1<html> 2 3<head> 4 <title>Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning</title> 5 <meta charset="utf-8"> 6 <meta http-equiv="X-UA-Compatible" content="IE=edge"> 7 <meta name="google-site-verification" content="xBT4GhYoi5qRD5tr338pgPM5OWHHIDR6mNg1a3euekI" /> 8 <meta name="viewport" content="width=device-width, initial-scale=1"> 9 <meta name="description" 10 content="About Machine Learning, Computer Vision, Life, Photo Gallery and Everything | Chi Zhang, Programmer, Machine Learning and Computer Vision"> 11 <meta name="keyword" content="Chi Zhang, å¼ é©°, Blog, Internet, Machine Learning, Computer Vision"> 12 <link rel="shortcut icon" href="/favicon.ico"> 13 <link href="https://fonts.googleapis.com/css?family=Lora:400,700,400italic,700italic" rel="stylesheet" 14 type="text/css"> 15 <link href="https://fonts.googleapis.com/css?family=Montserrat:400,700" rel="stylesheet" type="text/css"> 16 <link href='https://fonts.googleapis.com/css?family=Titillium+Web:400,600,400italic,600italic,300,300italic' 17 rel='stylesheet' type='text/css'> 18 <link rel="stylesheet" href="/css/project.css""> 19</head> 20 21<body> 22 23<div id=" Banner"> 24 <div height="80" id="header" style="background-color:#FFFFFF; color: #FFFFFF"> 25 <center> 26 <table width="1200" height="80" border="0"> 27 <tr> 28 <td halign="center"> 29 <p class=un>Learning Algebraic Representation for Systematic Generalization in Abstract 30 Reasoning</p> 31 <hr> 32 </td> 33 </tr> 34 </table> 35 </center> 36 </div> 37 </div> 38 39 <div id="main" 40 style="padding-bottom:1em; padding-top: 2em; width: 70em; max-width: 70em; margin-left: auto; margin-right: auto;"> 41 <center> 42 <img src="/img/in-post/ALANS/model.jpg" style="width: 100%;"> 43 </center> 44 <br> 45 <heading> 46 Abstract 47 </heading> 48 <p> 49 Is intelligence realized by connectionist or classicist? While connectionist approaches have achieved 50 superhuman performance, there has been growing evidence that such task-specific superiority is particularly 51 fragile in <i>systematic generalization</i>. This observation lies in the central debate between 52 connectionist and classicist, wherein the latter continually advocates an <i>algebraic</i> treatment in 53 cognitive architectures. In this work, we follow the classicist's call and propose a hybrid approach to 54 improve systematic generalization in reasoning. Specifically, we showcase a prototype with algebraic 55 representation for the abstract spatial-temporal reasoning task of Raven's Progressive Matrices (RPM) and 56 present the ALgebra-Aware Neuro-Semi-Symbolic (ALANS) learner. The ALANS learner is motivated by abstract 57 algebra and the representation theory. It consists of a neural visual perception frontend and an algebraic 58 abstract reasoning backend: the frontend summarizes the visual information from object-based representation, 59 while the backend transforms it into an algebraic structure and induces the hidden operator on the fly. The 60 induced operator is later executed to predict the answer's representation, and the choice most similar to 61 the prediction is selected as the solution. Extensive experiments show that by incorporating an algebraic 62 treatment, the ALANS learner outperforms various pure connectionist models in domains requiring systematic 63 generalization. We further show the generative nature of the learned algebraic representation; it can be 64 decoded by isomorphism to generate an answer. 65 </p> 66 </div> 67 68 <div id="main" 69 style="padding-bottom:0em; padding-top: 0em; width: 70em; max-width: 70em; margin-left: auto; margin-right: auto;"> 70 <heading> 71 Paper 72 </heading> 73 <p> 74 <papertitle>Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning 75 </papertitle><br>
76 Chi Zhang<sup>*</sup>, Sirui Xie<sup>*</sup>, Baoxiong Jia<sup>*</sup>, Ying Nian Wu, Song-Chun Zhu, Yixin 77 Zhu<br> 78 Proceedings of the European Conference on Computer Vision (ECCV), 2022<br> 79 (<sup>*</sup> indicates equal contribution.)<br> 80 <a href="https://drive.google.com/file/d/1KLvi_p1g3FRehAe9j2_rmXRux-uciQnZ/view?usp=sharing">Paper</a> / 81 <a href="https://drive.google.com/file/d/1cITYfNJ0UQlFE4l6ZE7gPgTcJL8jNN9H/view?usp=sharing">Supplementary</a> / 82 <a href="https://drive.google.com/file/d/1JcB0lYH_npAcGzXShEykjcQAb3RowDFT/view?usp=sharing">Poster</a> / 83 <a href="https://github.com/WellyZhang/ALANS">Code</a> / 84 <a href="/blog/2022/07/17/ALANS">Blog</a> 85 </p> 86 <p> 87 <center> 88 <a href="https://drive.google.com/file/d/1KLvi_p1g3FRehAe9j2_rmXRux-uciQnZ/view?usp=sharing"><img src="/img/project/alans_thumbnail.jpg" 89 style="width: 100%;" /></a> 90 </center> 91 </p> 92 </div> 93 94 <div id="main" 95 style="padding-bottom:0em; padding-top: 2em; width: 70em; max-width: 70em; margin-left: auto; margin-right: auto; align-content: center"> 96 <heading> 97 Team 98 </heading> 99 <div style="text-align: center; width: 100%; padding-top: 1em"> 100 <div style="display: inline-block; width: 180px;"> 101 <a href="http://wellyzhang.github.io"><img src="http://vcla.stat.ucla.edu/images/people/chiz.jpg" alt="" 102 style="border-radius: 50%; width:150px;"> 103 <p>Chi Zhang<sup>1</sup></p> 104 </a> 105 </div> 106 <div style="display: inline-block; width: 180px;"> 107 <a href="http://siruixie.com/"><img src="https://vcla.stat.ucla.edu/images/people/srxie.jpg" alt="" 108 style="border-radius: 50%; width:150px;"> 109 <p>Sirui Xie<sup>1</sup></p> 110 </a> 111 </div> 112 <div style="display: inline-block; width: 180px;"> 113 <a href="https://buzz-beater.github.io/"><img src="http://vcla.stat.ucla.edu/images/people/bxjia.jpg" 114 alt="" style="border-radius: 50%; width:150px;"> 115 <p>Baoxiong Jia<sup>1</sup></p> 116 </a> 117 </div> 118 <div style="display: inline-block; width: 180px;"> 119 <a href="http://www.stat.ucla.edu/~ywu/"><img src="https://vcla.stat.ucla.edu/images/people/ynwu.jpg" 120 alt="" style="border-radius: 50%; width:150px;"> 121 <p>Ying Nian Wu<sup>1</sup></p> 122 </a> 123 </div> 124 <div style="display: inline-block; width: 180px;"> 125 <a href="http://www.stat.ucla.edu/~sczhu/"><img 126 src="http://vcla.stat.ucla.edu/images/people/Zhu_UCLA.JPG" alt="" 127 style="border-radius: 50%; width:150px;"> 128 <p>Song-Chun Zhu<sup>1,2,3,4</sup></p> 129 </a> 130 </div> 131 <div style="display: inline-block; width: 180px;"> 132 <a href="http://www.yzhu.io/"><img src="https://vcla.stat.ucla.edu/images/people/yzhu.jpg" alt="" 133 style="border-radius: 50%; width:150px;"> 134 <p>Yixin Zhu<sup>2</sup></p> 135 </a> 136 </div> 137 </div> 138 <div style="text-align:center; width: 100%;"> 139 <div style="display: inline-block; width: 500px;"> 140 <p><sup>1 </sup>University of California, Los Angeles</p> 141 </div> 142 <div style="display: inline-block; width: 500px;"> 143 <p><sup>2 </sup>Peking University</p> 144 </div> 145 <div style="display: inline-block; width: 500px;"> 146 <p><sup>3 </sup>Tsinghua University</p> 147 </div> 148 <div style="display: inline-block; width: 500px;"> 149 <p><sup>4 </sup>Beijing Institute for General Artificial Intelligence (BIGAI)</p> 150 </div> 151 </div> 152 </div> 153 154 <div id="main" 155 style="padding-bottom:1em; padding-top: 0em; width: 80em; max-width: 70em; margin-left: auto; margin-right: auto;"> 156 <heading id="dataset"> 157 Dataset 158 </heading> 159 <p> 160 The new splits introduced in this work follow the same design in the original work of RAVEN and I-RAVEN, 161 except that the training set and the test set are sampled from different distributions of relations. All 162 the splits are of the 3x3 grid layout. See the <a href="https://drive.google.com/file/d/1cITYfNJ0UQlFE4l6ZE7gPgTcJL8jNN9H/view?usp=sharing">supplementary 163 material</a> for details. 164 </p> 165 <p> 166 Download the dataset from <a 167 href="https://drive.google.com/file/d/1dSUN5vmEK_1Rg-8Wwd8ZhUzB-i4Un-ZH/view?usp=sharing">Google Drive</a> or <a 168 href="https://pan.baidu.com/s/1OfQvskolholphXimqxAXdw?pwd=b2te">BaiduNetdisk</a>. The 169 zip file contains six folders (Systematicity, Productivity, and Localism for the two data-generating 170 methods). Those starting with "I" are generated from the I-RAVEN method. 171 </p> 172 </div> 173 174 <div id="main" 175 style="padding-bottom:1em; padding-top: 0em; width: 80em; max-width: 70em; margin-left: auto; margin-right: auto;"> 176 <heading> 177 Code 178 </heading> 179 <p> 180 View on <a href="https://github.com/WellyZhang/ALANS">GitHub</a> 181 </p> 182 </div> 183 184 <div id="main" 185 style="padding-bottom:1em; padding-top: 0em; width: 80em; max-width: 70em; margin-left: auto; margin-right: auto;"> 186 <heading> 187 Bibtex 188 </heading> 189 <p class=bibtax> 190 @inproceedings{zhang2022learning, 191 <br> title={Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning}, 192 <br> 
192author={Zhang, Chi and Xie, Sirui and Jia, Baoxiong and Wu, Ying Nian and Zhu, Song-Chun and Zhu, 193 Yixin}, 194 <br> booktitle={Proceedings of the European Conference on Computer Vision (ECCV)}, 195 <br> year={2022} 196 <br>} 197 </p> 198 </div> 199 200 </body> 201 202</html>
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