PageSourceSearch

https://jinglingli.github.io/publications/

html jinglingli.github.io collected 2026-10-03 09:23:32 UTC 27,275 bytes, 1,076 lines download raw bytes

1<!DOCTYPE html>
2<html>
3
4  <head>
5    
6    <meta charset="utf-8">
7<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
8<meta http-equiv="X-UA-Compatible" content="IE=edge">
9
10<title>
11
12  Jingling  Li
13
14
15  | publications
16
17</title>
18<meta name="description" content="Jingling's personal website
19">
20
21<!-- Open Graph -->
22
23
24<!-- Bootstrap & MDB -->
25<link href="https://stackpath.bootstrapcdn.com/bootstrap/4.5.2/css/bootstrap.min.css" rel="stylesheet" integrity="sha512-MoRNloxbStBcD8z3M/2BmnT+rg4IsMxPkXaGh2zD6LGNNFE80W3onsAhRcMAMrSoyWL9xD7Ert0men7vR8LUZg==" crossorigin="anonymous">
26<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/mdbootstrap/4.19.1/css/mdb.min.css" integrity="sha512-RO38pBRxYH3SoOprtPTD86JFOclM51/XTIdEPh5j8sj4tp8jmQIx26twG52UaLi//hQldfrh7e51WzP9wuP32Q==" crossorigin="anonymous" />
27
28<!-- Fonts & Icons -->
29<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.14.0/css/all.min.css"  integrity="sha512-1PKOgIY59xJ8Co8+NE6FZ+LOAZKjy+KY8iq0G4B3CyeY6wYHN3yt9PW0XpSriVlkMXe40PTKnXrLnZ9+fkDaog==" crossorigin="anonymous">
30<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/academicons/1.9.0/css/academicons.min.css" integrity="sha512-W4yqoT1+8NLkinBLBZko+dFB2ZbHsYLDdr50VElllRcNt2Q4/GSs6u71UHKxB7S6JEMCp5Ve4xjh3eGQl/HRvg==" crossorigin="anonymous">
31<link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Roboto:300,400,500,700|Roboto+Slab:100,300,400,500,700|Material+Icons">
32
33<!-- Code Syntax Highlighting -->
34<link rel="stylesheet" href="https://gitcdn.link/repo/jwarby/jekyll-pygments-themes/master/github.css" />
35
36<!-- Styles -->
37
38<link rel="icon" href="data:image/svg+xml,<svg xmlns=%22http://www.w3.org/2000/svg%22 viewBox=%220 0 100 100%22><text y=%22.9em%22 font-size=%2290%22>🌈</text></svg>">
39
40<link rel="stylesheet" href="/assets/css/main.css">
41<link rel="canonical" href="/publications/">
42
43<!-- JQuery -->
44<!-- jQuery -->
45<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.min.js" integrity="sha512-bLT0Qm9VnAYZDflyKcBaQ2gg0hSYNQrJ8RilYldYQ1FxQYoCLtUjuuRuZo+fjqhx/qtq/1itJ0C2ejDxltZVFg==" crossorigin="anonymous"></script>
45
46
47
48<!-- Theming-->
49
50<script src="/assets/js/theme.js"></script>
vendor: 1 bytes, line 50
50
51<script src="/assets/js/dark_mode.js"></script>
51
52
53
54
55
56
57
58    
59<!-- MathJax -->
60<script type="text/javascript">
61  window.MathJax = {
62    tex: {
63      tags: 'ams'
64    }
65  };
66</script>
vendor: 1 bytes, line 66
66
67<script defer type="text/javascript" id="MathJax-script" src="https://cdn.jsdelivr.net/npm/[email protected]/es5/tex-mml-chtml.js"></script>
vendor: 1 bytes, line 67
67
68<script defer src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
68
69
70
71  </head>
72
73  <body class="fixed-top-nav ">
74
75    <!-- Header -->
76
77    <header>
78
79    <!-- Nav Bar -->
80    <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top">
81    <div class="container">
82      
83      <a class="navbar-brand title font-weight-lighter" href="https://jinglingli.github.io/">
84       <span class="font-weight-bold">Jingling</span>   Li
85      </a>
86      
87      <!-- Navbar Toggle -->
88      <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation">
89        <span class="sr-only">Toggle navigation</span>
90        <span class="icon-bar top-bar"></span>
91        <span class="icon-bar middle-bar"></span>
92        <span class="icon-bar bottom-bar"></span>
93      </button>
94      <div class="collapse navbar-collapse text-right" id="navbarNav">
95        <ul class="navbar-nav ml-auto flex-nowrap">
96          <!-- About -->
97          <li class="nav-item ">
98            <a class="nav-link" href="/">
99              about
100              
101            </a>
102          </li>
103          
104          <!-- Other pages -->
105          
106          
107          
108          
109          
110          
111          
112          
113          
114          
115          
116          
117          
118          
119          
120          
121          
122          
123          
124          
125          
126          
127          
128          
129          <li class="nav-item active">
130              <a class="nav-link" href="/publications/">
131                publications
132                
133                <span class="sr-only">(current)</span>
134                
135              </a>
136          </li>
137          
138          
139          
140          
141          
142          
143            <div class="toggle-container">
144              <a id="light-toggle">
145                  <i class="fas fa-moon"></i>
146                  <i class="fas fa-sun"></i>
147              </a>
148            </div>
149          
150        </ul>
151      </div>
152    </div>
153  </nav>
154
155</header>
156
157
158    <!-- Content -->
159
160    <div class="container mt-5">
161      <div class="post">
162
163  <header class="post-header">
164    <h1 class="post-title">publications</h1>
165    <p class="post-description">\* denotes equal contributions or alphabetical order.</p>
166  </header>
167
168  <article>
169    <div class="publications">
170
171
172  <h2 class="year">2021</h2>
173  <ol class="bibliography">
174<li>
175<div class="row">
176  <div class="col-sm-2 abbr">
177  
178    
179    <abbr class="badge">Neurips</abbr>
180    
181  
182  </div>
183
184  <div id="Li2021How" class="col-sm-8">
185    
186      <div class="title">How Does a Neural Network’s Architecture Impact Its Robustness to Noisy Labels?</div>
187      <div class="author">
188        
189          
190          
191          
192          
193          
194          
195            
196              
197                <em>Li, Jingling</em>,
198              
199            
200          
201        
202          
203          
204          
205          
206          
207          
208            
209              
210                
211                  Zhang, Mozhi,
212                
213              
214            
215          
216        
217          
218          
219          
220          
221          
222          
223            
224              
225                
226                  Xu, Keyulu,
227                
228              
229            
230          
231        
232          
233          
234          
235          
236          
237          
238            
239              
240                
241                  Dickerson, John,
242                
243              
244            
245          
246        
247          
248          
249          
250          
251          
252          
253            
254              
255                
256                  and Ba, Jimmy
257                
258              
259            
260          
261        
262      </div>
263
264      <div class="periodical">
265      
266        <em>In Advances in Neural Information Processing Systems,</em>
267      
268      
269        2021
270      
271      </div>
272    
273
274    <div class="links">
275    
276      <a class="abstract btn btn-sm z-depth-0" role="button">Abs</a>
277    
278    
279    
280    
281      <a href="https://openreview.net/forum?id=Ir-WwGboFN-" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">HTML</a>
282    
283    
284    
285    
286    
287      <a href="https://github.com/jinglingli/alignment_noisy_label" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">
287Code</a>
288    
289    
290    
291    
292    </div>
293
294    <!-- Hidden abstract block -->
295    
296    <div class="abstract hidden">
297      <p>Noisy labels are inevitable in large real-world datasets. In this work, we explore an area understudied by previous works — how the network’s architecture impacts its robustness to noisy labels. We provide a formal framework connecting the robustness of a network to the alignments between its architecture and target/noise functions. Our framework measures a network’s robustness via the predictive power in its representations — the test performance of a linear model trained on the learned representations using a small set of clean labels. We hypothesize that a network is more robust to noisy labels if its architecture is more aligned with the target function than the noise. To support our hypothesis, we provide both theoretical and empirical evidence across various neural network architectures and different domains. We also find that when the network is well-aligned with the target function, its predictive power in representations could improve upon state-of-the-art (SOTA) noisy-label-training methods in terms of test accuracy and even outperform sophisticated methods that use clean labels.</p>
298    </div>
299    
300
301    <!-- Hidden bibtex block -->
302    
303  </div>
304</div>
305</li>
306<li>
307<div class="row">
308  <div class="col-sm-2 abbr">
309  
310    
311    <abbr class="badge">Neurips</abbr>
312    
313  
314  </div>
315
316  <div id="Ding2021Vq" class="col-sm-8">
317    
318      <div class="title">VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization</div>
319      <div class="author">
320        
321          
322          
323          
324          
325          
326          
327            
328              
329                
330                  Ding, Mucong*,
331                
332              
333            
334          
335        
336          
337          
338          
339          
340          
341          
342            
343              
344                
345                  Kong, Kezhi*,
346                
347              
348            
349          
350        
351          
352          
353          
354          
355          
356          
357            
358              
359                <em>Li, Jingling</em>,
360              
361            
362          
363        
364          
365          
366          
367          
368          
369          
370            
371              
372                
373                  Zhu, Chen,
374                
375              
376            
377          
378        
379          
380          
381          
382          
383          
384          
385            
386              
387                
388                  Dickerson, John P,
389                
390              
391            
392          
393        
394          
395          
396          
397          
398          
399          
400            
401              
402                
403                  Huang, Furong,
404                
405              
406            
407          
408        
409          
410          
411          
412          
413          
414          
415            
416              
417                
418                  and Goldstein, Tom
419                
420              
421            
422          
423        
424      </div>
425
426      <div class="periodical">
427      
428        <em>In Advances in Neural Information Processing Systems</em>
429      
430      
431        2021
432      
433      </div>
434    
435
436    <div class="links">
437    
438      <a class="abstract btn btn-sm z-depth-0" role="button">Abs</a>
439    
440    
441    
442    
443      <a href="https://openreview.net/forum?id=EO-CQzgcIxd" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">HTML</a>
444    
445    
446    
447    
448    
449      <a href="https://github.com/devnkong/VQ-GNN" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">Code</a>
450    
451    
452    
453    
454    </div>
455
456    <!-- Hidden abstract block -->
457    
458    <div class="abstract hidden">
459      <p>Most state-of-the-art Graph Neural Networks (GNNs) can be defined as a form of graph convolution which can be realized by message passing between direct neighbors or beyond. To scale such GNNs to large graphs, various neighbor-, layer-, or subgraph-sampling techniques are proposed to alleviate the "neighbor explosion" problem by considering only a small subset of messages passed to the nodes in a mini-batch. However, sampling-based methods are difficult to apply to GNNs that utilize many-hops-away or global context each layer, show unstable performance for different tasks and datasets, and do not speed up model inference. We propose a principled and fundamentally different approach, VQ-GNN, a universal framework to 
459scale up any convolution-based GNNs using Vector Quantization (VQ) without compromising the performance. In contrast to sampling-based techniques, our approach can effectively preserve all the messages passed to a mini-batch of nodes by learning and updating a small number of quantized reference vectors of global node representations, using VQ within each GNN layer. Our framework avoids the "neighbor explosion" problem of GNNs using quantized representations combined with a low-rank version of the graph convolution matrix. We show that such a compact low-rank version of the gigantic convolution matrix is sufficient both theoretically and experimentally. In company with VQ, we design a novel approximated message passing algorithm and a nontrivial back-propagation rule for our framework. Experiments on various types of GNN backbones demonstrate the scalability and competitive performance of our framework on large-graph node classification and link prediction benchmarks.</p>
460    </div>
461    
462
463    <!-- Hidden bibtex block -->
464    
465  </div>
466</div>
467</li>
468<li>
469<div class="row">
470  <div class="col-sm-2 abbr">
471  
472    
473    <abbr class="badge">ICLR</abbr>
474    
475  
476  </div>
477
478  <div id="Xu2021How" class="col-sm-8">
479    
480      <div class="title">How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks</div>
481      <div class="author">
482        
483          
484          
485          
486          
487          
488          
489            
490              
491                
492                  Xu, Keyulu,
493                
494              
495            
496          
497        
498          
499          
500          
501          
502          
503          
504            
505              
506                
507                  Zhang, Mozhi,
508                
509              
510            
511          
512        
513          
514          
515          
516          
517          
518          
519            
520              
521                <em>Li, Jingling</em>,
522              
523            
524          
525        
526          
527          
528          
529          
530          
531          
532            
533              
534                
535                  Du, Simon S.,
536                
537              
538            
539          
540        
541          
542          
543          
544          
545          
546          
547            
548              
549                
550                  Kawarabayashi, Ken-ichi,
551                
552              
553            
554          
555        
556          
557          
558          
559          
560          
561          
562            
563              
564                
565                  and Jegelka, Stefanie
566                
567              
568            
569          
570        
571      </div>
572
573      <div class="periodical">
574      
575        <em>In International Conference on Learning Representations (Oral)</em>
576      
577      
578        2021
579      
580      </div>
581    
582
583    <div class="links">
584    
585      <a class="abstract btn btn-sm z-depth-0" role="button">Abs</a>
586    
587    
588    
589    
590      <a href="https://openreview.net/forum?id=UH-cmocLJC" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">HTML</a>
591    
592    
593    
594    
595    
596      <a href="https://github.com/jinglingli/nn-extrapolate" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">Code</a>
597    
598    
599    
600    
601    </div>
602
603    <!-- Hidden abstract block -->
604    
605    <div class="abstract hidden">
606      <p>We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) – structured networks with MLP modules – have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify the observation that ReLU MLPs quickly converge to linear functions along any direction from the origin, which implies that ReLU MLPs do not extrapolate most nonlinear functions. But, they can provably learn a linear target function when the training distribution is sufficiently "diverse". Second, in connection to analyzing the successes and limitations of GNNs, these results suggest a hypothesis for which we provide theoretical and empirical evidence: the success of GNNs in extrapolating algorithmic tasks to new data (e.g., larger graphs or edge weights) relies on encoding task-s
606pecific non-linearities in the architecture or features. Our theoretical analysis builds on a connection of over-parameterized networks to the neural tangent kernel. Empirically, our theory holds across different training settings.</p>
607    </div>
608    
609
610    <!-- Hidden bibtex block -->
611    
612  </div>
613</div>
614</li>
615</ol>
616
617  <h2 class="year">2020</h2>
618  <ol class="bibliography">
619<li>
620<div class="row">
621  <div class="col-sm-2 abbr">
622  
623    
624    <abbr class="badge">ICLR</abbr>
625    
626  
627  </div>
628
629  <div id="Xu2020What" class="col-sm-8">
630    
631      <div class="title">What Can Neural Networks Reason About?</div>
632      <div class="author">
633        
634          
635          
636          
637          
638          
639          
640            
641              
642                
643                  Xu, Keyulu,
644                
645              
646            
647          
648        
649          
650          
651          
652          
653          
654          
655            
656              
657                <em>Li, Jingling</em>,
658              
659            
660          
661        
662          
663          
664          
665          
666          
667          
668            
669              
670                
671                  Zhang, Mozhi,
672                
673              
674            
675          
676        
677          
678          
679          
680          
681          
682          
683            
684              
685                
686                  Du, Simon S.,
687                
688              
689            
690          
691        
692          
693          
694          
695          
696          
697          
698            
699              
700                
701                  Kawarabayashi, Ken-ichi,
702                
703              
704            
705          
706        
707          
708          
709          
710          
711          
712          
713            
714              
715                
716                  and Jegelka, Stefanie
717                
718              
719            
720          
721        
722      </div>
723
724      <div class="periodical">
725      
726        <em>In International Conference on Learning Representations (Spotlight)</em>
727      
728      
729        2020
730      
731      </div>
732    
733
734    <div class="links">
735    
736      <a class="abstract btn btn-sm z-depth-0" role="button">Abs</a>
737    
738    
739    
740    
741      <a href="https://openreview.net/forum?id=rJxbJeHFPS" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">HTML</a>
742    
743    
744    
745    
746    
747      <a href="https://github.com/NNReasoning/What-Can-Neural-Networks-Reason-About" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">Code</a>
748    
749    
750    
751    
752    </div>
753
754    <!-- Hidden abstract block -->
755    
756    <div class="abstract hidden">
757      <p>Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically, there is limited understanding of why and when a network structure generalizes better than others, although they have equal expressive power. In this paper, we develop a framework to characterize which reasoning tasks a network can learn well, by studying how well its computation structure aligns with the algorithmic structure of the relevant reasoning process. We formally define this algorithmic alignment and derive a sample complexity bound that decreases with better alignment. This framework offers an explanation for the empirical success of popular reasoning models, and suggests their limitations. As an example, we unify seemingly different reasoning tasks, such as intuitive physics, visual question answering, and shortest paths, via the lens of a powerful algorithmic paradigm, dynamic programming (DP). We show that GNNs align with DP and thus are expected to solve these tasks. On several reasoning tasks, our theory is supported by empirical results.</p>
758    </div>
759    
760
761    <!-- Hidden bibtex block -->
762    
763  </div>
764</div>
765</li>
766<li>
767<div class="row">
768  <div class="col-sm-2 abbr">
769  
770    
771    <abbr class="badge">AISTATS</abbr>
772    
773  
774  </div>
775
776  <div id="Li2020Understanding" class="col-sm-8">
777    
778      <div class="title">Understanding Generalization in Deep Learning via Tensor Methods</div>
779      <div class="author">
780        
781          
782          
783          
784          
785          
786          
787            
788              
789                <em>Li, Jingling</em>,
790              
791            
792          
793        
794          
795          
796          
797          
798          
799          
800            
801              
802                
803                  Sun, Yanchao,
804                
805              
806            
807          
808        
809          
810          
811          
812          
813          
814          
815            
816              
817                
818                  Su, Jiahao,
819                
820              
821            
822          
823        
824          
825          
826          
827          
828          
829          
830            
831              
832                
833                  Suzuki, Taiji,
834                
835              
836            
837          
838        
839          
840          
841          
842          
843          
844          
845            
846              
847                
848                  and Huang, Furong
849                
850              
851            
852          
853        
854      </div>
855
856      <div class="periodical">
857      
858        <em>In International Conference on Artificial Intelligence and Statistics</em>
859      
860      
861        2020
862      
863      </div>
864    
865
866    <div class="links">
867    
868      <a class="abstract btn btn-sm z-depth-0" role="button">Abs</a>
869    
870    
871    
872    
873      <a href="http://proceedings.mlr.press/v108/li20c/li20c.pdf" class="btn btn-sm z-depth-0" role="button" target="_blank" rel="noopener noreferrer">HTML</a>
874    
875    
876    
877    
878    
879    
880    
881    
882    </div>
883
884    <!-- Hidden abstract block -->
885    
886    <div class="abstract hidden">
887      <p>Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have provided insights to understanding the generalizability in neural networks from perspectives of PAC-Bayes, robustness, overparametrization, compression and so on. In this work, we advance the understanding of the relations between the network’s architecture and its generalizability from the compression perspective. Using tensor analysis, we propose a series of intuitive, data-dependent and easily-measurable properties that tightly characterize the compressibility and generalizability of neural networks; thus, in practice, our generalization bound outperforms the previous compression-based ones, especially for neural networks using tensors as their weight kernels (e.g. CNNs). Moreover, these intuitive measurements provide further insights into designing neural network architectures with properties favorable for better/guaranteed generalizability. Our experimental results demonstrate that through the proposed measurable properties, our generalization error bound matches the trend of the test error well. Our theoretical analysis further provides justifications for the empirical success and limitations of some widely-used tensor-based compression approaches. We also discover the improvements to the compressibility and robustness of current neural networks when incorporating tensor operations via our proposed layer-wise structure.</p>
888    </div>
889    
890
891    <!-- Hidden bibtex block -->
892    
893  </div>
894</div>
895</li>
896</ol>
897
898  <h2 class="year">2019</h2>
899  <ol class="bibliography"><li>
900<div class="row">
901  <div class="col-sm-2 abbr">
902  
903    
904    <abbr class="badge">TCS</abbr>
905    
906  
907  </div>
908
909  <div id="khuller2019select" class="col-sm-8">
910    
911      <div class="title">Select and permute: An improved online framework for scheduling to minimize weighted completion time</div>
912      <div class="author">
913        
914          
915          
916          
917          
918          
919          
920            
921              
922                
923                  Khuller, Samir*,
924                
925              
926            
927          
928        
929          
930          
931          
932          
933          
934          
935            
936              
937                
938                  Li, Jingling*,
939                
940              
941            
942          
943        
944          
945          
946          
947          
948          
949          
950            
951              
952                
953                  Sturmfels, Pascal*,
954                
955              
956            
957          
958        
959          
960          
961          
962          
963          
964          
965            
966              
967                
968                  Sun, Kevin*,
969                
970              
971            
972          
973        
974          
975          
976          
977          
978          
979          
980            
981              
982                
983                  and Venkat, Prayaag*
984                
985              
986            
987          
988        
989      </div>
990
991      <div class="periodical">
992      
993        <em>Theoretical Computer Science</em>
994      
995      
996        2019
997      
998      </div>
999    
1000
1001    <div class="links">
1002    
1003    
1004    
1005    
1006    
1007    
1008    
1009    
1010    
1011    
1012    
1013    </div>
1014
1015    <!-- Hidden abstract block -->
1016    
1017
1018    <!-- Hidden bibtex block -->
1019    
1020  </div>
1021</div>
1022</li></ol>
1023
1024
1025</div>
1026
1027  </article>
1028
1029</div>
1030
1031    </div>
1032
1033    <!-- Footer -->
1034
1035    
1036<footer class="fixed-bottom">
1037  <div class="container mt-0">
1038    © Copyright 2022 Jingling  Li.
1039    Powered by <a href="http://jekyllrb.com/" target="_blank" rel="noopener noreferrer">Jekyll</a> with <a href="https://github.com/alshedivat/al-folio" target="_blank" rel="noopener noreferrer">al-folio</a> theme. Hosted by <a href="https://pages.github.com/" target="_blank" rel="noopener noreferrer">GitHub Pages</a>.
1040
1041    
1042    
1043    Last updated: November 22, 2022.
1044    
1045  </div>
1046</footer>
1047
1048
1049
1050  </body>
1051
1052  <!-- Bootsrap & MDB scripts -->
1053<script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/2.4.4/umd/popper.min.js" integrity="sha512-eUQ9hGdLjBjY3F41CScH3UX+4JDSI9zXeroz7hJ+RteoCaY+GP/LDoM8AO+Pt+DRFw3nXqsjh9Zsts8hnYv8/A==" crossorigin="anonymous"></script>
vendor: 1 bytes, line 1053
1053
1054<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.5.2/js/bootstrap.min.js" integrity="sha512-M5KW3ztuIICmVIhjSqXe01oV2bpe248gOxqmlcYrEzAvws7Pw3z6BK0iGbrwvdrUQUhi3eXgtxp5I8PDo9YfjQ==" crossorigin="anonymous"></script>
vendor: 1 bytes, line 1054
1054
1055<script src="https://cdnjs.cloudflare.com/ajax/libs/mdbootstrap/4.19.1/js/mdb.min.js" integrity="sha512-Mug9KHKmroQFMLm93zGrjhibM2z2Obg9l6qFG2qKjXEXkMp/VDkI4uju9m4QKPjWSwQ6O2qzZEnJDEeCw0Blcw==" crossorigin="anonymous"></script>
1055
1056
1057  
1058<!-- Mansory & imagesLoaded -->
1059<script defer src="https://unpkg.com/masonry-layout@4/dist/masonry.pkgd.min.js"></script>
vendor: 1 bytes, line 1059
1059
1060<script defer src="https://unpkg.com/imagesloaded@4/imagesloaded.pkgd.min.js"></script>
vendor: 1 bytes, line 1060
1060
1061<script defer src="/assets/js/mansory.js" type="text/javascript"></script>
1061
1062
1063
1064  
1065
1066
1067<!-- Medium Zoom JS -->
1068<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/medium-zoom.min.js" integrity="sha256-EdPgYcPk/IIrw7FYeuJQexva49pVRZNmt3LculEr7zM=" crossorigin="anonymous"></script>
vendor: 1 bytes, line 1068
1068
1069<script src="/assets/js/zoom.js"></script>
1069
1070
1071
1072<!-- Load Common JS -->
1073<script src="/assets/js/common.js"></script>
1073
1074
1075
1076</html>

Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.