0 , 2 ] ) } \\sum _ { j = 1 } ^ { | C _ { i } | } W _ { p } ( p , s ( i , j ) )", + "type": "interline_equation", + "image_path": "e41f71ea816eed4ff86ff64b32490bcc3db78eef95e6867af8384888b318d74e.jpg" + } + ] + } + ], + "index": 34.5, + "virtual_lines": [ + { + "bbox": [ + 229, + 676, + 382, + 694.5 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 229, + 694.5, + 382, + 713.0 + ], + "spans": [], + "index": 35 + } + ] + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 118, + 721, + 428, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 719, + 428, + 734 + ], + "spans": [ + { + "bbox": [ + 118, + 719, + 274, + 734 + ], + "score": 1.0, + "content": "3We used the seeding method suggested in", + "type": "text" + }, + { + "bbox": [ + 275, + 722, + 280, + 730 + ], + "score": 0.81, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 719, + 311, + 734 + ], + "score": 1.0, + "content": "-means+", + "type": "text" + }, + { + "bbox": [ + 311, + 725, + 316, + 730 + ], + "score": 0.42, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 317, + 719, + 428, + 734 + ], + "score": 1.0, + "content": "(Arthur & Vassilvitskii, 2007)", + "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": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 83, + 503, + 194 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 83, + 503, + 194 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 83, + 503, + 194 + ], + "spans": [ + { + "bbox": [ + 109, + 83, + 503, + 194 + ], + "score": 0.968, + "type": "image", + "image_path": "393d3119a11d19636ddb73ae543b4196b5496b3b1defea32cbff310a102d2d91.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 83, + 503, + 120.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 120.0, + 503, + 157.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 157.0, + 503, + 194.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 163, + 203, + 447, + 216 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 163, + 203, + 447, + 217 + ], + "spans": [ + { + "bbox": [ + 163, + 203, + 447, + 217 + ], + "score": 1.0, + "content": "Figure 1: The training (left) and fine-tuning (right) stages of our GNN.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 106, + 236, + 505, + 281 + ], + "lines": [ + { + "bbox": [ + 105, + 236, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 505, + 249 + ], + "score": 1.0, + "content": "These super-classes are then used in the creation of a super-graph used further down by our GNN.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 247, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 505, + 261 + ], + "score": 1.0, + "content": "Note that the creation of super-classes, followed by building a super-graph are a once-off process.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 257, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 104, + 257, + 506, + 272 + ], + "score": 1.0, + "content": "The prototype graphs as well as the super-classes for the base classes can be stored in memory for", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 269, + 155, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 269, + 155, + 282 + ], + "score": 1.0, + "content": "further use.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5, + "bbox_fs": [ + 104, + 236, + 506, + 282 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 286, + 505, + 342 + ], + "lines": [ + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "Next, we explain our graph neural network’s architecture which comprises of a feature extractor", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 107, + 297, + 506, + 310 + ], + "spans": [ + { + "bbox": [ + 107, + 298, + 129, + 309 + ], + "score": 0.91, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 129, + 297, + 193, + 310 + ], + "score": 1.0, + "content": "and a classifier", + "type": "text" + }, + { + "bbox": [ + 193, + 298, + 213, + 309 + ], + "score": 0.91, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 297, + 374, + 310 + ], + "score": 1.0, + "content": ", described in Section 4.2. The classifier", + "type": "text" + }, + { + "bbox": [ + 375, + 298, + 394, + 309 + ], + "score": 0.92, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 297, + 506, + 310 + ], + "score": 1.0, + "content": "is further subdivided into a", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 307, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 145, + 321 + ], + "score": 1.0, + "content": "classifier", + "type": "text" + }, + { + "bbox": [ + 145, + 309, + 167, + 318 + ], + "score": 0.87, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 307, + 506, + 321 + ], + "score": 1.0, + "content": "that predicts the superclass of a graph feature vector and a graph attention network", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 316, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 104, + 316, + 136, + 335 + ], + "score": 1.0, + "content": "(GAT)", + "type": "text" + }, + { + "bbox": [ + 136, + 319, + 164, + 330 + ], + "score": 0.88, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 316, + 506, + 335 + ], + "score": 1.0, + "content": "to predict the graph’s class label. Figure 1 illustrates the training and fine-tuning", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 330, + 189, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 189, + 342 + ], + "score": 1.0, + "content": "phases of our GNN.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10, + "bbox_fs": [ + 104, + 287, + 506, + 342 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 356, + 256, + 367 + ], + "lines": [ + { + "bbox": [ + 106, + 356, + 257, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 257, + 368 + ], + "score": 1.0, + "content": "4.1 COMPUTING SUPER CLASSES", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 376, + 505, + 414 + ], + "lines": [ + { + "bbox": [ + 105, + 376, + 504, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 504, + 389 + ], + "score": 1.0, + "content": "In order to exploit inter-class relationships between base-class labels, we cluster them in the follow-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 387, + 503, + 401 + ], + "spans": [ + { + "bbox": [ + 104, + 388, + 260, + 401 + ], + "score": 1.0, + "content": "ing manner. First, we partition the set", + "type": "text" + }, + { + "bbox": [ + 261, + 389, + 276, + 400 + ], + "score": 0.89, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 276, + 388, + 369, + 401 + ], + "score": 1.0, + "content": "into class-specific sets", + "type": "text" + }, + { + "bbox": [ + 370, + 387, + 388, + 399 + ], + "score": 0.9, + "content": "G ^ { ( i ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 388, + 406, + 401 + ], + "score": 1.0, + "content": ", for", + "type": "text" + }, + { + "bbox": [ + 406, + 389, + 454, + 399 + ], + "score": 0.88, + "content": "i = 1 \\dots K", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 388, + 485, + 401 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 486, + 388, + 503, + 399 + ], + "score": 0.91, + "content": "G ^ { ( i ) }", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 101, + 394, + 375, + 419 + ], + "spans": [ + { + "bbox": [ + 101, + 394, + 268, + 419 + ], + "score": 1.0, + "content": "is the set of graphs with base-class label", + "type": "text" + }, + { + "bbox": [ + 269, + 402, + 273, + 411 + ], + "score": 0.69, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 394, + 303, + 419 + ], + "score": 1.0, + "content": ". Thus,", + "type": "text" + }, + { + "bbox": [ + 303, + 400, + 372, + 415 + ], + "score": 0.93, + "content": "\\begin{array} { r } { G _ { B } = \\bigsqcup _ { i = 1 } ^ { K } G ^ { ( i ) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 373, + 394, + 375, + 419 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15, + "bbox_fs": [ + 101, + 376, + 504, + 419 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 418, + 504, + 442 + ], + "lines": [ + { + "bbox": [ + 106, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "Then, we compute class prototype graphs for each class-specific set. The class prototype graph for", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 429, + 252, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 128, + 443 + ], + "score": 1.0, + "content": "class", + "type": "text" + }, + { + "bbox": [ + 128, + 430, + 133, + 439 + ], + "score": 0.75, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 133, + 429, + 195, + 443 + ], + "score": 1.0, + "content": "represented by", + "type": "text" + }, + { + "bbox": [ + 195, + 431, + 205, + 441 + ], + "score": 0.84, + "content": "p _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 429, + 252, + 443 + ], + "score": 1.0, + "content": "is given by", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5, + "bbox_fs": [ + 105, + 418, + 505, + 443 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 447, + 386, + 485 + ], + "lines": [ + { + "bbox": [ + 225, + 447, + 386, + 485 + ], + "spans": [ + { + "bbox": [ + 225, + 447, + 386, + 485 + ], + "score": 0.95, + "content": "p _ { i } = \\operatorname * { a r g m i n } _ { g _ { i } \\in \\pi _ { 1 } ( G ^ { ( i ) } ) } \\frac { 1 } { | G ^ { ( i ) } | } \\sum _ { j = 1 } ^ { | G ^ { ( i ) } | } W ^ { p } ( g _ { i } , g _ { j } )", + "type": "interline_equation", + "image_path": "184a8c2a4d8c67644a73819913d2c42712d2ae5fc43d95dd4c9e69267eebce09.jpg" + } + ] + } + ], + "index": 19.5, + "virtual_lines": [ + { + "bbox": [ + 225, + 447, + 386, + 466.0 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 225, + 466.0, + 386, + 485.0 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 490, + 505, + 523 + ], + "lines": [ + { + "bbox": [ + 106, + 489, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 256, + 503 + ], + "score": 1.0, + "content": "Essentially, the class prototype graph", + "type": "text" + }, + { + "bbox": [ + 256, + 492, + 266, + 501 + ], + "score": 0.85, + "content": "p _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 266, + 489, + 295, + 503 + ], + "score": 1.0, + "content": "for the", + "type": "text" + }, + { + "bbox": [ + 296, + 491, + 300, + 500 + ], + "score": 0.77, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 489, + 505, + 503 + ], + "score": 1.0, + "content": "-th class is the graph with the least average spectral", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 501, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 357, + 514 + ], + "score": 1.0, + "content": "distance to the rest of the graphs in the same class. Given these", + "type": "text" + }, + { + "bbox": [ + 358, + 502, + 368, + 511 + ], + "score": 0.84, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 501, + 505, + 514 + ], + "score": 1.0, + "content": "prototypes, we cluster them using", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 512, + 280, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 234, + 523 + ], + "score": 1.0, + "content": "Lloyd’s method (also known as", + "type": "text" + }, + { + "bbox": [ + 234, + 513, + 240, + 522 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 512, + 280, + 523 + ], + "score": 1.0, + "content": "-means)3.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 489, + 505, + 523 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 528, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 266, + 542 + ], + "score": 1.0, + "content": "Clustering prototype graphs: Given", + "type": "text" + }, + { + "bbox": [ + 267, + 529, + 277, + 539 + ], + "score": 0.82, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 528, + 368, + 542 + ], + "score": 1.0, + "content": "unlabeled prototypes", + "type": "text" + }, + { + "bbox": [ + 368, + 529, + 464, + 541 + ], + "score": 0.9, + "content": "p _ { 1 } , \\dotsc , p _ { K } \\in \\pi _ { 1 } ( G _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 528, + 506, + 542 + ], + "score": 1.0, + "content": "and their", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 539, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 104, + 539, + 225, + 555 + ], + "score": 1.0, + "content": "associated spectral measures", + "type": "text" + }, + { + "bbox": [ + 225, + 540, + 351, + 553 + ], + "score": 0.91, + "content": " { \\mu } _ { \\sigma ( p _ { 1 } ) } , \\ldots , { \\mu } _ { \\sigma ( p _ { K } ) } \\in P ( [ 0 , 2 ] )", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 539, + 506, + 555 + ], + "score": 1.0, + "content": ". We rename the spectral measures as", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 107, + 551, + 504, + 563 + ], + "spans": [ + { + "bbox": [ + 107, + 553, + 151, + 562 + ], + "score": 0.9, + "content": "s _ { 1 } , \\ldots , s _ { K }", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 551, + 497, + 563 + ], + "score": 1.0, + "content": "to ease notation. Thus, our goal is to associate these spectral measures to at most", + "type": "text" + }, + { + "bbox": [ + 497, + 551, + 504, + 561 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 561, + 307, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 168, + 574 + ], + "score": 1.0, + "content": "clusters, where", + "type": "text" + }, + { + "bbox": [ + 169, + 562, + 194, + 573 + ], + "score": 0.91, + "content": "k \\geq 1", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 561, + 307, + 574 + ], + "score": 1.0, + "content": "is a user defined parameter.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25.5, + "bbox_fs": [ + 104, + 528, + 506, + 574 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 578, + 504, + 602 + ], + "lines": [ + { + "bbox": [ + 105, + 577, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 124, + 592 + ], + "score": 1.0, + "content": "The", + "type": "text" + }, + { + "bbox": [ + 124, + 579, + 131, + 589 + ], + "score": 0.81, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 577, + 225, + 592 + ], + "score": 1.0, + "content": "-means problem finds a", + "type": "text" + }, + { + "bbox": [ + 226, + 579, + 232, + 589 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 577, + 271, + 592 + ], + "score": 1.0, + "content": "-partition", + "type": "text" + }, + { + "bbox": [ + 271, + 579, + 349, + 591 + ], + "score": 0.95, + "content": "C = \\{ C _ { 1 } , \\ldots , C _ { k } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 577, + 505, + 592 + ], + "score": 1.0, + "content": "that minimizes the following objective", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 588, + 342, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 342, + 603 + ], + "score": 1.0, + "content": "that represents the overall distortion error of the clustering", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 28.5, + "bbox_fs": [ + 105, + 577, + 505, + 603 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 237, + 606, + 372, + 642 + ], + "lines": [ + { + "bbox": [ + 237, + 606, + 372, + 642 + ], + "spans": [ + { + "bbox": [ + 237, + 606, + 372, + 642 + ], + "score": 0.94, + "content": "\\underset { C } { \\operatorname { a r g m i n } } \\sum _ { i = 1 } ^ { k } \\sum _ { s _ { i } \\in C _ { i } } W _ { p } ( s _ { i } , B ( C _ { i } ) )", + "type": "interline_equation", + "image_path": "4073ea7dd99c2452de4f406f1a96a9e85bbfa50c9d7fcdccc4fe50e72615b66f.jpg" + } + ] + } + ], + "index": 30.5, + "virtual_lines": [ + { + "bbox": [ + 237, + 606, + 372, + 624.0 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 237, + 624.0, + 372, + 642.0 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 647, + 505, + 671 + ], + "lines": [ + { + "bbox": [ + 105, + 646, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 646, + 133, + 662 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 650, + 143, + 659 + ], + "score": 0.85, + "content": "s _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 646, + 269, + 662 + ], + "score": 1.0, + "content": "is a prototype graph in cluster", + "type": "text" + }, + { + "bbox": [ + 269, + 648, + 281, + 659 + ], + "score": 0.89, + "content": "C _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 646, + 300, + 662 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 300, + 648, + 327, + 660 + ], + "score": 0.93, + "content": "B ( C _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 646, + 506, + 662 + ], + "score": 1.0, + "content": "is the Wasserstein barycenter of the cluster", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 107, + 659, + 248, + 672 + ], + "spans": [ + { + "bbox": [ + 107, + 659, + 118, + 670 + ], + "score": 0.86, + "content": "C _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 118, + 659, + 248, + 672 + ], + "score": 1.0, + "content": ". The barycenter is computed as", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5, + "bbox_fs": [ + 105, + 646, + 506, + 672 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 229, + 676, + 382, + 713 + ], + "lines": [ + { + "bbox": [ + 229, + 676, + 382, + 713 + ], + "spans": [ + { + "bbox": [ + 229, + 676, + 382, + 713 + ], + "score": 0.95, + "content": "B ( C _ { i } ) = \\operatorname * { a r g m i n } _ { p \\in P ( [ 0 , 2 ] ) } \\sum _ { j = 1 } ^ { | C _ { i } | } W _ { p } ( p , s ( i , j ) )", + "type": "interline_equation", + "image_path": "e41f71ea816eed4ff86ff64b32490bcc3db78eef95e6867af8384888b318d74e.jpg" + } + ] + } + ], + "index": 34.5, + "virtual_lines": [ + { + "bbox": [ + 229, + 676, + 382, + 694.5 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 229, + 694.5, + 382, + 713.0 + ], + "spans": [], + "index": 35 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 89, + 486, + 242 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 89, + 486, + 242 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 89, + 486, + 242 + ], + "spans": [ + { + "bbox": [ + 109, + 89, + 486, + 242 + ], + "score": 0.97, + "type": "image", + "image_path": "0908b6d8353222c6cc3822778fc0d6149a35077983a3938dc8d0e1af7f456d8a.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 89, + 486, + 140.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 140.0, + 486, + 191.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 191.0, + 486, + 242.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 131, + 260, + 478, + 272 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 131, + 259, + 479, + 274 + ], + "spans": [ + { + "bbox": [ + 131, + 259, + 479, + 274 + ], + "score": 1.0, + "content": "Figure 2: An illustration of our proposed Wasserstein super-class clustering algorithm.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 107, + 294, + 381, + 306 + ], + "lines": [ + { + "bbox": [ + 106, + 294, + 383, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 133, + 308 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 294, + 159, + 307 + ], + "score": 0.93, + "content": "s ( i , j )", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 294, + 208, + 308 + ], + "score": 1.0, + "content": "denotes the", + "type": "text" + }, + { + "bbox": [ + 208, + 295, + 214, + 306 + ], + "score": 0.83, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 294, + 320, + 308 + ], + "score": 1.0, + "content": "-th spectral measure in the", + "type": "text" + }, + { + "bbox": [ + 321, + 295, + 325, + 304 + ], + "score": 0.76, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 294, + 366, + 308 + ], + "score": 1.0, + "content": "-th cluster", + "type": "text" + }, + { + "bbox": [ + 367, + 295, + 378, + 306 + ], + "score": 0.88, + "content": "C _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 378, + 294, + 383, + 308 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 312, + 505, + 347 + ], + "lines": [ + { + "bbox": [ + 105, + 311, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 391, + 326 + ], + "score": 1.0, + "content": "Lloyd’s algorithm: Given an initial set of Wasserstein barycenters", + "type": "text" + }, + { + "bbox": [ + 392, + 311, + 491, + 325 + ], + "score": 0.93, + "content": "B ^ { ( 1 ) } ( C _ { 1 } ) , \\ldots , B ^ { ( 1 ) } ( C _ { k } )", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 311, + 506, + 326 + ], + "score": 1.0, + "content": "of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 323, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 211, + 337 + ], + "score": 1.0, + "content": "spectral measures at step", + "type": "text" + }, + { + "bbox": [ + 212, + 324, + 239, + 334 + ], + "score": 0.89, + "content": "t = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 323, + 505, + 337 + ], + "score": 1.0, + "content": ", one uses the standard Lloyd’s algorithm to find the solution by", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 334, + 424, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 424, + 348 + ], + "score": 1.0, + "content": "alternating between the assignment (Equation 4) and update (Equation 5) steps", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + }, + { + "type": "interline_equation", + "bbox": [ + 134, + 352, + 477, + 393 + ], + "lines": [ + { + "bbox": [ + 134, + 352, + 477, + 393 + ], + "spans": [ + { + "bbox": [ + 134, + 352, + 477, + 393 + ], + "score": 0.91, + "content": "\\begin{array} { r l } & { \\quad C _ { i } ^ { ( t ) } = \\left\\{ s _ { p } : W _ { p } ( s _ { p } , B ^ { ( t ) } ( C _ { i } ) ) \\leq W _ { p } ( s _ { p } , B ^ { ( t ) } ( C _ { j } ) ) , \\forall j , 1 \\leq j \\leq k , 1 \\leq p \\leq K \\right\\} } \\\\ & { \\quad C _ { i } ^ { ( t + 1 ) } = B ( C _ { i } ^ { ( t ) } ) } \\end{array}", + "type": "interline_equation", + "image_path": "ad26653c6b604b388c4728b71459d97fa1b1aa7435fef4487de65c7c891e0de4.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 134, + 352, + 477, + 365.6666666666667 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 134, + 365.6666666666667, + 477, + 379.33333333333337 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 134, + 379.33333333333337, + 477, + 393.00000000000006 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 397, + 505, + 442 + ], + "lines": [ + { + "bbox": [ + 105, + 397, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 506, + 410 + ], + "score": 1.0, + "content": "Lloyd’s algorithm is known to converge to a local minimum (except in pathological cases, where it", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 408, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 505, + 421 + ], + "score": 1.0, + "content": "can oscillate between equivalent solutions). The final output is a grouping of the prototype graphs", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 418, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 125, + 432 + ], + "score": 1.0, + "content": "into", + "type": "text" + }, + { + "bbox": [ + 125, + 420, + 132, + 429 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 418, + 506, + 432 + ], + "score": 1.0, + "content": "groups, which also induces a grouping of the corresponding base classes. We denote these", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 430, + 400, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 430, + 374, + 443 + ], + "score": 1.0, + "content": "class groups as super-classes and denote the set of super-classes as", + "type": "text" + }, + { + "bbox": [ + 374, + 430, + 396, + 441 + ], + "score": 0.89, + "content": "y ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 430, + 400, + 443 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5 + }, + { + "type": "title", + "bbox": [ + 108, + 456, + 266, + 468 + ], + "lines": [ + { + "bbox": [ + 106, + 456, + 268, + 469 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 268, + 469 + ], + "score": 1.0, + "content": "4.2 OUR GRAPH NEURAL NETWORK", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 477, + 505, + 511 + ], + "lines": [ + { + "bbox": [ + 105, + 477, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 505, + 489 + ], + "score": 1.0, + "content": "Feature extractor: To apply standard neural network architectures for downstream tasks we must", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 488, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 501 + ], + "score": 1.0, + "content": "embed the graphs in a finite dimensional vector space. We consider graph neural networks (GNNs)", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 499, + 331, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 331, + 512 + ], + "score": 1.0, + "content": "that employ the following message-passing architecture", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17 + }, + { + "type": "interline_equation", + "bbox": [ + 247, + 517, + 363, + 532 + ], + "lines": [ + { + "bbox": [ + 247, + 517, + 363, + 532 + ], + "spans": [ + { + "bbox": [ + 247, + 517, + 363, + 532 + ], + "score": 0.92, + "content": "H ^ { ( j ) } = M ( A , H ^ { ( j - 1 ) } , \\theta ^ { ( j ) } )", + "type": "interline_equation", + "image_path": "a4db44c94ed2d34ff3fe4924ba2165185fceface82e7f5ec3ecdd6463052c7f7.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 247, + 517, + 363, + 532 + ], + "spans": [], + "index": 19 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 539, + 505, + 586 + ], + "lines": [ + { + "bbox": [ + 105, + 537, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 133, + 554 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 539, + 196, + 551 + ], + "score": 0.93, + "content": "H ^ { ( j ) } \\in \\mathbb { R } ^ { | V | \\times d }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 537, + 426, + 554 + ], + "score": 1.0, + "content": "are the node embeddings (i.e., messages) computed after", + "type": "text" + }, + { + "bbox": [ + 426, + 541, + 432, + 552 + ], + "score": 0.83, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 432, + 537, + 506, + 554 + ], + "score": 1.0, + "content": "steps of the GNN", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 551, + 504, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 551, + 124, + 563 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 552, + 136, + 561 + ], + "score": 0.83, + "content": "M", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 551, + 504, + 563 + ], + "score": 1.0, + "content": "is the message propagation function which depends on the adjacency matrix of the graph", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 107, + 562, + 504, + 576 + ], + "spans": [ + { + "bbox": [ + 107, + 564, + 115, + 573 + ], + "score": 0.73, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 562, + 244, + 576 + ], + "score": 1.0, + "content": ", the trainable parameters of the", + "type": "text" + }, + { + "bbox": [ + 245, + 563, + 259, + 575 + ], + "score": 0.9, + "content": "j ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 562, + 283, + 576 + ], + "score": 1.0, + "content": "layer", + "type": "text" + }, + { + "bbox": [ + 283, + 562, + 299, + 574 + ], + "score": 0.89, + "content": "\\theta ^ { ( j ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 562, + 394, + 576 + ], + "score": 1.0, + "content": ", and node embeddings", + "type": "text" + }, + { + "bbox": [ + 394, + 562, + 424, + 574 + ], + "score": 0.91, + "content": "H ^ { ( j - 1 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 562, + 504, + 576 + ], + "score": 1.0, + "content": "generated from the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 575, + 164, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 575, + 164, + 587 + ], + "score": 1.0, + "content": "previous step.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 106, + 590, + 505, + 658 + ], + "lines": [ + { + "bbox": [ + 106, + 591, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 418, + 604 + ], + "score": 1.0, + "content": "A recently proposed GNN called the graph isomorphism network (GIN) by", + "type": "text" + }, + { + "bbox": [ + 418, + 591, + 432, + 601 + ], + "score": 0.4, + "content": "\\mathrm { X u }", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 591, + 505, + 604 + ], + "score": 1.0, + "content": "et al. (2019) was", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 602, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 506, + 615 + ], + "score": 1.0, + "content": "shown to be stronger than several popular GNN variants like GCN Kipf & Welling (2016) and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 613, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 506, + 626 + ], + "score": 1.0, + "content": "GraphSAGE Hamilton et al. (2017). What makes GIN so powerful and sets it apart from the other", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 623, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 505, + 637 + ], + "score": 1.0, + "content": "GNN variants is its injective neighborhood aggregation scheme which allows it to be as powerful as", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 634, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 506, + 648 + ], + "score": 1.0, + "content": "the Weisfeiler-Lehman (WL) graph isomorphism test. Motivated by this finding, we chose GIN as", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 646, + 430, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 430, + 659 + ], + "score": 1.0, + "content": "our graph feature extractor. The message propagation scheme in GIN is given by", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26.5 + }, + { + "type": "interline_equation", + "bbox": [ + 205, + 663, + 405, + 679 + ], + "lines": [ + { + "bbox": [ + 205, + 663, + 405, + 679 + ], + "spans": [ + { + "bbox": [ + 205, + 663, + 405, + 679 + ], + "score": 0.91, + "content": "H ^ { ( j ) } = M L P ( ( 1 + \\epsilon ) ^ { j } \\odot H ^ { ( j - 1 ) } + A ^ { T } H ^ { ( j - 1 ) } )", + "type": "interline_equation", + "image_path": "ab87fbbec2534eec2d3ce3655b5c4dd0ba436535dfe260cc5acf999727c19ffe.jpg" + } + ] + } + ], + "index": 30, + "virtual_lines": [ + { + "bbox": [ + 205, + 663, + 405, + 679 + ], + "spans": [], + "index": 30 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 685, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 685, + 505, + 698 + ], + "spans": [ + { + "bbox": [ + 105, + 685, + 131, + 698 + ], + "score": 1.0, + "content": "Here,", + "type": "text" + }, + { + "bbox": [ + 131, + 688, + 136, + 695 + ], + "score": 0.73, + "content": "\\epsilon", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 685, + 317, + 698 + ], + "score": 1.0, + "content": "is a layer-wise learnable scalar parameter and", + "type": "text" + }, + { + "bbox": [ + 318, + 686, + 344, + 695 + ], + "score": 0.75, + "content": "M L P", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 685, + 505, + 698 + ], + "score": 1.0, + "content": "represents a multi-layer perceptron with", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 696, + 506, + 709 + ], + "spans": [ + { + "bbox": [ + 105, + 696, + 455, + 709 + ], + "score": 1.0, + "content": "layer-wise non-linearities for more expressive representations. The full GIN model run", + "type": "text" + }, + { + "bbox": [ + 456, + 697, + 464, + 707 + ], + "score": 0.8, + "content": "R", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 696, + 506, + 709 + ], + "score": 1.0, + "content": "iterations", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 707, + 506, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 707, + 404, + 721 + ], + "score": 1.0, + "content": "of Equation 6 to generate final node embeddings which we represent by", + "type": "text" + }, + { + "bbox": [ + 405, + 707, + 427, + 718 + ], + "score": 0.91, + "content": "H ^ { ( R ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 707, + 506, + 721 + ], + "score": 1.0, + "content": ". As features from", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 719, + 503, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 483, + 733 + ], + "score": 1.0, + "content": "earlier iterations can also be helpful in achieving higher discriminative power, embeddings", + "type": "text" + }, + { + "bbox": [ + 483, + 720, + 503, + 730 + ], + "score": 0.89, + "content": "H ^ { ( j ) }", + "type": "inline_equation" + } + ], + "index": 34 + } + ], + "index": 32.5 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 310, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 310, + 761 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 89, + 486, + 242 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 89, + 486, + 242 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 89, + 486, + 242 + ], + "spans": [ + { + "bbox": [ + 109, + 89, + 486, + 242 + ], + "score": 0.97, + "type": "image", + "image_path": "0908b6d8353222c6cc3822778fc0d6149a35077983a3938dc8d0e1af7f456d8a.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 89, + 486, + 140.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 140.0, + 486, + 191.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 191.0, + 486, + 242.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 131, + 260, + 478, + 272 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 131, + 259, + 479, + 274 + ], + "spans": [ + { + "bbox": [ + 131, + 259, + 479, + 274 + ], + "score": 1.0, + "content": "Figure 2: An illustration of our proposed Wasserstein super-class clustering algorithm.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 107, + 294, + 381, + 306 + ], + "lines": [ + { + "bbox": [ + 106, + 294, + 383, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 133, + 308 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 294, + 159, + 307 + ], + "score": 0.93, + "content": "s ( i , j )", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 294, + 208, + 308 + ], + "score": 1.0, + "content": "denotes the", + "type": "text" + }, + { + "bbox": [ + 208, + 295, + 214, + 306 + ], + "score": 0.83, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 294, + 320, + 308 + ], + "score": 1.0, + "content": "-th spectral measure in the", + "type": "text" + }, + { + "bbox": [ + 321, + 295, + 325, + 304 + ], + "score": 0.76, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 294, + 366, + 308 + ], + "score": 1.0, + "content": "-th cluster", + "type": "text" + }, + { + "bbox": [ + 367, + 295, + 378, + 306 + ], + "score": 0.88, + "content": "C _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 378, + 294, + 383, + 308 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4, + "bbox_fs": [ + 106, + 294, + 383, + 308 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 312, + 505, + 347 + ], + "lines": [ + { + "bbox": [ + 105, + 311, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 391, + 326 + ], + "score": 1.0, + "content": "Lloyd’s algorithm: Given an initial set of Wasserstein barycenters", + "type": "text" + }, + { + "bbox": [ + 392, + 311, + 491, + 325 + ], + "score": 0.93, + "content": "B ^ { ( 1 ) } ( C _ { 1 } ) , \\ldots , B ^ { ( 1 ) } ( C _ { k } )", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 311, + 506, + 326 + ], + "score": 1.0, + "content": "of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 323, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 211, + 337 + ], + "score": 1.0, + "content": "spectral measures at step", + "type": "text" + }, + { + "bbox": [ + 212, + 324, + 239, + 334 + ], + "score": 0.89, + "content": "t = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 323, + 505, + 337 + ], + "score": 1.0, + "content": ", one uses the standard Lloyd’s algorithm to find the solution by", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 334, + 424, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 424, + 348 + ], + "score": 1.0, + "content": "alternating between the assignment (Equation 4) and update (Equation 5) steps", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 311, + 506, + 348 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 134, + 352, + 477, + 393 + ], + "lines": [ + { + "bbox": [ + 134, + 352, + 477, + 393 + ], + "spans": [ + { + "bbox": [ + 134, + 352, + 477, + 393 + ], + "score": 0.91, + "content": "\\begin{array} { r l } & { \\quad C _ { i } ^ { ( t ) } = \\left\\{ s _ { p } : W _ { p } ( s _ { p } , B ^ { ( t ) } ( C _ { i } ) ) \\leq W _ { p } ( s _ { p } , B ^ { ( t ) } ( C _ { j } ) ) , \\forall j , 1 \\leq j \\leq k , 1 \\leq p \\leq K \\right\\} } \\\\ & { \\quad C _ { i } ^ { ( t + 1 ) } = B ( C _ { i } ^ { ( t ) } ) } \\end{array}", + "type": "interline_equation", + "image_path": "ad26653c6b604b388c4728b71459d97fa1b1aa7435fef4487de65c7c891e0de4.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 134, + 352, + 477, + 365.6666666666667 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 134, + 365.6666666666667, + 477, + 379.33333333333337 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 134, + 379.33333333333337, + 477, + 393.00000000000006 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 397, + 505, + 442 + ], + "lines": [ + { + "bbox": [ + 105, + 397, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 506, + 410 + ], + "score": 1.0, + "content": "Lloyd’s algorithm is known to converge to a local minimum (except in pathological cases, where it", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 408, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 505, + 421 + ], + "score": 1.0, + "content": "can oscillate between equivalent solutions). The final output is a grouping of the prototype graphs", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 418, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 125, + 432 + ], + "score": 1.0, + "content": "into", + "type": "text" + }, + { + "bbox": [ + 125, + 420, + 132, + 429 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 418, + 506, + 432 + ], + "score": 1.0, + "content": "groups, which also induces a grouping of the corresponding base classes. We denote these", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 430, + 400, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 430, + 374, + 443 + ], + "score": 1.0, + "content": "class groups as super-classes and denote the set of super-classes as", + "type": "text" + }, + { + "bbox": [ + 374, + 430, + 396, + 441 + ], + "score": 0.89, + "content": "y ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 430, + 400, + 443 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5, + "bbox_fs": [ + 104, + 397, + 506, + 443 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 456, + 266, + 468 + ], + "lines": [ + { + "bbox": [ + 106, + 456, + 268, + 469 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 268, + 469 + ], + "score": 1.0, + "content": "4.2 OUR GRAPH NEURAL NETWORK", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 477, + 505, + 511 + ], + "lines": [ + { + "bbox": [ + 105, + 477, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 505, + 489 + ], + "score": 1.0, + "content": "Feature extractor: To apply standard neural network architectures for downstream tasks we must", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 488, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 501 + ], + "score": 1.0, + "content": "embed the graphs in a finite dimensional vector space. We consider graph neural networks (GNNs)", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 499, + 331, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 331, + 512 + ], + "score": 1.0, + "content": "that employ the following message-passing architecture", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 477, + 505, + 512 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 247, + 517, + 363, + 532 + ], + "lines": [ + { + "bbox": [ + 247, + 517, + 363, + 532 + ], + "spans": [ + { + "bbox": [ + 247, + 517, + 363, + 532 + ], + "score": 0.92, + "content": "H ^ { ( j ) } = M ( A , H ^ { ( j - 1 ) } , \\theta ^ { ( j ) } )", + "type": "interline_equation", + "image_path": "a4db44c94ed2d34ff3fe4924ba2165185fceface82e7f5ec3ecdd6463052c7f7.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 247, + 517, + 363, + 532 + ], + "spans": [], + "index": 19 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 539, + 505, + 586 + ], + "lines": [ + { + "bbox": [ + 105, + 537, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 133, + 554 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 539, + 196, + 551 + ], + "score": 0.93, + "content": "H ^ { ( j ) } \\in \\mathbb { R } ^ { | V | \\times d }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 537, + 426, + 554 + ], + "score": 1.0, + "content": "are the node embeddings (i.e., messages) computed after", + "type": "text" + }, + { + "bbox": [ + 426, + 541, + 432, + 552 + ], + "score": 0.83, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 432, + 537, + 506, + 554 + ], + "score": 1.0, + "content": "steps of the GNN", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 551, + 504, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 551, + 124, + 563 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 552, + 136, + 561 + ], + "score": 0.83, + "content": "M", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 551, + 504, + 563 + ], + "score": 1.0, + "content": "is the message propagation function which depends on the adjacency matrix of the graph", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 107, + 562, + 504, + 576 + ], + "spans": [ + { + "bbox": [ + 107, + 564, + 115, + 573 + ], + "score": 0.73, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 562, + 244, + 576 + ], + "score": 1.0, + "content": ", the trainable parameters of the", + "type": "text" + }, + { + "bbox": [ + 245, + 563, + 259, + 575 + ], + "score": 0.9, + "content": "j ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 562, + 283, + 576 + ], + "score": 1.0, + "content": "layer", + "type": "text" + }, + { + "bbox": [ + 283, + 562, + 299, + 574 + ], + "score": 0.89, + "content": "\\theta ^ { ( j ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 562, + 394, + 576 + ], + "score": 1.0, + "content": ", and node embeddings", + "type": "text" + }, + { + "bbox": [ + 394, + 562, + 424, + 574 + ], + "score": 0.91, + "content": "H ^ { ( j - 1 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 562, + 504, + 576 + ], + "score": 1.0, + "content": "generated from the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 575, + 164, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 575, + 164, + 587 + ], + "score": 1.0, + "content": "previous step.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 537, + 506, + 587 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 590, + 505, + 658 + ], + "lines": [ + { + "bbox": [ + 106, + 591, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 418, + 604 + ], + "score": 1.0, + "content": "A recently proposed GNN called the graph isomorphism network (GIN) by", + "type": "text" + }, + { + "bbox": [ + 418, + 591, + 432, + 601 + ], + "score": 0.4, + "content": "\\mathrm { X u }", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 591, + 505, + 604 + ], + "score": 1.0, + "content": "et al. (2019) was", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 602, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 506, + 615 + ], + "score": 1.0, + "content": "shown to be stronger than several popular GNN variants like GCN Kipf & Welling (2016) and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 613, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 506, + 626 + ], + "score": 1.0, + "content": "GraphSAGE Hamilton et al. (2017). What makes GIN so powerful and sets it apart from the other", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 623, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 505, + 637 + ], + "score": 1.0, + "content": "GNN variants is its injective neighborhood aggregation scheme which allows it to be as powerful as", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 634, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 506, + 648 + ], + "score": 1.0, + "content": "the Weisfeiler-Lehman (WL) graph isomorphism test. Motivated by this finding, we chose GIN as", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 646, + 430, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 430, + 659 + ], + "score": 1.0, + "content": "our graph feature extractor. The message propagation scheme in GIN is given by", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 591, + 506, + 659 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 205, + 663, + 405, + 679 + ], + "lines": [ + { + "bbox": [ + 205, + 663, + 405, + 679 + ], + "spans": [ + { + "bbox": [ + 205, + 663, + 405, + 679 + ], + "score": 0.91, + "content": "H ^ { ( j ) } = M L P ( ( 1 + \\epsilon ) ^ { j } \\odot H ^ { ( j - 1 ) } + A ^ { T } H ^ { ( j - 1 ) } )", + "type": "interline_equation", + "image_path": "ab87fbbec2534eec2d3ce3655b5c4dd0ba436535dfe260cc5acf999727c19ffe.jpg" + } + ] + } + ], + "index": 30, + "virtual_lines": [ + { + "bbox": [ + 205, + 663, + 405, + 679 + ], + "spans": [], + "index": 30 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 685, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 685, + 505, + 698 + ], + "spans": [ + { + "bbox": [ + 105, + 685, + 131, + 698 + ], + "score": 1.0, + "content": "Here,", + "type": "text" + }, + { + "bbox": [ + 131, + 688, + 136, + 695 + ], + "score": 0.73, + "content": "\\epsilon", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 685, + 317, + 698 + ], + "score": 1.0, + "content": "is a layer-wise learnable scalar parameter and", + "type": "text" + }, + { + "bbox": [ + 318, + 686, + 344, + 695 + ], + "score": 0.75, + "content": "M L P", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 685, + 505, + 698 + ], + "score": 1.0, + "content": "represents a multi-layer perceptron with", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 696, + 506, + 709 + ], + "spans": [ + { + "bbox": [ + 105, + 696, + 455, + 709 + ], + "score": 1.0, + "content": "layer-wise non-linearities for more expressive representations. The full GIN model run", + "type": "text" + }, + { + "bbox": [ + 456, + 697, + 464, + 707 + ], + "score": 0.8, + "content": "R", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 696, + 506, + 709 + ], + "score": 1.0, + "content": "iterations", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 707, + 506, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 707, + 404, + 721 + ], + "score": 1.0, + "content": "of Equation 6 to generate final node embeddings which we represent by", + "type": "text" + }, + { + "bbox": [ + 405, + 707, + 427, + 718 + ], + "score": 0.91, + "content": "H ^ { ( R ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 707, + 506, + 721 + ], + "score": 1.0, + "content": ". As features from", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 719, + 503, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 483, + 733 + ], + "score": 1.0, + "content": "earlier iterations can also be helpful in achieving higher discriminative power, embeddings", + "type": "text" + }, + { + "bbox": [ + 483, + 720, + 503, + 730 + ], + "score": 0.89, + "content": "H ^ { ( j ) }", + "type": "inline_equation" + } + ], + "index": 34 + } + ], + "index": 32.5, + "bbox_fs": [ + 105, + 685, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 270, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 270, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 141, + 94 + ], + "score": 1.0, + "content": "from all", + "type": "text" + }, + { + "bbox": [ + 141, + 83, + 150, + 92 + ], + "score": 0.82, + "content": "R", + "type": "inline_equation" + }, + { + "bbox": [ + 150, + 82, + 270, + 94 + ], + "score": 1.0, + "content": "iterations are concatenated as", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 100, + 340, + 132 + ], + "lines": [ + { + "bbox": [ + 267, + 100, + 340, + 132 + ], + "spans": [ + { + "bbox": [ + 267, + 100, + 340, + 132 + ], + "score": 0.94, + "content": "H _ { g } = \\left\\| _ { j = 1 } ^ { R } H ^ { ( j ) } , \\right\\|", + "type": "interline_equation", + "image_path": "efd9868b636e27c4f3f13c23a86a3abe1b3f5758487b5acfc443c0f0c77fd42d.jpg" + } + ] + } + ], + "index": 1.5, + "virtual_lines": [ + { + "bbox": [ + 267, + 100, + 340, + 116.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 267, + 116.0, + 340, + 132.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 141, + 505, + 178 + ], + "lines": [ + { + "bbox": [ + 102, + 137, + 507, + 158 + ], + "spans": [ + { + "bbox": [ + 102, + 137, + 131, + 158 + ], + "score": 1.0, + "content": "Here,", + "type": "text" + }, + { + "bbox": [ + 132, + 141, + 216, + 156 + ], + "score": 0.93, + "content": "\\begin{array} { r } { H ^ { ( j ) } = \\sum _ { v \\in V } H _ { v } ^ { ( j ) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 137, + 248, + 158 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 248, + 141, + 269, + 156 + ], + "score": 0.93, + "content": "H _ { i } ^ { ( j ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 137, + 330, + 158 + ], + "score": 1.0, + "content": "represents the", + "type": "text" + }, + { + "bbox": [ + 330, + 145, + 335, + 154 + ], + "score": 0.73, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 137, + 450, + 158 + ], + "score": 1.0, + "content": "-th node’s embedding in the", + "type": "text" + }, + { + "bbox": [ + 450, + 145, + 456, + 155 + ], + "score": 0.83, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 137, + 507, + 158 + ], + "score": 1.0, + "content": "-th iteration", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 154, + 505, + 169 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 123, + 169 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 156, + 130, + 168 + ], + "score": 0.83, + "content": "\\parallel", + "type": "inline_equation" + }, + { + "bbox": [ + 131, + 154, + 268, + 169 + ], + "score": 1.0, + "content": "denotes a concatenation operator.", + "type": "text" + }, + { + "bbox": [ + 269, + 156, + 283, + 168 + ], + "score": 0.9, + "content": "H _ { g }", + "type": "inline_equation" + }, + { + "bbox": [ + 283, + 154, + 470, + 169 + ], + "score": 1.0, + "content": "now contains the graph embedding of a graph", + "type": "text" + }, + { + "bbox": [ + 471, + 158, + 478, + 167 + ], + "score": 0.79, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 154, + 505, + 169 + ], + "score": 1.0, + "content": "and is", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 167, + 213, + 179 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 213, + 179 + ], + "score": 1.0, + "content": "passed on to the classifier.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 183, + 505, + 228 + ], + "lines": [ + { + "bbox": [ + 106, + 183, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 505, + 196 + ], + "score": 1.0, + "content": "Classifier: Here, our objective is to improve the class separation produced by the graph embeddings", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 194, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 202, + 207 + ], + "score": 1.0, + "content": "of the feature extractor", + "type": "text" + }, + { + "bbox": [ + 202, + 195, + 225, + 207 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 194, + 506, + 207 + ], + "score": 1.0, + "content": "and we do this by building a “graph of graph embeddings”, called a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 205, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 104, + 205, + 158, + 219 + ], + "score": 1.0, + "content": "super-graph", + "type": "text" + }, + { + "bbox": [ + 158, + 206, + 177, + 217 + ], + "score": 0.9, + "content": "g ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 177, + 205, + 471, + 219 + ], + "score": 1.0, + "content": ", where each node is a graph feature vector. We then employ our classifier", + "type": "text" + }, + { + "bbox": [ + 472, + 205, + 491, + 218 + ], + "score": 0.91, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 205, + 505, + 219 + ], + "score": 1.0, + "content": "on", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 216, + 483, + 230 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 483, + 230 + ], + "score": 1.0, + "content": "this super-graph to achieve better separation among the graph classes in the embedding space.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 106, + 233, + 505, + 332 + ], + "lines": [ + { + "bbox": [ + 105, + 231, + 506, + 247 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 291, + 247 + ], + "score": 1.0, + "content": "During training, we first build the super-graph", + "type": "text" + }, + { + "bbox": [ + 291, + 234, + 311, + 245 + ], + "score": 0.91, + "content": "g ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 231, + 506, + 247 + ], + "score": 1.0, + "content": "on a batch of base-labeled graphs as a collection", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 244, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 106, + 244, + 118, + 257 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 245, + 124, + 254 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 125, + 244, + 272, + 257 + ], + "score": 1.0, + "content": "-NN graphs, where each constituent", + "type": "text" + }, + { + "bbox": [ + 272, + 245, + 279, + 254 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 244, + 506, + 257 + ], + "score": 1.0, + "content": "-NN graph is built on the graphs belonging to the same", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 253, + 507, + 268 + ], + "spans": [ + { + "bbox": [ + 104, + 253, + 156, + 268 + ], + "score": 1.0, + "content": "super-class.", + "type": "text" + }, + { + "bbox": [ + 156, + 256, + 176, + 267 + ], + "score": 0.9, + "content": "g ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 253, + 429, + 268 + ], + "score": 1.0, + "content": "is then passed through a multi-layered graph attention network", + "type": "text" + }, + { + "bbox": [ + 429, + 254, + 456, + 265 + ], + "score": 0.9, + "content": "C ^ { \\forall G A \\mathbf { \\breve { T } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 253, + 507, + 268 + ], + "score": 1.0, + "content": "to learn the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 344, + 279 + ], + "score": 1.0, + "content": "associated class probabilities. The features extracted from", + "type": "text" + }, + { + "bbox": [ + 344, + 266, + 366, + 277 + ], + "score": 0.89, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 266, + 505, + 279 + ], + "score": 1.0, + "content": "are passed into the MLP network", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 107, + 273, + 507, + 291 + ], + "spans": [ + { + "bbox": [ + 107, + 277, + 128, + 287 + ], + "score": 0.87, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 129, + 273, + 306, + 291 + ], + "score": 1.0, + "content": "to learn the associated super-class labels.", + "type": "text" + }, + { + "bbox": [ + 306, + 277, + 327, + 287 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 273, + 348, + 291 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 349, + 277, + 376, + 287 + ], + "score": 0.87, + "content": "C ^ { \\widecheck { G } A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 273, + 507, + 291 + ], + "score": 1.0, + "content": "combine to form our classifier", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 284, + 507, + 303 + ], + "spans": [ + { + "bbox": [ + 107, + 288, + 126, + 300 + ], + "score": 0.86, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 284, + 298, + 303 + ], + "score": 1.0, + "content": ". The cross-entropy losses associated with", + "type": "text" + }, + { + "bbox": [ + 299, + 289, + 321, + 299 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 284, + 340, + 303 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 340, + 288, + 367, + 298 + ], + "score": 0.89, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 368, + 284, + 507, + 303 + ], + "score": 1.0, + "content": "are added to give the overall loss", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 296, + 507, + 313 + ], + "spans": [ + { + "bbox": [ + 104, + 296, + 120, + 313 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 121, + 299, + 140, + 311 + ], + "score": 0.9, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 296, + 305, + 313 + ], + "score": 1.0, + "content": ". The intuition behind the construction of", + "type": "text" + }, + { + "bbox": [ + 305, + 300, + 324, + 311 + ], + "score": 0.91, + "content": "g ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 296, + 356, + 313 + ], + "score": 1.0, + "content": "to train", + "type": "text" + }, + { + "bbox": [ + 357, + 298, + 384, + 309 + ], + "score": 0.9, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 296, + 507, + 313 + ], + "score": 1.0, + "content": "on was to further improve the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 310, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 106, + 310, + 505, + 323 + ], + "score": 1.0, + "content": "existing cluster separation based on graph spectral measures by introducing a relational inductive", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 318, + 359, + 335 + ], + "spans": [ + { + "bbox": [ + 104, + 318, + 359, + 335 + ], + "score": 1.0, + "content": "bias (Battaglia et al., 2018) that is inherent to the GNN CGAT .", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 338, + 504, + 393 + ], + "lines": [ + { + "bbox": [ + 105, + 337, + 506, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 506, + 350 + ], + "score": 1.0, + "content": "Recall that we adopt an initialization method (described in 3). In our fine-tuning stage, novel class", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 348, + 506, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 188, + 362 + ], + "score": 1.0, + "content": "labeled graphs from", + "type": "text" + }, + { + "bbox": [ + 189, + 349, + 205, + 360 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 348, + 506, + 362 + ], + "score": 1.0, + "content": "are input to the network. The pre-trained parameters learned by the feature", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 358, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 145, + 373 + ], + "score": 1.0, + "content": "extractor", + "type": "text" + }, + { + "bbox": [ + 145, + 360, + 167, + 372 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 358, + 223, + 373 + ], + "score": 1.0, + "content": "are fixed and", + "type": "text" + }, + { + "bbox": [ + 223, + 360, + 245, + 370 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 358, + 506, + 373 + ], + "score": 1.0, + "content": "is used to infer the novel graph’s super-class label, followed by", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 103, + 366, + 507, + 387 + ], + "spans": [ + { + "bbox": [ + 103, + 366, + 507, + 387 + ], + "score": 1.0, + "content": "creation of super-graph on the novel graph samples and finally updating the parameters in CGAT", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 381, + 496, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 476, + 395 + ], + "score": 1.0, + "content": "through the loss. Finally the evaluation is performed on the samples from the unseen test set", + "type": "text" + }, + { + "bbox": [ + 476, + 382, + 492, + 393 + ], + "score": 0.87, + "content": "G _ { U }", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 381, + 496, + 395 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 404, + 505, + 492 + ], + "lines": [ + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "score": 1.0, + "content": "Discussion: We make the assumption that the novel test classes belong to the same set of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 415, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 506, + 427 + ], + "score": 1.0, + "content": "super-classes from the training graphs. The reason being that the novel class labeled samples are so", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "much fewer than the base class labeled samples, that the resulting super-graph ends up being ex-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 438, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 438, + 505, + 448 + ], + "score": 1.0, + "content": "tremely sparse and deviates a lot from the shape of the super-graph from the base classes; therefore", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 444, + 507, + 462 + ], + "spans": [ + { + "bbox": [ + 104, + 444, + 182, + 462 + ], + "score": 1.0, + "content": "it severely hinders", + "type": "text" + }, + { + "bbox": [ + 183, + 447, + 215, + 458 + ], + "score": 0.91, + "content": "C ^ { G A T } \\mathrm { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 444, + 507, + 462 + ], + "score": 1.0, + "content": "ability to effectively aggregate information from the embeddings of the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 457, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 104, + 457, + 464, + 471 + ], + "score": 1.0, + "content": "novel class labeled graphs. Instead, we pass the novel graph samples through our trained", + "type": "text" + }, + { + "bbox": [ + 465, + 459, + 487, + 469 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 457, + 506, + 471 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 469, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 483 + ], + "score": 1.0, + "content": "infer its super-class label and this works very effectively for us, as is evidenced by our empirical", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 481, + 138, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 138, + 492 + ], + "score": 1.0, + "content": "results.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 27.5 + }, + { + "type": "title", + "bbox": [ + 108, + 511, + 256, + 524 + ], + "lines": [ + { + "bbox": [ + 105, + 510, + 258, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 258, + 526 + ], + "score": 1.0, + "content": "5 EXPERIMENTAL RESULTS", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "title", + "bbox": [ + 108, + 538, + 248, + 550 + ], + "lines": [ + { + "bbox": [ + 106, + 539, + 249, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 249, + 551 + ], + "score": 1.0, + "content": "5.1 BASELINES AND DATASETS", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "The standard graph classification datasets do not adequately satisfy the requirements for few-shot", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "learning due to the dearth of unique class labels. Hence, we pick four new classification datasets,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 582, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 506, + 596 + ], + "score": 1.0, + "content": "namely, Letter-High, TRIANGLES, Reddit-12K, and ENZYMES. The details and statistics for these", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 594, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 607 + ], + "score": 1.0, + "content": "datasets are given in Appendix A.1. As there do not exist any standard state-of-the-art methods for", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "score": 1.0, + "content": "few-shot graph classification, we chose existing baselines for standard graph classification from both", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 616, + 262, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 262, + 628 + ], + "score": 1.0, + "content": "supervised and unsupervised methods.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 36.5 + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "For supervised deep learning baselines, we chose - GIN (Xu et al. (2019)), CapsGNN (Xinyi & Chen", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 642, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 506, + 657 + ], + "score": 1.0, + "content": "(2019)), and Diffpool (Lee et al. (2019)). We ran these methods with similar settings as ours, i.e.,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 655, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 506, + 668 + ], + "score": 1.0, + "content": "by partitioning the main model into feature extraction and classifier sub-models to compare them in", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 665, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 104, + 665, + 505, + 679 + ], + "score": 1.0, + "content": "a fair and informative manner. From the unsupervised category, we consider 4 powerful SOTA", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "methods - AWE (Ivanov & Burnaev (2018)), Graph2Vec (Narayanan et al. (2017)), Weisfeiler-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "Lehman subtree Kernel (Shervashidze et al. (2011)), and Graphlet count kernel (Shervashidze et al.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "(2009)). Since we want to analyze the few-shot classification abilities of these models, we essentially", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 425, + 722 + ], + "score": 1.0, + "content": "want to find out how well these algorithms can achieve class separation. We use", + "type": "text" + }, + { + "bbox": [ + 425, + 710, + 432, + 720 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 432, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "-NN search on the", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 721, + 266, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 266, + 733 + ], + "score": 1.0, + "content": "output embeddings of these algorithms.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 44 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 26, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 303, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 270, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 270, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 141, + 94 + ], + "score": 1.0, + "content": "from all", + "type": "text" + }, + { + "bbox": [ + 141, + 83, + 150, + 92 + ], + "score": 0.82, + "content": "R", + "type": "inline_equation" + }, + { + "bbox": [ + 150, + 82, + 270, + 94 + ], + "score": 1.0, + "content": "iterations are concatenated as", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0, + "bbox_fs": [ + 106, + 82, + 270, + 94 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 100, + 340, + 132 + ], + "lines": [ + { + "bbox": [ + 267, + 100, + 340, + 132 + ], + "spans": [ + { + "bbox": [ + 267, + 100, + 340, + 132 + ], + "score": 0.94, + "content": "H _ { g } = \\left\\| _ { j = 1 } ^ { R } H ^ { ( j ) } , \\right\\|", + "type": "interline_equation", + "image_path": "efd9868b636e27c4f3f13c23a86a3abe1b3f5758487b5acfc443c0f0c77fd42d.jpg" + } + ] + } + ], + "index": 1.5, + "virtual_lines": [ + { + "bbox": [ + 267, + 100, + 340, + 116.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 267, + 116.0, + 340, + 132.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 141, + 505, + 178 + ], + "lines": [ + { + "bbox": [ + 102, + 137, + 507, + 158 + ], + "spans": [ + { + "bbox": [ + 102, + 137, + 131, + 158 + ], + "score": 1.0, + "content": "Here,", + "type": "text" + }, + { + "bbox": [ + 132, + 141, + 216, + 156 + ], + "score": 0.93, + "content": "\\begin{array} { r } { H ^ { ( j ) } = \\sum _ { v \\in V } H _ { v } ^ { ( j ) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 137, + 248, + 158 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 248, + 141, + 269, + 156 + ], + "score": 0.93, + "content": "H _ { i } ^ { ( j ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 137, + 330, + 158 + ], + "score": 1.0, + "content": "represents the", + "type": "text" + }, + { + "bbox": [ + 330, + 145, + 335, + 154 + ], + "score": 0.73, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 137, + 450, + 158 + ], + "score": 1.0, + "content": "-th node’s embedding in the", + "type": "text" + }, + { + "bbox": [ + 450, + 145, + 456, + 155 + ], + "score": 0.83, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 137, + 507, + 158 + ], + "score": 1.0, + "content": "-th iteration", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 154, + 505, + 169 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 123, + 169 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 156, + 130, + 168 + ], + "score": 0.83, + "content": "\\parallel", + "type": "inline_equation" + }, + { + "bbox": [ + 131, + 154, + 268, + 169 + ], + "score": 1.0, + "content": "denotes a concatenation operator.", + "type": "text" + }, + { + "bbox": [ + 269, + 156, + 283, + 168 + ], + "score": 0.9, + "content": "H _ { g }", + "type": "inline_equation" + }, + { + "bbox": [ + 283, + 154, + 470, + 169 + ], + "score": 1.0, + "content": "now contains the graph embedding of a graph", + "type": "text" + }, + { + "bbox": [ + 471, + 158, + 478, + 167 + ], + "score": 0.79, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 154, + 505, + 169 + ], + "score": 1.0, + "content": "and is", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 167, + 213, + 179 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 213, + 179 + ], + "score": 1.0, + "content": "passed on to the classifier.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4, + "bbox_fs": [ + 102, + 137, + 507, + 179 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 183, + 505, + 228 + ], + "lines": [ + { + "bbox": [ + 106, + 183, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 505, + 196 + ], + "score": 1.0, + "content": "Classifier: Here, our objective is to improve the class separation produced by the graph embeddings", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 194, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 202, + 207 + ], + "score": 1.0, + "content": "of the feature extractor", + "type": "text" + }, + { + "bbox": [ + 202, + 195, + 225, + 207 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 194, + 506, + 207 + ], + "score": 1.0, + "content": "and we do this by building a “graph of graph embeddings”, called a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 205, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 104, + 205, + 158, + 219 + ], + "score": 1.0, + "content": "super-graph", + "type": "text" + }, + { + "bbox": [ + 158, + 206, + 177, + 217 + ], + "score": 0.9, + "content": "g ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 177, + 205, + 471, + 219 + ], + "score": 1.0, + "content": ", where each node is a graph feature vector. We then employ our classifier", + "type": "text" + }, + { + "bbox": [ + 472, + 205, + 491, + 218 + ], + "score": 0.91, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 205, + 505, + 219 + ], + "score": 1.0, + "content": "on", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 216, + 483, + 230 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 483, + 230 + ], + "score": 1.0, + "content": "this super-graph to achieve better separation among the graph classes in the embedding space.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5, + "bbox_fs": [ + 104, + 183, + 506, + 230 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 233, + 505, + 332 + ], + "lines": [ + { + "bbox": [ + 105, + 231, + 506, + 247 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 291, + 247 + ], + "score": 1.0, + "content": "During training, we first build the super-graph", + "type": "text" + }, + { + "bbox": [ + 291, + 234, + 311, + 245 + ], + "score": 0.91, + "content": "g ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 231, + 506, + 247 + ], + "score": 1.0, + "content": "on a batch of base-labeled graphs as a collection", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 244, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 106, + 244, + 118, + 257 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 245, + 124, + 254 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 125, + 244, + 272, + 257 + ], + "score": 1.0, + "content": "-NN graphs, where each constituent", + "type": "text" + }, + { + "bbox": [ + 272, + 245, + 279, + 254 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 244, + 506, + 257 + ], + "score": 1.0, + "content": "-NN graph is built on the graphs belonging to the same", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 253, + 507, + 268 + ], + "spans": [ + { + "bbox": [ + 104, + 253, + 156, + 268 + ], + "score": 1.0, + "content": "super-class.", + "type": "text" + }, + { + "bbox": [ + 156, + 256, + 176, + 267 + ], + "score": 0.9, + "content": "g ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 253, + 429, + 268 + ], + "score": 1.0, + "content": "is then passed through a multi-layered graph attention network", + "type": "text" + }, + { + "bbox": [ + 429, + 254, + 456, + 265 + ], + "score": 0.9, + "content": "C ^ { \\forall G A \\mathbf { \\breve { T } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 253, + 507, + 268 + ], + "score": 1.0, + "content": "to learn the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 344, + 279 + ], + "score": 1.0, + "content": "associated class probabilities. The features extracted from", + "type": "text" + }, + { + "bbox": [ + 344, + 266, + 366, + 277 + ], + "score": 0.89, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 266, + 505, + 279 + ], + "score": 1.0, + "content": "are passed into the MLP network", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 107, + 273, + 507, + 291 + ], + "spans": [ + { + "bbox": [ + 107, + 277, + 128, + 287 + ], + "score": 0.87, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 129, + 273, + 306, + 291 + ], + "score": 1.0, + "content": "to learn the associated super-class labels.", + "type": "text" + }, + { + "bbox": [ + 306, + 277, + 327, + 287 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 273, + 348, + 291 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 349, + 277, + 376, + 287 + ], + "score": 0.87, + "content": "C ^ { \\widecheck { G } A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 273, + 507, + 291 + ], + "score": 1.0, + "content": "combine to form our classifier", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 284, + 507, + 303 + ], + "spans": [ + { + "bbox": [ + 107, + 288, + 126, + 300 + ], + "score": 0.86, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 284, + 298, + 303 + ], + "score": 1.0, + "content": ". The cross-entropy losses associated with", + "type": "text" + }, + { + "bbox": [ + 299, + 289, + 321, + 299 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 284, + 340, + 303 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 340, + 288, + 367, + 298 + ], + "score": 0.89, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 368, + 284, + 507, + 303 + ], + "score": 1.0, + "content": "are added to give the overall loss", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 296, + 507, + 313 + ], + "spans": [ + { + "bbox": [ + 104, + 296, + 120, + 313 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 121, + 299, + 140, + 311 + ], + "score": 0.9, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 296, + 305, + 313 + ], + "score": 1.0, + "content": ". The intuition behind the construction of", + "type": "text" + }, + { + "bbox": [ + 305, + 300, + 324, + 311 + ], + "score": 0.91, + "content": "g ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 296, + 356, + 313 + ], + "score": 1.0, + "content": "to train", + "type": "text" + }, + { + "bbox": [ + 357, + 298, + 384, + 309 + ], + "score": 0.9, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 296, + 507, + 313 + ], + "score": 1.0, + "content": "on was to further improve the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 310, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 106, + 310, + 505, + 323 + ], + "score": 1.0, + "content": "existing cluster separation based on graph spectral measures by introducing a relational inductive", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 318, + 359, + 335 + ], + "spans": [ + { + "bbox": [ + 104, + 318, + 359, + 335 + ], + "score": 1.0, + "content": "bias (Battaglia et al., 2018) that is inherent to the GNN CGAT .", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 14, + "bbox_fs": [ + 104, + 231, + 507, + 335 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 338, + 504, + 393 + ], + "lines": [ + { + "bbox": [ + 105, + 337, + 506, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 506, + 350 + ], + "score": 1.0, + "content": "Recall that we adopt an initialization method (described in 3). In our fine-tuning stage, novel class", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 348, + 506, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 188, + 362 + ], + "score": 1.0, + "content": "labeled graphs from", + "type": "text" + }, + { + "bbox": [ + 189, + 349, + 205, + 360 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 348, + 506, + 362 + ], + "score": 1.0, + "content": "are input to the network. The pre-trained parameters learned by the feature", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 358, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 145, + 373 + ], + "score": 1.0, + "content": "extractor", + "type": "text" + }, + { + "bbox": [ + 145, + 360, + 167, + 372 + ], + "score": 0.92, + "content": "F _ { \\theta } ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 358, + 223, + 373 + ], + "score": 1.0, + "content": "are fixed and", + "type": "text" + }, + { + "bbox": [ + 223, + 360, + 245, + 370 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 358, + 506, + 373 + ], + "score": 1.0, + "content": "is used to infer the novel graph’s super-class label, followed by", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 103, + 366, + 507, + 387 + ], + "spans": [ + { + "bbox": [ + 103, + 366, + 507, + 387 + ], + "score": 1.0, + "content": "creation of super-graph on the novel graph samples and finally updating the parameters in CGAT", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 381, + 496, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 476, + 395 + ], + "score": 1.0, + "content": "through the loss. Finally the evaluation is performed on the samples from the unseen test set", + "type": "text" + }, + { + "bbox": [ + 476, + 382, + 492, + 393 + ], + "score": 0.87, + "content": "G _ { U }", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 381, + 496, + 395 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21, + "bbox_fs": [ + 103, + 337, + 507, + 395 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 404, + 505, + 492 + ], + "lines": [ + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "score": 1.0, + "content": "Discussion: We make the assumption that the novel test classes belong to the same set of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 415, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 506, + 427 + ], + "score": 1.0, + "content": "super-classes from the training graphs. The reason being that the novel class labeled samples are so", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "much fewer than the base class labeled samples, that the resulting super-graph ends up being ex-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 438, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 438, + 505, + 448 + ], + "score": 1.0, + "content": "tremely sparse and deviates a lot from the shape of the super-graph from the base classes; therefore", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 444, + 507, + 462 + ], + "spans": [ + { + "bbox": [ + 104, + 444, + 182, + 462 + ], + "score": 1.0, + "content": "it severely hinders", + "type": "text" + }, + { + "bbox": [ + 183, + 447, + 215, + 458 + ], + "score": 0.91, + "content": "C ^ { G A T } \\mathrm { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 444, + 507, + 462 + ], + "score": 1.0, + "content": "ability to effectively aggregate information from the embeddings of the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 457, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 104, + 457, + 464, + 471 + ], + "score": 1.0, + "content": "novel class labeled graphs. Instead, we pass the novel graph samples through our trained", + "type": "text" + }, + { + "bbox": [ + 465, + 459, + 487, + 469 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 457, + 506, + 471 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 469, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 483 + ], + "score": 1.0, + "content": "infer its super-class label and this works very effectively for us, as is evidenced by our empirical", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 481, + 138, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 138, + 492 + ], + "score": 1.0, + "content": "results.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 27.5, + "bbox_fs": [ + 104, + 403, + 507, + 492 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 511, + 256, + 524 + ], + "lines": [ + { + "bbox": [ + 105, + 510, + 258, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 258, + 526 + ], + "score": 1.0, + "content": "5 EXPERIMENTAL RESULTS", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "title", + "bbox": [ + 108, + 538, + 248, + 550 + ], + "lines": [ + { + "bbox": [ + 106, + 539, + 249, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 249, + 551 + ], + "score": 1.0, + "content": "5.1 BASELINES AND DATASETS", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "The standard graph classification datasets do not adequately satisfy the requirements for few-shot", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "learning due to the dearth of unique class labels. Hence, we pick four new classification datasets,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 582, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 506, + 596 + ], + "score": 1.0, + "content": "namely, Letter-High, TRIANGLES, Reddit-12K, and ENZYMES. The details and statistics for these", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 594, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 607 + ], + "score": 1.0, + "content": "datasets are given in Appendix A.1. As there do not exist any standard state-of-the-art methods for", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "score": 1.0, + "content": "few-shot graph classification, we chose existing baselines for standard graph classification from both", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 616, + 262, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 262, + 628 + ], + "score": 1.0, + "content": "supervised and unsupervised methods.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 36.5, + "bbox_fs": [ + 105, + 561, + 506, + 628 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "For supervised deep learning baselines, we chose - GIN (Xu et al. (2019)), CapsGNN (Xinyi & Chen", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 642, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 506, + 657 + ], + "score": 1.0, + "content": "(2019)), and Diffpool (Lee et al. (2019)). We ran these methods with similar settings as ours, i.e.,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 655, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 506, + 668 + ], + "score": 1.0, + "content": "by partitioning the main model into feature extraction and classifier sub-models to compare them in", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 665, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 104, + 665, + 505, + 679 + ], + "score": 1.0, + "content": "a fair and informative manner. From the unsupervised category, we consider 4 powerful SOTA", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "methods - AWE (Ivanov & Burnaev (2018)), Graph2Vec (Narayanan et al. (2017)), Weisfeiler-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "Lehman subtree Kernel (Shervashidze et al. (2011)), and Graphlet count kernel (Shervashidze et al.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "(2009)). Since we want to analyze the few-shot classification abilities of these models, we essentially", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 425, + 722 + ], + "score": 1.0, + "content": "want to find out how well these algorithms can achieve class separation. We use", + "type": "text" + }, + { + "bbox": [ + 425, + 710, + 432, + 720 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 432, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "-NN search on the", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 721, + 266, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 266, + 733 + ], + "score": 1.0, + "content": "output embeddings of these algorithms.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 44, + "bbox_fs": [ + 104, + 633, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 116, + 119, + 495, + 219 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 80, + 504, + 103 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 80, + 505, + 93 + ], + "spans": [ + { + "bbox": [ + 106, + 80, + 505, + 93 + ], + "score": 1.0, + "content": "Table 1: Results for various few-shot scenarios on Letter-High and TRIANGLES datasets. The best", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 91, + 407, + 103 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 407, + 103 + ], + "score": 1.0, + "content": "results are highlighted in bold while the second best results are underlined.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "table_body", + "bbox": [ + 116, + 119, + 495, + 219 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 116, + 119, + 495, + 219 + ], + "spans": [ + { + "bbox": [ + 116, + 119, + 495, + 219 + ], + "score": 0.982, + "html": "
MethodLetter-HighTRIANGLES
5-shot10-shot20-shot5-shot10-shot20-shot
WL65.27 ± 7.6768.39± 4.6972.69±3.0251.25± 4.0253.26 ± 2.9557.74 ± 2.88
Graphlet33.76 ± 6.9437.59 ± 4.6041.11 ± 3.7140.17 ± 3.1843.76 ± 3.0945.90 ±2.65
AWE40.60 ± 3.9142.20 ±2.8743.12 ± 1.0039.36± 3.8542.58 ± 3.1144.98 ± 1.54
Graph2Vec66.12 ± 5.2168.17 ± 4.2670.28 ± 2.8148.38 ± 3.8550.16 ± 4.1554.90 ± 3.01
Diffpool58.69 ± 6.3961.59 ± 5.2164.67 ± 3.2164.17 ± 5.8767.12 ± 4.2973.27 ± 3.29
CapsGNN56.60 ± 7.8660.67 ± 5.2463.97 ± 3.6965.40 ± 6.1368.37 ± 3.6773.06 ± 3.64
GIN65.83 ± 7.1769.16 ± 5.1473.28 ± 2.1763.80 ± 5.6167.30 ± 4.3572.55 ± 1.97
GIN-k-NN63.52 ± 7.2765.66± 8.6967.45± 8.7658.34 ± 3.9161.55± 3.1963.45± 2.76
OurMethod-GCN68.69 ± 6.5072.80 ± 4.1275.17 ± 3.1169.37 ± 4.9273.11 ± 3.9477.86 ± 2.84
OurMethod-GAT69.91 ± 5.9073.28± 3.4677.38 ± 1.5871.40 ± 4.3475.60± 3.6780.04 ± 2.20
", + "type": "table", + "image_path": "8342046b53e913f031efd7336ea4bc6015e333001246da39f501904f0b0e11e3.jpg" + } + ] + } + ], + "index": 3, + "virtual_lines": [ + { + "bbox": [ + 116, + 119, + 495, + 152.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 116, + 152.33333333333334, + 495, + 185.66666666666669 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 116, + 185.66666666666669, + 495, + 219.00000000000003 + ], + "spans": [], + "index": 4 + } + ] + } + ], + "index": 1.75 + }, + { + "type": "text", + "bbox": [ + 108, + 240, + 504, + 273 + ], + "lines": [ + { + "bbox": [ + 106, + 240, + 504, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 504, + 252 + ], + "score": 1.0, + "content": "Further configuration and implementation details for the baselines can be found in Appendix A.2.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 250, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 250, + 505, + 263 + ], + "score": 1.0, + "content": "We also emphasize the benefit of using a GNN as a classifier by showing the adaptation of our model", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 261, + 495, + 275 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 495, + 275 + ], + "score": 1.0, + "content": "to semi-supervised fine-tuning (in Appendix A.5) and active learning (in Appendix A.6) settings.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + }, + { + "type": "title", + "bbox": [ + 108, + 288, + 217, + 299 + ], + "lines": [ + { + "bbox": [ + 105, + 286, + 219, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 219, + 301 + ], + "score": 1.0, + "content": "5.2 FEW-SHOT RESULTS", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 109, + 309, + 504, + 342 + ], + "lines": [ + { + "bbox": [ + 107, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 107, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "We consider two variants of our model as naive baselines. In the first variant, we replace our GAT", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 107, + 320, + 505, + 332 + ], + "spans": [ + { + "bbox": [ + 107, + 320, + 505, + 332 + ], + "score": 1.0, + "content": "classifier with GCN Kipf & Welling (2016). We call this model OurMethod-GCN. This variant is", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 331, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 287, + 343 + ], + "score": 1.0, + "content": "used to justify the choice of GAT over GCN.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 347, + 505, + 392 + ], + "lines": [ + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 365, + 360 + ], + "score": 1.0, + "content": "In the second variant, we replace the entire classifier with the", + "type": "text" + }, + { + "bbox": [ + 365, + 348, + 372, + 358 + ], + "score": 0.78, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 347, + 505, + 360 + ], + "score": 1.0, + "content": "-NN algorithm over the features", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 360, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 434, + 370 + ], + "score": 1.0, + "content": "extracted from various layers of the feature extractor. We call this variant GIN-", + "type": "text" + }, + { + "bbox": [ + 435, + 360, + 441, + 369 + ], + "score": 0.57, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 360, + 505, + 370 + ], + "score": 1.0, + "content": "-NN and this is", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "score": 1.0, + "content": "introduced to emphasize the significance of building a super-graph and using a GAT on it as a", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 381, + 300, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 300, + 392 + ], + "score": 1.0, + "content": "classifier to exploit the relational inductive bias.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 397, + 505, + 464 + ], + "lines": [ + { + "bbox": [ + 106, + 396, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 266, + 410 + ], + "score": 1.0, + "content": "The results for all the datasets in various", + "type": "text" + }, + { + "bbox": [ + 266, + 399, + 272, + 409 + ], + "score": 0.78, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 396, + 361, + 410 + ], + "score": 1.0, + "content": "-shot scenarios, where", + "type": "text" + }, + { + "bbox": [ + 361, + 397, + 423, + 410 + ], + "score": 0.93, + "content": "q \\in \\{ 5 , 1 0 , 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 423, + 396, + 505, + 410 + ], + "score": 1.0, + "content": "are given in Table 1.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "score": 1.0, + "content": "We run each model 50 times and report averaged results. In every run, we select a different novel", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 420, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 167, + 431 + ], + "score": 1.0, + "content": "labeled subset", + "type": "text" + }, + { + "bbox": [ + 167, + 420, + 184, + 430 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 420, + 505, + 431 + ], + "score": 1.0, + "content": "for fine-tuning the classifiers of the models. The evaluation for all models is", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 405, + 443 + ], + "score": 1.0, + "content": "done by randomly selecting a subset of 500 samples from the testing set", + "type": "text" + }, + { + "bbox": [ + 405, + 431, + 421, + 442 + ], + "score": 0.9, + "content": "G _ { U }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "for Letter-High and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 441, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 505, + 453 + ], + "score": 1.0, + "content": "TRIANGLES, whereas over 150 for ENZYMES and 300 for Reddit dataset and averaging over 10", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 451, + 204, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 204, + 464 + ], + "score": 1.0, + "content": "such random selections.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5 + }, + { + "type": "table", + "bbox": [ + 117, + 523, + 494, + 624 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 484, + 504, + 507 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 485, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 485, + 344, + 496 + ], + "score": 1.0, + "content": "Table 2: Results for various few-shot scenarios on Reddit-", + "type": "text" + }, + { + "bbox": [ + 345, + 485, + 363, + 495 + ], + "score": 0.52, + "content": "I 2 K", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 485, + 505, + 496 + ], + "score": 1.0, + "content": "and ENZYMES datasets. The best", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 496, + 407, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 407, + 508 + ], + "score": 1.0, + "content": "results are highlighted in bold while the second best results are underlined.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5 + }, + { + "type": "table_body", + "bbox": [ + 117, + 523, + 494, + 624 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 117, + 523, + 494, + 624 + ], + "spans": [ + { + "bbox": [ + 117, + 523, + 494, + 624 + ], + "score": 0.98, + "html": "
MethodReddit-12KENZYMES
5-shot10-shot20-shot5-shot10-shot20-shot
WL40.26± 5.1742.57±3.6944.41±3.4355.78± 4.7258.47±3.8460.1±3.18
Graphlet33.76 ± 6.9437.59 ± 4.6041.11 ± 3.7153.17 ± 5.9255.30 ±3.7856.90 ±3.79
AWE30.24± 2.3433.44 ±2.0436.13 ± 1.8943.75 ±1.8545.58 ± 2.1149.98 ± 1.54
Graph2Vec27.85 ± 4.2129.97 ± 3.1732.75 ± 2.0255.88 ± 4.8658.22 ± 4.3062.28 ± 4.14
Diffpool35.24 ± 5.6937.43 ± 3.9439.11 ± 3.5245.64 ± 4.5649.64 ± 4.2354.27 ± 3.94
CapsGNN36.58 ±4.2839.16 ± 3.7341.27 ± 3.1252.67 ± 5.5155.31 ± 4.2359.34 ± 4.02
GIN40.36 ± 4.6943.70 ± 3.9846.28 ± 3.4955.73 ± 5.8058.83 ±5.3261.12 ± 4.64
GIN-k-NN41.31± 2.8443.58±2.8045.12 ± 2.1957.24 ± 7.0659.34± 5.2460.49±3.48
OurMethod-GCN40.77 ± 4.3244.28 ± 3.8648.67 ± 4.2254.34 ± 5.6458.16 ± 4.3960.86 ± 3.74
OurMethod-GAT41.59 ± 4.1245.67± 3.6850.34± 2.7155.42 ± 5.7460.64 ± 3.8462.81 ± 3.56
", + "type": "table", + "image_path": "b955792ef88c002b65b8845aeab3812c807e8919a39ab39ae60f47bbce68009d.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 117, + 523, + 494, + 556.6666666666666 + ], + "spans": [], + "index": 24 + }, + { + "bbox": [ + 117, + 556.6666666666666, + 494, + 590.3333333333333 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 117, + 590.3333333333333, + 494, + 623.9999999999999 + ], + "spans": [], + "index": 26 + } + ] + } + ], + "index": 23.75 + }, + { + "type": "text", + "bbox": [ + 106, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 643, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 505, + 657 + ], + "score": 1.0, + "content": "The results clearly show that our proposed method and its GCN variant (i.e., OurMethod-GCN)", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 654, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 231, + 666 + ], + "score": 1.0, + "content": "outperform the baselines. GIN-", + "type": "text" + }, + { + "bbox": [ + 232, + 655, + 238, + 665 + ], + "score": 0.76, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 654, + 505, + 666 + ], + "score": 1.0, + "content": "-NN shows significant degradation in results on nearly all the three", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "paradigms for all datasets with exceptions on 5-shot and 10-shot on ENZYMES dataset, thus strongly", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "indicating that the improvements of our method can primarily be attributed to our GNN classifier", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 686, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 506, + 701 + ], + "score": 1.0, + "content": "fed with the super-graph constructed from our proposed method. The improvements in results are", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "higher on TRIANGLES and Reddit datasets in contrast to Letter-High and ENZYMES, which can be", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "attributed to the smaller size of the graphs in Letter-High making it difficult to distinguish based on", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "graph spectra alone, whereas the complex and highly inter-related structure of enzymes makes it dif-", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 300, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 300, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 116, + 119, + 495, + 219 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 80, + 504, + 103 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 80, + 505, + 93 + ], + "spans": [ + { + "bbox": [ + 106, + 80, + 505, + 93 + ], + "score": 1.0, + "content": "Table 1: Results for various few-shot scenarios on Letter-High and TRIANGLES datasets. The best", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 91, + 407, + 103 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 407, + 103 + ], + "score": 1.0, + "content": "results are highlighted in bold while the second best results are underlined.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "table_body", + "bbox": [ + 116, + 119, + 495, + 219 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 116, + 119, + 495, + 219 + ], + "spans": [ + { + "bbox": [ + 116, + 119, + 495, + 219 + ], + "score": 0.982, + "html": "
MethodLetter-HighTRIANGLES
5-shot10-shot20-shot5-shot10-shot20-shot
WL65.27 ± 7.6768.39± 4.6972.69±3.0251.25± 4.0253.26 ± 2.9557.74 ± 2.88
Graphlet33.76 ± 6.9437.59 ± 4.6041.11 ± 3.7140.17 ± 3.1843.76 ± 3.0945.90 ±2.65
AWE40.60 ± 3.9142.20 ±2.8743.12 ± 1.0039.36± 3.8542.58 ± 3.1144.98 ± 1.54
Graph2Vec66.12 ± 5.2168.17 ± 4.2670.28 ± 2.8148.38 ± 3.8550.16 ± 4.1554.90 ± 3.01
Diffpool58.69 ± 6.3961.59 ± 5.2164.67 ± 3.2164.17 ± 5.8767.12 ± 4.2973.27 ± 3.29
CapsGNN56.60 ± 7.8660.67 ± 5.2463.97 ± 3.6965.40 ± 6.1368.37 ± 3.6773.06 ± 3.64
GIN65.83 ± 7.1769.16 ± 5.1473.28 ± 2.1763.80 ± 5.6167.30 ± 4.3572.55 ± 1.97
GIN-k-NN63.52 ± 7.2765.66± 8.6967.45± 8.7658.34 ± 3.9161.55± 3.1963.45± 2.76
OurMethod-GCN68.69 ± 6.5072.80 ± 4.1275.17 ± 3.1169.37 ± 4.9273.11 ± 3.9477.86 ± 2.84
OurMethod-GAT69.91 ± 5.9073.28± 3.4677.38 ± 1.5871.40 ± 4.3475.60± 3.6780.04 ± 2.20
", + "type": "table", + "image_path": "8342046b53e913f031efd7336ea4bc6015e333001246da39f501904f0b0e11e3.jpg" + } + ] + } + ], + "index": 3, + "virtual_lines": [ + { + "bbox": [ + 116, + 119, + 495, + 152.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 116, + 152.33333333333334, + 495, + 185.66666666666669 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 116, + 185.66666666666669, + 495, + 219.00000000000003 + ], + "spans": [], + "index": 4 + } + ] + } + ], + "index": 1.75 + }, + { + "type": "text", + "bbox": [ + 108, + 240, + 504, + 273 + ], + "lines": [ + { + "bbox": [ + 106, + 240, + 504, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 504, + 252 + ], + "score": 1.0, + "content": "Further configuration and implementation details for the baselines can be found in Appendix A.2.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 250, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 250, + 505, + 263 + ], + "score": 1.0, + "content": "We also emphasize the benefit of using a GNN as a classifier by showing the adaptation of our model", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 261, + 495, + 275 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 495, + 275 + ], + "score": 1.0, + "content": "to semi-supervised fine-tuning (in Appendix A.5) and active learning (in Appendix A.6) settings.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 240, + 505, + 275 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 288, + 217, + 299 + ], + "lines": [ + { + "bbox": [ + 105, + 286, + 219, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 219, + 301 + ], + "score": 1.0, + "content": "5.2 FEW-SHOT RESULTS", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 109, + 309, + 504, + 342 + ], + "lines": [ + { + "bbox": [ + 107, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 107, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "We consider two variants of our model as naive baselines. In the first variant, we replace our GAT", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 107, + 320, + 505, + 332 + ], + "spans": [ + { + "bbox": [ + 107, + 320, + 505, + 332 + ], + "score": 1.0, + "content": "classifier with GCN Kipf & Welling (2016). We call this model OurMethod-GCN. This variant is", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 331, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 287, + 343 + ], + "score": 1.0, + "content": "used to justify the choice of GAT over GCN.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10, + "bbox_fs": [ + 106, + 309, + 505, + 343 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 347, + 505, + 392 + ], + "lines": [ + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 365, + 360 + ], + "score": 1.0, + "content": "In the second variant, we replace the entire classifier with the", + "type": "text" + }, + { + "bbox": [ + 365, + 348, + 372, + 358 + ], + "score": 0.78, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 347, + 505, + 360 + ], + "score": 1.0, + "content": "-NN algorithm over the features", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 360, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 434, + 370 + ], + "score": 1.0, + "content": "extracted from various layers of the feature extractor. We call this variant GIN-", + "type": "text" + }, + { + "bbox": [ + 435, + 360, + 441, + 369 + ], + "score": 0.57, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 360, + 505, + 370 + ], + "score": 1.0, + "content": "-NN and this is", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "score": 1.0, + "content": "introduced to emphasize the significance of building a super-graph and using a GAT on it as a", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 381, + 300, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 300, + 392 + ], + "score": 1.0, + "content": "classifier to exploit the relational inductive bias.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 347, + 506, + 392 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 397, + 505, + 464 + ], + "lines": [ + { + "bbox": [ + 106, + 396, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 266, + 410 + ], + "score": 1.0, + "content": "The results for all the datasets in various", + "type": "text" + }, + { + "bbox": [ + 266, + 399, + 272, + 409 + ], + "score": 0.78, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 396, + 361, + 410 + ], + "score": 1.0, + "content": "-shot scenarios, where", + "type": "text" + }, + { + "bbox": [ + 361, + 397, + 423, + 410 + ], + "score": 0.93, + "content": "q \\in \\{ 5 , 1 0 , 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 423, + 396, + 505, + 410 + ], + "score": 1.0, + "content": "are given in Table 1.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "score": 1.0, + "content": "We run each model 50 times and report averaged results. In every run, we select a different novel", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 420, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 167, + 431 + ], + "score": 1.0, + "content": "labeled subset", + "type": "text" + }, + { + "bbox": [ + 167, + 420, + 184, + 430 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 420, + 505, + 431 + ], + "score": 1.0, + "content": "for fine-tuning the classifiers of the models. The evaluation for all models is", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 405, + 443 + ], + "score": 1.0, + "content": "done by randomly selecting a subset of 500 samples from the testing set", + "type": "text" + }, + { + "bbox": [ + 405, + 431, + 421, + 442 + ], + "score": 0.9, + "content": "G _ { U }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "for Letter-High and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 441, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 505, + 453 + ], + "score": 1.0, + "content": "TRIANGLES, whereas over 150 for ENZYMES and 300 for Reddit dataset and averaging over 10", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 451, + 204, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 204, + 464 + ], + "score": 1.0, + "content": "such random selections.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 396, + 506, + 464 + ] + }, + { + "type": "table", + "bbox": [ + 117, + 523, + 494, + 624 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 484, + 504, + 507 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 485, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 485, + 344, + 496 + ], + "score": 1.0, + "content": "Table 2: Results for various few-shot scenarios on Reddit-", + "type": "text" + }, + { + "bbox": [ + 345, + 485, + 363, + 495 + ], + "score": 0.52, + "content": "I 2 K", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 485, + 505, + 496 + ], + "score": 1.0, + "content": "and ENZYMES datasets. The best", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 496, + 407, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 407, + 508 + ], + "score": 1.0, + "content": "results are highlighted in bold while the second best results are underlined.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5 + }, + { + "type": "table_body", + "bbox": [ + 117, + 523, + 494, + 624 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 117, + 523, + 494, + 624 + ], + "spans": [ + { + "bbox": [ + 117, + 523, + 494, + 624 + ], + "score": 0.98, + "html": "
MethodReddit-12KENZYMES
5-shot10-shot20-shot5-shot10-shot20-shot
WL40.26± 5.1742.57±3.6944.41±3.4355.78± 4.7258.47±3.8460.1±3.18
Graphlet33.76 ± 6.9437.59 ± 4.6041.11 ± 3.7153.17 ± 5.9255.30 ±3.7856.90 ±3.79
AWE30.24± 2.3433.44 ±2.0436.13 ± 1.8943.75 ±1.8545.58 ± 2.1149.98 ± 1.54
Graph2Vec27.85 ± 4.2129.97 ± 3.1732.75 ± 2.0255.88 ± 4.8658.22 ± 4.3062.28 ± 4.14
Diffpool35.24 ± 5.6937.43 ± 3.9439.11 ± 3.5245.64 ± 4.5649.64 ± 4.2354.27 ± 3.94
CapsGNN36.58 ±4.2839.16 ± 3.7341.27 ± 3.1252.67 ± 5.5155.31 ± 4.2359.34 ± 4.02
GIN40.36 ± 4.6943.70 ± 3.9846.28 ± 3.4955.73 ± 5.8058.83 ±5.3261.12 ± 4.64
GIN-k-NN41.31± 2.8443.58±2.8045.12 ± 2.1957.24 ± 7.0659.34± 5.2460.49±3.48
OurMethod-GCN40.77 ± 4.3244.28 ± 3.8648.67 ± 4.2254.34 ± 5.6458.16 ± 4.3960.86 ± 3.74
OurMethod-GAT41.59 ± 4.1245.67± 3.6850.34± 2.7155.42 ± 5.7460.64 ± 3.8462.81 ± 3.56
", + "type": "table", + "image_path": "b955792ef88c002b65b8845aeab3812c807e8919a39ab39ae60f47bbce68009d.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 117, + 523, + 494, + 556.6666666666666 + ], + "spans": [], + "index": 24 + }, + { + "bbox": [ + 117, + 556.6666666666666, + 494, + 590.3333333333333 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 117, + 590.3333333333333, + 494, + 623.9999999999999 + ], + "spans": [], + "index": 26 + } + ] + } + ], + "index": 23.75 + }, + { + "type": "text", + "bbox": [ + 106, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 643, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 505, + 657 + ], + "score": 1.0, + "content": "The results clearly show that our proposed method and its GCN variant (i.e., OurMethod-GCN)", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 654, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 231, + 666 + ], + "score": 1.0, + "content": "outperform the baselines. GIN-", + "type": "text" + }, + { + "bbox": [ + 232, + 655, + 238, + 665 + ], + "score": 0.76, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 654, + 505, + 666 + ], + "score": 1.0, + "content": "-NN shows significant degradation in results on nearly all the three", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "paradigms for all datasets with exceptions on 5-shot and 10-shot on ENZYMES dataset, thus strongly", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "indicating that the improvements of our method can primarily be attributed to our GNN classifier", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 686, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 506, + 701 + ], + "score": 1.0, + "content": "fed with the super-graph constructed from our proposed method. The improvements in results are", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "higher on TRIANGLES and Reddit datasets in contrast to Letter-High and ENZYMES, which can be", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "attributed to the smaller size of the graphs in Letter-High making it difficult to distinguish based on", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "graph spectra alone, whereas the complex and highly inter-related structure of enzymes makes it dif-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 247, + 505, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 247, + 505, + 259 + ], + "score": 1.0, + "content": "ficult for the DL based feature extractors as well as the graph kernel methods to segregate the classes", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 258, + 506, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 506, + 270 + ], + "score": 1.0, + "content": "in the feature and graph space respectively. GIN and WL show much better results as compared to", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 268, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 212, + 282 + ], + "score": 1.0, + "content": "other baselines for all the", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 213, + 271, + 219, + 281 + ], + "score": 0.8, + "content": "q", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 219, + 268, + 505, + 282 + ], + "score": 1.0, + "content": "-shot scenarios, whereas AWE and Graphlet Kernel show significantly", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "score": 1.0, + "content": "low results, unable to capture the properties of the graphs well. The DL baselines apart from GIN", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 291, + 505, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 505, + 303 + ], + "score": 1.0, + "content": "on the other hand show improvements on the TRIANGLES dataset performing close to GIN, where", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 301, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 505, + 315 + ], + "score": 1.0, + "content": "the unsupervised methods fails to capture the local node properties, however still perform poorly on", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 312, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 506, + 326 + ], + "score": 1.0, + "content": "other datasets. For the 20-shot scenario on TRIANGLES, our GAT variant shows an improvement", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 323, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 147, + 337 + ], + "score": 1.0, + "content": "of around", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 147, + 324, + 162, + 334 + ], + "score": 0.88, + "content": "7 \\%", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 162, + 323, + 296, + 337 + ], + "score": 1.0, + "content": "over DL baselines and more than", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 297, + 324, + 316, + 334 + ], + "score": 0.89, + "content": "2 0 \\%", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 316, + 323, + 505, + 337 + ], + "score": 1.0, + "content": "when compared to unsupervised methods. The", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 254, + 347 + ], + "score": 1.0, + "content": "substantial improvements of around", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 254, + 334, + 270, + 345 + ], + "score": 0.86, + "content": "4 \\%", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 270, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "on Reddit dataset shows the superiority of our model for", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 315, + 358 + ], + "score": 1.0, + "content": "both the variants - GAT and GCN. Furthermore, the", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 316, + 347, + 321, + 356 + ], + "score": 0.66, + "content": "t", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 321, + 345, + 506, + 358 + ], + "score": 1.0, + "content": "-SNE plots in Figure 3 show a substantial and", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 357, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 505, + 369 + ], + "score": 1.0, + "content": "interesting separation of class labels which strongly indicate that a good feature extractor in con-", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "junction with a GNN perform well as a combination. The t-SNE plots for ENZYMES, Reddit, and", + "type": "text", + "cross_page": true + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 378, + 333, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 333, + 392 + ], + "score": 1.0, + "content": "Letter-High are shown in figures 4, 5 and 6 respectively.", + "type": "text", + "cross_page": true + } + ], + "index": 18 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 643, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 123, + 61, + 489, + 182 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 123, + 61, + 489, + 182 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 61, + 489, + 182 + ], + "spans": [ + { + "bbox": [ + 123, + 61, + 489, + 182 + ], + "score": 0.899, + "type": "image", + "image_path": "c52ff756e9f560ae3e4f1bc969a402fd9e4832578474fe3bc86a8e21779491da.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 123, + 61, + 489, + 101.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 123, + 101.33333333333334, + 489, + 141.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 123, + 141.66666666666669, + 489, + 182.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 191, + 506, + 225 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 191, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 505, + 204 + ], + "score": 1.0, + "content": "Figure 3: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 202, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 106, + 202, + 505, + 214 + ], + "score": 1.0, + "content": "from OurMethod-GAT (left), GIN (middle) and WL Kernel (right) on TRIANGLES dataset. The", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 213, + 495, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 495, + 226 + ], + "score": 1.0, + "content": "embeddings for both our model and GIN are taken from the final layers of the respective models.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 106, + 247, + 505, + 389 + ], + "lines": [ + { + "bbox": [ + 106, + 247, + 505, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 247, + 505, + 259 + ], + "score": 1.0, + "content": "ficult for the DL based feature extractors as well as the graph kernel methods to segregate the classes", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 258, + 506, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 506, + 270 + ], + "score": 1.0, + "content": "in the feature and graph space respectively. GIN and WL show much better results as compared to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 268, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 212, + 282 + ], + "score": 1.0, + "content": "other baselines for all the", + "type": "text" + }, + { + "bbox": [ + 213, + 271, + 219, + 281 + ], + "score": 0.8, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 268, + 505, + 282 + ], + "score": 1.0, + "content": "-shot scenarios, whereas AWE and Graphlet Kernel show significantly", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "score": 1.0, + "content": "low results, unable to capture the properties of the graphs well. The DL baselines apart from GIN", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 291, + 505, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 505, + 303 + ], + "score": 1.0, + "content": "on the other hand show improvements on the TRIANGLES dataset performing close to GIN, where", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 301, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 505, + 315 + ], + "score": 1.0, + "content": "the unsupervised methods fails to capture the local node properties, however still perform poorly on", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 312, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 506, + 326 + ], + "score": 1.0, + "content": "other datasets. For the 20-shot scenario on TRIANGLES, our GAT variant shows an improvement", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 323, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 147, + 337 + ], + "score": 1.0, + "content": "of around", + "type": "text" + }, + { + "bbox": [ + 147, + 324, + 162, + 334 + ], + "score": 0.88, + "content": "7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 323, + 296, + 337 + ], + "score": 1.0, + "content": "over DL baselines and more than", + "type": "text" + }, + { + "bbox": [ + 297, + 324, + 316, + 334 + ], + "score": 0.89, + "content": "2 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 323, + 505, + 337 + ], + "score": 1.0, + "content": "when compared to unsupervised methods. The", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 254, + 347 + ], + "score": 1.0, + "content": "substantial improvements of around", + "type": "text" + }, + { + "bbox": [ + 254, + 334, + 270, + 345 + ], + "score": 0.86, + "content": "4 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "on Reddit dataset shows the superiority of our model for", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 315, + 358 + ], + "score": 1.0, + "content": "both the variants - GAT and GCN. Furthermore, the", + "type": "text" + }, + { + "bbox": [ + 316, + 347, + 321, + 356 + ], + "score": 0.66, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 345, + 506, + 358 + ], + "score": 1.0, + "content": "-SNE plots in Figure 3 show a substantial and", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 357, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 505, + 369 + ], + "score": 1.0, + "content": "interesting separation of class labels which strongly indicate that a good feature extractor in con-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "junction with a GNN perform well as a combination. The t-SNE plots for ENZYMES, Reddit, and", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 378, + 333, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 333, + 392 + ], + "score": 1.0, + "content": "Letter-High are shown in figures 4, 5 and 6 respectively.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 12 + }, + { + "type": "title", + "bbox": [ + 107, + 404, + 352, + 415 + ], + "lines": [ + { + "bbox": [ + 106, + 403, + 353, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 403, + 353, + 416 + ], + "score": 1.0, + "content": "5.3 ABLATION STUDY ON NUMBER OF SUPER-CLASSES", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 424, + 505, + 535 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 505, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 479, + 437 + ], + "score": 1.0, + "content": "Here, we study the behavior of our proposed network model without the super-class classifier", + "type": "text" + }, + { + "bbox": [ + 479, + 425, + 501, + 435 + ], + "score": 0.88, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 424, + 505, + 437 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "score": 1.0, + "content": "In Table 3 (10 and 20-shot setting), we observe a marked increase with the addition of our classifier", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 446, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 505, + 460 + ], + "score": 1.0, + "content": "which uses the super-class information and the super-graph based on spectral measures to guide", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 455, + 506, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 457, + 134, + 468 + ], + "score": 0.88, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 455, + 506, + 473 + ], + "score": 1.0, + "content": "towards improving the class separation of the graphs during both the training and fine-tuning", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 468, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 104, + 468, + 506, + 482 + ], + "score": 1.0, + "content": "stages. Using super-classes help in reducing the sample complexity of the large Hypothesis space", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 480, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 506, + 492 + ], + "score": 1.0, + "content": "and makes tuning of the model parameters easier during fine-tuning stage with less samples and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 491, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 505, + 502 + ], + "score": 1.0, + "content": "few iterations. Negligible differences are observed on ENZYMES dataset since both the number of", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 500, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 104, + 500, + 505, + 516 + ], + "score": 1.0, + "content": "training classes as well as test classes are low, thus, the model performs equally well on removing", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 513, + 505, + 525 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 505, + 525 + ], + "score": 1.0, + "content": "super-classes. This is because of the latent inter-class representations can still be captured between", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 524, + 313, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 313, + 536 + ], + "score": 1.0, + "content": "few classes especially during the fine-tuning phase.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 24.5 + }, + { + "type": "table", + "bbox": [ + 137, + 588, + 474, + 659 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 546, + 504, + 570 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 545, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 358, + 559 + ], + "score": 1.0, + "content": "Table 3: Ablation Study: “No-SC” represents our classifier", + "type": "text" + }, + { + "bbox": [ + 359, + 547, + 378, + 559 + ], + "score": 0.88, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 545, + 415, + 559 + ], + "score": 1.0, + "content": "without", + "type": "text" + }, + { + "bbox": [ + 416, + 547, + 437, + 557 + ], + "score": 0.84, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 545, + 505, + 559 + ], + "score": 1.0, + "content": "and “With-SC”", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 556, + 313, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 280, + 571 + ], + "score": 1.0, + "content": "represents C(.) with both Csup and CGAT", + "type": "text" + }, + { + "bbox": [ + 279, + 558, + 313, + 570 + ], + "score": 1.0, + "content": "present.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30.5 + }, + { + "type": "table_body", + "bbox": [ + 137, + 588, + 474, + 659 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 137, + 588, + 474, + 659 + ], + "spans": [ + { + "bbox": [ + 137, + 588, + 474, + 659 + ], + "score": 0.974, + "html": "
Dataset10-shot20-shot
No-SCWith-SCNo-SCWith-SC
Letter-High71.13 ± 3.6473.61 ± 3.1975.23 ± 2.4877.42 ± 1.47
TRIANGLES74.03 ± 3.8976.49 ± 3.2676.89 ± 2.6380.14 ± 1.88
Reddit-12K43.76 ± 4.3445.35 ± 4.0648.19 ± 4.0150.36 ± 3.04
ENZYMES59.97 ± 3.9859.58 ± 4.3262.7 ± 3.6362.39 ± 3.48
", + "type": "table", + "image_path": "e052f38d2b04a5429a0c303b7baded7ce27984a6f914d9210609d5da78404829.jpg" + } + ] + } + ], + "index": 33, + "virtual_lines": [ + { + "bbox": [ + 137, + 588, + 474, + 611.6666666666666 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 137, + 611.6666666666666, + 474, + 635.3333333333333 + ], + "spans": [], + "index": 33 + }, + { + "bbox": [ + 137, + 635.3333333333333, + 474, + 658.9999999999999 + ], + "spans": [], + "index": 34 + } + ] + } + ], + "index": 31.75 + }, + { + "type": "title", + "bbox": [ + 107, + 678, + 345, + 689 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 346, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 346, + 690 + ], + "score": 1.0, + "content": "5.4 SENSITIVITY ANALYSIS OF VARIOUS ATTRIBUTES", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 699, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "Our proposed method contains two crucial attributes. We analyze our model by varying: (i) the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 709, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 250, + 721 + ], + "score": 1.0, + "content": "number of super-classes and (ii) the", + "type": "text" + }, + { + "bbox": [ + 250, + 710, + 257, + 720 + ], + "score": 0.83, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 709, + 505, + 721 + ], + "score": 1.0, + "content": "-value in super-graph construction. The effect of varying these", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "attributes on model accuracy are shown in Tables 4 and 5, respectively. For TRIANGLES and Letter-", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "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": "image", + "bbox": [ + 123, + 61, + 489, + 182 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 123, + 61, + 489, + 182 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 61, + 489, + 182 + ], + "spans": [ + { + "bbox": [ + 123, + 61, + 489, + 182 + ], + "score": 0.899, + "type": "image", + "image_path": "c52ff756e9f560ae3e4f1bc969a402fd9e4832578474fe3bc86a8e21779491da.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 123, + 61, + 489, + 101.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 123, + 101.33333333333334, + 489, + 141.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 123, + 141.66666666666669, + 489, + 182.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 191, + 506, + 225 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 191, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 505, + 204 + ], + "score": 1.0, + "content": "Figure 3: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 202, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 106, + 202, + 505, + 214 + ], + "score": 1.0, + "content": "from OurMethod-GAT (left), GIN (middle) and WL Kernel (right) on TRIANGLES dataset. The", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 213, + 495, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 495, + 226 + ], + "score": 1.0, + "content": "embeddings for both our model and GIN are taken from the final layers of the respective models.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 106, + 247, + 505, + 389 + ], + "lines": [], + "index": 12, + "bbox_fs": [ + 105, + 247, + 506, + 392 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 404, + 352, + 415 + ], + "lines": [ + { + "bbox": [ + 106, + 403, + 353, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 403, + 353, + 416 + ], + "score": 1.0, + "content": "5.3 ABLATION STUDY ON NUMBER OF SUPER-CLASSES", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 424, + 505, + 535 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 505, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 479, + 437 + ], + "score": 1.0, + "content": "Here, we study the behavior of our proposed network model without the super-class classifier", + "type": "text" + }, + { + "bbox": [ + 479, + 425, + 501, + 435 + ], + "score": 0.88, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 424, + 505, + 437 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "score": 1.0, + "content": "In Table 3 (10 and 20-shot setting), we observe a marked increase with the addition of our classifier", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 446, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 505, + 460 + ], + "score": 1.0, + "content": "which uses the super-class information and the super-graph based on spectral measures to guide", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 455, + 506, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 457, + 134, + 468 + ], + "score": 0.88, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 455, + 506, + 473 + ], + "score": 1.0, + "content": "towards improving the class separation of the graphs during both the training and fine-tuning", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 468, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 104, + 468, + 506, + 482 + ], + "score": 1.0, + "content": "stages. Using super-classes help in reducing the sample complexity of the large Hypothesis space", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 480, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 506, + 492 + ], + "score": 1.0, + "content": "and makes tuning of the model parameters easier during fine-tuning stage with less samples and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 491, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 505, + 502 + ], + "score": 1.0, + "content": "few iterations. Negligible differences are observed on ENZYMES dataset since both the number of", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 500, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 104, + 500, + 505, + 516 + ], + "score": 1.0, + "content": "training classes as well as test classes are low, thus, the model performs equally well on removing", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 513, + 505, + 525 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 505, + 525 + ], + "score": 1.0, + "content": "super-classes. This is because of the latent inter-class representations can still be captured between", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 524, + 313, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 313, + 536 + ], + "score": 1.0, + "content": "few classes especially during the fine-tuning phase.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 24.5, + "bbox_fs": [ + 104, + 424, + 506, + 536 + ] + }, + { + "type": "table", + "bbox": [ + 137, + 588, + 474, + 659 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 546, + 504, + 570 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 545, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 358, + 559 + ], + "score": 1.0, + "content": "Table 3: Ablation Study: “No-SC” represents our classifier", + "type": "text" + }, + { + "bbox": [ + 359, + 547, + 378, + 559 + ], + "score": 0.88, + "content": "C ( . )", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 545, + 415, + 559 + ], + "score": 1.0, + "content": "without", + "type": "text" + }, + { + "bbox": [ + 416, + 547, + 437, + 557 + ], + "score": 0.84, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 545, + 505, + 559 + ], + "score": 1.0, + "content": "and “With-SC”", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 556, + 313, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 280, + 571 + ], + "score": 1.0, + "content": "represents C(.) with both Csup and CGAT", + "type": "text" + }, + { + "bbox": [ + 279, + 558, + 313, + 570 + ], + "score": 1.0, + "content": "present.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30.5 + }, + { + "type": "table_body", + "bbox": [ + 137, + 588, + 474, + 659 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 137, + 588, + 474, + 659 + ], + "spans": [ + { + "bbox": [ + 137, + 588, + 474, + 659 + ], + "score": 0.974, + "html": "
Dataset10-shot20-shot
No-SCWith-SCNo-SCWith-SC
Letter-High71.13 ± 3.6473.61 ± 3.1975.23 ± 2.4877.42 ± 1.47
TRIANGLES74.03 ± 3.8976.49 ± 3.2676.89 ± 2.6380.14 ± 1.88
Reddit-12K43.76 ± 4.3445.35 ± 4.0648.19 ± 4.0150.36 ± 3.04
ENZYMES59.97 ± 3.9859.58 ± 4.3262.7 ± 3.6362.39 ± 3.48
", + "type": "table", + "image_path": "e052f38d2b04a5429a0c303b7baded7ce27984a6f914d9210609d5da78404829.jpg" + } + ] + } + ], + "index": 33, + "virtual_lines": [ + { + "bbox": [ + 137, + 588, + 474, + 611.6666666666666 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 137, + 611.6666666666666, + 474, + 635.3333333333333 + ], + "spans": [], + "index": 33 + }, + { + "bbox": [ + 137, + 635.3333333333333, + 474, + 658.9999999999999 + ], + "spans": [], + "index": 34 + } + ] + } + ], + "index": 31.75 + }, + { + "type": "title", + "bbox": [ + 107, + 678, + 345, + 689 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 346, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 346, + 690 + ], + "score": 1.0, + "content": "5.4 SENSITIVITY ANALYSIS OF VARIOUS ATTRIBUTES", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 699, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "Our proposed method contains two crucial attributes. We analyze our model by varying: (i) the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 709, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 250, + 721 + ], + "score": 1.0, + "content": "number of super-classes and (ii) the", + "type": "text" + }, + { + "bbox": [ + 250, + 710, + 257, + 720 + ], + "score": 0.83, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 709, + 505, + 721 + ], + "score": 1.0, + "content": "-value in super-graph construction. The effect of varying these", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "attributes on model accuracy are shown in Tables 4 and 5, respectively. For TRIANGLES and Letter-", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 698, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 112, + 145, + 501, + 203 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 80, + 505, + 113 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 79, + 505, + 92 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 505, + 92 + ], + "score": 1.0, + "content": "Table 4: Model analysis over number of super-classes in 20-shot scenario. There is no evaluation for", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 91, + 506, + 103 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 506, + 103 + ], + "score": 1.0, + "content": "5 super-classes on ENZYMES since the number of training classes is 4. Default value of parameter", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 102, + 165, + 113 + ], + "spans": [ + { + "bbox": [ + 106, + 103, + 113, + 112 + ], + "score": 0.7, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 102, + 165, + 113 + ], + "score": 1.0, + "content": "is fixed at 2.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "table_caption", + "bbox": [ + 117, + 134, + 151, + 145 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 117, + 133, + 153, + 146 + ], + "spans": [ + { + "bbox": [ + 117, + 133, + 153, + 146 + ], + "score": 1.0, + "content": "Dataset", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "table_caption", + "bbox": [ + 321, + 134, + 353, + 144 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 320, + 133, + 355, + 146 + ], + "spans": [ + { + "bbox": [ + 320, + 133, + 355, + 146 + ], + "score": 1.0, + "content": "20-shot", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "table_body", + "bbox": [ + 112, + 145, + 501, + 203 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 112, + 145, + 501, + 203 + ], + "spans": [ + { + "bbox": [ + 112, + 145, + 501, + 203 + ], + "score": 0.932, + "html": "
12345
Letter-High74.43± 2.6176.61 ± 1.6777.51 ± 1.4976.31 ± 1.9875.05 ± 2.29
TRIANGLES76.43 ± 2.8779.55 ± 1.9180.51 ± 1.7278.91 ± 2.0978.25 ± 2.40
Reddit-12K48.32 ± 4.0950.67 ± 2.9450.10 ± 3.0249.52 ± 4.0248.33 ± 4.08
ENZYMES62.34 ± 4.1162.13 ± 4.0160.16 ± 3.8159.34 ± 3.98
", + "type": "table", + "image_path": "9297c3837aad9fbb9b836f8f7340cdcabaf13a6f26dc6e5a9682212b53b232ae.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 112, + 145, + 501, + 164.33333333333334 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 112, + 164.33333333333334, + 501, + 183.66666666666669 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 112, + 183.66666666666669, + 501, + 203.00000000000003 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 106, + 223, + 504, + 246 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 312, + 236 + ], + "score": 1.0, + "content": "Table 5: Model analysis over number of neighbors", + "type": "text" + }, + { + "bbox": [ + 312, + 224, + 325, + 235 + ], + "score": 0.61, + "content": "( k )", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 223, + 505, + 236 + ], + "score": 1.0, + "content": "in super-graph for 20-shot scenario. Default", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 234, + 308, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 308, + 246 + ], + "score": 1.0, + "content": "value for the number of super-classes is fixed at 3.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 112, + 277, + 500, + 335 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 117, + 267, + 151, + 277 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 116, + 265, + 153, + 279 + ], + "spans": [ + { + "bbox": [ + 116, + 265, + 153, + 279 + ], + "score": 1.0, + "content": "Dataset", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "table_caption", + "bbox": [ + 321, + 267, + 354, + 277 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 320, + 266, + 355, + 279 + ], + "spans": [ + { + "bbox": [ + 320, + 266, + 355, + 279 + ], + "score": 1.0, + "content": "20-shot", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "table_body", + "bbox": [ + 112, + 277, + 500, + 335 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 112, + 277, + 500, + 335 + ], + "spans": [ + { + "bbox": [ + 112, + 277, + 500, + 335 + ], + "score": 0.961, + "html": "
2468Heuristic
Letter-High77.33 ± 1.7176.61 ± 1.6775.63 ± 2.4974.66 ± 2.6174.35 ± 2.48
TRIANGLES80.77 ± 1.5779.85 ± 1.5979.45 ± 1.9778.93 ± 2.0479.42 ± 3.16
Reddit-12K50.48 ± 3.0246.37 ± 3.0344.12 ± 2.9843.88 ± 3.2444.82 ± 2.83
ENZYMES62.34 ± 4.1161.42 ± 4.4260.23 ± 5.1059.67 ± 4.7761.07 ± 4.68
", + "type": "table", + "image_path": "239ed734fe3bd68fda8888be536259aa30b7bbc47460f944ed1eafdd58b397e4.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 112, + 277, + 500, + 296.3333333333333 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 112, + 296.3333333333333, + 500, + 315.66666666666663 + ], + "spans": [], + "index": 13 + }, + { + "bbox": [ + 112, + 315.66666666666663, + 500, + 334.99999999999994 + ], + "spans": [], + "index": 14 + } + ] + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 366, + 505, + 465 + ], + "lines": [ + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "score": 1.0, + "content": "High datasets, as we increase the number of super-classes, we observe the accuracy improving", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 378, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 505, + 389 + ], + "score": 1.0, + "content": "steadily up to 3 super-classes and then dropping from there onwards. For super-classes less than", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 389, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 198, + 400 + ], + "score": 1.0, + "content": "3, we observe that the", + "type": "text" + }, + { + "bbox": [ + 199, + 389, + 205, + 398 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 389, + 505, + 400 + ], + "score": 1.0, + "content": "-NN graph does not respect the class boundaries that are already imposed", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 399, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 506, + 412 + ], + "score": 1.0, + "content": "by the graph spectral measures, thus connecting more arbitrary classes. For Reddit we observe", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "score": 1.0, + "content": "the performance is slightly better on using 2 super-classes and for ENZYMES similar performances", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "score": 1.0, + "content": "are observed for both 1 and 2 super-classes as described in the ablation study. On the other hand,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 432, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 445 + ], + "score": 1.0, + "content": "increasing the number of super-classes past 3, makes each super-class cluster very sparse with few", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "score": 1.0, + "content": "graph classes within, leading to an underflow of information between the graph classes. The same", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 454, + 242, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 242, + 466 + ], + "score": 1.0, + "content": "effect is observed for all datasets.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 106, + 470, + 505, + 570 + ], + "lines": [ + { + "bbox": [ + 106, + 470, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 124, + 483 + ], + "score": 1.0, + "content": "The", + "type": "text" + }, + { + "bbox": [ + 125, + 471, + 132, + 481 + ], + "score": 0.82, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 470, + 505, + 483 + ], + "score": 1.0, + "content": "-value or the number of neighbors of each node belonging to the same connected component", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 481, + 505, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 505, + 495 + ], + "score": 1.0, + "content": "in the super-graph (i.e., belonging to the same super-class) is another salient parameter upon which", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 493, + 506, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 506, + 506 + ], + "score": 1.0, + "content": "hinges the information flow (via message passing) between the graphs of the same super-class. We", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 504, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 208, + 516 + ], + "score": 1.0, + "content": "analyze our model with", + "type": "text" + }, + { + "bbox": [ + 208, + 504, + 216, + 514 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 504, + 290, + 516 + ], + "score": 1.0, + "content": "values in the set", + "type": "text" + }, + { + "bbox": [ + 290, + 504, + 334, + 516 + ], + "score": 0.93, + "content": "\\{ 2 , 4 , 6 , 8 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 504, + 505, + 516 + ], + "score": 1.0, + "content": "and a commonly used heuristic method,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 250, + 529 + ], + "score": 1.0, + "content": "whereby each graph is connected to", + "type": "text" + }, + { + "bbox": [ + 250, + 515, + 268, + 527 + ], + "score": 0.94, + "content": "\\sqrt { b _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "nearest neighboring graphs based on the Euclidean similar-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 527, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 272, + 540 + ], + "score": 1.0, + "content": "ity of their feature representations, where", + "type": "text" + }, + { + "bbox": [ + 272, + 527, + 282, + 538 + ], + "score": 0.88, + "content": "b _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 527, + 505, + 540 + ], + "score": 1.0, + "content": "is the number of samples in the mini-batch correspond-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 538, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 189, + 551 + ], + "score": 1.0, + "content": "ing to super-classes", + "type": "text" + }, + { + "bbox": [ + 190, + 540, + 196, + 548 + ], + "score": 0.5, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 538, + 505, + 551 + ], + "score": 1.0, + "content": ". We achieve best results with 2-NN graphs per super-class and increasing", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 548, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 113, + 559 + ], + "score": 0.78, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 548, + 505, + 562 + ], + "score": 1.0, + "content": "beyond it leads to denser graphs with unnecessary connections between classes belonging to the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 560, + 178, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 178, + 572 + ], + "score": 1.0, + "content": "same super-class.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 28 + }, + { + "type": "title", + "bbox": [ + 107, + 600, + 195, + 613 + ], + "lines": [ + { + "bbox": [ + 105, + 599, + 197, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 197, + 616 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "score": 1.0, + "content": "In this paper, we investigated the problem of few-shot learning on graphs for the graph classification", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "task. We explicitly created a super-graph on the base-labeled graphs and then grouped / clustered", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "their associated class labels into super-classes, based on the graph spectral measures attributed to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 187, + 678 + ], + "score": 1.0, + "content": "each graph and the", + "type": "text" + }, + { + "bbox": [ + 187, + 666, + 199, + 676 + ], + "score": 0.85, + "content": "L ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "-Wasserstein distances between them. We found that training our GNN on", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "the super-graph along with the auxiliary super-classes resulted in a marked improvement over state-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 687, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 701 + ], + "score": 1.0, + "content": "of-the-art GNNs. A promising future work is to propose new GNN models that break away from", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "current neighborhood aggregation schemes to specifically overcome the obstacle posed by few-shot", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "learning on graphs. Our source-code and dataset splits have been made public in an attempt to attract", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 721, + 349, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 349, + 734 + ], + "score": 1.0, + "content": "more attention to the context of few-shot learning on graphs.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 38 + } + ], + "page_idx": 9, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 301, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 765 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 765 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 15, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 112, + 145, + 501, + 203 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 80, + 505, + 113 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 79, + 505, + 92 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 505, + 92 + ], + "score": 1.0, + "content": "Table 4: Model analysis over number of super-classes in 20-shot scenario. There is no evaluation for", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 91, + 506, + 103 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 506, + 103 + ], + "score": 1.0, + "content": "5 super-classes on ENZYMES since the number of training classes is 4. Default value of parameter", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 102, + 165, + 113 + ], + "spans": [ + { + "bbox": [ + 106, + 103, + 113, + 112 + ], + "score": 0.7, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 102, + 165, + 113 + ], + "score": 1.0, + "content": "is fixed at 2.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "table_caption", + "bbox": [ + 117, + 134, + 151, + 145 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 117, + 133, + 153, + 146 + ], + "spans": [ + { + "bbox": [ + 117, + 133, + 153, + 146 + ], + "score": 1.0, + "content": "Dataset", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "table_caption", + "bbox": [ + 321, + 134, + 353, + 144 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 320, + 133, + 355, + 146 + ], + "spans": [ + { + "bbox": [ + 320, + 133, + 355, + 146 + ], + "score": 1.0, + "content": "20-shot", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "table_body", + "bbox": [ + 112, + 145, + 501, + 203 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 112, + 145, + 501, + 203 + ], + "spans": [ + { + "bbox": [ + 112, + 145, + 501, + 203 + ], + "score": 0.932, + "html": "
12345
Letter-High74.43± 2.6176.61 ± 1.6777.51 ± 1.4976.31 ± 1.9875.05 ± 2.29
TRIANGLES76.43 ± 2.8779.55 ± 1.9180.51 ± 1.7278.91 ± 2.0978.25 ± 2.40
Reddit-12K48.32 ± 4.0950.67 ± 2.9450.10 ± 3.0249.52 ± 4.0248.33 ± 4.08
ENZYMES62.34 ± 4.1162.13 ± 4.0160.16 ± 3.8159.34 ± 3.98
", + "type": "table", + "image_path": "9297c3837aad9fbb9b836f8f7340cdcabaf13a6f26dc6e5a9682212b53b232ae.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 112, + 145, + 501, + 164.33333333333334 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 112, + 164.33333333333334, + 501, + 183.66666666666669 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 112, + 183.66666666666669, + 501, + 203.00000000000003 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 106, + 223, + 504, + 246 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 223, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 312, + 236 + ], + "score": 1.0, + "content": "Table 5: Model analysis over number of neighbors", + "type": "text" + }, + { + "bbox": [ + 312, + 224, + 325, + 235 + ], + "score": 0.61, + "content": "( k )", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 223, + 505, + 236 + ], + "score": 1.0, + "content": "in super-graph for 20-shot scenario. Default", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 234, + 308, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 308, + 246 + ], + "score": 1.0, + "content": "value for the number of super-classes is fixed at 3.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 112, + 277, + 500, + 335 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 117, + 267, + 151, + 277 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 116, + 265, + 153, + 279 + ], + "spans": [ + { + "bbox": [ + 116, + 265, + 153, + 279 + ], + "score": 1.0, + "content": "Dataset", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "table_caption", + "bbox": [ + 321, + 267, + 354, + 277 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 320, + 266, + 355, + 279 + ], + "spans": [ + { + "bbox": [ + 320, + 266, + 355, + 279 + ], + "score": 1.0, + "content": "20-shot", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "table_body", + "bbox": [ + 112, + 277, + 500, + 335 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 112, + 277, + 500, + 335 + ], + "spans": [ + { + "bbox": [ + 112, + 277, + 500, + 335 + ], + "score": 0.961, + "html": "
2468Heuristic
Letter-High77.33 ± 1.7176.61 ± 1.6775.63 ± 2.4974.66 ± 2.6174.35 ± 2.48
TRIANGLES80.77 ± 1.5779.85 ± 1.5979.45 ± 1.9778.93 ± 2.0479.42 ± 3.16
Reddit-12K50.48 ± 3.0246.37 ± 3.0344.12 ± 2.9843.88 ± 3.2444.82 ± 2.83
ENZYMES62.34 ± 4.1161.42 ± 4.4260.23 ± 5.1059.67 ± 4.7761.07 ± 4.68
", + "type": "table", + "image_path": "239ed734fe3bd68fda8888be536259aa30b7bbc47460f944ed1eafdd58b397e4.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 112, + 277, + 500, + 296.3333333333333 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 112, + 296.3333333333333, + 500, + 315.66666666666663 + ], + "spans": [], + "index": 13 + }, + { + "bbox": [ + 112, + 315.66666666666663, + 500, + 334.99999999999994 + ], + "spans": [], + "index": 14 + } + ] + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 366, + 505, + 465 + ], + "lines": [ + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "score": 1.0, + "content": "High datasets, as we increase the number of super-classes, we observe the accuracy improving", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 378, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 505, + 389 + ], + "score": 1.0, + "content": "steadily up to 3 super-classes and then dropping from there onwards. For super-classes less than", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 389, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 198, + 400 + ], + "score": 1.0, + "content": "3, we observe that the", + "type": "text" + }, + { + "bbox": [ + 199, + 389, + 205, + 398 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 389, + 505, + 400 + ], + "score": 1.0, + "content": "-NN graph does not respect the class boundaries that are already imposed", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 399, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 506, + 412 + ], + "score": 1.0, + "content": "by the graph spectral measures, thus connecting more arbitrary classes. For Reddit we observe", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "score": 1.0, + "content": "the performance is slightly better on using 2 super-classes and for ENZYMES similar performances", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "score": 1.0, + "content": "are observed for both 1 and 2 super-classes as described in the ablation study. On the other hand,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 432, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 445 + ], + "score": 1.0, + "content": "increasing the number of super-classes past 3, makes each super-class cluster very sparse with few", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "score": 1.0, + "content": "graph classes within, leading to an underflow of information between the graph classes. The same", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 454, + 242, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 242, + 466 + ], + "score": 1.0, + "content": "effect is observed for all datasets.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19, + "bbox_fs": [ + 105, + 365, + 506, + 466 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 470, + 505, + 570 + ], + "lines": [ + { + "bbox": [ + 106, + 470, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 124, + 483 + ], + "score": 1.0, + "content": "The", + "type": "text" + }, + { + "bbox": [ + 125, + 471, + 132, + 481 + ], + "score": 0.82, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 470, + 505, + 483 + ], + "score": 1.0, + "content": "-value or the number of neighbors of each node belonging to the same connected component", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 481, + 505, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 505, + 495 + ], + "score": 1.0, + "content": "in the super-graph (i.e., belonging to the same super-class) is another salient parameter upon which", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 493, + 506, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 506, + 506 + ], + "score": 1.0, + "content": "hinges the information flow (via message passing) between the graphs of the same super-class. We", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 504, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 208, + 516 + ], + "score": 1.0, + "content": "analyze our model with", + "type": "text" + }, + { + "bbox": [ + 208, + 504, + 216, + 514 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 504, + 290, + 516 + ], + "score": 1.0, + "content": "values in the set", + "type": "text" + }, + { + "bbox": [ + 290, + 504, + 334, + 516 + ], + "score": 0.93, + "content": "\\{ 2 , 4 , 6 , 8 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 504, + 505, + 516 + ], + "score": 1.0, + "content": "and a commonly used heuristic method,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 250, + 529 + ], + "score": 1.0, + "content": "whereby each graph is connected to", + "type": "text" + }, + { + "bbox": [ + 250, + 515, + 268, + 527 + ], + "score": 0.94, + "content": "\\sqrt { b _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "nearest neighboring graphs based on the Euclidean similar-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 527, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 272, + 540 + ], + "score": 1.0, + "content": "ity of their feature representations, where", + "type": "text" + }, + { + "bbox": [ + 272, + 527, + 282, + 538 + ], + "score": 0.88, + "content": "b _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 527, + 505, + 540 + ], + "score": 1.0, + "content": "is the number of samples in the mini-batch correspond-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 538, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 189, + 551 + ], + "score": 1.0, + "content": "ing to super-classes", + "type": "text" + }, + { + "bbox": [ + 190, + 540, + 196, + 548 + ], + "score": 0.5, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 538, + 505, + 551 + ], + "score": 1.0, + "content": ". We achieve best results with 2-NN graphs per super-class and increasing", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 548, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 113, + 559 + ], + "score": 0.78, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 548, + 505, + 562 + ], + "score": 1.0, + "content": "beyond it leads to denser graphs with unnecessary connections between classes belonging to the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 560, + 178, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 178, + 572 + ], + "score": 1.0, + "content": "same super-class.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 28, + "bbox_fs": [ + 105, + 470, + 506, + 572 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 600, + 195, + 613 + ], + "lines": [ + { + "bbox": [ + 105, + 599, + 197, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 197, + 616 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "score": 1.0, + "content": "In this paper, we investigated the problem of few-shot learning on graphs for the graph classification", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "task. We explicitly created a super-graph on the base-labeled graphs and then grouped / clustered", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "their associated class labels into super-classes, based on the graph spectral measures attributed to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 187, + 678 + ], + "score": 1.0, + "content": "each graph and the", + "type": "text" + }, + { + "bbox": [ + 187, + 666, + 199, + 676 + ], + "score": 0.85, + "content": "L ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "-Wasserstein distances between them. We found that training our GNN on", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "the super-graph along with the auxiliary super-classes resulted in a marked improvement over state-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 687, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 701 + ], + "score": 1.0, + "content": "of-the-art GNNs. A promising future work is to propose new GNN models that break away from", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "current neighborhood aggregation schemes to specifically overcome the obstacle posed by few-shot", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "learning on graphs. Our source-code and dataset splits have been made public in an attempt to attract", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 721, + 349, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 349, + 734 + ], + "score": 1.0, + "content": "more attention to the context of few-shot learning on graphs.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 633, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 81, + 176, + 94 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 176, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 176, + 94 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 100, + 504, + 122 + ], + "lines": [ + { + "bbox": [ + 105, + 98, + 505, + 113 + ], + "spans": [ + { + "bbox": [ + 105, + 98, + 505, + 113 + ], + "score": 1.0, + "content": "Martial Agueh and Guillaume Carlier. Barycenters in the wasserstein space. SIAM J. Math. Analysis,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 116, + 110, + 206, + 123 + ], + "spans": [ + { + "bbox": [ + 116, + 110, + 206, + 123 + ], + "score": 1.0, + "content": "43(2):904–924, 2011.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1.5 + }, + { + "type": "text", + "bbox": [ + 106, + 128, + 505, + 162 + ], + "lines": [ + { + "bbox": [ + 106, + 129, + 504, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 129, + 298, + 141 + ], + "score": 1.0, + "content": "David Arthur and Sergei Vassilvitskii. K-means", + "type": "text" + }, + { + "bbox": [ + 298, + 130, + 309, + 139 + ], + "score": 0.58, + "content": "^ { + + }", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 129, + 504, + 141 + ], + "score": 1.0, + "content": ": The advantages of careful seeding. In Proceed-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 138, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 115, + 138, + 505, + 154 + ], + "score": 1.0, + "content": "ings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’07, pp.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 117, + 151, + 192, + 162 + ], + "spans": [ + { + "bbox": [ + 117, + 151, + 192, + 162 + ], + "score": 1.0, + "content": "1027–1035, 2007.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 169, + 504, + 202 + ], + "lines": [ + { + "bbox": [ + 105, + 169, + 504, + 181 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 504, + 181 + ], + "score": 1.0, + "content": "Lars Backstrom and Jure Leskovec. Supervised random walks: Predicting and recommending links", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 180, + 503, + 192 + ], + "spans": [ + { + "bbox": [ + 115, + 180, + 503, + 192 + ], + "score": 1.0, + "content": "in social networks. CoRR, abs/1011.4071, 2010. URL http://arxiv.org/abs/1011.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 115, + 191, + 146, + 203 + ], + "spans": [ + { + "bbox": [ + 115, + 191, + 146, + 203 + ], + "score": 1.0, + "content": "4071.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 106, + 209, + 505, + 287 + ], + "lines": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "Peter Battaglia, Jessica Blake Chandler Hamrick, Victor Bapst, Alvaro Sanchez, Vinicius Zam-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 219, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 115, + 219, + 505, + 233 + ], + "score": 1.0, + "content": "baldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 115, + 231, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 115, + 231, + 505, + 244 + ], + "score": 1.0, + "content": "Caglar Gulcehre, Francis Song, Andy Ballard, Justin Gilmer, George E. Dahl, Ashish Vaswani,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 116, + 242, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 116, + 242, + 505, + 255 + ], + "score": 1.0, + "content": "Kelsey Allen, Charles Nash, Victoria Jayne Langston, Chris Dyer, Nicolas Heess, Daan Wier-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 115, + 253, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 115, + 253, + 505, + 265 + ], + "score": 1.0, + "content": "stra, Pushmeet Kohli, Matt Botvinick, Oriol Vinyals, Yujia Li, and Razvan Pascanu. Re-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 115, + 263, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 115, + 263, + 504, + 277 + ], + "score": 1.0, + "content": "lational inductive biases, deep learning, and graph networks. arXiv, 2018. URL https:", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 117, + 276, + 301, + 287 + ], + "spans": [ + { + "bbox": [ + 117, + 276, + 301, + 287 + ], + "score": 1.0, + "content": "//arxiv.org/pdf/1806.01261.pdf.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 106, + 293, + 505, + 338 + ], + "lines": [ + { + "bbox": [ + 106, + 293, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 106, + 293, + 506, + 306 + ], + "score": 1.0, + "content": "Karsten M. Borgwardt, Cheng Soon Ong, Stefan Schonauer, S. V. N. Vishwanathan, Alex J. Smola, ¨", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 115, + 304, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 115, + 304, + 505, + 317 + ], + "score": 1.0, + "content": "and Hans-Peter Kriegel. Protein function prediction via graph kernels. Bioinformatics, 21(1):", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 315, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 115, + 315, + 505, + 329 + ], + "score": 1.0, + "content": "47–56, January 2005. ISSN 1367-4803. doi: 10.1093/bioinformatics/bti1007. URL http:", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 117, + 327, + 379, + 338 + ], + "spans": [ + { + "bbox": [ + 117, + 327, + 379, + 338 + ], + "score": 1.0, + "content": "//dx.doi.org/10.1093/bioinformatics/bti1007.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17.5 + }, + { + "type": "text", + "bbox": [ + 106, + 344, + 505, + 378 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 505, + 356 + ], + "score": 1.0, + "content": "Michael M. Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. Ge-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 115, + 356, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 115, + 356, + 505, + 367 + ], + "score": 1.0, + "content": "ometric deep learning: going beyond euclidean data. CoRR, abs/1611.08097, 2016. URL", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 117, + 367, + 307, + 379 + ], + "spans": [ + { + "bbox": [ + 117, + 367, + 307, + 379 + ], + "score": 1.0, + "content": "http://arxiv.org/abs/1611.08097.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 384, + 505, + 418 + ], + "lines": [ + { + "bbox": [ + 105, + 384, + 504, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 504, + 397 + ], + "score": 1.0, + "content": "Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann Lecun. Spectral networks and lo-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 116, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 116, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "cally connected networks on graphs. In International Conference on Learning Representations", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 116, + 407, + 271, + 419 + ], + "spans": [ + { + "bbox": [ + 116, + 407, + 271, + 419 + ], + "score": 1.0, + "content": "(ICLR2014), CBLS, April 2014, 2014.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 424, + 505, + 459 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 505, + 438 + ], + "score": 1.0, + "content": "Duen Horng Chau, Carey Nachenberg, Jeffrey Wilhelm, Adam Wright, and Christos Faloutsos.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 115, + 435, + 505, + 449 + ], + "spans": [ + { + "bbox": [ + 115, + 435, + 505, + 449 + ], + "score": 1.0, + "content": "Polonium: Tera-scale graph mining and inference for malware detection. In SIAM INTERNA-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 116, + 446, + 412, + 459 + ], + "spans": [ + { + "bbox": [ + 116, + 446, + 412, + 459 + ], + "score": 1.0, + "content": "TIONAL CONFERENCE ON DATA MINING (SDM), pp. 131–142, 2011.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 464, + 505, + 498 + ], + "lines": [ + { + "bbox": [ + 106, + 464, + 506, + 478 + ], + "spans": [ + { + "bbox": [ + 106, + 464, + 506, + 478 + ], + "score": 1.0, + "content": "Wei-Yu Chen, Yen-Cheng Liu, Zsolt Kira, Yu-Chiang Frank Wang, and Jia-Bin Huang. A closer", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 116, + 476, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 116, + 476, + 505, + 488 + ], + "score": 1.0, + "content": "look at few-shot classification. In International Conference on Learning Representations, 2019.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 116, + 486, + 394, + 500 + ], + "spans": [ + { + "bbox": [ + 116, + 486, + 325, + 500 + ], + "score": 1.0, + "content": "URL https://openreview.net/forum?id", + "type": "text" + }, + { + "bbox": [ + 325, + 488, + 331, + 496 + ], + "score": 0.53, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 486, + 394, + 500 + ], + "score": 1.0, + "content": "HkxLXnAcFQ.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 505, + 505, + 549 + ], + "lines": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "Michael Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on ¨", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 115, + 515, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 115, + 515, + 506, + 529 + ], + "score": 1.0, + "content": "graphs with fast localized spectral filtering. In D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon,", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 115, + 527, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 115, + 527, + 505, + 540 + ], + "score": 1.0, + "content": "and R. Garnett (eds.), Advances in Neural Information Processing Systems 29, pp. 3844–3852.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 117, + 538, + 239, + 550 + ], + "spans": [ + { + "bbox": [ + 117, + 538, + 239, + 550 + ], + "score": 1.0, + "content": "Curran Associates, Inc., 2016.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 106, + 556, + 505, + 611 + ], + "lines": [ + { + "bbox": [ + 106, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "David K Duvenaud, Dougal Maclaurin, Jorge Iparraguirre, Rafael Bombarell, Timothy Hirzel, Alan", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 117, + 567, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 117, + 567, + 505, + 579 + ], + "score": 1.0, + "content": "Aspuru-Guzik, and Ryan P Adams. Convolutional networks on graphs for learning molecular", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 115, + 578, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 115, + 578, + 506, + 591 + ], + "score": 1.0, + "content": "fingerprints. In C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, and R. Garnett (eds.),", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 114, + 587, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 114, + 587, + 506, + 603 + ], + "score": 1.0, + "content": "Advances in Neural Information Processing Systems 28, pp. 2224–2232. Curran Associates, Inc.,", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 115, + 599, + 142, + 612 + ], + "spans": [ + { + "bbox": [ + 115, + 599, + 142, + 612 + ], + "score": 1.0, + "content": "2015.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 108, + 618, + 503, + 652 + ], + "lines": [ + { + "bbox": [ + 105, + 617, + 504, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 504, + 631 + ], + "score": 1.0, + "content": "Li Fei-Fei, Rob Fergus, and Pietro Perona. One-shot learning of object categories. IEEE Trans.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 116, + 629, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 116, + 629, + 505, + 641 + ], + "score": 1.0, + "content": "Pattern Anal. Mach. Intell., 28(4):594–611, April 2006. ISSN 0162-8828. doi: 10.1109/TPAMI.", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 116, + 639, + 404, + 653 + ], + "spans": [ + { + "bbox": [ + 116, + 639, + 404, + 653 + ], + "score": 1.0, + "content": "2006.79. URL https://doi.org/10.1109/TPAMI.2006.79.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 105, + 658, + 504, + 691 + ], + "lines": [ + { + "bbox": [ + 105, + 657, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 105, + 657, + 505, + 671 + ], + "score": 1.0, + "content": "Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 116, + 669, + 504, + 681 + ], + "spans": [ + { + "bbox": [ + 116, + 669, + 504, + 681 + ], + "score": 1.0, + "content": "of deep networks. CoRR, abs/1703.03400, 2017. URL http://arxiv.org/abs/1703.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 116, + 680, + 152, + 692 + ], + "spans": [ + { + "bbox": [ + 116, + 680, + 152, + 692 + ], + "score": 1.0, + "content": "03400.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45 + }, + { + "type": "text", + "bbox": [ + 107, + 698, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 696, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 696, + 505, + 713 + ], + "score": 1.0, + "content": "Aude Genevay, Marco Cuturi, Gabriel Peyre, and Francis Bach. Stochastic optimization for large- ´", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 115, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 115, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "scale optimal transport. In Advances in Neural Information Processing Systems 29, pp. 3440–", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 115, + 719, + 167, + 732 + ], + "spans": [ + { + "bbox": [ + 115, + 719, + 167, + 732 + ], + "score": 1.0, + "content": "3448. 2016.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48 + } + ], + "page_idx": 10, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 765 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 765 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 15, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 81, + 176, + 94 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 176, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 176, + 94 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 100, + 504, + 122 + ], + "lines": [ + { + "bbox": [ + 105, + 98, + 505, + 113 + ], + "spans": [ + { + "bbox": [ + 105, + 98, + 505, + 113 + ], + "score": 1.0, + "content": "Martial Agueh and Guillaume Carlier. Barycenters in the wasserstein space. SIAM J. Math. Analysis,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 116, + 110, + 206, + 123 + ], + "spans": [ + { + "bbox": [ + 116, + 110, + 206, + 123 + ], + "score": 1.0, + "content": "43(2):904–924, 2011.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1.5, + "bbox_fs": [ + 105, + 98, + 505, + 123 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 128, + 505, + 162 + ], + "lines": [ + { + "bbox": [ + 106, + 129, + 504, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 129, + 298, + 141 + ], + "score": 1.0, + "content": "David Arthur and Sergei Vassilvitskii. K-means", + "type": "text" + }, + { + "bbox": [ + 298, + 130, + 309, + 139 + ], + "score": 0.58, + "content": "^ { + + }", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 129, + 504, + 141 + ], + "score": 1.0, + "content": ": The advantages of careful seeding. In Proceed-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 138, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 115, + 138, + 505, + 154 + ], + "score": 1.0, + "content": "ings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’07, pp.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 117, + 151, + 192, + 162 + ], + "spans": [ + { + "bbox": [ + 117, + 151, + 192, + 162 + ], + "score": 1.0, + "content": "1027–1035, 2007.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4, + "bbox_fs": [ + 106, + 129, + 505, + 162 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 169, + 504, + 202 + ], + "lines": [ + { + "bbox": [ + 105, + 169, + 504, + 181 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 504, + 181 + ], + "score": 1.0, + "content": "Lars Backstrom and Jure Leskovec. Supervised random walks: Predicting and recommending links", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 180, + 503, + 192 + ], + "spans": [ + { + "bbox": [ + 115, + 180, + 503, + 192 + ], + "score": 1.0, + "content": "in social networks. CoRR, abs/1011.4071, 2010. URL http://arxiv.org/abs/1011.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 115, + 191, + 146, + 203 + ], + "spans": [ + { + "bbox": [ + 115, + 191, + 146, + 203 + ], + "score": 1.0, + "content": "4071.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7, + "bbox_fs": [ + 105, + 169, + 504, + 203 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 209, + 505, + 287 + ], + "lines": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "Peter Battaglia, Jessica Blake Chandler Hamrick, Victor Bapst, Alvaro Sanchez, Vinicius Zam-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 219, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 115, + 219, + 505, + 233 + ], + "score": 1.0, + "content": "baldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 115, + 231, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 115, + 231, + 505, + 244 + ], + "score": 1.0, + "content": "Caglar Gulcehre, Francis Song, Andy Ballard, Justin Gilmer, George E. Dahl, Ashish Vaswani,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 116, + 242, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 116, + 242, + 505, + 255 + ], + "score": 1.0, + "content": "Kelsey Allen, Charles Nash, Victoria Jayne Langston, Chris Dyer, Nicolas Heess, Daan Wier-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 115, + 253, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 115, + 253, + 505, + 265 + ], + "score": 1.0, + "content": "stra, Pushmeet Kohli, Matt Botvinick, Oriol Vinyals, Yujia Li, and Razvan Pascanu. Re-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 115, + 263, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 115, + 263, + 504, + 277 + ], + "score": 1.0, + "content": "lational inductive biases, deep learning, and graph networks. arXiv, 2018. URL https:", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 117, + 276, + 301, + 287 + ], + "spans": [ + { + "bbox": [ + 117, + 276, + 301, + 287 + ], + "score": 1.0, + "content": "//arxiv.org/pdf/1806.01261.pdf.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 209, + 505, + 287 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 293, + 505, + 338 + ], + "lines": [ + { + "bbox": [ + 106, + 293, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 106, + 293, + 506, + 306 + ], + "score": 1.0, + "content": "Karsten M. Borgwardt, Cheng Soon Ong, Stefan Schonauer, S. V. N. Vishwanathan, Alex J. Smola, ¨", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 115, + 304, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 115, + 304, + 505, + 317 + ], + "score": 1.0, + "content": "and Hans-Peter Kriegel. Protein function prediction via graph kernels. Bioinformatics, 21(1):", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 315, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 115, + 315, + 505, + 329 + ], + "score": 1.0, + "content": "47–56, January 2005. ISSN 1367-4803. doi: 10.1093/bioinformatics/bti1007. URL http:", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 117, + 327, + 379, + 338 + ], + "spans": [ + { + "bbox": [ + 117, + 327, + 379, + 338 + ], + "score": 1.0, + "content": "//dx.doi.org/10.1093/bioinformatics/bti1007.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17.5, + "bbox_fs": [ + 106, + 293, + 506, + 338 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 344, + 505, + 378 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 505, + 356 + ], + "score": 1.0, + "content": "Michael M. Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. Ge-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 115, + 356, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 115, + 356, + 505, + 367 + ], + "score": 1.0, + "content": "ometric deep learning: going beyond euclidean data. CoRR, abs/1611.08097, 2016. URL", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 117, + 367, + 307, + 379 + ], + "spans": [ + { + "bbox": [ + 117, + 367, + 307, + 379 + ], + "score": 1.0, + "content": "http://arxiv.org/abs/1611.08097.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21, + "bbox_fs": [ + 106, + 344, + 505, + 379 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 384, + 505, + 418 + ], + "lines": [ + { + "bbox": [ + 105, + 384, + 504, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 504, + 397 + ], + "score": 1.0, + "content": "Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann Lecun. Spectral networks and lo-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 116, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 116, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "cally connected networks on graphs. In International Conference on Learning Representations", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 116, + 407, + 271, + 419 + ], + "spans": [ + { + "bbox": [ + 116, + 407, + 271, + 419 + ], + "score": 1.0, + "content": "(ICLR2014), CBLS, April 2014, 2014.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 384, + 505, + 419 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 424, + 505, + 459 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 505, + 438 + ], + "score": 1.0, + "content": "Duen Horng Chau, Carey Nachenberg, Jeffrey Wilhelm, Adam Wright, and Christos Faloutsos.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 115, + 435, + 505, + 449 + ], + "spans": [ + { + "bbox": [ + 115, + 435, + 505, + 449 + ], + "score": 1.0, + "content": "Polonium: Tera-scale graph mining and inference for malware detection. In SIAM INTERNA-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 116, + 446, + 412, + 459 + ], + "spans": [ + { + "bbox": [ + 116, + 446, + 412, + 459 + ], + "score": 1.0, + "content": "TIONAL CONFERENCE ON DATA MINING (SDM), pp. 131–142, 2011.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 424, + 505, + 459 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 464, + 505, + 498 + ], + "lines": [ + { + "bbox": [ + 106, + 464, + 506, + 478 + ], + "spans": [ + { + "bbox": [ + 106, + 464, + 506, + 478 + ], + "score": 1.0, + "content": "Wei-Yu Chen, Yen-Cheng Liu, Zsolt Kira, Yu-Chiang Frank Wang, and Jia-Bin Huang. A closer", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 116, + 476, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 116, + 476, + 505, + 488 + ], + "score": 1.0, + "content": "look at few-shot classification. In International Conference on Learning Representations, 2019.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 116, + 486, + 394, + 500 + ], + "spans": [ + { + "bbox": [ + 116, + 486, + 325, + 500 + ], + "score": 1.0, + "content": "URL https://openreview.net/forum?id", + "type": "text" + }, + { + "bbox": [ + 325, + 488, + 331, + 496 + ], + "score": 0.53, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 486, + 394, + 500 + ], + "score": 1.0, + "content": "HkxLXnAcFQ.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30, + "bbox_fs": [ + 106, + 464, + 506, + 500 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 505, + 505, + 549 + ], + "lines": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "Michael Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on ¨", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 115, + 515, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 115, + 515, + 506, + 529 + ], + "score": 1.0, + "content": "graphs with fast localized spectral filtering. In D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon,", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 115, + 527, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 115, + 527, + 505, + 540 + ], + "score": 1.0, + "content": "and R. Garnett (eds.), Advances in Neural Information Processing Systems 29, pp. 3844–3852.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 117, + 538, + 239, + 550 + ], + "spans": [ + { + "bbox": [ + 117, + 538, + 239, + 550 + ], + "score": 1.0, + "content": "Curran Associates, Inc., 2016.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 505, + 506, + 550 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 556, + 505, + 611 + ], + "lines": [ + { + "bbox": [ + 106, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "David K Duvenaud, Dougal Maclaurin, Jorge Iparraguirre, Rafael Bombarell, Timothy Hirzel, Alan", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 117, + 567, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 117, + 567, + 505, + 579 + ], + "score": 1.0, + "content": "Aspuru-Guzik, and Ryan P Adams. Convolutional networks on graphs for learning molecular", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 115, + 578, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 115, + 578, + 506, + 591 + ], + "score": 1.0, + "content": "fingerprints. In C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, and R. Garnett (eds.),", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 114, + 587, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 114, + 587, + 506, + 603 + ], + "score": 1.0, + "content": "Advances in Neural Information Processing Systems 28, pp. 2224–2232. Curran Associates, Inc.,", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 115, + 599, + 142, + 612 + ], + "spans": [ + { + "bbox": [ + 115, + 599, + 142, + 612 + ], + "score": 1.0, + "content": "2015.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38, + "bbox_fs": [ + 106, + 556, + 506, + 612 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 618, + 503, + 652 + ], + "lines": [ + { + "bbox": [ + 105, + 617, + 504, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 504, + 631 + ], + "score": 1.0, + "content": "Li Fei-Fei, Rob Fergus, and Pietro Perona. One-shot learning of object categories. IEEE Trans.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 116, + 629, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 116, + 629, + 505, + 641 + ], + "score": 1.0, + "content": "Pattern Anal. Mach. Intell., 28(4):594–611, April 2006. ISSN 0162-8828. doi: 10.1109/TPAMI.", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 116, + 639, + 404, + 653 + ], + "spans": [ + { + "bbox": [ + 116, + 639, + 404, + 653 + ], + "score": 1.0, + "content": "2006.79. URL https://doi.org/10.1109/TPAMI.2006.79.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 617, + 505, + 653 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 658, + 504, + 691 + ], + "lines": [ + { + "bbox": [ + 105, + 657, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 105, + 657, + 505, + 671 + ], + "score": 1.0, + "content": "Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 116, + 669, + 504, + 681 + ], + "spans": [ + { + "bbox": [ + 116, + 669, + 504, + 681 + ], + "score": 1.0, + "content": "of deep networks. CoRR, abs/1703.03400, 2017. URL http://arxiv.org/abs/1703.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 116, + 680, + 152, + 692 + ], + "spans": [ + { + "bbox": [ + 116, + 680, + 152, + 692 + ], + "score": 1.0, + "content": "03400.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 657, + 505, + 692 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 698, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 696, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 696, + 505, + 713 + ], + "score": 1.0, + "content": "Aude Genevay, Marco Cuturi, Gabriel Peyre, and Francis Bach. Stochastic optimization for large- ´", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 115, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 115, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "scale optimal transport. In Advances in Neural Information Processing Systems 29, pp. 3440–", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 115, + 719, + 167, + 732 + ], + "spans": [ + { + "bbox": [ + 115, + 719, + 167, + 732 + ], + "score": 1.0, + "content": "3448. 2016.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48, + "bbox_fs": [ + 105, + 696, + 505, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Marco Gori, Gabriele Monfardini, and Franco Scarselli. A new model for learning in graph domains.", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "In Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005., volume 2,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 105, + 223, + 116 + ], + "spans": [ + { + "bbox": [ + 115, + 105, + 223, + 116 + ], + "score": 1.0, + "content": "pp. 729–734. IEEE, 2005.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 104, + 123, + 504, + 147 + ], + "lines": [ + { + "bbox": [ + 104, + 122, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 104, + 122, + 505, + 138 + ], + "score": 1.0, + "content": "Jiao Gu, Bobo Hua, and Shiping Liu. Spectral distances on graphs. Discrete Applied Mathematics,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 117, + 135, + 212, + 147 + ], + "spans": [ + { + "bbox": [ + 117, + 135, + 212, + 147 + ], + "score": 1.0, + "content": "190-191:56 – 74, 2015.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + }, + { + "type": "text", + "bbox": [ + 106, + 155, + 504, + 178 + ], + "lines": [ + { + "bbox": [ + 105, + 153, + 506, + 169 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 506, + 169 + ], + "score": 1.0, + "content": "William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 165, + 486, + 179 + ], + "spans": [ + { + "bbox": [ + 115, + 165, + 486, + 179 + ], + "score": 1.0, + "content": "graphs. CoRR, abs/1706.02216, 2017. URL http://arxiv.org/abs/1706.02216.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 105, + 186, + 504, + 209 + ], + "lines": [ + { + "bbox": [ + 105, + 185, + 505, + 198 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 505, + 198 + ], + "score": 1.0, + "content": "Mikael Henaff, Joan Bruna, and Yann LeCun. Deep convolutional networks on graph-structured", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 196, + 476, + 209 + ], + "spans": [ + { + "bbox": [ + 116, + 196, + 476, + 209 + ], + "score": 1.0, + "content": "data. CoRR, abs/1506.05163, 2015. URL http://arxiv.org/abs/1506.05163.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 106, + 216, + 505, + 272 + ], + "lines": [ + { + "bbox": [ + 106, + 217, + 505, + 229 + ], + "spans": [ + { + "bbox": [ + 106, + 217, + 505, + 229 + ], + "score": 1.0, + "content": "Sergey Ivanov and Evgeny Burnaev. Anonymous walk embeddings. In Jennifer Dy and An-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 226, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 115, + 226, + 506, + 241 + ], + "score": 1.0, + "content": "dreas Krause (eds.), Proceedings of the 35th International Conference on Machine Learning,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 116, + 239, + 505, + 251 + ], + "spans": [ + { + "bbox": [ + 116, + 239, + 505, + 251 + ], + "score": 1.0, + "content": "volume 80 of Proceedings of Machine Learning Research, pp. 2186–2195, Stockholmsmssan,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 115, + 248, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 115, + 248, + 505, + 263 + ], + "score": 1.0, + "content": "Stockholm Sweden, 10–15 Jul 2018. PMLR. URL http://proceedings.mlr.press/", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 116, + 261, + 229, + 272 + ], + "spans": [ + { + "bbox": [ + 116, + 261, + 229, + 272 + ], + "score": 1.0, + "content": "v80/ivanov18a.html.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 280, + 503, + 315 + ], + "lines": [ + { + "bbox": [ + 106, + 280, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 280, + 505, + 293 + ], + "score": 1.0, + "content": "Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization, 2014. URL", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 116, + 291, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 116, + 291, + 505, + 304 + ], + "score": 1.0, + "content": "http://arxiv.org/abs/1412.6980. cite arxiv:1412.6980Comment: Published as a con-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 116, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 116, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "ference paper at the 3rd International Conference for Learning Representations, San Diego, 2015.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 322, + 502, + 345 + ], + "lines": [ + { + "bbox": [ + 106, + 322, + 504, + 335 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 504, + 335 + ], + "score": 1.0, + "content": "Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional net-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 116, + 333, + 483, + 346 + ], + "spans": [ + { + "bbox": [ + 116, + 333, + 483, + 346 + ], + "score": 1.0, + "content": "works. CoRR, abs/1609.02907, 2016. URL http://arxiv.org/abs/1609.02907.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5 + }, + { + "type": "text", + "bbox": [ + 106, + 352, + 503, + 376 + ], + "lines": [ + { + "bbox": [ + 104, + 351, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 104, + 351, + 505, + 367 + ], + "score": 1.0, + "content": "Nils M. Kriege, Fredrik D. Johansson, and Christopher Morris. A survey on graph kernels. ArXiv,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 116, + 364, + 210, + 376 + ], + "spans": [ + { + "bbox": [ + 116, + 364, + 210, + 376 + ], + "score": 1.0, + "content": "abs/1903.11835, 2019.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 106, + 384, + 505, + 440 + ], + "lines": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "score": 1.0, + "content": "Junhyun Lee, Inyeop Lee, and Jaewoo Kang. Self-attention graph pooling. In Kamalika Chaud-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 115, + 393, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 115, + 393, + 505, + 408 + ], + "score": 1.0, + "content": "huri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th International Conference on", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 115, + 405, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 115, + 405, + 505, + 419 + ], + "score": 1.0, + "content": "Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp. 3734–3743,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 115, + 416, + 504, + 429 + ], + "spans": [ + { + "bbox": [ + 115, + 416, + 504, + 429 + ], + "score": 1.0, + "content": "Long Beach, California, USA, 09–15 Jun 2019. PMLR. URL http://proceedings.mlr.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 115, + 429, + 247, + 440 + ], + "spans": [ + { + "bbox": [ + 115, + 429, + 247, + 440 + ], + "score": 1.0, + "content": "press/v97/lee19c.html.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 447, + 504, + 481 + ], + "lines": [ + { + "bbox": [ + 105, + 447, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 506, + 460 + ], + "score": 1.0, + "content": "Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper insights into graph convolutional networks for", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 115, + 459, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 115, + 459, + 505, + 471 + ], + "score": 1.0, + "content": "semi-supervised learning. CoRR, abs/1801.07606, 2018a. URL http://arxiv.org/abs/", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 116, + 469, + 182, + 481 + ], + "spans": [ + { + "bbox": [ + 116, + 469, + 182, + 481 + ], + "score": 1.0, + "content": "1801.07606.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 105, + 489, + 504, + 512 + ], + "lines": [ + { + "bbox": [ + 107, + 489, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 107, + 489, + 505, + 502 + ], + "score": 1.0, + "content": "Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper insights into graph convolutional networks for", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 116, + 501, + 289, + 512 + ], + "spans": [ + { + "bbox": [ + 116, + 501, + 289, + 512 + ], + "score": 1.0, + "content": "semi-supervised learning. In AAAI, 2018b.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29.5 + }, + { + "type": "text", + "bbox": [ + 106, + 520, + 504, + 554 + ], + "lines": [ + { + "bbox": [ + 105, + 519, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 505, + 534 + ], + "score": 1.0, + "content": "Annamalai Narayanan, Mahinthan Chandramohan, Rajasekar Venkatesan, Lihui Chen, Yang Liu,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 116, + 532, + 505, + 544 + ], + "spans": [ + { + "bbox": [ + 116, + 532, + 505, + 544 + ], + "score": 1.0, + "content": "and Shantanu Jaiswal. graph2vec: Learning distributed representations of graphs. CoRR,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 116, + 542, + 424, + 554 + ], + "spans": [ + { + "bbox": [ + 116, + 542, + 424, + 554 + ], + "score": 1.0, + "content": "abs/1707.05005, 2017. URL http://arxiv.org/abs/1707.05005.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 106, + 561, + 503, + 585 + ], + "lines": [ + { + "bbox": [ + 106, + 562, + 504, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 504, + 574 + ], + "score": 1.0, + "content": "Alex Nichol, Joshua Achiam, and John Schulman. On first-order meta-learning algorithms. CoRR,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 116, + 573, + 424, + 585 + ], + "spans": [ + { + "bbox": [ + 116, + 573, + 424, + 585 + ], + "score": 1.0, + "content": "abs/1803.02999, 2018. URL http://arxiv.org/abs/1803.02999.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5 + }, + { + "type": "text", + "bbox": [ + 106, + 592, + 505, + 638 + ], + "lines": [ + { + "bbox": [ + 106, + 592, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 505, + 605 + ], + "score": 1.0, + "content": "Sachin Ravi and Hugo Larochelle. Optimization as a model for few-shot learning. In 5th Interna-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 116, + 604, + 505, + 616 + ], + "spans": [ + { + "bbox": [ + 116, + 604, + 505, + 616 + ], + "score": 1.0, + "content": "tional Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 116, + 614, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 116, + 614, + 505, + 628 + ], + "score": 1.0, + "content": "Conference Track Proceedings. OpenReview.net, 2017. URL https://openreview.net/", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 116, + 626, + 229, + 637 + ], + "spans": [ + { + "bbox": [ + 116, + 626, + 164, + 637 + ], + "score": 1.0, + "content": "forum?id", + "type": "text" + }, + { + "bbox": [ + 165, + 627, + 171, + 636 + ], + "score": 0.5, + "content": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } } =", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 626, + 229, + 637 + ], + "score": 1.0, + "content": "rJY0-Kcll.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5 + }, + { + "type": "text", + "bbox": [ + 106, + 645, + 505, + 680 + ], + "lines": [ + { + "bbox": [ + 106, + 645, + 505, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 505, + 659 + ], + "score": 1.0, + "content": "Andrei A. Rusu, Dushyant Rao, Jakub Sygnowski, Oriol Vinyals, Razvan Pascanu, Simon Osindero,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 115, + 656, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 115, + 656, + 505, + 669 + ], + "score": 1.0, + "content": "and Raia Hadsell. Meta-learning with latent embedding optimization. CoRR, abs/1807.05960,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 116, + 667, + 356, + 680 + ], + "spans": [ + { + "bbox": [ + 116, + 667, + 356, + 680 + ], + "score": 1.0, + "content": "2018. URL http://arxiv.org/abs/1807.05960.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 106, + 687, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 116, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 116, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "The graph neural network model. Trans. Neur. Netw., 20(1):61–80, January 2009. ISSN 1045-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 115, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 115, + 709, + 504, + 722 + ], + "score": 1.0, + "content": "9227. doi: 10.1109/TNN.2008.2005605. URL http://dx.doi.org/10.1109/TNN.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 116, + 721, + 193, + 732 + ], + "spans": [ + { + "bbox": [ + 116, + 721, + 193, + 732 + ], + "score": 1.0, + "content": "2008.2005605.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 44.5 + } + ], + "page_idx": 11, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 294, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "12", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Marco Gori, Gabriele Monfardini, and Franco Scarselli. A new model for learning in graph domains.", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "In Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005., volume 2,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 105, + 223, + 116 + ], + "spans": [ + { + "bbox": [ + 115, + 105, + 223, + 116 + ], + "score": 1.0, + "content": "pp. 729–734. IEEE, 2005.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1, + "bbox_fs": [ + 106, + 82, + 505, + 116 + ] + }, + { + "type": "text", + "bbox": [ + 104, + 123, + 504, + 147 + ], + "lines": [ + { + "bbox": [ + 104, + 122, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 104, + 122, + 505, + 138 + ], + "score": 1.0, + "content": "Jiao Gu, Bobo Hua, and Shiping Liu. Spectral distances on graphs. Discrete Applied Mathematics,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 117, + 135, + 212, + 147 + ], + "spans": [ + { + "bbox": [ + 117, + 135, + 212, + 147 + ], + "score": 1.0, + "content": "190-191:56 – 74, 2015.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5, + "bbox_fs": [ + 104, + 122, + 505, + 147 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 155, + 504, + 178 + ], + "lines": [ + { + "bbox": [ + 105, + 153, + 506, + 169 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 506, + 169 + ], + "score": 1.0, + "content": "William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 165, + 486, + 179 + ], + "spans": [ + { + "bbox": [ + 115, + 165, + 486, + 179 + ], + "score": 1.0, + "content": "graphs. CoRR, abs/1706.02216, 2017. URL http://arxiv.org/abs/1706.02216.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 153, + 506, + 179 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 186, + 504, + 209 + ], + "lines": [ + { + "bbox": [ + 105, + 185, + 505, + 198 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 505, + 198 + ], + "score": 1.0, + "content": "Mikael Henaff, Joan Bruna, and Yann LeCun. Deep convolutional networks on graph-structured", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 196, + 476, + 209 + ], + "spans": [ + { + "bbox": [ + 116, + 196, + 476, + 209 + ], + "score": 1.0, + "content": "data. CoRR, abs/1506.05163, 2015. URL http://arxiv.org/abs/1506.05163.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5, + "bbox_fs": [ + 105, + 185, + 505, + 209 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 216, + 505, + 272 + ], + "lines": [ + { + "bbox": [ + 106, + 217, + 505, + 229 + ], + "spans": [ + { + "bbox": [ + 106, + 217, + 505, + 229 + ], + "score": 1.0, + "content": "Sergey Ivanov and Evgeny Burnaev. Anonymous walk embeddings. In Jennifer Dy and An-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 226, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 115, + 226, + 506, + 241 + ], + "score": 1.0, + "content": "dreas Krause (eds.), Proceedings of the 35th International Conference on Machine Learning,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 116, + 239, + 505, + 251 + ], + "spans": [ + { + "bbox": [ + 116, + 239, + 505, + 251 + ], + "score": 1.0, + "content": "volume 80 of Proceedings of Machine Learning Research, pp. 2186–2195, Stockholmsmssan,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 115, + 248, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 115, + 248, + 505, + 263 + ], + "score": 1.0, + "content": "Stockholm Sweden, 10–15 Jul 2018. PMLR. URL http://proceedings.mlr.press/", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 116, + 261, + 229, + 272 + ], + "spans": [ + { + "bbox": [ + 116, + 261, + 229, + 272 + ], + "score": 1.0, + "content": "v80/ivanov18a.html.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11, + "bbox_fs": [ + 106, + 217, + 506, + 272 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 280, + 503, + 315 + ], + "lines": [ + { + "bbox": [ + 106, + 280, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 280, + 505, + 293 + ], + "score": 1.0, + "content": "Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization, 2014. URL", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 116, + 291, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 116, + 291, + 505, + 304 + ], + "score": 1.0, + "content": "http://arxiv.org/abs/1412.6980. cite arxiv:1412.6980Comment: Published as a con-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 116, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 116, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "ference paper at the 3rd International Conference for Learning Representations, San Diego, 2015.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15, + "bbox_fs": [ + 106, + 280, + 505, + 315 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 322, + 502, + 345 + ], + "lines": [ + { + "bbox": [ + 106, + 322, + 504, + 335 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 504, + 335 + ], + "score": 1.0, + "content": "Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional net-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 116, + 333, + 483, + 346 + ], + "spans": [ + { + "bbox": [ + 116, + 333, + 483, + 346 + ], + "score": 1.0, + "content": "works. CoRR, abs/1609.02907, 2016. URL http://arxiv.org/abs/1609.02907.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5, + "bbox_fs": [ + 106, + 322, + 504, + 346 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 352, + 503, + 376 + ], + "lines": [ + { + "bbox": [ + 104, + 351, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 104, + 351, + 505, + 367 + ], + "score": 1.0, + "content": "Nils M. Kriege, Fredrik D. Johansson, and Christopher Morris. A survey on graph kernels. ArXiv,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 116, + 364, + 210, + 376 + ], + "spans": [ + { + "bbox": [ + 116, + 364, + 210, + 376 + ], + "score": 1.0, + "content": "abs/1903.11835, 2019.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 19.5, + "bbox_fs": [ + 104, + 351, + 505, + 376 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 384, + 505, + 440 + ], + "lines": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "score": 1.0, + "content": "Junhyun Lee, Inyeop Lee, and Jaewoo Kang. Self-attention graph pooling. In Kamalika Chaud-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 115, + 393, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 115, + 393, + 505, + 408 + ], + "score": 1.0, + "content": "huri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th International Conference on", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 115, + 405, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 115, + 405, + 505, + 419 + ], + "score": 1.0, + "content": "Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp. 3734–3743,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 115, + 416, + 504, + 429 + ], + "spans": [ + { + "bbox": [ + 115, + 416, + 504, + 429 + ], + "score": 1.0, + "content": "Long Beach, California, USA, 09–15 Jun 2019. PMLR. URL http://proceedings.mlr.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 115, + 429, + 247, + 440 + ], + "spans": [ + { + "bbox": [ + 115, + 429, + 247, + 440 + ], + "score": 1.0, + "content": "press/v97/lee19c.html.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23, + "bbox_fs": [ + 105, + 383, + 505, + 440 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 447, + 504, + 481 + ], + "lines": [ + { + "bbox": [ + 105, + 447, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 506, + 460 + ], + "score": 1.0, + "content": "Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper insights into graph convolutional networks for", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 115, + 459, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 115, + 459, + 505, + 471 + ], + "score": 1.0, + "content": "semi-supervised learning. CoRR, abs/1801.07606, 2018a. URL http://arxiv.org/abs/", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 116, + 469, + 182, + 481 + ], + "spans": [ + { + "bbox": [ + 116, + 469, + 182, + 481 + ], + "score": 1.0, + "content": "1801.07606.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 447, + 506, + 481 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 489, + 504, + 512 + ], + "lines": [ + { + "bbox": [ + 107, + 489, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 107, + 489, + 505, + 502 + ], + "score": 1.0, + "content": "Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper insights into graph convolutional networks for", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 116, + 501, + 289, + 512 + ], + "spans": [ + { + "bbox": [ + 116, + 501, + 289, + 512 + ], + "score": 1.0, + "content": "semi-supervised learning. In AAAI, 2018b.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29.5, + "bbox_fs": [ + 107, + 489, + 505, + 512 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 520, + 504, + 554 + ], + "lines": [ + { + "bbox": [ + 105, + 519, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 505, + 534 + ], + "score": 1.0, + "content": "Annamalai Narayanan, Mahinthan Chandramohan, Rajasekar Venkatesan, Lihui Chen, Yang Liu,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 116, + 532, + 505, + 544 + ], + "spans": [ + { + "bbox": [ + 116, + 532, + 505, + 544 + ], + "score": 1.0, + "content": "and Shantanu Jaiswal. graph2vec: Learning distributed representations of graphs. CoRR,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 116, + 542, + 424, + 554 + ], + "spans": [ + { + "bbox": [ + 116, + 542, + 424, + 554 + ], + "score": 1.0, + "content": "abs/1707.05005, 2017. URL http://arxiv.org/abs/1707.05005.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 519, + 505, + 554 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 561, + 503, + 585 + ], + "lines": [ + { + "bbox": [ + 106, + 562, + 504, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 504, + 574 + ], + "score": 1.0, + "content": "Alex Nichol, Joshua Achiam, and John Schulman. On first-order meta-learning algorithms. CoRR,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 116, + 573, + 424, + 585 + ], + "spans": [ + { + "bbox": [ + 116, + 573, + 424, + 585 + ], + "score": 1.0, + "content": "abs/1803.02999, 2018. URL http://arxiv.org/abs/1803.02999.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5, + "bbox_fs": [ + 106, + 562, + 504, + 585 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 592, + 505, + 638 + ], + "lines": [ + { + "bbox": [ + 106, + 592, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 505, + 605 + ], + "score": 1.0, + "content": "Sachin Ravi and Hugo Larochelle. Optimization as a model for few-shot learning. In 5th Interna-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 116, + 604, + 505, + 616 + ], + "spans": [ + { + "bbox": [ + 116, + 604, + 505, + 616 + ], + "score": 1.0, + "content": "tional Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 116, + 614, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 116, + 614, + 505, + 628 + ], + "score": 1.0, + "content": "Conference Track Proceedings. OpenReview.net, 2017. URL https://openreview.net/", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 116, + 626, + 229, + 637 + ], + "spans": [ + { + "bbox": [ + 116, + 626, + 164, + 637 + ], + "score": 1.0, + "content": "forum?id", + "type": "text" + }, + { + "bbox": [ + 165, + 627, + 171, + 636 + ], + "score": 0.5, + "content": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } } =", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 626, + 229, + 637 + ], + "score": 1.0, + "content": "rJY0-Kcll.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5, + "bbox_fs": [ + 106, + 592, + 505, + 637 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 645, + 505, + 680 + ], + "lines": [ + { + "bbox": [ + 106, + 645, + 505, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 505, + 659 + ], + "score": 1.0, + "content": "Andrei A. Rusu, Dushyant Rao, Jakub Sygnowski, Oriol Vinyals, Razvan Pascanu, Simon Osindero,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 115, + 656, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 115, + 656, + 505, + 669 + ], + "score": 1.0, + "content": "and Raia Hadsell. Meta-learning with latent embedding optimization. CoRR, abs/1807.05960,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 116, + 667, + 356, + 680 + ], + "spans": [ + { + "bbox": [ + 116, + 667, + 356, + 680 + ], + "score": 1.0, + "content": "2018. URL http://arxiv.org/abs/1807.05960.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41, + "bbox_fs": [ + 106, + 645, + 505, + 680 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 687, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 116, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 116, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "The graph neural network model. Trans. Neur. Netw., 20(1):61–80, January 2009. ISSN 1045-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 115, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 115, + 709, + 504, + 722 + ], + "score": 1.0, + "content": "9227. doi: 10.1109/TNN.2008.2005605. URL http://dx.doi.org/10.1109/TNN.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 116, + 721, + 193, + 732 + ], + "spans": [ + { + "bbox": [ + 116, + 721, + 193, + 732 + ], + "score": 1.0, + "content": "2008.2005605.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 44.5, + "bbox_fs": [ + 105, + 687, + 505, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 126 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "N. Shervashidze, SVN. Vishwanathan, TH. Petri, K. Mehlhorn, and KM. Borgwardt. Efficient", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "graphlet kernels for large graph comparison. In JMLR Workshop and Conference Proceed-", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 115, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "ings Volume 5: AISTATS 2009, pp. 488–495, Cambridge, MA, USA, April 2009. Max-Planck-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 114, + 218, + 127 + ], + "spans": [ + { + "bbox": [ + 115, + 114, + 218, + 127 + ], + "score": 1.0, + "content": "Gesellschaft, MIT Press.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "text", + "bbox": [ + 106, + 134, + 505, + 178 + ], + "lines": [ + { + "bbox": [ + 105, + 134, + 505, + 146 + ], + "spans": [ + { + "bbox": [ + 105, + 134, + 505, + 146 + ], + "score": 1.0, + "content": "Nino Shervashidze, Pascal Schweitzer, Erik Jan van Leeuwen, Kurt Mehlhorn, and Karsten M.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 145, + 505, + 157 + ], + "spans": [ + { + "bbox": [ + 115, + 145, + 505, + 157 + ], + "score": 1.0, + "content": "Borgwardt. Weisfeiler-lehman graph kernels. J. Mach. Learn. Res., 12:2539–2561, Novem-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 156, + 504, + 168 + ], + "spans": [ + { + "bbox": [ + 115, + 156, + 449, + 168 + ], + "score": 1.0, + "content": "ber 2011. ISSN 1532-4435. URL http://dl.acm.org/citation.cfm?id", + "type": "text" + }, + { + "bbox": [ + 449, + 157, + 456, + 166 + ], + "score": 0.35, + "content": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } } =", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 156, + 504, + 168 + ], + "score": 1.0, + "content": "1953048.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 167, + 164, + 178 + ], + "spans": [ + { + "bbox": [ + 115, + 167, + 164, + 178 + ], + "score": 1.0, + "content": "2078187.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 106, + 186, + 505, + 220 + ], + "lines": [ + { + "bbox": [ + 105, + 185, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 505, + 199 + ], + "score": 1.0, + "content": "Petar Velikovi, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li, and Yoshua Ben-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 115, + 197, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 115, + 197, + 505, + 210 + ], + "score": 1.0, + "content": "gio. Graph attention networks. In International Conference on Learning Representations, 2018.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 207, + 389, + 222 + ], + "spans": [ + { + "bbox": [ + 115, + 207, + 325, + 222 + ], + "score": 1.0, + "content": "URL https://openreview.net/forum?id", + "type": "text" + }, + { + "bbox": [ + 325, + 209, + 331, + 218 + ], + "score": 0.53, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 207, + 389, + 222 + ], + "score": 1.0, + "content": "rJXMpikCZ.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 226, + 503, + 249 + ], + "lines": [ + { + "bbox": [ + 105, + 225, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 225, + 505, + 241 + ], + "score": 1.0, + "content": "B. Yu. Weisfeiler and A. A. Leman. Reduction of a graph to a canonical form and an algebra arising", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 116, + 238, + 230, + 250 + ], + "spans": [ + { + "bbox": [ + 116, + 238, + 230, + 250 + ], + "score": 1.0, + "content": "during this reduction. 1968.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5 + }, + { + "type": "text", + "bbox": [ + 106, + 256, + 503, + 280 + ], + "lines": [ + { + "bbox": [ + 106, + 255, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 106, + 255, + 505, + 270 + ], + "score": 1.0, + "content": "Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and Philip S. Yu. A", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 115, + 268, + 437, + 280 + ], + "spans": [ + { + "bbox": [ + 115, + 268, + 437, + 280 + ], + "score": 1.0, + "content": "comprehensive survey on graph neural networks. CoRR, abs/1901.00596, 2019.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 106, + 286, + 504, + 309 + ], + "lines": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "score": 1.0, + "content": "Zhang Xinyi and Lihui Chen. Capsule graph neural network. In International Conference on Learn-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 116, + 297, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 116, + 297, + 434, + 311 + ], + "score": 1.0, + "content": "ing Representations, 2019. URL https://openreview.net/forum?id", + "type": "text" + }, + { + "bbox": [ + 435, + 299, + 441, + 307 + ], + "score": 0.38, + "content": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 297, + 505, + 311 + ], + "score": 1.0, + "content": "Byl8BnRcYm.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 106, + 316, + 505, + 350 + ], + "lines": [ + { + "bbox": [ + 106, + 316, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 505, + 329 + ], + "score": 1.0, + "content": "Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 115, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "networks? In International Conference on Learning Representations, 2019. URL https:", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 117, + 338, + 337, + 351 + ], + "spans": [ + { + "bbox": [ + 117, + 338, + 266, + 351 + ], + "score": 1.0, + "content": "//openreview.net/forum?id", + "type": "text" + }, + { + "bbox": [ + 267, + 340, + 273, + 348 + ], + "score": 0.58, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 338, + 337, + 351 + ], + "score": 1.0, + "content": "ryGs6iA5Km.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 357, + 504, + 390 + ], + "lines": [ + { + "bbox": [ + 106, + 357, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 506, + 370 + ], + "score": 1.0, + "content": "Shengzhong Zhang, Ziang Zhou, Zengfeng Huang, and Zhongyu Wei. Few-shot classification on", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 115, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 115, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "graphs with structural regularized GCNs, 2019. URL https://openreview.net/forum?", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 116, + 380, + 199, + 391 + ], + "spans": [ + { + "bbox": [ + 116, + 380, + 199, + 391 + ], + "score": 1.0, + "content": "id=r1znKiAcY7.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + } + ], + "page_idx": 12, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "13", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 126 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "N. Shervashidze, SVN. Vishwanathan, TH. Petri, K. Mehlhorn, and KM. Borgwardt. Efficient", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "graphlet kernels for large graph comparison. In JMLR Workshop and Conference Proceed-", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 115, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "ings Volume 5: AISTATS 2009, pp. 488–495, Cambridge, MA, USA, April 2009. Max-Planck-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 114, + 218, + 127 + ], + "spans": [ + { + "bbox": [ + 115, + 114, + 218, + 127 + ], + "score": 1.0, + "content": "Gesellschaft, MIT Press.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5, + "bbox_fs": [ + 105, + 82, + 505, + 127 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 134, + 505, + 178 + ], + "lines": [ + { + "bbox": [ + 105, + 134, + 505, + 146 + ], + "spans": [ + { + "bbox": [ + 105, + 134, + 505, + 146 + ], + "score": 1.0, + "content": "Nino Shervashidze, Pascal Schweitzer, Erik Jan van Leeuwen, Kurt Mehlhorn, and Karsten M.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 145, + 505, + 157 + ], + "spans": [ + { + "bbox": [ + 115, + 145, + 505, + 157 + ], + "score": 1.0, + "content": "Borgwardt. Weisfeiler-lehman graph kernels. J. Mach. Learn. Res., 12:2539–2561, Novem-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 156, + 504, + 168 + ], + "spans": [ + { + "bbox": [ + 115, + 156, + 449, + 168 + ], + "score": 1.0, + "content": "ber 2011. ISSN 1532-4435. URL http://dl.acm.org/citation.cfm?id", + "type": "text" + }, + { + "bbox": [ + 449, + 157, + 456, + 166 + ], + "score": 0.35, + "content": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } } =", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 156, + 504, + 168 + ], + "score": 1.0, + "content": "1953048.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 167, + 164, + 178 + ], + "spans": [ + { + "bbox": [ + 115, + 167, + 164, + 178 + ], + "score": 1.0, + "content": "2078187.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 134, + 505, + 178 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 186, + 505, + 220 + ], + "lines": [ + { + "bbox": [ + 105, + 185, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 505, + 199 + ], + "score": 1.0, + "content": "Petar Velikovi, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li, and Yoshua Ben-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 115, + 197, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 115, + 197, + 505, + 210 + ], + "score": 1.0, + "content": "gio. Graph attention networks. In International Conference on Learning Representations, 2018.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 207, + 389, + 222 + ], + "spans": [ + { + "bbox": [ + 115, + 207, + 325, + 222 + ], + "score": 1.0, + "content": "URL https://openreview.net/forum?id", + "type": "text" + }, + { + "bbox": [ + 325, + 209, + 331, + 218 + ], + "score": 0.53, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 207, + 389, + 222 + ], + "score": 1.0, + "content": "rJXMpikCZ.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 185, + 505, + 222 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 226, + 503, + 249 + ], + "lines": [ + { + "bbox": [ + 105, + 225, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 225, + 505, + 241 + ], + "score": 1.0, + "content": "B. Yu. Weisfeiler and A. A. Leman. Reduction of a graph to a canonical form and an algebra arising", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 116, + 238, + 230, + 250 + ], + "spans": [ + { + "bbox": [ + 116, + 238, + 230, + 250 + ], + "score": 1.0, + "content": "during this reduction. 1968.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5, + "bbox_fs": [ + 105, + 225, + 505, + 250 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 256, + 503, + 280 + ], + "lines": [ + { + "bbox": [ + 106, + 255, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 106, + 255, + 505, + 270 + ], + "score": 1.0, + "content": "Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and Philip S. Yu. A", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 115, + 268, + 437, + 280 + ], + "spans": [ + { + "bbox": [ + 115, + 268, + 437, + 280 + ], + "score": 1.0, + "content": "comprehensive survey on graph neural networks. CoRR, abs/1901.00596, 2019.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5, + "bbox_fs": [ + 106, + 255, + 505, + 280 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 286, + 504, + 309 + ], + "lines": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "score": 1.0, + "content": "Zhang Xinyi and Lihui Chen. Capsule graph neural network. In International Conference on Learn-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 116, + 297, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 116, + 297, + 434, + 311 + ], + "score": 1.0, + "content": "ing Representations, 2019. URL https://openreview.net/forum?id", + "type": "text" + }, + { + "bbox": [ + 435, + 299, + 441, + 307 + ], + "score": 0.38, + "content": "\\underline { { \\underline { { \\mathbf { \\Pi } } } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 297, + 505, + 311 + ], + "score": 1.0, + "content": "Byl8BnRcYm.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 286, + 505, + 311 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 316, + 505, + 350 + ], + "lines": [ + { + "bbox": [ + 106, + 316, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 505, + 329 + ], + "score": 1.0, + "content": "Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 115, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "networks? In International Conference on Learning Representations, 2019. URL https:", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 117, + 338, + 337, + 351 + ], + "spans": [ + { + "bbox": [ + 117, + 338, + 266, + 351 + ], + "score": 1.0, + "content": "//openreview.net/forum?id", + "type": "text" + }, + { + "bbox": [ + 267, + 340, + 273, + 348 + ], + "score": 0.58, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 338, + 337, + 351 + ], + "score": 1.0, + "content": "ryGs6iA5Km.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 106, + 316, + 505, + 351 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 357, + 504, + 390 + ], + "lines": [ + { + "bbox": [ + 106, + 357, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 506, + 370 + ], + "score": 1.0, + "content": "Shengzhong Zhang, Ziang Zhou, Zengfeng Huang, and Zhongyu Wei. Few-shot classification on", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 115, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 115, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "graphs with structural regularized GCNs, 2019. URL https://openreview.net/forum?", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 116, + 380, + 199, + 391 + ], + "spans": [ + { + "bbox": [ + 116, + 380, + 199, + 391 + ], + "score": 1.0, + "content": "id=r1znKiAcY7.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21, + "bbox_fs": [ + 106, + 357, + 506, + 391 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 182, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 79, + 185, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 185, + 97 + ], + "score": 1.0, + "content": "A APPENDIX", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "title", + "bbox": [ + 108, + 110, + 212, + 121 + ], + "lines": [ + { + "bbox": [ + 106, + 110, + 213, + 122 + ], + "spans": [ + { + "bbox": [ + 106, + 110, + 213, + 122 + ], + "score": 1.0, + "content": "A.1 DATASET DETAILS", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 107, + 133, + 505, + 188 + ], + "lines": [ + { + "bbox": [ + 106, + 133, + 505, + 146 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 146 + ], + "score": 1.0, + "content": "We use 4 different datasets namely - Reddit-12K, ENZYMES, Letter-High and TRIANGLES to per-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "form exhaustive empirical evaluation of our model on various real-world datasets varying from small", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 155, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 155, + 505, + 168 + ], + "score": 1.0, + "content": "average graph size on Letter-High to large graphs like Reddit-12K. These datasets can be down-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 164, + 505, + 179 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 179 + ], + "score": 1.0, + "content": "loaded here 4. The dataset statistics are provided in Table 6, while the split statistics are provided in", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 175, + 140, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 175, + 140, + 189 + ], + "score": 1.0, + "content": "Table 7", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 153, + 234, + 457, + 304 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 253, + 203, + 358, + 215 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 253, + 203, + 358, + 215 + ], + "spans": [ + { + "bbox": [ + 253, + 203, + 358, + 215 + ], + "score": 1.0, + "content": "Table 6: Dataset Statistics", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "table_body", + "bbox": [ + 153, + 234, + 457, + 304 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 153, + 234, + 457, + 304 + ], + "spans": [ + { + "bbox": [ + 153, + 234, + 457, + 304 + ], + "score": 0.958, + "html": "
DatasetName# Classes# GraphsAvg # NodesAvg #Edges
Reddit-12K11929391.41456.89
ENZYMES11 660032.6362.14
Letter-High1522504.674.50
TRIANGLES104500020.8535.50
", + "type": "table", + "image_path": "7f2a202ef08fea6e3b49b3ef6526d917c6df6c3f47300c2899ddc24614d5646d.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 153, + 234, + 457, + 257.3333333333333 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 153, + 257.3333333333333, + 457, + 280.66666666666663 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 153, + 280.66666666666663, + 457, + 303.99999999999994 + ], + "spans": [], + "index": 10 + } + ] + } + ], + "index": 8.0 + }, + { + "type": "text", + "bbox": [ + 107, + 328, + 504, + 372 + ], + "lines": [ + { + "bbox": [ + 105, + 327, + 506, + 341 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 506, + 341 + ], + "score": 1.0, + "content": "Dataset Description: Reddit-12K datasets contains 11929 graphs where each graph corresponds to", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 339, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 506, + 352 + ], + "score": 1.0, + "content": "a thread in which each node represents a user and each edge represents that one user has responded", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 349, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 104, + 349, + 506, + 363 + ], + "score": 1.0, + "content": "to a comment from some other user. There are 11 different types of discussion forums corresponding", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 360, + 208, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 208, + 373 + ], + "score": 1.0, + "content": "to each of the 11 classes.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 108, + 372, + 503, + 405 + ], + "lines": [ + { + "bbox": [ + 106, + 372, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 505, + 384 + ], + "score": 1.0, + "content": "ENZYMES is a dataset of protein tertiary structures consisting of 600 enzymes from the BRENDA", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 382, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 505, + 396 + ], + "score": 1.0, + "content": "enzyme database. The dataset contains 6 different graph categories corresponding to each different", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 393, + 196, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 196, + 408 + ], + "score": 1.0, + "content": "top-level EC enzyme.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 405, + 504, + 427 + ], + "lines": [ + { + "bbox": [ + 106, + 405, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 505, + 417 + ], + "score": 1.0, + "content": "TRIANGLES dataset contain 10 different classes where the classes are numbered from 1 to 10", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 416, + 425, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 425, + 429 + ], + "score": 1.0, + "content": "corresponding to the number of triangles/3-cliques in each graph of the dataset.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 107, + 428, + 502, + 460 + ], + "lines": [ + { + "bbox": [ + 105, + 426, + 504, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 504, + 440 + ], + "score": 1.0, + "content": "Letter-High dataset contains graphs which represent distorted letter drawings from the english al-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 438, + 503, + 450 + ], + "spans": [ + { + "bbox": [ + 106, + 438, + 145, + 450 + ], + "score": 1.0, + "content": "phabets -", + "type": "text" + }, + { + "bbox": [ + 145, + 438, + 323, + 450 + ], + "score": 0.92, + "content": "A , E , F , H , I , K , L , M , N , T , V , W , X , Y , Z", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 438, + 503, + 450 + ], + "score": 1.0, + "content": ". Each graph is a prototype manual construc-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 449, + 192, + 461 + ], + "spans": [ + { + "bbox": [ + 106, + 449, + 192, + 461 + ], + "score": 1.0, + "content": "tion of the alphabets.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 133, + 507, + 478, + 589 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 259, + 477, + 352, + 489 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 258, + 476, + 352, + 490 + ], + "spans": [ + { + "bbox": [ + 258, + 476, + 352, + 490 + ], + "score": 1.0, + "content": "Table 7: Dataset Splits", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "table_body", + "bbox": [ + 133, + 507, + 478, + 589 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 133, + 507, + 478, + 589 + ], + "spans": [ + { + "bbox": [ + 133, + 507, + 478, + 589 + ], + "score": 0.977, + "html": "
Dataset Name#Train Classes#Test Classes# Training Graphs# Validation Graphs#Test Graphs
Reddit-12K74566141404
ENZYMES4 112 4320 133080 320200 600
Letter-High TRIANGLES731126271603
", + "type": "table", + "image_path": "6d74ff990d783464ac74a44d21f0162800cf54953df543089fc8a0b3e9c03ed8.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 133, + 507, + 478, + 534.3333333333334 + ], + "spans": [], + "index": 24 + }, + { + "bbox": [ + 133, + 534.3333333333334, + 478, + 561.6666666666667 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 133, + 561.6666666666667, + 478, + 589.0000000000001 + ], + "spans": [], + "index": 26 + } + ] + } + ], + "index": 24.0 + }, + { + "type": "text", + "bbox": [ + 106, + 613, + 505, + 702 + ], + "lines": [ + { + "bbox": [ + 105, + 612, + 505, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 505, + 626 + ], + "score": 1.0, + "content": "The validation graphs are used to assess model performance on training classes itself to check over-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 624, + 506, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 506, + 637 + ], + "score": 1.0, + "content": "fitting as well as for grid-search over hyperparameters. The actual train-testing class splits used for", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "score": 1.0, + "content": "this paper are provided with the code. Since the TRIANGLES dataset has a large number of sam-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 646, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 506, + 659 + ], + "score": 1.0, + "content": "ples, this makes it infeasible to run many baselines including DL and non-DL methods. Hence, we", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 657, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 505, + 669 + ], + "score": 1.0, + "content": "sample 200 graphs from each class, making the total sample size 2000. Similarly we downsample", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 667, + 506, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 506, + 681 + ], + "score": 1.0, + "content": "the number of graphs from 11929 to 1111 (nearly 101 graphs per class). Downsampling is per-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 678, + 505, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 505, + 692 + ], + "score": 1.0, + "content": "formed for Reddit-12K given extremely large graph sizes which makes the graph kernels as well as", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 691, + 290, + 703 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 290, + 703 + ], + "score": 1.0, + "content": "some deep learning baselines extremely slow.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5 + } + ], + "page_idx": 13, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 118, + 721, + 371, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 719, + 372, + 734 + ], + "spans": [ + { + "bbox": [ + 118, + 719, + 372, + 734 + ], + "score": 1.0, + "content": "4https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 752, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 182, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 79, + 185, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 185, + 97 + ], + "score": 1.0, + "content": "A APPENDIX", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "title", + "bbox": [ + 108, + 110, + 212, + 121 + ], + "lines": [ + { + "bbox": [ + 106, + 110, + 213, + 122 + ], + "spans": [ + { + "bbox": [ + 106, + 110, + 213, + 122 + ], + "score": 1.0, + "content": "A.1 DATASET DETAILS", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 107, + 133, + 505, + 188 + ], + "lines": [ + { + "bbox": [ + 106, + 133, + 505, + 146 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 146 + ], + "score": 1.0, + "content": "We use 4 different datasets namely - Reddit-12K, ENZYMES, Letter-High and TRIANGLES to per-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "form exhaustive empirical evaluation of our model on various real-world datasets varying from small", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 155, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 155, + 505, + 168 + ], + "score": 1.0, + "content": "average graph size on Letter-High to large graphs like Reddit-12K. These datasets can be down-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 164, + 505, + 179 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 179 + ], + "score": 1.0, + "content": "loaded here 4. The dataset statistics are provided in Table 6, while the split statistics are provided in", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 175, + 140, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 175, + 140, + 189 + ], + "score": 1.0, + "content": "Table 7", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4, + "bbox_fs": [ + 105, + 133, + 505, + 189 + ] + }, + { + "type": "table", + "bbox": [ + 153, + 234, + 457, + 304 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 253, + 203, + 358, + 215 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 253, + 203, + 358, + 215 + ], + "spans": [ + { + "bbox": [ + 253, + 203, + 358, + 215 + ], + "score": 1.0, + "content": "Table 6: Dataset Statistics", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "table_body", + "bbox": [ + 153, + 234, + 457, + 304 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 153, + 234, + 457, + 304 + ], + "spans": [ + { + "bbox": [ + 153, + 234, + 457, + 304 + ], + "score": 0.958, + "html": "
DatasetName# Classes# GraphsAvg # NodesAvg #Edges
Reddit-12K11929391.41456.89
ENZYMES11 660032.6362.14
Letter-High1522504.674.50
TRIANGLES104500020.8535.50
", + "type": "table", + "image_path": "7f2a202ef08fea6e3b49b3ef6526d917c6df6c3f47300c2899ddc24614d5646d.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 153, + 234, + 457, + 257.3333333333333 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 153, + 257.3333333333333, + 457, + 280.66666666666663 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 153, + 280.66666666666663, + 457, + 303.99999999999994 + ], + "spans": [], + "index": 10 + } + ] + } + ], + "index": 8.0 + }, + { + "type": "text", + "bbox": [ + 107, + 328, + 504, + 372 + ], + "lines": [ + { + "bbox": [ + 105, + 327, + 506, + 341 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 506, + 341 + ], + "score": 1.0, + "content": "Dataset Description: Reddit-12K datasets contains 11929 graphs where each graph corresponds to", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 339, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 506, + 352 + ], + "score": 1.0, + "content": "a thread in which each node represents a user and each edge represents that one user has responded", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 349, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 104, + 349, + 506, + 363 + ], + "score": 1.0, + "content": "to a comment from some other user. There are 11 different types of discussion forums corresponding", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 360, + 208, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 208, + 373 + ], + "score": 1.0, + "content": "to each of the 11 classes.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5, + "bbox_fs": [ + 104, + 327, + 506, + 373 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 372, + 503, + 405 + ], + "lines": [ + { + "bbox": [ + 106, + 372, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 505, + 384 + ], + "score": 1.0, + "content": "ENZYMES is a dataset of protein tertiary structures consisting of 600 enzymes from the BRENDA", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 382, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 505, + 396 + ], + "score": 1.0, + "content": "enzyme database. The dataset contains 6 different graph categories corresponding to each different", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 393, + 196, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 196, + 408 + ], + "score": 1.0, + "content": "top-level EC enzyme.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 372, + 505, + 408 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 405, + 504, + 427 + ], + "lines": [ + { + "bbox": [ + 106, + 405, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 505, + 417 + ], + "score": 1.0, + "content": "TRIANGLES dataset contain 10 different classes where the classes are numbered from 1 to 10", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 416, + 425, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 425, + 429 + ], + "score": 1.0, + "content": "corresponding to the number of triangles/3-cliques in each graph of the dataset.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5, + "bbox_fs": [ + 106, + 405, + 505, + 429 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 428, + 502, + 460 + ], + "lines": [ + { + "bbox": [ + 105, + 426, + 504, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 504, + 440 + ], + "score": 1.0, + "content": "Letter-High dataset contains graphs which represent distorted letter drawings from the english al-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 438, + 503, + 450 + ], + "spans": [ + { + "bbox": [ + 106, + 438, + 145, + 450 + ], + "score": 1.0, + "content": "phabets -", + "type": "text" + }, + { + "bbox": [ + 145, + 438, + 323, + 450 + ], + "score": 0.92, + "content": "A , E , F , H , I , K , L , M , N , T , V , W , X , Y , Z", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 438, + 503, + 450 + ], + "score": 1.0, + "content": ". Each graph is a prototype manual construc-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 449, + 192, + 461 + ], + "spans": [ + { + "bbox": [ + 106, + 449, + 192, + 461 + ], + "score": 1.0, + "content": "tion of the alphabets.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 426, + 504, + 461 + ] + }, + { + "type": "table", + "bbox": [ + 133, + 507, + 478, + 589 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 259, + 477, + 352, + 489 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 258, + 476, + 352, + 490 + ], + "spans": [ + { + "bbox": [ + 258, + 476, + 352, + 490 + ], + "score": 1.0, + "content": "Table 7: Dataset Splits", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "table_body", + "bbox": [ + 133, + 507, + 478, + 589 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 133, + 507, + 478, + 589 + ], + "spans": [ + { + "bbox": [ + 133, + 507, + 478, + 589 + ], + "score": 0.977, + "html": "
Dataset Name#Train Classes#Test Classes# Training Graphs# Validation Graphs#Test Graphs
Reddit-12K74566141404
ENZYMES4 112 4320 133080 320200 600
Letter-High TRIANGLES731126271603
", + "type": "table", + "image_path": "6d74ff990d783464ac74a44d21f0162800cf54953df543089fc8a0b3e9c03ed8.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 133, + 507, + 478, + 534.3333333333334 + ], + "spans": [], + "index": 24 + }, + { + "bbox": [ + 133, + 534.3333333333334, + 478, + 561.6666666666667 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 133, + 561.6666666666667, + 478, + 589.0000000000001 + ], + "spans": [], + "index": 26 + } + ] + } + ], + "index": 24.0 + }, + { + "type": "text", + "bbox": [ + 106, + 613, + 505, + 702 + ], + "lines": [ + { + "bbox": [ + 105, + 612, + 505, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 505, + 626 + ], + "score": 1.0, + "content": "The validation graphs are used to assess model performance on training classes itself to check over-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 624, + 506, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 506, + 637 + ], + "score": 1.0, + "content": "fitting as well as for grid-search over hyperparameters. The actual train-testing class splits used for", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "score": 1.0, + "content": "this paper are provided with the code. Since the TRIANGLES dataset has a large number of sam-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 646, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 506, + 659 + ], + "score": 1.0, + "content": "ples, this makes it infeasible to run many baselines including DL and non-DL methods. Hence, we", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 657, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 505, + 669 + ], + "score": 1.0, + "content": "sample 200 graphs from each class, making the total sample size 2000. Similarly we downsample", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 667, + 506, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 506, + 681 + ], + "score": 1.0, + "content": "the number of graphs from 11929 to 1111 (nearly 101 graphs per class). Downsampling is per-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 678, + 505, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 505, + 692 + ], + "score": 1.0, + "content": "formed for Reddit-12K given extremely large graph sizes which makes the graph kernels as well as", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 691, + 290, + 703 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 290, + 703 + ], + "score": 1.0, + "content": "some deep learning baselines extremely slow.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 612, + 506, + 703 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 82, + 217, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 81, + 219, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 81, + 219, + 95 + ], + "score": 1.0, + "content": "A.2 BASELINE DETAILS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 105, + 505, + 205 + ], + "lines": [ + { + "bbox": [ + 106, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "This section details the implementation of the baseline methods. Since, DL-based methods - GIN,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 116, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 505, + 129 + ], + "score": 1.0, + "content": "CapsGNN and DIFFPOOL have not been previously run on these datasets, we select the crucial", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 128, + 505, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 505, + 139 + ], + "score": 1.0, + "content": "hyper-parameters - such as number of layers heuristically based on the results of standard graph", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 137, + 505, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 505, + 151 + ], + "score": 1.0, + "content": "classification datasets on the best performing variants of these models. For these three methods we", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 150, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 505, + 162 + ], + "score": 1.0, + "content": "take the novel layers proposed in the corresponding papers as their feature extractors, while down-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "score": 1.0, + "content": "stream MLP layers are chosen as the classifier. The training and evaluation strategies are similar to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 467, + 183 + ], + "score": 1.0, + "content": "our model, i.e., the models are first trained in an end-to-end fashion on the training dataset", + "type": "text" + }, + { + "bbox": [ + 467, + 172, + 483, + 182 + ], + "score": 0.89, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 483, + 172, + 505, + 183 + ], + "score": 1.0, + "content": "until", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "score": 1.0, + "content": "convergence with learning rate decay on loss plateau and then the classifier layers are fine-tuned", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 386, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 126, + 206 + ], + "score": 1.0, + "content": "over", + "type": "text" + }, + { + "bbox": [ + 127, + 194, + 143, + 204 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 193, + 386, + 206 + ], + "score": 1.0, + "content": ", keeping the parameters of the feature extractor layers fixed.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 210, + 505, + 342 + ], + "lines": [ + { + "bbox": [ + 105, + 210, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 505, + 222 + ], + "score": 1.0, + "content": "For the unsupervised models - WL subtree kernel, Graphlet Count kernel, AWE and Graph2Vec, the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 221, + 506, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 221, + 203, + 234 + ], + "score": 1.0, + "content": "evaluation is done using", + "type": "text" + }, + { + "bbox": [ + 204, + 222, + 210, + 231 + ], + "score": 0.78, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 210, + 221, + 506, + 234 + ], + "score": 1.0, + "content": "-NN search to assess the clustering quality of these models in our few-shot", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 231, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 506, + 245 + ], + "score": 1.0, + "content": "scenario. We refrain from using high-level classifier models such as SVM or MLPs, since training", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 243, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 505, + 255 + ], + "score": 1.0, + "content": "these classifiers on few-shot regime will not properly assess the abilities of these models to cluster", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 254, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 266 + ], + "score": 1.0, + "content": "together graphs of similar class labels. We empirically found that using high level classifiers resulted", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 265, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 265, + 505, + 277 + ], + "score": 1.0, + "content": "in higher deviations and lower mean accuracies. We choose the hyper-parameters for these models", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "score": 1.0, + "content": "using grid-search, since they are significantly faster and each one of these models have few highly", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "sensitive parameters which affect the model significantly. For these models, we perform a grid", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 298, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 199, + 310 + ], + "score": 1.0, + "content": "search for selection of", + "type": "text" + }, + { + "bbox": [ + 199, + 298, + 206, + 308 + ], + "score": 0.82, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 298, + 234, + 310 + ], + "score": 1.0, + "content": "in the", + "type": "text" + }, + { + "bbox": [ + 234, + 298, + 240, + 308 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 298, + 354, + 310 + ], + "score": 1.0, + "content": "-NN algorithm from the set", + "type": "text" + }, + { + "bbox": [ + 354, + 298, + 407, + 309 + ], + "score": 0.93, + "content": "\\{ 1 , 2 , 3 , 4 , 5 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 298, + 505, + 310 + ], + "score": 1.0, + "content": "for the 5-shot scenario,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 144, + 321 + ], + "score": 1.0, + "content": "of which", + "type": "text" + }, + { + "bbox": [ + 144, + 309, + 170, + 319 + ], + "score": 0.9, + "content": "k = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "was found to perform the best. For higher shot scenario, the search was performed", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 320, + 505, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 155, + 332 + ], + "score": 1.0, + "content": "over the set", + "type": "text" + }, + { + "bbox": [ + 156, + 320, + 261, + 332 + ], + "score": 0.91, + "content": "\\{ 1 , 2 , 3 , 4 , 5 , 6 , 7 , \\bar { 8 } , 9 , 1 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 320, + 357, + 332 + ], + "score": 1.0, + "content": ", where we again found", + "type": "text" + }, + { + "bbox": [ + 357, + 320, + 383, + 330 + ], + "score": 0.9, + "content": "k = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 320, + 505, + 332 + ], + "score": 1.0, + "content": "to be the best. The validation", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 331, + 453, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 453, + 343 + ], + "score": 1.0, + "content": "set is used to check overfitting and hyper-parameter selection on the baseline methods.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 15.5 + }, + { + "type": "title", + "bbox": [ + 108, + 362, + 228, + 373 + ], + "lines": [ + { + "bbox": [ + 106, + 361, + 230, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 361, + 230, + 375 + ], + "score": 1.0, + "content": "A.3 OUR MODEL DETAILS", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 106, + 385, + 505, + 506 + ], + "lines": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "score": 1.0, + "content": "This section provides the implementation details of our proposed model. Since, our feature extractor", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 396, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 505, + 409 + ], + "score": 1.0, + "content": "model is GIN, we maintain similar parameter settings as recommended by their paper. As mentioned", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "in section 4.2, using embeddings from all iterations of the message passing network helps achieve", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "better discriminative power and improved gradient flow, therefore we employ the same strategy in", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 428, + 506, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 428, + 425, + 443 + ], + "score": 1.0, + "content": "our feature extractor. The number of super-classes are selected from the set", + "type": "text" + }, + { + "bbox": [ + 425, + 429, + 479, + 441 + ], + "score": 0.91, + "content": "\\{ 1 , 2 , 3 , 4 , 5 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 479, + 428, + 506, + 443 + ], + "score": 1.0, + "content": "using", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 440, + 175, + 452 + ], + "score": 1.0, + "content": "grid-search. The", + "type": "text" + }, + { + "bbox": [ + 175, + 441, + 182, + 450 + ], + "score": 0.82, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 440, + 438, + 452 + ], + "score": 1.0, + "content": "-value for construction of super-graph was selected from the set", + "type": "text" + }, + { + "bbox": [ + 438, + 441, + 482, + 452 + ], + "score": 0.9, + "content": "\\{ 2 , 4 , 6 , 8 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 483, + 440, + 506, + 452 + ], + "score": 1.0, + "content": ". The", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 450, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 506, + 464 + ], + "score": 1.0, + "content": "feature extractor model uses batch-normalization between subsequent message passing layers. We", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 459, + 506, + 476 + ], + "spans": [ + { + "bbox": [ + 104, + 459, + 209, + 476 + ], + "score": 1.0, + "content": "use dropout of 0.5 in the", + "type": "text" + }, + { + "bbox": [ + 209, + 462, + 231, + 472 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 459, + 281, + 476 + ], + "score": 1.0, + "content": "layers. The", + "type": "text" + }, + { + "bbox": [ + 282, + 461, + 309, + 472 + ], + "score": 0.9, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 459, + 506, + 476 + ], + "score": 1.0, + "content": "layers undergo normalization of inputs between", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 473, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 485 + ], + "score": 1.0, + "content": "subsequent layers along with a dropout of 0.5, however, the normalization mechanism in classifier", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 483, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 505, + 497 + ], + "score": 1.0, + "content": "layers is different from batch-norm. We normalize each feature embedding to have Euclidean norm", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 495, + 209, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 209, + 507 + ], + "score": 1.0, + "content": "with value 1. Essentially,", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 28 + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 513, + 344, + 543 + ], + "lines": [ + { + "bbox": [ + 267, + 513, + 344, + 543 + ], + "spans": [ + { + "bbox": [ + 267, + 513, + 344, + 543 + ], + "score": 0.94, + "content": "\\mathbf { x } _ { i n p u t } ^ { j + 1 } = \\frac { \\mathbf { x } _ { o u t } ^ { j } } { | | \\mathbf { x } _ { o u t } ^ { j } | | _ { 2 } }", + "type": "interline_equation", + "image_path": "3ae89ef6953aa96bd243b83d2892c1e11485b0e15e9c2d90ac6788465304f328.jpg" + } + ] + } + ], + "index": 34.5, + "virtual_lines": [ + { + "bbox": [ + 267, + 513, + 344, + 528.0 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 267, + 528.0, + 344, + 543.0 + ], + "spans": [], + "index": 35 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 554, + 505, + 701 + ], + "lines": [ + { + "bbox": [ + 103, + 554, + 507, + 573 + ], + "spans": [ + { + "bbox": [ + 103, + 554, + 133, + 573 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 555, + 159, + 570 + ], + "score": 0.93, + "content": "\\mathbf { x } _ { i n p u t } ^ { j + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 554, + 218, + 573 + ], + "score": 1.0, + "content": "is the input of", + "type": "text" + }, + { + "bbox": [ + 218, + 555, + 249, + 568 + ], + "score": 0.92, + "content": "j + 1 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 554, + 323, + 573 + ], + "score": 1.0, + "content": "layer of classifier,", + "type": "text" + }, + { + "bbox": [ + 323, + 554, + 342, + 569 + ], + "score": 0.92, + "content": "\\mathbf { x } _ { o u t } ^ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 554, + 420, + 573 + ], + "score": 1.0, + "content": "is the output of the", + "type": "text" + }, + { + "bbox": [ + 420, + 555, + 434, + 568 + ], + "score": 0.9, + "content": "j ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 554, + 507, + 573 + ], + "score": 1.0, + "content": "layer. The inputs", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 566, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 104, + 566, + 189, + 583 + ], + "score": 1.0, + "content": "of the first layer of", + "type": "text" + }, + { + "bbox": [ + 189, + 568, + 216, + 580 + ], + "score": 0.9, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 566, + 506, + 583 + ], + "score": 1.0, + "content": "also undergo the same transformation over the outputs of the feature", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 581, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 505, + 593 + ], + "score": 1.0, + "content": "extractor model. We train our models with Adam (Kingma & Ba (2014)) with an initial learning rate", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 591, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 117, + 604 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 591, + 139, + 602 + ], + "score": 0.89, + "content": "1 0 ^ { - 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 591, + 505, + 604 + ], + "score": 1.0, + "content": "for 50 epochs. Each epoch has 10 iterations, where we randomly select a mini-batch from", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 603, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 106, + 603, + 174, + 615 + ], + "score": 1.0, + "content": "the training data", + "type": "text" + }, + { + "bbox": [ + 174, + 603, + 190, + 614 + ], + "score": 0.88, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 603, + 505, + 615 + ], + "score": 1.0, + "content": ". The fine-tuning stage consists of 20 epochs with 10 iterations per epoch. We", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 610, + 506, + 627 + ], + "spans": [ + { + "bbox": [ + 104, + 610, + 321, + 627 + ], + "score": 1.0, + "content": "use a two-layer MLP over the final attention layer of", + "type": "text" + }, + { + "bbox": [ + 321, + 612, + 348, + 624 + ], + "score": 0.91, + "content": "C ^ { G A T ^ { \\bf 1 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 610, + 506, + 627 + ], + "score": 1.0, + "content": "for classification. The attention layers", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 624, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 505, + 637 + ], + "score": 1.0, + "content": "use multi-head attention with 2 heads and leaky ReLU slope of 0.1 . The embeddings from both the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 636, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 636, + 320, + 647 + ], + "score": 1.0, + "content": "attention heads are concatenated. For 20-shot, we set", + "type": "text" + }, + { + "bbox": [ + 320, + 636, + 327, + 645 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 636, + 505, + 647 + ], + "score": 1.0, + "content": "to 2, number of super-classes to 3 and batch", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 647, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 647, + 290, + 658 + ], + "score": 1.0, + "content": "size to 128 on the Letter-High dataset, while", + "type": "text" + }, + { + "bbox": [ + 290, + 647, + 297, + 656 + ], + "score": 0.81, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 647, + 505, + 658 + ], + "score": 1.0, + "content": "is set to 2 and batch size 64 on Reddit, ENZYMES", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 657, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 506, + 669 + ], + "score": 1.0, + "content": "and TRIANGLES datasets. The number of super-classes for Reddit are set to 2, for ENZYMES it", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "is set to 1 and for TRIANGLES are 3. For ENZYMES, there are negligible differences on using 1", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 678, + 506, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 692 + ], + "score": 1.0, + "content": "and 2 super-classes as shown in table 4. We used Python Optimal Transport (POT) library 5 for", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 690, + 303, + 703 + ], + "spans": [ + { + "bbox": [ + 106, + 690, + 197, + 703 + ], + "score": 1.0, + "content": "implementation of the", + "type": "text" + }, + { + "bbox": [ + 197, + 691, + 203, + 702 + ], + "score": 0.79, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 690, + 303, + 703 + ], + "score": 1.0, + "content": "-th Wasserstein distance.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 42 + } + ], + "page_idx": 14, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 119, + 721, + 279, + 731 + ], + "lines": [ + { + "bbox": [ + 119, + 720, + 280, + 733 + ], + "spans": [ + { + "bbox": [ + 119, + 720, + 280, + 733 + ], + "score": 1.0, + "content": "5https://pot.readthedocs.io/en/stable/all.html", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "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": "15", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 82, + 217, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 81, + 219, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 81, + 219, + 95 + ], + "score": 1.0, + "content": "A.2 BASELINE DETAILS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 105, + 505, + 205 + ], + "lines": [ + { + "bbox": [ + 106, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "This section details the implementation of the baseline methods. Since, DL-based methods - GIN,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 116, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 505, + 129 + ], + "score": 1.0, + "content": "CapsGNN and DIFFPOOL have not been previously run on these datasets, we select the crucial", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 128, + 505, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 505, + 139 + ], + "score": 1.0, + "content": "hyper-parameters - such as number of layers heuristically based on the results of standard graph", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 137, + 505, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 505, + 151 + ], + "score": 1.0, + "content": "classification datasets on the best performing variants of these models. For these three methods we", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 150, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 505, + 162 + ], + "score": 1.0, + "content": "take the novel layers proposed in the corresponding papers as their feature extractors, while down-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "score": 1.0, + "content": "stream MLP layers are chosen as the classifier. The training and evaluation strategies are similar to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 467, + 183 + ], + "score": 1.0, + "content": "our model, i.e., the models are first trained in an end-to-end fashion on the training dataset", + "type": "text" + }, + { + "bbox": [ + 467, + 172, + 483, + 182 + ], + "score": 0.89, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 483, + 172, + 505, + 183 + ], + "score": 1.0, + "content": "until", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "score": 1.0, + "content": "convergence with learning rate decay on loss plateau and then the classifier layers are fine-tuned", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 386, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 126, + 206 + ], + "score": 1.0, + "content": "over", + "type": "text" + }, + { + "bbox": [ + 127, + 194, + 143, + 204 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 193, + 386, + 206 + ], + "score": 1.0, + "content": ", keeping the parameters of the feature extractor layers fixed.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 105, + 505, + 206 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 210, + 505, + 342 + ], + "lines": [ + { + "bbox": [ + 105, + 210, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 505, + 222 + ], + "score": 1.0, + "content": "For the unsupervised models - WL subtree kernel, Graphlet Count kernel, AWE and Graph2Vec, the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 221, + 506, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 221, + 203, + 234 + ], + "score": 1.0, + "content": "evaluation is done using", + "type": "text" + }, + { + "bbox": [ + 204, + 222, + 210, + 231 + ], + "score": 0.78, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 210, + 221, + 506, + 234 + ], + "score": 1.0, + "content": "-NN search to assess the clustering quality of these models in our few-shot", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 231, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 506, + 245 + ], + "score": 1.0, + "content": "scenario. We refrain from using high-level classifier models such as SVM or MLPs, since training", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 243, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 505, + 255 + ], + "score": 1.0, + "content": "these classifiers on few-shot regime will not properly assess the abilities of these models to cluster", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 254, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 266 + ], + "score": 1.0, + "content": "together graphs of similar class labels. We empirically found that using high level classifiers resulted", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 265, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 265, + 505, + 277 + ], + "score": 1.0, + "content": "in higher deviations and lower mean accuracies. We choose the hyper-parameters for these models", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "score": 1.0, + "content": "using grid-search, since they are significantly faster and each one of these models have few highly", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "sensitive parameters which affect the model significantly. For these models, we perform a grid", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 298, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 199, + 310 + ], + "score": 1.0, + "content": "search for selection of", + "type": "text" + }, + { + "bbox": [ + 199, + 298, + 206, + 308 + ], + "score": 0.82, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 298, + 234, + 310 + ], + "score": 1.0, + "content": "in the", + "type": "text" + }, + { + "bbox": [ + 234, + 298, + 240, + 308 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 298, + 354, + 310 + ], + "score": 1.0, + "content": "-NN algorithm from the set", + "type": "text" + }, + { + "bbox": [ + 354, + 298, + 407, + 309 + ], + "score": 0.93, + "content": "\\{ 1 , 2 , 3 , 4 , 5 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 298, + 505, + 310 + ], + "score": 1.0, + "content": "for the 5-shot scenario,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 144, + 321 + ], + "score": 1.0, + "content": "of which", + "type": "text" + }, + { + "bbox": [ + 144, + 309, + 170, + 319 + ], + "score": 0.9, + "content": "k = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "was found to perform the best. For higher shot scenario, the search was performed", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 320, + 505, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 155, + 332 + ], + "score": 1.0, + "content": "over the set", + "type": "text" + }, + { + "bbox": [ + 156, + 320, + 261, + 332 + ], + "score": 0.91, + "content": "\\{ 1 , 2 , 3 , 4 , 5 , 6 , 7 , \\bar { 8 } , 9 , 1 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 320, + 357, + 332 + ], + "score": 1.0, + "content": ", where we again found", + "type": "text" + }, + { + "bbox": [ + 357, + 320, + 383, + 330 + ], + "score": 0.9, + "content": "k = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 320, + 505, + 332 + ], + "score": 1.0, + "content": "to be the best. The validation", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 331, + 453, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 453, + 343 + ], + "score": 1.0, + "content": "set is used to check overfitting and hyper-parameter selection on the baseline methods.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 210, + 506, + 343 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 362, + 228, + 373 + ], + "lines": [ + { + "bbox": [ + 106, + 361, + 230, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 361, + 230, + 375 + ], + "score": 1.0, + "content": "A.3 OUR MODEL DETAILS", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 106, + 385, + 505, + 506 + ], + "lines": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "score": 1.0, + "content": "This section provides the implementation details of our proposed model. Since, our feature extractor", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 396, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 505, + 409 + ], + "score": 1.0, + "content": "model is GIN, we maintain similar parameter settings as recommended by their paper. As mentioned", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "in section 4.2, using embeddings from all iterations of the message passing network helps achieve", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "better discriminative power and improved gradient flow, therefore we employ the same strategy in", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 428, + 506, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 428, + 425, + 443 + ], + "score": 1.0, + "content": "our feature extractor. The number of super-classes are selected from the set", + "type": "text" + }, + { + "bbox": [ + 425, + 429, + 479, + 441 + ], + "score": 0.91, + "content": "\\{ 1 , 2 , 3 , 4 , 5 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 479, + 428, + 506, + 443 + ], + "score": 1.0, + "content": "using", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 440, + 175, + 452 + ], + "score": 1.0, + "content": "grid-search. The", + "type": "text" + }, + { + "bbox": [ + 175, + 441, + 182, + 450 + ], + "score": 0.82, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 440, + 438, + 452 + ], + "score": 1.0, + "content": "-value for construction of super-graph was selected from the set", + "type": "text" + }, + { + "bbox": [ + 438, + 441, + 482, + 452 + ], + "score": 0.9, + "content": "\\{ 2 , 4 , 6 , 8 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 483, + 440, + 506, + 452 + ], + "score": 1.0, + "content": ". The", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 450, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 506, + 464 + ], + "score": 1.0, + "content": "feature extractor model uses batch-normalization between subsequent message passing layers. We", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 459, + 506, + 476 + ], + "spans": [ + { + "bbox": [ + 104, + 459, + 209, + 476 + ], + "score": 1.0, + "content": "use dropout of 0.5 in the", + "type": "text" + }, + { + "bbox": [ + 209, + 462, + 231, + 472 + ], + "score": 0.89, + "content": "C ^ { s u p }", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 459, + 281, + 476 + ], + "score": 1.0, + "content": "layers. The", + "type": "text" + }, + { + "bbox": [ + 282, + 461, + 309, + 472 + ], + "score": 0.9, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 459, + 506, + 476 + ], + "score": 1.0, + "content": "layers undergo normalization of inputs between", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 473, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 485 + ], + "score": 1.0, + "content": "subsequent layers along with a dropout of 0.5, however, the normalization mechanism in classifier", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 483, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 505, + 497 + ], + "score": 1.0, + "content": "layers is different from batch-norm. We normalize each feature embedding to have Euclidean norm", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 495, + 209, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 209, + 507 + ], + "score": 1.0, + "content": "with value 1. Essentially,", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 28, + "bbox_fs": [ + 104, + 385, + 506, + 507 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 513, + 344, + 543 + ], + "lines": [ + { + "bbox": [ + 267, + 513, + 344, + 543 + ], + "spans": [ + { + "bbox": [ + 267, + 513, + 344, + 543 + ], + "score": 0.94, + "content": "\\mathbf { x } _ { i n p u t } ^ { j + 1 } = \\frac { \\mathbf { x } _ { o u t } ^ { j } } { | | \\mathbf { x } _ { o u t } ^ { j } | | _ { 2 } }", + "type": "interline_equation", + "image_path": "3ae89ef6953aa96bd243b83d2892c1e11485b0e15e9c2d90ac6788465304f328.jpg" + } + ] + } + ], + "index": 34.5, + "virtual_lines": [ + { + "bbox": [ + 267, + 513, + 344, + 528.0 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 267, + 528.0, + 344, + 543.0 + ], + "spans": [], + "index": 35 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 554, + 505, + 701 + ], + "lines": [ + { + "bbox": [ + 103, + 554, + 507, + 573 + ], + "spans": [ + { + "bbox": [ + 103, + 554, + 133, + 573 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 555, + 159, + 570 + ], + "score": 0.93, + "content": "\\mathbf { x } _ { i n p u t } ^ { j + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 554, + 218, + 573 + ], + "score": 1.0, + "content": "is the input of", + "type": "text" + }, + { + "bbox": [ + 218, + 555, + 249, + 568 + ], + "score": 0.92, + "content": "j + 1 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 554, + 323, + 573 + ], + "score": 1.0, + "content": "layer of classifier,", + "type": "text" + }, + { + "bbox": [ + 323, + 554, + 342, + 569 + ], + "score": 0.92, + "content": "\\mathbf { x } _ { o u t } ^ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 554, + 420, + 573 + ], + "score": 1.0, + "content": "is the output of the", + "type": "text" + }, + { + "bbox": [ + 420, + 555, + 434, + 568 + ], + "score": 0.9, + "content": "j ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 554, + 507, + 573 + ], + "score": 1.0, + "content": "layer. The inputs", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 566, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 104, + 566, + 189, + 583 + ], + "score": 1.0, + "content": "of the first layer of", + "type": "text" + }, + { + "bbox": [ + 189, + 568, + 216, + 580 + ], + "score": 0.9, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 566, + 506, + 583 + ], + "score": 1.0, + "content": "also undergo the same transformation over the outputs of the feature", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 581, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 505, + 593 + ], + "score": 1.0, + "content": "extractor model. We train our models with Adam (Kingma & Ba (2014)) with an initial learning rate", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 591, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 117, + 604 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 591, + 139, + 602 + ], + "score": 0.89, + "content": "1 0 ^ { - 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 591, + 505, + 604 + ], + "score": 1.0, + "content": "for 50 epochs. Each epoch has 10 iterations, where we randomly select a mini-batch from", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 603, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 106, + 603, + 174, + 615 + ], + "score": 1.0, + "content": "the training data", + "type": "text" + }, + { + "bbox": [ + 174, + 603, + 190, + 614 + ], + "score": 0.88, + "content": "G _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 603, + 505, + 615 + ], + "score": 1.0, + "content": ". The fine-tuning stage consists of 20 epochs with 10 iterations per epoch. We", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 610, + 506, + 627 + ], + "spans": [ + { + "bbox": [ + 104, + 610, + 321, + 627 + ], + "score": 1.0, + "content": "use a two-layer MLP over the final attention layer of", + "type": "text" + }, + { + "bbox": [ + 321, + 612, + 348, + 624 + ], + "score": 0.91, + "content": "C ^ { G A T ^ { \\bf 1 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 610, + 506, + 627 + ], + "score": 1.0, + "content": "for classification. The attention layers", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 624, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 505, + 637 + ], + "score": 1.0, + "content": "use multi-head attention with 2 heads and leaky ReLU slope of 0.1 . The embeddings from both the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 636, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 636, + 320, + 647 + ], + "score": 1.0, + "content": "attention heads are concatenated. For 20-shot, we set", + "type": "text" + }, + { + "bbox": [ + 320, + 636, + 327, + 645 + ], + "score": 0.79, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 636, + 505, + 647 + ], + "score": 1.0, + "content": "to 2, number of super-classes to 3 and batch", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 647, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 647, + 290, + 658 + ], + "score": 1.0, + "content": "size to 128 on the Letter-High dataset, while", + "type": "text" + }, + { + "bbox": [ + 290, + 647, + 297, + 656 + ], + "score": 0.81, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 647, + 505, + 658 + ], + "score": 1.0, + "content": "is set to 2 and batch size 64 on Reddit, ENZYMES", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 657, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 506, + 669 + ], + "score": 1.0, + "content": "and TRIANGLES datasets. The number of super-classes for Reddit are set to 2, for ENZYMES it", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "is set to 1 and for TRIANGLES are 3. For ENZYMES, there are negligible differences on using 1", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 678, + 506, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 692 + ], + "score": 1.0, + "content": "and 2 super-classes as shown in table 4. We used Python Optimal Transport (POT) library 5 for", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 690, + 303, + 703 + ], + "spans": [ + { + "bbox": [ + 106, + 690, + 197, + 703 + ], + "score": 1.0, + "content": "implementation of the", + "type": "text" + }, + { + "bbox": [ + 197, + 691, + 203, + 702 + ], + "score": 0.79, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 690, + 303, + 703 + ], + "score": 1.0, + "content": "-th Wasserstein distance.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 42, + "bbox_fs": [ + 103, + 554, + 507, + 703 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 122, + 49, + 493, + 197 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 49, + 493, + 197 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 49, + 493, + 197 + ], + "spans": [ + { + "bbox": [ + 122, + 49, + 493, + 197 + ], + "score": 0.882, + "type": "image", + "image_path": "29fdd17a77c3e8e015beb1724b352f5089f6e6dae91756dba71ded23dab355b7.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 122, + 49, + 493, + 98.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 122, + 98.33333333333334, + 493, + 147.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 122, + 147.66666666666669, + 493, + 197.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 205, + 505, + 228 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 106, + 205, + 505, + 218 + ], + "score": 1.0, + "content": "Figure 4: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 216, + 465, + 229 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 465, + 229 + ], + "score": 1.0, + "content": "from OurMethod-GAT (left), GIN (middle) and WL Kernel (right) on ENZYMES dataset.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "image", + "bbox": [ + 122, + 260, + 490, + 366 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 260, + 490, + 366 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 122, + 260, + 490, + 366 + ], + "spans": [ + { + "bbox": [ + 122, + 260, + 490, + 366 + ], + "score": 0.942, + "type": "image", + "image_path": "562f5e73ca715f0b27d1079b212c127e5869fabcb2d041d7a1dfb57df4883ff6.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 122, + 260, + 490, + 295.3333333333333 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 122, + 295.3333333333333, + 490, + 330.66666666666663 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 122, + 330.66666666666663, + 490, + 365.99999999999994 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 375, + 506, + 397 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "Figure 5: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 385, + 448, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 448, + 398 + ], + "score": 1.0, + "content": "from OurMethod-GAT (left), GIN (middle) and WL Kernel (right) on Reddit dataset.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + } + ], + "index": 7.25 + }, + { + "type": "image", + "bbox": [ + 122, + 428, + 489, + 535 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 428, + 489, + 535 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 122, + 428, + 489, + 535 + ], + "spans": [ + { + "bbox": [ + 122, + 428, + 489, + 535 + ], + "score": 0.962, + "type": "image", + "image_path": "5cc4f83d20953c2ca1efcadb37047fc6947a35899155b9dcb5b918db26496726.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 122, + 428, + 489, + 463.6666666666667 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 122, + 463.6666666666667, + 489, + 499.33333333333337 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 122, + 499.33333333333337, + 489, + 535.0 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 544, + 505, + 567 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 106, + 544, + 505, + 557 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 505, + 557 + ], + "score": 1.0, + "content": "Figure 6: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 555, + 468, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 468, + 568 + ], + "score": 1.0, + "content": "from OurMethod-GAT (left), GIN (middle) and WL Kernel (right) on Letter-High dataset.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + } + ], + "index": 12.25 + }, + { + "type": "title", + "bbox": [ + 108, + 586, + 225, + 597 + ], + "lines": [ + { + "bbox": [ + 106, + 585, + 226, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 226, + 598 + ], + "score": 1.0, + "content": "A.4 SILHOUETTE SCORES", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 606, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 606, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 505, + 618 + ], + "score": 1.0, + "content": "To assess the clustering abilities of the models we analyze the silhouette scores of the test embed-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 618, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 506, + 630 + ], + "score": 1.0, + "content": "dings produced by the GAT variant of our method, GIN and WL Kernel. Silhouette coefficient", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 628, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 506, + 641 + ], + "score": 1.0, + "content": "essentially measures the ratio of intra-class versus inter-class distance. The Silhouette Coefficient", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 640, + 504, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 504, + 651 + ], + "score": 1.0, + "content": "is calculated using the mean intra-cluster distance (a) and the mean nearest-cluster distance (b) for", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 102, + 649, + 509, + 672 + ], + "spans": [ + { + "bbox": [ + 102, + 649, + 371, + 672 + ], + "score": 1.0, + "content": "each sample. The Silhouette Coefficient for a sample is given by", + "type": "text" + }, + { + "bbox": [ + 371, + 650, + 407, + 667 + ], + "score": 0.94, + "content": "\\frac { ( b - a ) } { m a x ( a , b ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 649, + 438, + 672 + ], + "score": 1.0, + "content": ",where", + "type": "text" + }, + { + "bbox": [ + 438, + 653, + 444, + 663 + ], + "score": 0.73, + "content": "b", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 649, + 509, + 672 + ], + "score": 1.0, + "content": "is the distance", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "between a sample and the nearest cluster that the sample is not a part of. The results for mean", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "silhouette coefficient over the test samples averaged over multiple runs are shown in Table 8. We", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "normalize the embeddings before calculating the silhouette coefficient. We can clearly see that our", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "model creates better clusters with low intra-cluster distance as well as high inter-cluster distance.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "Note that the coefficient value for WL remains the same for all scenarios since it computes fixed", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 720, + 335, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 335, + 734 + ], + "score": 1.0, + "content": "embeddings attributed to absence of any DL component.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 21 + } + ], + "page_idx": 15, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "16", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 122, + 49, + 493, + 197 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 49, + 493, + 197 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 49, + 493, + 197 + ], + "spans": [ + { + "bbox": [ + 122, + 49, + 493, + 197 + ], + "score": 0.882, + "type": "image", + "image_path": "29fdd17a77c3e8e015beb1724b352f5089f6e6dae91756dba71ded23dab355b7.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 122, + 49, + 493, + 98.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 122, + 98.33333333333334, + 493, + 147.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 122, + 147.66666666666669, + 493, + 197.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 205, + 505, + 228 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 106, + 205, + 505, + 218 + ], + "score": 1.0, + "content": "Figure 4: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 216, + 465, + 229 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 465, + 229 + ], + "score": 1.0, + "content": "from OurMethod-GAT (left), GIN (middle) and WL Kernel (right) on ENZYMES dataset.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "image", + "bbox": [ + 122, + 260, + 490, + 366 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 260, + 490, + 366 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 122, + 260, + 490, + 366 + ], + "spans": [ + { + "bbox": [ + 122, + 260, + 490, + 366 + ], + "score": 0.942, + "type": "image", + "image_path": "562f5e73ca715f0b27d1079b212c127e5869fabcb2d041d7a1dfb57df4883ff6.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 122, + 260, + 490, + 295.3333333333333 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 122, + 295.3333333333333, + 490, + 330.66666666666663 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 122, + 330.66666666666663, + 490, + 365.99999999999994 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 375, + 506, + 397 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "Figure 5: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 385, + 448, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 448, + 398 + ], + "score": 1.0, + "content": "from OurMethod-GAT (left), GIN (middle) and WL Kernel (right) on Reddit dataset.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + } + ], + "index": 7.25 + }, + { + "type": "image", + "bbox": [ + 122, + 428, + 489, + 535 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 428, + 489, + 535 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 122, + 428, + 489, + 535 + ], + "spans": [ + { + "bbox": [ + 122, + 428, + 489, + 535 + ], + "score": 0.962, + "type": "image", + "image_path": "5cc4f83d20953c2ca1efcadb37047fc6947a35899155b9dcb5b918db26496726.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 122, + 428, + 489, + 463.6666666666667 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 122, + 463.6666666666667, + 489, + 499.33333333333337 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 122, + 499.33333333333337, + 489, + 535.0 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 544, + 505, + 567 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 106, + 544, + 505, + 557 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 505, + 557 + ], + "score": 1.0, + "content": "Figure 6: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 555, + 468, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 468, + 568 + ], + "score": 1.0, + "content": "from OurMethod-GAT (left), GIN (middle) and WL Kernel (right) on Letter-High dataset.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + } + ], + "index": 12.25 + }, + { + "type": "title", + "bbox": [ + 108, + 586, + 225, + 597 + ], + "lines": [ + { + "bbox": [ + 106, + 585, + 226, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 226, + 598 + ], + "score": 1.0, + "content": "A.4 SILHOUETTE SCORES", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 606, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 606, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 505, + 618 + ], + "score": 1.0, + "content": "To assess the clustering abilities of the models we analyze the silhouette scores of the test embed-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 618, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 506, + 630 + ], + "score": 1.0, + "content": "dings produced by the GAT variant of our method, GIN and WL Kernel. Silhouette coefficient", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 628, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 506, + 641 + ], + "score": 1.0, + "content": "essentially measures the ratio of intra-class versus inter-class distance. The Silhouette Coefficient", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 640, + 504, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 504, + 651 + ], + "score": 1.0, + "content": "is calculated using the mean intra-cluster distance (a) and the mean nearest-cluster distance (b) for", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 102, + 649, + 509, + 672 + ], + "spans": [ + { + "bbox": [ + 102, + 649, + 371, + 672 + ], + "score": 1.0, + "content": "each sample. The Silhouette Coefficient for a sample is given by", + "type": "text" + }, + { + "bbox": [ + 371, + 650, + 407, + 667 + ], + "score": 0.94, + "content": "\\frac { ( b - a ) } { m a x ( a , b ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 649, + 438, + 672 + ], + "score": 1.0, + "content": ",where", + "type": "text" + }, + { + "bbox": [ + 438, + 653, + 444, + 663 + ], + "score": 0.73, + "content": "b", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 649, + 509, + 672 + ], + "score": 1.0, + "content": "is the distance", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "between a sample and the nearest cluster that the sample is not a part of. The results for mean", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "silhouette coefficient over the test samples averaged over multiple runs are shown in Table 8. We", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "normalize the embeddings before calculating the silhouette coefficient. We can clearly see that our", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "model creates better clusters with low intra-cluster distance as well as high inter-cluster distance.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "Note that the coefficient value for WL remains the same for all scenarios since it computes fixed", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 720, + 335, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 335, + 734 + ], + "score": 1.0, + "content": "embeddings attributed to absence of any DL component.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 21, + "bbox_fs": [ + 102, + 606, + 509, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 124, + 119, + 487, + 162 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 80, + 504, + 103 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 80, + 506, + 93 + ], + "spans": [ + { + "bbox": [ + 106, + 80, + 506, + 93 + ], + "score": 1.0, + "content": "Table 8: Silhouette coefficients of the test classes for the three dominant models - GAT variant of", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 91, + 376, + 103 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 376, + 103 + ], + "score": 1.0, + "content": "Our Method, GIN and WL. The best scores are highlighted in bold.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "table_body", + "bbox": [ + 124, + 119, + 487, + 162 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 124, + 119, + 487, + 162 + ], + "spans": [ + { + "bbox": [ + 124, + 119, + 487, + 162 + ], + "score": 0.966, + "html": "
MethodReddit-12KENZYMESLetter-HighTRIANGLES
10-shot20-shot10-shot20-shot10-shot20-shot10-shot20-shot
GIN-0.0566-0.06520.01680.04320.21570.23160.03730.1256
WLKernel-0.0626-0.06260.03660.03660.24900.24900.01860.0186
OurMethod-GAT-0.0553-0.05590.02960.11720.34940.37870.38240.4508
", + "type": "table", + "image_path": "47003b584db4ec8d671af55bb420905906ffbb2b85e175dedc50ef2660beaad4.jpg" + } + ] + } + ], + "index": 3, + "virtual_lines": [ + { + "bbox": [ + 124, + 119, + 487, + 133.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 124, + 133.33333333333334, + 487, + 147.66666666666669 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 124, + 147.66666666666669, + 487, + 162.00000000000003 + ], + "spans": [], + "index": 4 + } + ] + } + ], + "index": 1.75 + }, + { + "type": "text", + "bbox": [ + 107, + 173, + 505, + 195 + ], + "lines": [ + { + "bbox": [ + 106, + 173, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 106, + 173, + 332, + 185 + ], + "score": 1.0, + "content": "Table 9: Semi-supervised fine-tuning results for various", + "type": "text" + }, + { + "bbox": [ + 333, + 175, + 339, + 184 + ], + "score": 0.79, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 173, + 505, + 185 + ], + "score": 1.0, + "content": "values on 10-shot and 20-shot scenarios,", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 183, + 469, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 469, + 196 + ], + "score": 1.0, + "content": "where “No Semi-Sup” represents the fine-tuning stage without additional labeled samples.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5 + }, + { + "type": "table", + "bbox": [ + 126, + 212, + 485, + 289 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 126, + 212, + 485, + 289 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 126, + 212, + 485, + 289 + ], + "spans": [ + { + "bbox": [ + 126, + 212, + 485, + 289 + ], + "score": 0.947, + "html": "
Dataset10-shot20-shot
No Semi-Sup2550No Semi-Sup2550
Letter-High73.21± 3.1974.18 ± 2.5874.65 ± 2.1676.95 ± 1.7977.79 ± 1.5278.31 ± 1.11
TRIANGLES75.83 ± 2.9776.36± 2.5977.8 ± 2.0480.09 ±1.7881.29 ± 1.9881.87 ± 1.45
Dataset10-shot20-shot
No Semi-Sup1020No Semi-Sup1020
Reddit45.41± 3.7945.88±3.3246.01± 2.9950.34± 2.7750.76±2.5251.17 ± 2.21
ENZYMES60.13 ± 3.9860.87 ± 3.2461.25 ± 3.1762.74 ± 3.6463.10± 3.4763.67 ± 3.18
", + "type": "table", + "image_path": "bbca2369fa72335fc5638686c7581496db6b789c5859f356022902292405a991.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 126, + 212, + 485, + 237.66666666666666 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 126, + 237.66666666666666, + 485, + 263.3333333333333 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 126, + 263.3333333333333, + 485, + 289.0 + ], + "spans": [], + "index": 9 + } + ] + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 108, + 309, + 274, + 320 + ], + "lines": [ + { + "bbox": [ + 106, + 308, + 275, + 321 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 275, + 321 + ], + "score": 1.0, + "content": "A.5 SEMI-SUPERVISED FINE-TUNING", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 108, + 330, + 504, + 363 + ], + "lines": [ + { + "bbox": [ + 106, + 330, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 505, + 342 + ], + "score": 1.0, + "content": "In many real-world learning scenarios, it is quite common to find abundant unlabelled data. Since", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 340, + 504, + 353 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 504, + 353 + ], + "score": 1.0, + "content": "our model uses a GNN classifier, this makes it possible to use unlabelled data while learning through", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 351, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 505, + 365 + ], + "score": 1.0, + "content": "message passing, where the fine tuning stage of our method is performed in semi-supervised settings.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 368, + 505, + 457 + ], + "lines": [ + { + "bbox": [ + 104, + 365, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 104, + 365, + 402, + 382 + ], + "score": 1.0, + "content": "Essentially, while fine tuning the model, i.e., only training the classifier", + "type": "text" + }, + { + "bbox": [ + 403, + 367, + 430, + 379 + ], + "score": 0.91, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 365, + 445, + 382 + ], + "score": 1.0, + "content": "on", + "type": "text" + }, + { + "bbox": [ + 446, + 369, + 462, + 380 + ], + "score": 0.9, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 365, + 506, + 382 + ], + "score": 1.0, + "content": ", we addi-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 155, + 392 + ], + "score": 1.0, + "content": "tionally use", + "type": "text" + }, + { + "bbox": [ + 156, + 382, + 163, + 391 + ], + "score": 0.75, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 379, + 263, + 392 + ], + "score": 1.0, + "content": "more graphs along with", + "type": "text" + }, + { + "bbox": [ + 263, + 380, + 279, + 390 + ], + "score": 0.9, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 379, + 505, + 392 + ], + "score": 1.0, + "content": ", whose labels are unknown. The learning objective for", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "fine tuning stage doesn’t change since the gradients are back-propagated from the labeled samples", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "score": 1.0, + "content": "only. In this setting, each node in the attention classifier can aggregate information from unlabelled", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 415, + 425 + ], + "score": 1.0, + "content": "samples as well, thus allowing improved learning of the graphs features in", + "type": "text" + }, + { + "bbox": [ + 415, + 411, + 442, + 423 + ], + "score": 0.93, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 443, + 411, + 506, + 425 + ], + "score": 1.0, + "content": ". We show the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 423, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 148, + 435 + ], + "score": 1.0, + "content": "results for", + "type": "text" + }, + { + "bbox": [ + 149, + 425, + 155, + 435 + ], + "score": 0.77, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 423, + 441, + 435 + ], + "score": 1.0, + "content": "values 25 and 50 on Letter-High and TRIANGLES datasets, whereas for", + "type": "text" + }, + { + "bbox": [ + 441, + 425, + 448, + 435 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 423, + 505, + 435 + ], + "score": 1.0, + "content": "values 10 and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 434, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 505, + 446 + ], + "score": 1.0, + "content": "20 on Reddit and ENZYMES datasets. The results are shown in Table 9. We observe an increase in", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 445, + 447, + 458 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 447, + 458 + ], + "score": 1.0, + "content": "the accuracy with increase in number of unlabeled samples during fine-tuning phase.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 17.5 + }, + { + "type": "title", + "bbox": [ + 108, + 471, + 289, + 482 + ], + "lines": [ + { + "bbox": [ + 106, + 470, + 290, + 483 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 290, + 483 + ], + "score": 1.0, + "content": "A.6 ADAPTATION TO ACTIVE-LEARNING", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 107, + 491, + 505, + 547 + ], + "lines": [ + { + "bbox": [ + 105, + 490, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 505, + 505 + ], + "score": 1.0, + "content": "In this section, we show the adaptation of our model to highly practical active learning scenario.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 503, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 503, + 505, + 515 + ], + "score": 1.0, + "content": "In many real world applications, we might start with few samples per class, however as the number", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 513, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 505, + 527 + ], + "score": 1.0, + "content": "of samples to classify from these classes increase over time, some of these samples can be used by", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 524, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 505, + 537 + ], + "score": 1.0, + "content": "the model to adaptively learn and improve with very less human intervention, since the number of", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 536, + 402, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 402, + 547 + ], + "score": 1.0, + "content": "number of samples to be queried for theirs label can always be controlled.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 552, + 505, + 586 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "score": 1.0, + "content": "To perform active-learning, we first select a random subset of size 100 for Letter-High and TRI-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 564, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 574 + ], + "score": 1.0, + "content": "ANGLES datasets as well as a random subset of size 40 for Reddit and ENZYMES datasets, which", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 572, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 153, + 588 + ], + "score": 1.0, + "content": "we term as", + "type": "text" + }, + { + "bbox": [ + 153, + 574, + 190, + 586 + ], + "score": 0.9, + "content": "G _ { r a n d o m }", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 572, + 307, + 588 + ], + "score": 1.0, + "content": ", then fine tune the model on", + "type": "text" + }, + { + "bbox": [ + 308, + 574, + 324, + 585 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 572, + 463, + 588 + ], + "score": 1.0, + "content": "and further evaluate the model on", + "type": "text" + }, + { + "bbox": [ + 464, + 574, + 501, + 586 + ], + "score": 0.86, + "content": "G _ { r a n d o m }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 572, + 506, + 588 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29 + }, + { + "type": "table", + "bbox": [ + 126, + 654, + 485, + 731 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 604, + 505, + 637 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 604, + 505, + 616 + ], + "spans": [ + { + "bbox": [ + 106, + 604, + 496, + 616 + ], + "score": 1.0, + "content": "Table 10: Active Learning Results. The value below each shot represents the number samples", + "type": "text" + }, + { + "bbox": [ + 497, + 604, + 501, + 614 + ], + "score": 0.47, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 604, + 505, + 616 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 614, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 144, + 628 + ], + "score": 1.0, + "content": "added to", + "type": "text" + }, + { + "bbox": [ + 144, + 615, + 160, + 626 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 614, + 506, + 628 + ], + "score": 1.0, + "content": "for second fine-tuning step, where “No AL” represents the model evaluation without", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 625, + 217, + 638 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 217, + 638 + ], + "score": 1.0, + "content": "additional labeled samples.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32 + }, + { + "type": "table_body", + "bbox": [ + 126, + 654, + 485, + 731 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 126, + 654, + 485, + 731 + ], + "spans": [ + { + "bbox": [ + 126, + 654, + 485, + 731 + ], + "score": 0.945, + "html": "
Dataset10-shot20-shot
No AL1525No AL1525
Letter-High73.34± 3.3775.03 ± 3.2476.89 ± 2.1677.06 ± 1.7378.44 ± 1.5279.28 ± 1.36
TRIANGLES76.02 ± 2.5478.44 ± 1.8479.91 ± 1.2880.27 ±1.8481.74 ± 2.0382.58 ± 1.57
Dataset10-shot20-shot
No AL1020No AL1020
Reddit45.41± 3.7946.88±3.1447.91± 2.9950.43±2.6651.76± 2.3253.07± 2.21
ENZYMES60.13 ± 3.9861.57 ± 3.4862.25 ± 3.0662.74 ± 3.6463.60±3.3064.97 ± 3.11
", + "type": "table", + "image_path": "8a7cc9daae3583429066fddac91f1e1cd620856b408f3ed283bb8bd95e385ddf.jpg" + } + ] + } + ], + "index": 35, + "virtual_lines": [ + { + "bbox": [ + 126, + 654, + 485, + 679.6666666666666 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 126, + 679.6666666666666, + 485, + 705.3333333333333 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 126, + 705.3333333333333, + 485, + 730.9999999999999 + ], + "spans": [], + "index": 36 + } + ] + } + ], + "index": 33.5 + } + ], + "page_idx": 16, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 765 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 765 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 15, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 124, + 119, + 487, + 162 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 80, + 504, + 103 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 80, + 506, + 93 + ], + "spans": [ + { + "bbox": [ + 106, + 80, + 506, + 93 + ], + "score": 1.0, + "content": "Table 8: Silhouette coefficients of the test classes for the three dominant models - GAT variant of", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 91, + 376, + 103 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 376, + 103 + ], + "score": 1.0, + "content": "Our Method, GIN and WL. The best scores are highlighted in bold.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "table_body", + "bbox": [ + 124, + 119, + 487, + 162 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 124, + 119, + 487, + 162 + ], + "spans": [ + { + "bbox": [ + 124, + 119, + 487, + 162 + ], + "score": 0.966, + "html": "
MethodReddit-12KENZYMESLetter-HighTRIANGLES
10-shot20-shot10-shot20-shot10-shot20-shot10-shot20-shot
GIN-0.0566-0.06520.01680.04320.21570.23160.03730.1256
WLKernel-0.0626-0.06260.03660.03660.24900.24900.01860.0186
OurMethod-GAT-0.0553-0.05590.02960.11720.34940.37870.38240.4508
", + "type": "table", + "image_path": "47003b584db4ec8d671af55bb420905906ffbb2b85e175dedc50ef2660beaad4.jpg" + } + ] + } + ], + "index": 3, + "virtual_lines": [ + { + "bbox": [ + 124, + 119, + 487, + 133.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 124, + 133.33333333333334, + 487, + 147.66666666666669 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 124, + 147.66666666666669, + 487, + 162.00000000000003 + ], + "spans": [], + "index": 4 + } + ] + } + ], + "index": 1.75 + }, + { + "type": "text", + "bbox": [ + 107, + 173, + 505, + 195 + ], + "lines": [ + { + "bbox": [ + 106, + 173, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 106, + 173, + 332, + 185 + ], + "score": 1.0, + "content": "Table 9: Semi-supervised fine-tuning results for various", + "type": "text" + }, + { + "bbox": [ + 333, + 175, + 339, + 184 + ], + "score": 0.79, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 173, + 505, + 185 + ], + "score": 1.0, + "content": "values on 10-shot and 20-shot scenarios,", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 183, + 469, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 469, + 196 + ], + "score": 1.0, + "content": "where “No Semi-Sup” represents the fine-tuning stage without additional labeled samples.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5, + "bbox_fs": [ + 106, + 173, + 505, + 196 + ] + }, + { + "type": "table", + "bbox": [ + 126, + 212, + 485, + 289 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 126, + 212, + 485, + 289 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 126, + 212, + 485, + 289 + ], + "spans": [ + { + "bbox": [ + 126, + 212, + 485, + 289 + ], + "score": 0.947, + "html": "
Dataset10-shot20-shot
No Semi-Sup2550No Semi-Sup2550
Letter-High73.21± 3.1974.18 ± 2.5874.65 ± 2.1676.95 ± 1.7977.79 ± 1.5278.31 ± 1.11
TRIANGLES75.83 ± 2.9776.36± 2.5977.8 ± 2.0480.09 ±1.7881.29 ± 1.9881.87 ± 1.45
Dataset10-shot20-shot
No Semi-Sup1020No Semi-Sup1020
Reddit45.41± 3.7945.88±3.3246.01± 2.9950.34± 2.7750.76±2.5251.17 ± 2.21
ENZYMES60.13 ± 3.9860.87 ± 3.2461.25 ± 3.1762.74 ± 3.6463.10± 3.4763.67 ± 3.18
", + "type": "table", + "image_path": "bbca2369fa72335fc5638686c7581496db6b789c5859f356022902292405a991.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 126, + 212, + 485, + 237.66666666666666 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 126, + 237.66666666666666, + 485, + 263.3333333333333 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 126, + 263.3333333333333, + 485, + 289.0 + ], + "spans": [], + "index": 9 + } + ] + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 108, + 309, + 274, + 320 + ], + "lines": [ + { + "bbox": [ + 106, + 308, + 275, + 321 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 275, + 321 + ], + "score": 1.0, + "content": "A.5 SEMI-SUPERVISED FINE-TUNING", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 108, + 330, + 504, + 363 + ], + "lines": [ + { + "bbox": [ + 106, + 330, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 505, + 342 + ], + "score": 1.0, + "content": "In many real-world learning scenarios, it is quite common to find abundant unlabelled data. Since", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 340, + 504, + 353 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 504, + 353 + ], + "score": 1.0, + "content": "our model uses a GNN classifier, this makes it possible to use unlabelled data while learning through", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 351, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 505, + 365 + ], + "score": 1.0, + "content": "message passing, where the fine tuning stage of our method is performed in semi-supervised settings.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 330, + 505, + 365 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 368, + 505, + 457 + ], + "lines": [ + { + "bbox": [ + 104, + 365, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 104, + 365, + 402, + 382 + ], + "score": 1.0, + "content": "Essentially, while fine tuning the model, i.e., only training the classifier", + "type": "text" + }, + { + "bbox": [ + 403, + 367, + 430, + 379 + ], + "score": 0.91, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 365, + 445, + 382 + ], + "score": 1.0, + "content": "on", + "type": "text" + }, + { + "bbox": [ + 446, + 369, + 462, + 380 + ], + "score": 0.9, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 365, + 506, + 382 + ], + "score": 1.0, + "content": ", we addi-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 155, + 392 + ], + "score": 1.0, + "content": "tionally use", + "type": "text" + }, + { + "bbox": [ + 156, + 382, + 163, + 391 + ], + "score": 0.75, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 379, + 263, + 392 + ], + "score": 1.0, + "content": "more graphs along with", + "type": "text" + }, + { + "bbox": [ + 263, + 380, + 279, + 390 + ], + "score": 0.9, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 379, + 505, + 392 + ], + "score": 1.0, + "content": ", whose labels are unknown. The learning objective for", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "fine tuning stage doesn’t change since the gradients are back-propagated from the labeled samples", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "score": 1.0, + "content": "only. In this setting, each node in the attention classifier can aggregate information from unlabelled", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 415, + 425 + ], + "score": 1.0, + "content": "samples as well, thus allowing improved learning of the graphs features in", + "type": "text" + }, + { + "bbox": [ + 415, + 411, + 442, + 423 + ], + "score": 0.93, + "content": "C ^ { G A T }", + "type": "inline_equation" + }, + { + "bbox": [ + 443, + 411, + 506, + 425 + ], + "score": 1.0, + "content": ". We show the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 423, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 148, + 435 + ], + "score": 1.0, + "content": "results for", + "type": "text" + }, + { + "bbox": [ + 149, + 425, + 155, + 435 + ], + "score": 0.77, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 423, + 441, + 435 + ], + "score": 1.0, + "content": "values 25 and 50 on Letter-High and TRIANGLES datasets, whereas for", + "type": "text" + }, + { + "bbox": [ + 441, + 425, + 448, + 435 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 423, + 505, + 435 + ], + "score": 1.0, + "content": "values 10 and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 434, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 505, + 446 + ], + "score": 1.0, + "content": "20 on Reddit and ENZYMES datasets. The results are shown in Table 9. We observe an increase in", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 445, + 447, + 458 + ], + "spans": [ + { + "bbox": [ + 106, + 445, + 447, + 458 + ], + "score": 1.0, + "content": "the accuracy with increase in number of unlabeled samples during fine-tuning phase.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 17.5, + "bbox_fs": [ + 104, + 365, + 506, + 458 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 471, + 289, + 482 + ], + "lines": [ + { + "bbox": [ + 106, + 470, + 290, + 483 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 290, + 483 + ], + "score": 1.0, + "content": "A.6 ADAPTATION TO ACTIVE-LEARNING", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 107, + 491, + 505, + 547 + ], + "lines": [ + { + "bbox": [ + 105, + 490, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 505, + 505 + ], + "score": 1.0, + "content": "In this section, we show the adaptation of our model to highly practical active learning scenario.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 503, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 503, + 505, + 515 + ], + "score": 1.0, + "content": "In many real world applications, we might start with few samples per class, however as the number", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 513, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 505, + 527 + ], + "score": 1.0, + "content": "of samples to classify from these classes increase over time, some of these samples can be used by", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 524, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 505, + 537 + ], + "score": 1.0, + "content": "the model to adaptively learn and improve with very less human intervention, since the number of", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 536, + 402, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 402, + 547 + ], + "score": 1.0, + "content": "number of samples to be queried for theirs label can always be controlled.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 490, + 505, + 547 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 552, + 505, + 586 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "score": 1.0, + "content": "To perform active-learning, we first select a random subset of size 100 for Letter-High and TRI-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 564, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 574 + ], + "score": 1.0, + "content": "ANGLES datasets as well as a random subset of size 40 for Reddit and ENZYMES datasets, which", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 572, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 153, + 588 + ], + "score": 1.0, + "content": "we term as", + "type": "text" + }, + { + "bbox": [ + 153, + 574, + 190, + 586 + ], + "score": 0.9, + "content": "G _ { r a n d o m }", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 572, + 307, + 588 + ], + "score": 1.0, + "content": ", then fine tune the model on", + "type": "text" + }, + { + "bbox": [ + 308, + 574, + 324, + 585 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 572, + 463, + 588 + ], + "score": 1.0, + "content": "and further evaluate the model on", + "type": "text" + }, + { + "bbox": [ + 464, + 574, + 501, + 586 + ], + "score": 0.86, + "content": "G _ { r a n d o m }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 572, + 506, + 588 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 552, + 506, + 588 + ] + }, + { + "type": "table", + "bbox": [ + 126, + 654, + 485, + 731 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 604, + 505, + 637 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 604, + 505, + 616 + ], + "spans": [ + { + "bbox": [ + 106, + 604, + 496, + 616 + ], + "score": 1.0, + "content": "Table 10: Active Learning Results. The value below each shot represents the number samples", + "type": "text" + }, + { + "bbox": [ + 497, + 604, + 501, + 614 + ], + "score": 0.47, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 604, + 505, + 616 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 614, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 144, + 628 + ], + "score": 1.0, + "content": "added to", + "type": "text" + }, + { + "bbox": [ + 144, + 615, + 160, + 626 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 614, + 506, + 628 + ], + "score": 1.0, + "content": "for second fine-tuning step, where “No AL” represents the model evaluation without", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 625, + 217, + 638 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 217, + 638 + ], + "score": 1.0, + "content": "additional labeled samples.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32 + }, + { + "type": "table_body", + "bbox": [ + 126, + 654, + 485, + 731 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 126, + 654, + 485, + 731 + ], + "spans": [ + { + "bbox": [ + 126, + 654, + 485, + 731 + ], + "score": 0.945, + "html": "
Dataset10-shot20-shot
No AL1525No AL1525
Letter-High73.34± 3.3775.03 ± 3.2476.89 ± 2.1677.06 ± 1.7378.44 ± 1.5279.28 ± 1.36
TRIANGLES76.02 ± 2.5478.44 ± 1.8479.91 ± 1.2880.27 ±1.8481.74 ± 2.0382.58 ± 1.57
Dataset10-shot20-shot
No AL1020No AL1020
Reddit45.41± 3.7946.88±3.1447.91± 2.9950.43±2.6651.76± 2.3253.07± 2.21
ENZYMES60.13 ± 3.9861.57 ± 3.4862.25 ± 3.0662.74 ± 3.6463.60±3.3064.97 ± 3.11
", + "type": "table", + "image_path": "8a7cc9daae3583429066fddac91f1e1cd620856b408f3ed283bb8bd95e385ddf.jpg" + } + ] + } + ], + "index": 35, + "virtual_lines": [ + { + "bbox": [ + 126, + 654, + 485, + 679.6666666666666 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 126, + 679.6666666666666, + 485, + 705.3333333333333 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 126, + 705.3333333333333, + 485, + 730.9999999999999 + ], + "spans": [], + "index": 36 + } + ] + } + ], + "index": 33.5 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 214 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 345, + 96 + ], + "score": 1.0, + "content": "Thereafter, l relatively important samples are chosen from", + "type": "text" + }, + { + "bbox": [ + 345, + 83, + 383, + 94 + ], + "score": 0.91, + "content": "G _ { r a n d o m }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 81, + 439, + 96 + ], + "score": 1.0, + "content": "and added to", + "type": "text" + }, + { + "bbox": [ + 440, + 83, + 456, + 93 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 81, + 506, + 96 + ], + "score": 1.0, + "content": "for another", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 95, + 504, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 504, + 105 + ], + "score": 1.0, + "content": "step of fine-tuning. There can be multiple strategies for defining relative importance of a sample.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "For our purpose, we define a sample’s relative importance via its predicted class probability distri-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "bution. We sort these samples in increasing order of the difference between their highest and second", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 331, + 138 + ], + "score": 1.0, + "content": "highest predicted class probabilities and choose the first", + "type": "text" + }, + { + "bbox": [ + 331, + 127, + 336, + 136 + ], + "score": 0.51, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 126, + 505, + 138 + ], + "score": 1.0, + "content": "samples from this sorted ranking. We call", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 417, + 150 + ], + "score": 1.0, + "content": "this importance relative, since each sample is evaluated with respect to the set", + "type": "text" + }, + { + "bbox": [ + 417, + 137, + 434, + 148 + ], + "score": 0.9, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "and thus, there is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "score": 1.0, + "content": "transductive flow of information among the samples, hence defining the relative embeddings in the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 505, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 505, + 172 + ], + "score": 1.0, + "content": "space. Intuitively speaking, we have chosen the samples lying closer to separation boundary with", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 169, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 147, + 183 + ], + "score": 1.0, + "content": "respect to", + "type": "text" + }, + { + "bbox": [ + 148, + 171, + 164, + 181 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 169, + 301, + 183 + ], + "score": 1.0, + "content": ". The results for various values of", + "type": "text" + }, + { + "bbox": [ + 301, + 171, + 306, + 180 + ], + "score": 0.65, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 169, + 506, + 183 + ], + "score": 1.0, + "content": "are shown in Table 10. The evaluation is done as", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 253, + 194 + ], + "score": 1.0, + "content": "mentioned earlier on the unseen set", + "type": "text" + }, + { + "bbox": [ + 253, + 181, + 269, + 192 + ], + "score": 0.87, + "content": "G _ { U }", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 181, + 505, + 194 + ], + "score": 1.0, + "content": ". We observe significant improvement for all the datasets.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "score": 1.0, + "content": "This shows our model is capable of selecting important samples with respect to the few existing", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 204, + 216, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 216, + 216 + ], + "score": 1.0, + "content": "samples and learn actively.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 5.5 + }, + { + "type": "title", + "bbox": [ + 107, + 236, + 344, + 248 + ], + "lines": [ + { + "bbox": [ + 105, + 236, + 346, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 346, + 249 + ], + "score": 1.0, + "content": "A.7 PERFORMANCE OF MODEL WITH 1 SUPER-CLASS", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 105, + 259, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 505, + 275 + ], + "score": 1.0, + "content": "From table 4 in correspondence to tables 1 and 2, one can observe that the results obtained by using", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 272, + 505, + 285 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 505, + 285 + ], + "score": 1.0, + "content": "only 1 super-class which is equivalent to removing the super-classes are still better in comparison", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 283, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 283, + 505, + 296 + ], + "score": 1.0, + "content": "with many GNN and graph kernel baselines. By removing the super-classes and thus forming the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 294, + 505, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 220, + 306 + ], + "score": 1.0, + "content": "super-graph solely based on", + "type": "text" + }, + { + "bbox": [ + 221, + 295, + 228, + 304 + ], + "score": 0.27, + "content": "\\mathbf { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 294, + 505, + 306 + ], + "score": 1.0, + "content": "-nearest neighbor heuristic the GAT still learns latent inter class con-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 304, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 318 + ], + "score": 1.0, + "content": "nections via information flow better than the GNNs which use MLP as their classifier. The super", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 315, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 330 + ], + "score": 1.0, + "content": "graph constructed in such scenario will have arbitrary connections between classes in the beginning,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 327, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 505, + 339 + ], + "score": 1.0, + "content": "however as the GIN feature extractor learns over time the segregation in the feature space increases", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 337, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 351 + ], + "score": 1.0, + "content": "leading to better inter as well intra-class connections. Despite this, the performance with super-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 348, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 505, + 361 + ], + "score": 1.0, + "content": "classes is better as this inductive bias allows the model to initiate with a better alignment in the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 360, + 505, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 505, + 372 + ], + "score": 1.0, + "content": "feature space. The silhouette score comparison for OurMethod-GAT with 1 super-class and with the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 371, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 106, + 371, + 505, + 383 + ], + "score": 1.0, + "content": "best performing number of super-classes to GIN and WL clearly indicates the multifold benefits of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 382, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 505, + 393 + ], + "score": 1.0, + "content": "using GNNs as a classifier via super-graph construction. The t-SNE plots for OurMethod-GAT with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "only 1 super-class, GIN and WL kernel on the datasets TRIANGLES, Reddit and Letter-High are", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 403, + 293, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 293, + 417 + ], + "score": 1.0, + "content": "provided in the figures 7, 8 and 9 respectively.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 19.5 + }, + { + "type": "table", + "bbox": [ + 129, + 494, + 483, + 538 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 433, + 505, + 478 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 433, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 505, + 445 + ], + "score": 1.0, + "content": "Table 11: Silhouette coefficients of the test classes for three models - GAT variant of Our Method", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 443, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 506, + 457 + ], + "score": 1.0, + "content": "for 1 super-class which is equivalent to not using any super-classes vs the best performing number of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "super-classes as well as GIN and WL on 20-shot scenario. For GIN and WL both the sub-columns", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 467, + 396, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 396, + 479 + ], + "score": 1.0, + "content": "contain the same values as they don’t have any concept of super-classes.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28.5 + }, + { + "type": "table_body", + "bbox": [ + 129, + 494, + 483, + 538 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 129, + 494, + 483, + 538 + ], + "spans": [ + { + "bbox": [ + 129, + 494, + 483, + 538 + ], + "score": 0.729, + "html": "
MethodReddit-12KENZYMESLetter-HighTRIANGLES
1-SC2-SC1-SC2-SC1-SC3-SC1-SC3-SC
GIN-0.0652-0.06520.04320.04320.23160.23160.12560.1256
WLKernel-0.0626-0.06260.03660.03660.24900.24900.01860.0186
OurMethod-GAT-0.0593-0.05590.11720.09890.35190.37870.39750.4508
", + "type": "table", + "image_path": "c644275b549300264d9b69267a41dfc443e44a9e18a8ec592f85fda7c7f5a611.jpg" + } + ] + } + ], + "index": 32, + "virtual_lines": [ + { + "bbox": [ + 129, + 494, + 483, + 508.6666666666667 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 129, + 508.6666666666667, + 483, + 523.3333333333334 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 129, + 523.3333333333334, + 483, + 538.0 + ], + "spans": [], + "index": 33 + } + ] + } + ], + "index": 30.25 + }, + { + "type": "image", + "bbox": [ + 122, + 580, + 489, + 686 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 580, + 489, + 686 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 580, + 489, + 686 + ], + "spans": [ + { + "bbox": [ + 122, + 580, + 489, + 686 + ], + "score": 0.369, + "type": "image", + "image_path": "1bafd2a3349ea4e2fe9c394cca4ab791a2cd1f65cf071a516bbd1c14891f4fbb.jpg" + } + ] + } + ], + "index": 35, + "virtual_lines": [ + { + "bbox": [ + 122, + 580, + 489, + 615.3333333333334 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 122, + 615.3333333333334, + 489, + 650.6666666666667 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 122, + 650.6666666666667, + 489, + 686.0000000000001 + ], + "spans": [], + "index": 36 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 695, + 505, + 729 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 694, + 505, + 709 + ], + "spans": [ + { + "bbox": [ + 105, + 694, + 505, + 709 + ], + "score": 1.0, + "content": "Figure 7: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot sce-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 706, + 505, + 718 + ], + "spans": [ + { + "bbox": [ + 105, + 706, + 505, + 718 + ], + "score": 1.0, + "content": "nario from OurMethod-GAT with only 1 super-class (left), GIN (middle) and WL Kernel (right) on", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 716, + 193, + 729 + ], + "spans": [ + { + "bbox": [ + 106, + 716, + 193, + 729 + ], + "score": 1.0, + "content": "TRIANGLES dataset.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38 + } + ], + "index": 36.5 + } + ], + "page_idx": 17, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 763 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 763 + ], + "score": 1.0, + "content": "18", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 214 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 345, + 96 + ], + "score": 1.0, + "content": "Thereafter, l relatively important samples are chosen from", + "type": "text" + }, + { + "bbox": [ + 345, + 83, + 383, + 94 + ], + "score": 0.91, + "content": "G _ { r a n d o m }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 81, + 439, + 96 + ], + "score": 1.0, + "content": "and added to", + "type": "text" + }, + { + "bbox": [ + 440, + 83, + 456, + 93 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 81, + 506, + 96 + ], + "score": 1.0, + "content": "for another", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 95, + 504, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 504, + 105 + ], + "score": 1.0, + "content": "step of fine-tuning. There can be multiple strategies for defining relative importance of a sample.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "For our purpose, we define a sample’s relative importance via its predicted class probability distri-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "bution. We sort these samples in increasing order of the difference between their highest and second", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 331, + 138 + ], + "score": 1.0, + "content": "highest predicted class probabilities and choose the first", + "type": "text" + }, + { + "bbox": [ + 331, + 127, + 336, + 136 + ], + "score": 0.51, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 126, + 505, + 138 + ], + "score": 1.0, + "content": "samples from this sorted ranking. We call", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 417, + 150 + ], + "score": 1.0, + "content": "this importance relative, since each sample is evaluated with respect to the set", + "type": "text" + }, + { + "bbox": [ + 417, + 137, + 434, + 148 + ], + "score": 0.9, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "and thus, there is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "score": 1.0, + "content": "transductive flow of information among the samples, hence defining the relative embeddings in the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 505, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 505, + 172 + ], + "score": 1.0, + "content": "space. Intuitively speaking, we have chosen the samples lying closer to separation boundary with", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 169, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 147, + 183 + ], + "score": 1.0, + "content": "respect to", + "type": "text" + }, + { + "bbox": [ + 148, + 171, + 164, + 181 + ], + "score": 0.89, + "content": "G _ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 169, + 301, + 183 + ], + "score": 1.0, + "content": ". The results for various values of", + "type": "text" + }, + { + "bbox": [ + 301, + 171, + 306, + 180 + ], + "score": 0.65, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 169, + 506, + 183 + ], + "score": 1.0, + "content": "are shown in Table 10. The evaluation is done as", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 253, + 194 + ], + "score": 1.0, + "content": "mentioned earlier on the unseen set", + "type": "text" + }, + { + "bbox": [ + 253, + 181, + 269, + 192 + ], + "score": 0.87, + "content": "G _ { U }", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 181, + 505, + 194 + ], + "score": 1.0, + "content": ". We observe significant improvement for all the datasets.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "score": 1.0, + "content": "This shows our model is capable of selecting important samples with respect to the few existing", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 204, + 216, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 216, + 216 + ], + "score": 1.0, + "content": "samples and learn actively.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 81, + 506, + 216 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 236, + 344, + 248 + ], + "lines": [ + { + "bbox": [ + 105, + 236, + 346, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 346, + 249 + ], + "score": 1.0, + "content": "A.7 PERFORMANCE OF MODEL WITH 1 SUPER-CLASS", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 105, + 259, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 505, + 275 + ], + "score": 1.0, + "content": "From table 4 in correspondence to tables 1 and 2, one can observe that the results obtained by using", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 272, + 505, + 285 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 505, + 285 + ], + "score": 1.0, + "content": "only 1 super-class which is equivalent to removing the super-classes are still better in comparison", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 283, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 283, + 505, + 296 + ], + "score": 1.0, + "content": "with many GNN and graph kernel baselines. By removing the super-classes and thus forming the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 294, + 505, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 220, + 306 + ], + "score": 1.0, + "content": "super-graph solely based on", + "type": "text" + }, + { + "bbox": [ + 221, + 295, + 228, + 304 + ], + "score": 0.27, + "content": "\\mathbf { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 294, + 505, + 306 + ], + "score": 1.0, + "content": "-nearest neighbor heuristic the GAT still learns latent inter class con-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 304, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 318 + ], + "score": 1.0, + "content": "nections via information flow better than the GNNs which use MLP as their classifier. The super", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 315, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 330 + ], + "score": 1.0, + "content": "graph constructed in such scenario will have arbitrary connections between classes in the beginning,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 327, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 505, + 339 + ], + "score": 1.0, + "content": "however as the GIN feature extractor learns over time the segregation in the feature space increases", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 337, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 351 + ], + "score": 1.0, + "content": "leading to better inter as well intra-class connections. Despite this, the performance with super-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 348, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 505, + 361 + ], + "score": 1.0, + "content": "classes is better as this inductive bias allows the model to initiate with a better alignment in the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 360, + 505, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 505, + 372 + ], + "score": 1.0, + "content": "feature space. The silhouette score comparison for OurMethod-GAT with 1 super-class and with the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 371, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 106, + 371, + 505, + 383 + ], + "score": 1.0, + "content": "best performing number of super-classes to GIN and WL clearly indicates the multifold benefits of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 382, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 505, + 393 + ], + "score": 1.0, + "content": "using GNNs as a classifier via super-graph construction. The t-SNE plots for OurMethod-GAT with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "only 1 super-class, GIN and WL kernel on the datasets TRIANGLES, Reddit and Letter-High are", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 403, + 293, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 293, + 417 + ], + "score": 1.0, + "content": "provided in the figures 7, 8 and 9 respectively.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 19.5, + "bbox_fs": [ + 105, + 259, + 505, + 417 + ] + }, + { + "type": "table", + "bbox": [ + 129, + 494, + 483, + 538 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 433, + 505, + 478 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 433, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 505, + 445 + ], + "score": 1.0, + "content": "Table 11: Silhouette coefficients of the test classes for three models - GAT variant of Our Method", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 443, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 506, + 457 + ], + "score": 1.0, + "content": "for 1 super-class which is equivalent to not using any super-classes vs the best performing number of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "super-classes as well as GIN and WL on 20-shot scenario. For GIN and WL both the sub-columns", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 467, + 396, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 396, + 479 + ], + "score": 1.0, + "content": "contain the same values as they don’t have any concept of super-classes.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28.5 + }, + { + "type": "table_body", + "bbox": [ + 129, + 494, + 483, + 538 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 129, + 494, + 483, + 538 + ], + "spans": [ + { + "bbox": [ + 129, + 494, + 483, + 538 + ], + "score": 0.729, + "html": "
MethodReddit-12KENZYMESLetter-HighTRIANGLES
1-SC2-SC1-SC2-SC1-SC3-SC1-SC3-SC
GIN-0.0652-0.06520.04320.04320.23160.23160.12560.1256
WLKernel-0.0626-0.06260.03660.03660.24900.24900.01860.0186
OurMethod-GAT-0.0593-0.05590.11720.09890.35190.37870.39750.4508
", + "type": "table", + "image_path": "c644275b549300264d9b69267a41dfc443e44a9e18a8ec592f85fda7c7f5a611.jpg" + } + ] + } + ], + "index": 32, + "virtual_lines": [ + { + "bbox": [ + 129, + 494, + 483, + 508.6666666666667 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 129, + 508.6666666666667, + 483, + 523.3333333333334 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 129, + 523.3333333333334, + 483, + 538.0 + ], + "spans": [], + "index": 33 + } + ] + } + ], + "index": 30.25 + }, + { + "type": "image", + "bbox": [ + 122, + 580, + 489, + 686 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 580, + 489, + 686 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 580, + 489, + 686 + ], + "spans": [ + { + "bbox": [ + 122, + 580, + 489, + 686 + ], + "score": 0.369, + "type": "image", + "image_path": "1bafd2a3349ea4e2fe9c394cca4ab791a2cd1f65cf071a516bbd1c14891f4fbb.jpg" + } + ] + } + ], + "index": 35, + "virtual_lines": [ + { + "bbox": [ + 122, + 580, + 489, + 615.3333333333334 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 122, + 615.3333333333334, + 489, + 650.6666666666667 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 122, + 650.6666666666667, + 489, + 686.0000000000001 + ], + "spans": [], + "index": 36 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 695, + 505, + 729 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 694, + 505, + 709 + ], + "spans": [ + { + "bbox": [ + 105, + 694, + 505, + 709 + ], + "score": 1.0, + "content": "Figure 7: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot sce-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 706, + 505, + 718 + ], + "spans": [ + { + "bbox": [ + 105, + 706, + 505, + 718 + ], + "score": 1.0, + "content": "nario from OurMethod-GAT with only 1 super-class (left), GIN (middle) and WL Kernel (right) on", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 716, + 193, + 729 + ], + "spans": [ + { + "bbox": [ + 106, + 716, + 193, + 729 + ], + "score": 1.0, + "content": "TRIANGLES dataset.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38 + } + ], + "index": 36.5 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 123, + 53, + 491, + 197 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 123, + 53, + 491, + 197 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 53, + 491, + 197 + ], + "spans": [ + { + "bbox": [ + 123, + 53, + 491, + 197 + ], + "score": 0.9, + "type": "image", + "image_path": "2c26d5078ecb3af998cfa6a0df81aaa3205653b35f692f0d5124b1eb6194c0bd.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 123, + 53, + 491, + 101.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 123, + 101.0, + 491, + 149.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 123, + 149.0, + 491, + 197.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 205, + 505, + 239 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "score": 1.0, + "content": "Figure 8: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 215, + 505, + 229 + ], + "spans": [ + { + "bbox": [ + 104, + 215, + 505, + 229 + ], + "score": 1.0, + "content": "from OurMethod-GAT with only 1 super-class (left), GIN (middle) and WL Kernel (right) on Reddit", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 226, + 140, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 140, + 240 + ], + "score": 1.0, + "content": "dataset.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "image", + "bbox": [ + 122, + 270, + 489, + 379 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 270, + 489, + 379 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 122, + 270, + 489, + 379 + ], + "spans": [ + { + "bbox": [ + 122, + 270, + 489, + 379 + ], + "score": 0.953, + "type": "image", + "image_path": "6612059db44bda00c40722071d4b3b857b74cec9b39a0f864e9338819d122eed.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 122, + 270, + 489, + 306.3333333333333 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 122, + 306.3333333333333, + 489, + 342.66666666666663 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 122, + 342.66666666666663, + 489, + 378.99999999999994 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 388, + 504, + 422 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 387, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 506, + 401 + ], + "score": 1.0, + "content": "Figure 9: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 398, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 505, + 412 + ], + "score": 1.0, + "content": "from OurMethod-GAT with only 1 super-class (left), GIN (middle) and WL Kernel (right) on Letter-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 408, + 163, + 424 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 163, + 424 + ], + "score": 1.0, + "content": "High dataset.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + } + ], + "index": 8.5 + } + ], + "page_idx": 18, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "19", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 123, + 53, + 491, + 197 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 123, + 53, + 491, + 197 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 53, + 491, + 197 + ], + "spans": [ + { + "bbox": [ + 123, + 53, + 491, + 197 + ], + "score": 0.9, + "type": "image", + "image_path": "2c26d5078ecb3af998cfa6a0df81aaa3205653b35f692f0d5124b1eb6194c0bd.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 123, + 53, + 491, + 101.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 123, + 101.0, + 491, + 149.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 123, + 149.0, + 491, + 197.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 205, + 505, + 239 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "score": 1.0, + "content": "Figure 8: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 215, + 505, + 229 + ], + "spans": [ + { + "bbox": [ + 104, + 215, + 505, + 229 + ], + "score": 1.0, + "content": "from OurMethod-GAT with only 1 super-class (left), GIN (middle) and WL Kernel (right) on Reddit", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 226, + 140, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 140, + 240 + ], + "score": 1.0, + "content": "dataset.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "image", + "bbox": [ + 122, + 270, + 489, + 379 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 270, + 489, + 379 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 122, + 270, + 489, + 379 + ], + "spans": [ + { + "bbox": [ + 122, + 270, + 489, + 379 + ], + "score": 0.953, + "type": "image", + "image_path": "6612059db44bda00c40722071d4b3b857b74cec9b39a0f864e9338819d122eed.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 122, + 270, + 489, + 306.3333333333333 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 122, + 306.3333333333333, + 489, + 342.66666666666663 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 122, + 342.66666666666663, + 489, + 378.99999999999994 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 388, + 504, + 422 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 387, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 506, + 401 + ], + "score": 1.0, + "content": "Figure 9: Visualization: t-SNE plots of the computed embeddings of test graphs on 20-shot scenario", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 398, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 505, + 412 + ], + "score": 1.0, + "content": "from OurMethod-GAT with only 1 super-class (left), GIN (middle) and WL Kernel (right) on Letter-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 408, + 163, + 424 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 163, + 424 + ], + "score": 1.0, + "content": "High dataset.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + } + ], + "index": 8.5 + } + ] + } + ], + "_backend": "pipeline", + "_version_name": "2.2.2" +} \ No newline at end of file