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<script src="http://www.google.com/jsapi" type="text/javascript"></script>
<script type="text/javascript">google.load("jquery", "1.3.2");</script>
<style type="text/css">
body {
font-family: "HelveticaNeue-Light", "Helvetica Neue Light", "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;
font-weight:300;
font-size:18px;
margin-left: auto;
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</style>
<html>
<head>
<title>CATWalk</title>
<meta property="og:image" content="Path to my teaser.png"/> <!-- Facebook automatically scrapes this. Go to https://developers.facebook.com/tools/debug/ if you update and want to force Facebook to rescrape. -->
<meta property="og:title" content="Creative and Descriptive Paper Title." />
<meta property="og:description" content="Paper description." />
<!-- Get from Google Analytics -->
<!-- Global site tag (gtag.js) - Google Analytics -->
<script async src=""></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());
gtag('config', 'UA-75863369-6');
</script>
</head>
<body>
<br>
<center>
<span style="font-size:36px">CAT-Walk: Inductive Hypergraph Learning via Set Walks</span>
<br>
<br>
<table align=center width=1200px>
<table align=center width=900px>
<tr>
<td align=center width=300px>
<center>
<span style="font-size:24px"><a href="https://abehrouz.github.io/">Ali Behrouz</a></span>
</center>
</td>
<td align=center width=300px>
<center>
<span style="font-size:24px"><a href="https://farnooshha.github.io/">Farnoosh Hashemi*</a></span>
</center>
</td>
<td align=center width=300px>
<center>
<span style="font-size:24px"><a href="https://www.linkedin.com/in/sadaf-sadeghian-53b8b4174/">Sadaf Sadeghian*</a></span>
</center>
</td>
<td align=center width=300px>
<center>
<span style="font-size:24px"><a href="https://www.seltzer.com/margo/">Margo Seltzer</a></span>
</center>
</td>
</tr>
</table>
<br>
<table align=center width=490px>
<tr>
<td align=center width=120px>
<center>
<span style="font-size:24px"><a href='https://openreview.net/pdf?id=QG4nJBNEar'>[Paper]</a></span>
</center>
</td>
<td align=center width=120px>
<center>
<span style="font-size:24px"><a href='https://github.com/ubc-systopia/CATWalk'>[Code]</a></span>
</center>
</td>
<td align=center width=120px>
<center>
<span style="font-size:24px"><a href='./resources/bibtex.txt'>[Bibtex]</a></span>
</center>
</td>
<td align=center width=120px>
<center>
<span style="font-size:24px"><a href='./resources/Slides.pdf'>[Slides]</a></span><br>
</center>
</td>
</tr>
</table>
<br>
<table align=center width=490px>
<tr>
<td align=center width=120px>
<center>
<span style="font-size:24px">NeurIPS 2023</span>
</center>
</td>
</tr>
</table>
</table>
</center>
<br>
<br>
<center>
<table align=center width=1200px>
<tr>
<td width=600px>
<center>
<img class="round" style="width:950px" src="./resources/teaser.png"/>
</center>
</td>
</tr>
</table>
<!-- <table align=center width=850px>
<tr>
<td>
This was a template originally made for <a href="http://richzhang.github.io/colorization/">Colorful Image Colorization</a>. The code can be found in this <a href="https://github.com/richzhang/webpage-template">repository</a>.
</td>
</tr>
</table> -->
</center>
<hr>
<table align=center width=850px>
<center><h1>Abstract</h1></center>
<tr>
<td>
<p align="justify">Temporal hypergraphs provide a powerful paradigm for modeling time-dependent, higher-order interactions in complex systems. Representation learning for hypergraphs is essential for extracting patterns of the higher-order interactions that are critically important in real-world problems in social network analysis, neuroscience, finance, etc. However, existing methods are typically designed only for specific tasks or static hypergraphs. We present CAT-Walk, an inductive method that learns the underlying dynamic laws that govern the temporal and structural processes underlying a temporal hypergraph. CAT-Walk introduces a temporal, higher-order walk on hypergraphs, SetWalk, that extracts higher-order causal patterns. CAT-Walk uses a novel adaptive and permutation invariant pooling strategy, SetMixer, along with a set-based anonymization process that hides the identity of hyperedges. Finally, we present a simple yet effective neural network model to encode hyperedges. Our evaluation on 10 hypergraph benchmark datasets shows that CAT-Walk attains outstanding performance on temporal hyperedge prediction benchmarks in both inductive and transductive settings. It also shows competitive performance with state-of-the-art methods for node classification.</p>
</td>
</tr>
</table>
<br>
<hr>
<center><h1>Talk</h1></center>
<center><h3>Talk will be available soon!</h3></center>
<!-- <p align="center"> -->
<!-- <iframe width="660" height="395" src="https://www.youtube.com/embed/dQw4w9WgXcQ" frameborder="0" allow="autoplay; encrypted-media" allowfullscreen align="center"></iframe> -->
<!-- </p> -->
<hr>
<table align=center width=850px>
<center><h1>Motivation</h1></center>
<tr>
<td>
<h3>Capturing underlying temporal and higher-order structure</h3>
<p align="justify"> Many recent attempts to design representation learning methods for hypergraphs are equivalent to applying Graph Neural Networks (GNNs) to the clique-expansion (CE) of a hypergraph. CE is a straightforward way to generalize graph algorithms to hypergraphs by replacing hyperedges with (weighted) cliques. However, we prove that this decomposition of hyperedges limits expressiveness, leading to suboptimal performance. New methods that encode hypergraphs directly partially address this issue but these methods suffer from some combination of the following three limitations: they are designed for (1) learning the structural properties of static hypergraphs and do not consider temporal properties, (2) the transductive setting, limiting their performance on unseen patterns and data, and (3) a specific downstream task (e.g., node classification, hyperedge prediction, or subgraph classification) and cannot easily be extended to other downstream tasks, limiting their application. To address these challenges, we propose a higher-order temporal walk, called SetWalk, to capture both higher-order and temporal properties, and then design a provably powerful permutation invariant pooling method to learn the hyperedge representations. </p>
<br>
<h3>SetWalks</h3>
<p align="justify"> One possible solution to capturing underlying temporal and higher-order structure is to extend the concept of a hypergraph random walk to its temporal counterpart by letting the walker walk over time. However, existing definitions of random walks on hypergraphs offer limited expressivity and sometimes degenerate to simple walks on the CE of the hypergraph. There are two reasons for this: (1) Random walks are composed of a sequence of pair-wise interconnected vertices, even though edges in a hypergraph connect sets of vertices. Decomposing them into sequences of simple pair-wise interactions loses the semantic meaning of the hyperedges. (2) A sampling probability of a walk on a hypergraph must be different from its sampling probability on the CE of the hypergraph. To this end, we present a new temporal higher-order walks, called SetWalk, where each random walk is a sequence of hyperedges (i.e., in each step of walk sampling, we sample an adjacent hyperedge). </p>
<br>
<h3>SetMixer</h3>
<p align="justify"> </p>
</td>
</tr>
</table>
<br>
<hr>
<table align=center width=850px>
<center><h1>Method</h1></center>
<tr>
<center>
<table align=center width=1200px>
<tr>
<td width=600px>
<center>
<img class="round" style="width:800px" src="./resources/method_diagram.png"/>
</center>
</td>
</tr>
</table>
</center>
</tr>
</table>
<br>
<hr>
<table align=center width=850px>
<center><h1>Experiments</h1></center>
<tr>
<td>
<h3>Hyperedge Prediction:</h3>
<p align="justify"> </p>
<center>
<table align=center width=1200px>
<tr>
<td width=600px>
<center>
<img class="round" style="width:900px" src="./resources/he_result.png"/>
</center>
</td>
</tr>
</table>
</center>
<br>
<h3>Node Classification:</h3>
<p align="justify"> </p>
<center>
<table align=center width=1200px>
<tr>
<td width=600px>
<center>
<img class="round" style="width:550px" src="./resources/node_result.png"/>
</center>
</td>
</tr>
</table>
</center>
<br>
<h3>MLP-Mixer vs RNNs:</h3>
<p align="justify"> </p>
<center>
<table align=center width=1200px>
<tr>
<td width=600px>
<center>
<img class="round" style="width:800px" src="./resources/rnn_result.png"/>
</center>
</td>
</tr>
</table>
</center>
</td>
</tr>
</table>
<br>
<hr>
<table align=center width=800px>
<br>
<tr><center>
<span style="font-size:28px"> <a href='https://github.com/ubc-systopia/CATWalk'>Code, Data, and Trained Models</a>
</center>
</span>
</table>
<table align=center width=400px>
<tr>
<td align=center width=400px>
<center>
<a href="https://github.com/ubc-systopia/CATWalk">
<img class="round" style="width:300px" src="./resources/Github.png"/>
</a>
</center>
</td>
</tr>
</table>
<br>
<hr>
<table align=center width=1000px>
<center><h1>Paper and Supplementary Material</h1></center>
<tr>
<td><a href=""><img class="layered-paper-big" style="height:175px" src="./resources/paper.png"/></a></td>
<td><span style="font-size:14pt">A. Behrouz, F. Hashemi, S. Sadeghian, M. Seltzer.<br>
<b>CAT-Walk: Inductive Hypergraph Learning via Set Walks.</b><br>
In Thirty-seventh Conference on Neural Information Processing Systems, NeurIPS 2023.<br>
(<a href="https://openreview.net/forum?id=QG4nJBNEar">Openreview</a>)<br>
<!-- (<a href="./resources/camera-ready.pdf">camera ready</a>)<br> -->
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</td>
</tr>
</table>
<br>
<hr>
<br>
<table align=center width=900px>
<tr>
<td width=400px>
<left>
<center><h1>Acknowledgements</h1></center>
This template was originally made by <a href="http://web.mit.edu/phillipi/">Phillip Isola</a> and <a href="http://richzhang.github.io/">Richard Zhang</a> for a <a href="http://richzhang.github.io/colorization/">colorful</a> ECCV project; the code can be found <a href="https://github.com/richzhang/webpage-template">here</a>.
</left>
</td>
</tr>
</table>
<br>
</body>
</html>