modeling conversation structure and temporal dynamics for ...4789 qazvinian et al.,2011;procter et...

Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processingand the 9th International Joint Conference on Natural Language Processing, pages 4787–4798,Hong Kong, China, November 3–7, 2019. c©2019 Association for Computational Linguistics

4787

Modeling Conversation Structure and Temporal Dynamics for JointlyPredicting Rumor Stance and Veracity

Penghui Wei, Nan Xu, Wenji Mao†SKL-MCCS, Institute of Automation, Chinese Academy of Sciences (CASIA)

‡University of Chinese Academy of Sciences{weipenghui2016,xunan2015,wenji.mao}@ia.ac.cn

Abstract

Automatically verifying rumorous informa-tion has become an important and challeng-ing task in natural language processing and so-cial media analytics. Previous studies revealthat people’s stances towards rumorous mes-sages can provide indicative clues for identi-fying the veracity of rumors, and thus deter-mining the stances of public reactions is a cru-cial preceding step for rumor veracity predic-tion. In this paper, we propose a hierarchicalmulti-task learning framework for jointly pre-dicting rumor stance and veracity on Twitter,which consists of two components. The bot-tom component of our framework classifies thestances of tweets in a conversation discussinga rumor via modeling the structural propertybased on a novel graph convolutional network.The top component predicts the rumor veracityby exploiting the temporal dynamics of stanceevolution. Experimental results on two bench-mark datasets show that our method outper-forms previous methods in both rumor stanceclassification and veracity prediction.

1 Introduction

Social media websites have become the main plat-form for users to browse information and shareopinions, facilitating news dissemination greatly.However, the characteristics of social media alsoaccelerate the rapid spread and dissemination of un-verified information, i.e., rumors (Shu et al., 2017).The definition of rumor is “items of informationthat are unverified at the time of posting” (Zubi-aga et al., 2018). Ubiquitous false rumors bringabout harmful effects, which has seriously affectedpublic and individual lives, and caused panic insociety (Zhou and Zafarani, 2018; Sharma et al.,2019). Because online content is massive and de-bunking rumors manually is time-consuming, thereis a great need for automatic methods to identifyfalse rumors (Oshikawa et al., 2018).

Timeline1

2

3

4

5

6

Source tweet (originating a rumor): 1. Reply tweets: 2, 3, 4, 5, and 6.

Support<latexit sha1_base64="LmF7uylmEdUT0h/2SzQhZJC2F10=">AAAB7nicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48RzQOSJcxOZpMhszPDTK8QQj7CiwdFvPo93vwbJ8keNLGgoajqprsr1oJbDIJvr7C2vrG5Vdwu7ezu7R+UD4+aVmWGsgZVQpl2TCwTXLIGchSsrQ0jaSxYKx7dzvzWEzOWK/mIY82ilAwkTzgl6KTWQ6a1MtgrV4JqMIe/SsKcVCBHvVf+6vYVzVImkQpibScMNEYTYpBTwaalbmaZJnREBqzjqCQps9Fkfu7UP3NK30+UcSXRn6u/JyYktXacxq4zJTi0y95M/M/rZJhcRxMudYZM0sWiJBM+Kn/2u9/nhlEUY0cINdzd6tMhMYSiS6jkQgiXX14lzYtqGFTD+8tK7SaPowgncArnEMIV1OAO6tAACiN4hld487T34r17H4vWgpfPHMMfeJ8/nimPvQ==</latexit><latexit sha1_base64="LmF7uylmEdUT0h/2SzQhZJC2F10=">AAAB7nicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48RzQOSJcxOZpMhszPDTK8QQj7CiwdFvPo93vwbJ8keNLGgoajqprsr1oJbDIJvr7C2vrG5Vdwu7ezu7R+UD4+aVmWGsgZVQpl2TCwTXLIGchSsrQ0jaSxYKx7dzvzWEzOWK/mIY82ilAwkTzgl6KTWQ6a1MtgrV4JqMIe/SsKcVCBHvVf+6vYVzVImkQpibScMNEYTYpBTwaalbmaZJnREBqzjqCQps9Fkfu7UP3NK30+UcSXRn6u/JyYktXacxq4zJTi0y95M/M/rZJhcRxMudYZM0sWiJBM+Kn/2u9/nhlEUY0cINdzd6tMhMYSiS6jkQgiXX14lzYtqGFTD+8tK7SaPowgncArnEMIV1OAO6tAACiN4hld487T34r17H4vWgpfPHMMfeJ8/nimPvQ==</latexit><latexit sha1_base64="LmF7uylmEdUT0h/2SzQhZJC2F10=">AAAB7nicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48RzQOSJcxOZpMhszPDTK8QQj7CiwdFvPo93vwbJ8keNLGgoajqprsr1oJbDIJvr7C2vrG5Vdwu7ezu7R+UD4+aVmWGsgZVQpl2TCwTXLIGchSsrQ0jaSxYKx7dzvzWEzOWK/mIY82ilAwkTzgl6KTWQ6a1MtgrV4JqMIe/SsKcVCBHvVf+6vYVzVImkQpibScMNEYTYpBTwaalbmaZJnREBqzjqCQps9Fkfu7UP3NK30+UcSXRn6u/JyYktXacxq4zJTi0y95M/M/rZJhcRxMudYZM0sWiJBM+Kn/2u9/nhlEUY0cINdzd6tMhMYSiS6jkQgiXX14lzYtqGFTD+8tK7SaPowgncArnEMIV1OAO6tAACiN4hld487T34r17H4vWgpfPHMMfeJ8/nimPvQ==</latexit><latexit sha1_base64="LmF7uylmEdUT0h/2SzQhZJC2F10=">AAAB7nicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48RzQOSJcxOZpMhszPDTK8QQj7CiwdFvPo93vwbJ8keNLGgoajqprsr1oJbDIJvr7C2vrG5Vdwu7ezu7R+UD4+aVmWGsgZVQpl2TCwTXLIGchSsrQ0jaSxYKx7dzvzWEzOWK/mIY82ilAwkTzgl6KTWQ6a1MtgrV4JqMIe/SsKcVCBHvVf+6vYVzVImkQpibScMNEYTYpBTwaalbmaZJnREBqzjqCQps9Fkfu7UP3NK30+UcSXRn6u/JyYktXacxq4zJTi0y95M/M/rZJhcRxMudYZM0sWiJBM+Kn/2u9/nhlEUY0cINdzd6tMhMYSiS6jkQgiXX14lzYtqGFTD+8tK7SaPowgncArnEMIV1OAO6tAACiN4hld487T34r17H4vWgpfPHMMfeJ8/nimPvQ==</latexit>

Deny<latexit sha1_base64="8ekNGixclA8ONaWdNJoQQqMbz68=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNRDx4r2A9oQ9lsJ+3SzSbsboRQ+he8eFDEq3/Im//GTZuDtj4YeLw3w8y8IBFcG9f9dkpr6xubW+Xtys7u3v5B9fCoreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJbe53nlBpHstHkyXoR3QkecgZNbl0hzIbVGtu3Z2DrBKvIDUo0BxUv/rDmKURSsME1brnuYnxp1QZzgTOKv1UY0LZhI6wZ6mkEWp/Or91Rs6sMiRhrGxJQ+bq74kpjbTOosB2RtSM9bKXi/95vdSE1/6UyyQ1KNliUZgKYmKSP06GXCEzIrOEMsXtrYSNqaLM2HgqNgRv+eVV0r6oe27de7isNW6KOMpwAqdwDh5cQQPuoQktYDCGZ3iFNydyXpx352PRWnKKmWP4A+fzB/9tjjI=</latexit><latexit sha1_base64="8ekNGixclA8ONaWdNJoQQqMbz68=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNRDx4r2A9oQ9lsJ+3SzSbsboRQ+he8eFDEq3/Im//GTZuDtj4YeLw3w8y8IBFcG9f9dkpr6xubW+Xtys7u3v5B9fCoreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJbe53nlBpHstHkyXoR3QkecgZNbl0hzIbVGtu3Z2DrBKvIDUo0BxUv/rDmKURSsME1brnuYnxp1QZzgTOKv1UY0LZhI6wZ6mkEWp/Or91Rs6sMiRhrGxJQ+bq74kpjbTOosB2RtSM9bKXi/95vdSE1/6UyyQ1KNliUZgKYmKSP06GXCEzIrOEMsXtrYSNqaLM2HgqNgRv+eVV0r6oe27de7isNW6KOMpwAqdwDh5cQQPuoQktYDCGZ3iFNydyXpx352PRWnKKmWP4A+fzB/9tjjI=</latexit><latexit sha1_base64="8ekNGixclA8ONaWdNJoQQqMbz68=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNRDx4r2A9oQ9lsJ+3SzSbsboRQ+he8eFDEq3/Im//GTZuDtj4YeLw3w8y8IBFcG9f9dkpr6xubW+Xtys7u3v5B9fCoreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJbe53nlBpHstHkyXoR3QkecgZNbl0hzIbVGtu3Z2DrBKvIDUo0BxUv/rDmKURSsME1brnuYnxp1QZzgTOKv1UY0LZhI6wZ6mkEWp/Or91Rs6sMiRhrGxJQ+bq74kpjbTOosB2RtSM9bKXi/95vdSE1/6UyyQ1KNliUZgKYmKSP06GXCEzIrOEMsXtrYSNqaLM2HgqNgRv+eVV0r6oe27de7isNW6KOMpwAqdwDh5cQQPuoQktYDCGZ3iFNydyXpx352PRWnKKmWP4A+fzB/9tjjI=</latexit><latexit sha1_base64="8ekNGixclA8ONaWdNJoQQqMbz68=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNRDx4r2A9oQ9lsJ+3SzSbsboRQ+he8eFDEq3/Im//GTZuDtj4YeLw3w8y8IBFcG9f9dkpr6xubW+Xtys7u3v5B9fCoreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJbe53nlBpHstHkyXoR3QkecgZNbl0hzIbVGtu3Z2DrBKvIDUo0BxUv/rDmKURSsME1brnuYnxp1QZzgTOKv1UY0LZhI6wZ6mkEWp/Or91Rs6sMiRhrGxJQ+bq74kpjbTOosB2RtSM9bKXi/95vdSE1/6UyyQ1KNliUZgKYmKSP06GXCEzIrOEMsXtrYSNqaLM2HgqNgRv+eVV0r6oe27de7isNW6KOMpwAqdwDh5cQQPuoQktYDCGZ3iFNydyXpx352PRWnKKmWP4A+fzB/9tjjI=</latexit>

Query<latexit sha1_base64="tcn3XJLk8U1N6KP5fFc5SCaEEKE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cWTFtoQ9lsp+3SzSbsboQQ+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dkobm1vbO+Xdyt7+weFR9fikreNUMfRZLGLVDalGwSX6hhuB3UQhjUKBnXB6P/c7T6g0j+WjyRIMIjqWfMQZNVbyWymqbFCtuXV3AbJOvILUoEBzUP3qD2OWRigNE1TrnucmJsipMpwJnFX6qcaEsikdY89SSSPUQb44dkYurDIko1jZkoYs1N8TOY20zqLQdkbUTPSqNxf/83qpGd0GOZdJalCy5aJRKoiJyfxzMuQKmRGZJZQpbm8lbEIVZcbmU7EheKsvr5P2Vd1z617ruta4K+IowxmcwyV4cAMNeIAm+MCAwzO8wpsjnRfn3flYtpacYuYU/sD5/AHxWY7C</latexit><latexit sha1_base64="tcn3XJLk8U1N6KP5fFc5SCaEEKE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cWTFtoQ9lsp+3SzSbsboQQ+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dkobm1vbO+Xdyt7+weFR9fikreNUMfRZLGLVDalGwSX6hhuB3UQhjUKBnXB6P/c7T6g0j+WjyRIMIjqWfMQZNVbyWymqbFCtuXV3AbJOvILUoEBzUP3qD2OWRigNE1TrnucmJsipMpwJnFX6qcaEsikdY89SSSPUQb44dkYurDIko1jZkoYs1N8TOY20zqLQdkbUTPSqNxf/83qpGd0GOZdJalCy5aJRKoiJyfxzMuQKmRGZJZQpbm8lbEIVZcbmU7EheKsvr5P2Vd1z617ruta4K+IowxmcwyV4cAMNeIAm+MCAwzO8wpsjnRfn3flYtpacYuYU/sD5/AHxWY7C</latexit><latexit sha1_base64="tcn3XJLk8U1N6KP5fFc5SCaEEKE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cWTFtoQ9lsp+3SzSbsboQQ+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dkobm1vbO+Xdyt7+weFR9fikreNUMfRZLGLVDalGwSX6hhuB3UQhjUKBnXB6P/c7T6g0j+WjyRIMIjqWfMQZNVbyWymqbFCtuXV3AbJOvILUoEBzUP3qD2OWRigNE1TrnucmJsipMpwJnFX6qcaEsikdY89SSSPUQb44dkYurDIko1jZkoYs1N8TOY20zqLQdkbUTPSqNxf/83qpGd0GOZdJalCy5aJRKoiJyfxzMuQKmRGZJZQpbm8lbEIVZcbmU7EheKsvr5P2Vd1z617ruta4K+IowxmcwyV4cAMNeIAm+MCAwzO8wpsjnRfn3flYtpacYuYU/sD5/AHxWY7C</latexit><latexit sha1_base64="tcn3XJLk8U1N6KP5fFc5SCaEEKE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cWTFtoQ9lsp+3SzSbsboQQ+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dkobm1vbO+Xdyt7+weFR9fikreNUMfRZLGLVDalGwSX6hhuB3UQhjUKBnXB6P/c7T6g0j+WjyRIMIjqWfMQZNVbyWymqbFCtuXV3AbJOvILUoEBzUP3qD2OWRigNE1TrnucmJsipMpwJnFX6qcaEsikdY89SSSPUQb44dkYurDIko1jZkoYs1N8TOY20zqLQdkbUTPSqNxf/83qpGd0GOZdJalCy5aJRKoiJyfxzMuQKmRGZJZQpbm8lbEIVZcbmU7EheKsvr5P2Vd1z617ruta4K+IowxmcwyV4cAMNeIAm+MCAwzO8wpsjnRfn3flYtpacYuYU/sD5/AHxWY7C</latexit>

Comment<latexit sha1_base64="DMnalIG6O30mTYHReP1CxLydbXY=">AAAB7nicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMtiNy4r2Ae0Q8mkmTY0jyHJCGXoR7hxoYhbv8edf2OmnYW2HggczrmH3HuihDNjff/bK21sbm3vlHcre/sHh0fV45OOUakmtE0UV7oXYUM5k7RtmeW0l2iKRcRpN5o2c7/7RLVhSj7aWUJDgceSxYxg66RuUwlBpR1Wa37dXwCtk6AgNSjQGla/BiNF0jxLODamH/iJDTOsLSOcziuD1NAEkyke076jEgtqwmyx7hxdOGWEYqXdkxYt1N+JDAtjZiJykwLbiVn1cvE/r5/a+DbMmExSSyVZfhSnHFmF8tvRiGlKLJ85golmbldEJlhjYl1DFVdCsHryOulc1QO/Hjxc1xp3RR1lOINzuIQAbqAB99CCNhCYwjO8wpuXeC/eu/exHC15ReYU/sD7/AFd1o+T</latexit><latexit sha1_base64="DMnalIG6O30mTYHReP1CxLydbXY=">AAAB7nicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMtiNy4r2Ae0Q8mkmTY0jyHJCGXoR7hxoYhbv8edf2OmnYW2HggczrmH3HuihDNjff/bK21sbm3vlHcre/sHh0fV45OOUakmtE0UV7oXYUM5k7RtmeW0l2iKRcRpN5o2c7/7RLVhSj7aWUJDgceSxYxg66RuUwlBpR1Wa37dXwCtk6AgNSjQGla/BiNF0jxLODamH/iJDTOsLSOcziuD1NAEkyke076jEgtqwmyx7hxdOGWEYqXdkxYt1N+JDAtjZiJykwLbiVn1cvE/r5/a+DbMmExSSyVZfhSnHFmF8tvRiGlKLJ85golmbldEJlhjYl1DFVdCsHryOulc1QO/Hjxc1xp3RR1lOINzuIQAbqAB99CCNhCYwjO8wpuXeC/eu/exHC15ReYU/sD7/AFd1o+T</latexit><latexit sha1_base64="DMnalIG6O30mTYHReP1CxLydbXY=">AAAB7nicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMtiNy4r2Ae0Q8mkmTY0jyHJCGXoR7hxoYhbv8edf2OmnYW2HggczrmH3HuihDNjff/bK21sbm3vlHcre/sHh0fV45OOUakmtE0UV7oXYUM5k7RtmeW0l2iKRcRpN5o2c7/7RLVhSj7aWUJDgceSxYxg66RuUwlBpR1Wa37dXwCtk6AgNSjQGla/BiNF0jxLODamH/iJDTOsLSOcziuD1NAEkyke076jEgtqwmyx7hxdOGWEYqXdkxYt1N+JDAtjZiJykwLbiVn1cvE/r5/a+DbMmExSSyVZfhSnHFmF8tvRiGlKLJ85golmbldEJlhjYl1DFVdCsHryOulc1QO/Hjxc1xp3RR1lOINzuIQAbqAB99CCNhCYwjO8wpuXeC/eu/exHC15ReYU/sD7/AFd1o+T</latexit><latexit sha1_base64="DMnalIG6O30mTYHReP1CxLydbXY=">AAAB7nicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMtiNy4r2Ae0Q8mkmTY0jyHJCGXoR7hxoYhbv8edf2OmnYW2HggczrmH3HuihDNjff/bK21sbm3vlHcre/sHh0fV45OOUakmtE0UV7oXYUM5k7RtmeW0l2iKRcRpN5o2c7/7RLVhSj7aWUJDgceSxYxg66RuUwlBpR1Wa37dXwCtk6AgNSjQGla/BiNF0jxLODamH/iJDTOsLSOcziuD1NAEkyke076jEgtqwmyx7hxdOGWEYqXdkxYt1N+JDAtjZiJykwLbiVn1cvE/r5/a+DbMmExSSyVZfhSnHFmF8tvRiGlKLJ85golmbldEJlhjYl1DFVdCsHryOulc1QO/Hjxc1xp3RR1lOINzuIQAbqAB99CCNhCYwjO8wpuXeC/eu/exHC15ReYU/sD7/AFd1o+T</latexit>



Stance1

2

3

4

5

6

Sequential based:

Temporal based:

Aggregation based:

1! 2! 5, 1! 2! 4! 6<latexit sha1_base64="kDIHHf0RWbPC/QkBBl3vI8szd3Q=">AAACI3icbVC7TsMwFHV4lvIKMLJYVEgMqEqq8hBTBQtjkehDaqLKcdzWquMEP5CqqP/Cwq+wMIAqFgb+BafNAG2vZOvonHuvfU6QMCqV43xbK6tr6xubha3i9s7u3r59cNiUsRaYNHDMYtEOkCSMctJQVDHSTgRBUcBIKxjeZXrrmQhJY/6oRgnxI9TntEcxUobq2jeup2LoaR4Ske1IK+OMuDj3njQK4XK1ml2XXbvklJ1pwUXg5qAE8qp37YkXxlhHhCvMkJQd10mUnyKhKGZkXPS0JAnCQ9QnHQM5ioj006nHMTw1TAh7sTCHKzhl/06kKJJyFAWmM0JqIOe1jFymdbTqXfsp5YlWhOPZQz3NoLGYBQZDKghWbGQAwoKav0I8QAJhZWItmhDcecuLoFkpu07ZfaiWard5HAVwDE7AGXDBFaiBe1AHDYDBC3gDH+DTerXerYn1NWtdsfKZI/CvrJ9fyVOjtg==</latexit><latexit sha1_base64="kDIHHf0RWbPC/QkBBl3vI8szd3Q=">AAACI3icbVC7TsMwFHV4lvIKMLJYVEgMqEqq8hBTBQtjkehDaqLKcdzWquMEP5CqqP/Cwq+wMIAqFgb+BafNAG2vZOvonHuvfU6QMCqV43xbK6tr6xubha3i9s7u3r59cNiUsRaYNHDMYtEOkCSMctJQVDHSTgRBUcBIKxjeZXrrmQhJY/6oRgnxI9TntEcxUobq2jeup2LoaR4Ske1IK+OMuDj3njQK4XK1ml2XXbvklJ1pwUXg5qAE8qp37YkXxlhHhCvMkJQd10mUnyKhKGZkXPS0JAnCQ9QnHQM5ioj006nHMTw1TAh7sTCHKzhl/06kKJJyFAWmM0JqIOe1jFymdbTqXfsp5YlWhOPZQz3NoLGYBQZDKghWbGQAwoKav0I8QAJhZWItmhDcecuLoFkpu07ZfaiWard5HAVwDE7AGXDBFaiBe1AHDYDBC3gDH+DTerXerYn1NWtdsfKZI/CvrJ9fyVOjtg==</latexit><latexit sha1_base64="kDIHHf0RWbPC/QkBBl3vI8szd3Q=">AAACI3icbVC7TsMwFHV4lvIKMLJYVEgMqEqq8hBTBQtjkehDaqLKcdzWquMEP5CqqP/Cwq+wMIAqFgb+BafNAG2vZOvonHuvfU6QMCqV43xbK6tr6xubha3i9s7u3r59cNiUsRaYNHDMYtEOkCSMctJQVDHSTgRBUcBIKxjeZXrrmQhJY/6oRgnxI9TntEcxUobq2jeup2LoaR4Ske1IK+OMuDj3njQK4XK1ml2XXbvklJ1pwUXg5qAE8qp37YkXxlhHhCvMkJQd10mUnyKhKGZkXPS0JAnCQ9QnHQM5ioj006nHMTw1TAh7sTCHKzhl/06kKJJyFAWmM0JqIOe1jFymdbTqXfsp5YlWhOPZQz3NoLGYBQZDKghWbGQAwoKav0I8QAJhZWItmhDcecuLoFkpu07ZfaiWard5HAVwDE7AGXDBFaiBe1AHDYDBC3gDH+DTerXerYn1NWtdsfKZI/CvrJ9fyVOjtg==</latexit><latexit sha1_base64="kDIHHf0RWbPC/QkBBl3vI8szd3Q=">AAACI3icbVC7TsMwFHV4lvIKMLJYVEgMqEqq8hBTBQtjkehDaqLKcdzWquMEP5CqqP/Cwq+wMIAqFgb+BafNAG2vZOvonHuvfU6QMCqV43xbK6tr6xubha3i9s7u3r59cNiUsRaYNHDMYtEOkCSMctJQVDHSTgRBUcBIKxjeZXrrmQhJY/6oRgnxI9TntEcxUobq2jeup2LoaR4Ske1IK+OMuDj3njQK4XK1ml2XXbvklJ1pwUXg5qAE8qp37YkXxlhHhCvMkJQd10mUnyKhKGZkXPS0JAnCQ9QnHQM5ioj006nHMTw1TAh7sTCHKzhl/06kKJJyFAWmM0JqIOe1jFymdbTqXfsp5YlWhOPZQz3NoLGYBQZDKghWbGQAwoKav0I8QAJhZWItmhDcecuLoFkpu07ZfaiWard5HAVwDE7AGXDBFaiBe1AHDYDBC3gDH+DTerXerYn1NWtdsfKZI/CvrJ9fyVOjtg==</latexit>

1<latexit sha1_base64="l9eImvYcFOKpzEDji/n9jPDeWb8=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==</latexit><latexit sha1_base64="l9eImvYcFOKpzEDji/n9jPDeWb8=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==</latexit><latexit sha1_base64="l9eImvYcFOKpzEDji/n9jPDeWb8=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==</latexit><latexit sha1_base64="l9eImvYcFOKpzEDji/n9jPDeWb8=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==</latexit>

2<latexit sha1_base64="xAoQ0JyvZfnKwgaw5bZ39aOSpsA=">AAAB9HicbVDLSsNAFL2pr1pfVZdugkVwVZIi6LLoxmUF+4A2lMnkph06mcSZSaGEfocbF4q49WPc+TdO2iy09cDA4Zx7uHeOn3CmtON8W6WNza3tnfJuZW//4PCoenzSUXEqKbZpzGPZ84lCzgS2NdMce4lEEvkcu/7kLve7U5SKxeJRzxL0IjISLGSUaCN5g1QEKPNw1pgPqzWn7ixgrxO3IDUo0BpWvwZBTNMIhaacKNV3nUR7GZGaUY7zyiBVmBA6ISPsGypIhMrLFkfP7QujBHYYS/OEthfq70RGIqVmkW8mI6LHatXLxf+8fqrDGy9jIkk1CrpcFKbc1rGdN2AHTCLVfGYIoZKZW206JpJQbXqqmBLc1S+vk06j7jp19+Gq1rwt6ijDGZzDJbhwDU24hxa0gcITPMMrvFlT68V6tz6WoyWryJzCH1ifPxNkkkg=</latexit><latexit sha1_base64="xAoQ0JyvZfnKwgaw5bZ39aOSpsA=">AAAB9HicbVDLSsNAFL2pr1pfVZdugkVwVZIi6LLoxmUF+4A2lMnkph06mcSZSaGEfocbF4q49WPc+TdO2iy09cDA4Zx7uHeOn3CmtON8W6WNza3tnfJuZW//4PCoenzSUXEqKbZpzGPZ84lCzgS2NdMce4lEEvkcu/7kLve7U5SKxeJRzxL0IjISLGSUaCN5g1QEKPNw1pgPqzWn7ixgrxO3IDUo0BpWvwZBTNMIhaacKNV3nUR7GZGaUY7zyiBVmBA6ISPsGypIhMrLFkfP7QujBHYYS/OEthfq70RGIqVmkW8mI6LHatXLxf+8fqrDGy9jIkk1CrpcFKbc1rGdN2AHTCLVfGYIoZKZW206JpJQbXqqmBLc1S+vk06j7jp19+Gq1rwt6ijDGZzDJbhwDU24hxa0gcITPMMrvFlT68V6tz6WoyWryJzCH1ifPxNkkkg=</latexit><latexit sha1_base64="xAoQ0JyvZfnKwgaw5bZ39aOSpsA=">AAAB9HicbVDLSsNAFL2pr1pfVZdugkVwVZIi6LLoxmUF+4A2lMnkph06mcSZSaGEfocbF4q49WPc+TdO2iy09cDA4Zx7uHeOn3CmtON8W6WNza3tnfJuZW//4PCoenzSUXEqKbZpzGPZ84lCzgS2NdMce4lEEvkcu/7kLve7U5SKxeJRzxL0IjISLGSUaCN5g1QEKPNw1pgPqzWn7ixgrxO3IDUo0BpWvwZBTNMIhaacKNV3nUR7GZGaUY7zyiBVmBA6ISPsGypIhMrLFkfP7QujBHYYS/OEthfq70RGIqVmkW8mI6LHatXLxf+8fqrDGy9jIkk1CrpcFKbc1rGdN2AHTCLVfGYIoZKZW206JpJQbXqqmBLc1S+vk06j7jp19+Gq1rwt6ijDGZzDJbhwDU24hxa0gcITPMMrvFlT68V6tz6WoyWryJzCH1ifPxNkkkg=</latexit><latexit sha1_base64="xAoQ0JyvZfnKwgaw5bZ39aOSpsA=">AAAB9HicbVDLSsNAFL2pr1pfVZdugkVwVZIi6LLoxmUF+4A2lMnkph06mcSZSaGEfocbF4q49WPc+TdO2iy09cDA4Zx7uHeOn3CmtON8W6WNza3tnfJuZW//4PCoenzSUXEqKbZpzGPZ84lCzgS2NdMce4lEEvkcu/7kLve7U5SKxeJRzxL0IjISLGSUaCN5g1QEKPNw1pgPqzWn7ixgrxO3IDUo0BpWvwZBTNMIhaacKNV3nUR7GZGaUY7zyiBVmBA6ISPsGypIhMrLFkfP7QujBHYYS/OEthfq70RGIqVmkW8mI6LHatXLxf+8fqrDGy9jIkk1CrpcFKbc1rGdN2AHTCLVfGYIoZKZW206JpJQbXqqmBLc1S+vk06j7jp19+Gq1rwt6ijDGZzDJbhwDU24hxa0gcITPMMrvFlT68V6tz6WoyWryJzCH1ifPxNkkkg=</latexit>

!<latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit><latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit><latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit><latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit>

!<latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit> <latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit> <latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit> <latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit>!<latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit><latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit><latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit><latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit> 4<latexit sha1_base64="bERoMPi7jsjoiO8mzWJ5ledolrw=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipWRuUK27VXYCsEy8nFcjRGJS/+sOYpRFKwwTVuue5ifEzqgxnAmelfqoxoWxCR9izVNIItZ8tDp2RC6sMSRgrW9KQhfp7IqOR1tMosJ0RNWO96s3F/7xeasIbP+MySQ1KtlwUpoKYmMy/JkOukBkxtYQyxe2thI2poszYbEo2BG/15XXSvqp6btVr1ir12zyOIpzBOVyCB9dQh3toQAsYIDzDK7w5j86L8+58LFsLTj5zCn/gfP4AfymMuA==</latexit><latexit sha1_base64="ntM2nJNqqkFdIzXRO2Lr9nOLg/g=">AAAB5HicbVBNS8NAEJ3Urxq/qlcvi0XwVBIR9Fj04rGCaQttKJvtpF272YTdjVBCf4EXD4pXf5M3/43bNgdtfTDweG+GmXlRJrg2nvftVDY2t7Z3qrvu3v7B4VHNPW7rNFcMA5aKVHUjqlFwiYHhRmA3U0iTSGAnmtzN/c4zKs1T+WimGYYJHUkec0aNlR6uBrW61/AWIOvEL0kdSrQGta/+MGV5gtIwQbXu+V5mwoIqw5nAmdvPNWaUTegIe5ZKmqAOi8WhM3JulSGJU2VLGrJQf08UNNF6mkS2M6FmrFe9ufif18tNfBMWXGa5QcmWi+JcEJOS+ddkyBUyI6aWUKa4vZWwMVWUGZuNa0PwV19eJ+3Lhu81/HrztgyjCqdwBhfgwzU04R5aEAADhBd4g3fnyXl1PpaNFaecOIE/cD5/ABTTi44=</latexit><latexit sha1_base64="ntM2nJNqqkFdIzXRO2Lr9nOLg/g=">AAAB5HicbVBNS8NAEJ3Urxq/qlcvi0XwVBIR9Fj04rGCaQttKJvtpF272YTdjVBCf4EXD4pXf5M3/43bNgdtfTDweG+GmXlRJrg2nvftVDY2t7Z3qrvu3v7B4VHNPW7rNFcMA5aKVHUjqlFwiYHhRmA3U0iTSGAnmtzN/c4zKs1T+WimGYYJHUkec0aNlR6uBrW61/AWIOvEL0kdSrQGta/+MGV5gtIwQbXu+V5mwoIqw5nAmdvPNWaUTegIe5ZKmqAOi8WhM3JulSGJU2VLGrJQf08UNNF6mkS2M6FmrFe9ufif18tNfBMWXGa5QcmWi+JcEJOS+ddkyBUyI6aWUKa4vZWwMVWUGZuNa0PwV19eJ+3Lhu81/HrztgyjCqdwBhfgwzU04R5aEAADhBd4g3fnyXl1PpaNFaecOIE/cD5/ABTTi44=</latexit><latexit sha1_base64="ntM2nJNqqkFdIzXRO2Lr9nOLg/g=">AAAB5HicbVBNS8NAEJ3Urxq/qlcvi0XwVBIR9Fj04rGCaQttKJvtpF272YTdjVBCf4EXD4pXf5M3/43bNgdtfTDweG+GmXlRJrg2nvftVDY2t7Z3qrvu3v7B4VHNPW7rNFcMA5aKVHUjqlFwiYHhRmA3U0iTSGAnmtzN/c4zKs1T+WimGYYJHUkec0aNlR6uBrW61/AWIOvEL0kdSrQGta/+MGV5gtIwQbXu+V5mwoIqw5nAmdvPNWaUTegIe5ZKmqAOi8WhM3JulSGJU2VLGrJQf08UNNF6mkS2M6FmrFe9ufif18tNfBMWXGa5QcmWi+JcEJOS+ddkyBUyI6aWUKa4vZWwMVWUGZuNa0PwV19eJ+3Lhu81/HrztgyjCqdwBhfgwzU04R5aEAADhBd4g3fnyXl1PpaNFaecOIE/cD5/ABTTi44=</latexit>5<latexit sha1_base64="N8f4lxeEEDz/qiLuXS+43TBm1YA=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzUuOqXK27VnYOsEi8nFchR75e/eoOYpRFKwwTVuuu5ifEzqgxnAqelXqoxoWxMh9i1VNIItZ/ND52SM6sMSBgrW9KQufp7IqOR1pMosJ0RNSO97M3E/7xuasIbP+MySQ1KtlgUpoKYmMy+JgOukBkxsYQyxe2thI2ooszYbEo2BG/55VXSuqh6btVrXFZqt3kcRTiBUzgHD66hBvdQhyYwQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBgK2MuQ==</latexit><latexit sha1_base64="N8f4lxeEEDz/qiLuXS+43TBm1YA=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzUuOqXK27VnYOsEi8nFchR75e/eoOYpRFKwwTVuuu5ifEzqgxnAqelXqoxoWxMh9i1VNIItZ/ND52SM6sMSBgrW9KQufp7IqOR1pMosJ0RNSO97M3E/7xuasIbP+MySQ1KtlgUpoKYmMy+JgOukBkxsYQyxe2thI2ooszYbEo2BG/55VXSuqh6btVrXFZqt3kcRTiBUzgHD66hBvdQhyYwQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBgK2MuQ==</latexit><latexit sha1_base64="N8f4lxeEEDz/qiLuXS+43TBm1YA=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzUuOqXK27VnYOsEi8nFchR75e/eoOYpRFKwwTVuuu5ifEzqgxnAqelXqoxoWxMh9i1VNIItZ/ND52SM6sMSBgrW9KQufp7IqOR1pMosJ0RNSO97M3E/7xuasIbP+MySQ1KtlgUpoKYmMy+JgOukBkxsYQyxe2thI2ooszYbEo2BG/55VXSuqh6btVrXFZqt3kcRTiBUzgHD66hBvdQhyYwQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBgK2MuQ==</latexit><latexit sha1_base64="N8f4lxeEEDz/qiLuXS+43TBm1YA=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzUuOqXK27VnYOsEi8nFchR75e/eoOYpRFKwwTVuuu5ifEzqgxnAqelXqoxoWxMh9i1VNIItZ/ND52SM6sMSBgrW9KQufp7IqOR1pMosJ0RNSO97M3E/7xuasIbP+MySQ1KtlgUpoKYmMy+JgOukBkxsYQyxe2thI2ooszYbEo2BG/55VXSuqh6btVrXFZqt3kcRTiBUzgHD66hBvdQhyYwQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBgK2MuQ==</latexit>

1! 2! 3! 4! . . .<latexit sha1_base64="gtjndtTOlbWz/3Id1eKGkdZEO0c=">AAACD3icbVC7TsMwFHV4lvIKMLJYVCCmKimVYKxgYSwSfUhNVDmO01p17Mh2kKqof8DCr7AwgBArKxt/g5NmgJYr2To6595rnxMkjCrtON/Wyura+sZmZau6vbO7t28fHHaVSCUmHSyYkP0AKcIoJx1NNSP9RBIUB4z0gslNrvceiFRU8Hs9TYgfoxGnEcVIG2pon7meFtBLeUhkviNrzHLiIr+ahcRCodXQrjl1pyi4DNwS1EBZ7aH95YUCpzHhGjOk1MB1Eu1nSGqKGZlVvVSRBOEJGpGBgRzFRPlZ4WcGTw0TwkhIc7iGBft7IkOxUtM4MJ0x0mO1qOXkf9og1dGVn1GepJpwPH8oShk0PvNwYEglwZpNDUBYUvNXiMdIIqxNhFUTgrtoeRl0G3XXqbt3zVrruoyjAo7BCTgHLrgELXAL2qADMHgEz+AVvFlP1ov1bn3MW1escuYI/Cnr8wcRapwJ</latexit><latexit sha1_base64="gtjndtTOlbWz/3Id1eKGkdZEO0c=">AAACD3icbVC7TsMwFHV4lvIKMLJYVCCmKimVYKxgYSwSfUhNVDmO01p17Mh2kKqof8DCr7AwgBArKxt/g5NmgJYr2To6595rnxMkjCrtON/Wyura+sZmZau6vbO7t28fHHaVSCUmHSyYkP0AKcIoJx1NNSP9RBIUB4z0gslNrvceiFRU8Hs9TYgfoxGnEcVIG2pon7meFtBLeUhkviNrzHLiIr+ahcRCodXQrjl1pyi4DNwS1EBZ7aH95YUCpzHhGjOk1MB1Eu1nSGqKGZlVvVSRBOEJGpGBgRzFRPlZ4WcGTw0TwkhIc7iGBft7IkOxUtM4MJ0x0mO1qOXkf9og1dGVn1GepJpwPH8oShk0PvNwYEglwZpNDUBYUvNXiMdIIqxNhFUTgrtoeRl0G3XXqbt3zVrruoyjAo7BCTgHLrgELXAL2qADMHgEz+AVvFlP1ov1bn3MW1escuYI/Cnr8wcRapwJ</latexit><latexit sha1_base64="gtjndtTOlbWz/3Id1eKGkdZEO0c=">AAACD3icbVC7TsMwFHV4lvIKMLJYVCCmKimVYKxgYSwSfUhNVDmO01p17Mh2kKqof8DCr7AwgBArKxt/g5NmgJYr2To6595rnxMkjCrtON/Wyura+sZmZau6vbO7t28fHHaVSCUmHSyYkP0AKcIoJx1NNSP9RBIUB4z0gslNrvceiFRU8Hs9TYgfoxGnEcVIG2pon7meFtBLeUhkviNrzHLiIr+ahcRCodXQrjl1pyi4DNwS1EBZ7aH95YUCpzHhGjOk1MB1Eu1nSGqKGZlVvVSRBOEJGpGBgRzFRPlZ4WcGTw0TwkhIc7iGBft7IkOxUtM4MJ0x0mO1qOXkf9og1dGVn1GepJpwPH8oShk0PvNwYEglwZpNDUBYUvNXiMdIIqxNhFUTgrtoeRl0G3XXqbt3zVrruoyjAo7BCTgHLrgELXAL2qADMHgEz+AVvFlP1ov1bn3MW1escuYI/Cnr8wcRapwJ</latexit><latexit sha1_base64="gtjndtTOlbWz/3Id1eKGkdZEO0c=">AAACD3icbVC7TsMwFHV4lvIKMLJYVCCmKimVYKxgYSwSfUhNVDmO01p17Mh2kKqof8DCr7AwgBArKxt/g5NmgJYr2To6595rnxMkjCrtON/Wyura+sZmZau6vbO7t28fHHaVSCUmHSyYkP0AKcIoJx1NNSP9RBIUB4z0gslNrvceiFRU8Hs9TYgfoxGnEcVIG2pon7meFtBLeUhkviNrzHLiIr+ahcRCodXQrjl1pyi4DNwS1EBZ7aH95YUCpzHhGjOk1MB1Eu1nSGqKGZlVvVSRBOEJGpGBgRzFRPlZ4WcGTw0TwkhIc7iGBft7IkOxUtM4MJ0x0mO1qOXkf9og1dGVn1GepJpwPH8oShk0PvNwYEglwZpNDUBYUvNXiMdIIqxNhFUTgrtoeRl0G3XXqbt3zVrruoyjAo7BCTgHLrgELXAL2qADMHgEz+AVvFlP1ov1bn3MW1escuYI/Cnr8wcRapwJ</latexit>

!<latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit> <latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit> <latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit> <latexit sha1_base64="8tQZlBzaoa+vzXmUrPcUKIz5lFM=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKoMegF48RzQOSJcxOZpMhszPLTK8QQj7BiwdFvPpF3vwbJ8keNLGgoajqprsrSqWw6PvfXmFtfWNzq7hd2tnd2z8oHx41rc4M4w2mpTbtiFouheINFCh5OzWcJpHkrWh0O/NbT9xYodUjjlMeJnSgRCwYRSc9dFH3yhW/6s9BVkmQkwrkqPfKX92+ZlnCFTJJre0EforhhBoUTPJpqZtZnlI2ogPecVTRhNtwMj91Ss6c0iexNq4Ukrn6e2JCE2vHSeQ6E4pDu+zNxP+8TobxdTgRKs2QK7ZYFGeSoCazv0lfGM5Qjh2hzAh3K2FDaihDl07JhRAsv7xKmhfVwK8G95eV2k0eRxFO4BTOIYArqMEd1KEBDAbwDK/w5knvxXv3PhatBS+fOYY/8D5/AF7pjdc=</latexit>



..<latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit><latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit><latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit><latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit>

..<latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit><latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit><latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit><latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit>

..<latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit> <latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit> <latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit> <latexit sha1_base64="cWFa8E+s41dd5yD6riPqvj6XktY=">AAAB6XicbVBNS8NAEJ3Ur1q/qh69LBbBU0hE0GPRi8cq9gPaUDbbSbt0swm7G6GE/gMvHhTx6j/y5r9x2+agrQ8GHu/NMDMvTAXXxvO+ndLa+sbmVnm7srO7t39QPTxq6SRTDJssEYnqhFSj4BKbhhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVZ6cN1+tea53hxklfgFqUGBRr/61RskLItRGiao1l3fS02QU2U4Ezit9DKNKWVjOsSupZLGqIN8fumUnFllQKJE2ZKGzNXfEzmNtZ7Eoe2MqRnpZW8m/ud1MxNdBzmXaWZQssWiKBPEJGT2NhlwhcyIiSWUKW5vJWxEFWXGhlOxIfjLL6+S1oXre65/f1mr3xRxlOEETuEcfLiCOtxBA5rAIIJneIU3Z+y8OO/Ox6K15BQzx/AHzucP4NuM6g==</latexit>

Figure 1: A conversation thread discussing the rumor-ous tweet “1”. Three different perspectives for learningthe stance feature of the reply tweet “2” are illustrated.

Previous studies have observed that publicstances towards rumorous messages are crucial sig-nals to detect trending rumors (Qazvinian et al.,2011; Zhao et al., 2015) and indicate the veracityof them (Mendoza et al., 2010; Procter et al., 2013;Liu et al., 2015; Jin et al., 2016; Glenski et al.,2018). Therefore, stance classification towards ru-mors is viewed as an important preceding step ofrumor veracity prediction, especially in the contextof Twitter conversations (Zubiaga et al., 2016a).

The state-of-the-art methods for rumor stanceclassification are proposed to model the sequentialproperty (Kochkina et al., 2017) or the temporalproperty (Veyseh et al., 2017) of a Twitter con-versation thread. In this paper, we propose a newperspective based on structural property: learningtweet representations through aggregating informa-tion from their neighboring tweets. Intuitively, atweet’s nearer neighbors in its conversation threadare more informative than farther neighbors be-cause the replying relationships of them are closer,and their stance expressions can help classify thestance of the center tweet (e.g., in Figure 1, tweets“1”, “4” and “5” are the one-hop neighbors of thetweet “2”, and their influences on predicting thestance of “2” are larger than that of the two-hopneighbor “3”). To achieve this, we represent both

4788

Stan

ce d

istri

butio

n

Time (hour)Time (hour) Time (hour)

True Rumors False Rumors Unverified Rumors

Figure 2: Stance distributions of tweets discussing true rumors, false rumors, and unverified rumors, respec-tively (Better viewed in color). The horizontal axis is the spreading time of the first rumor. It is visualized basedon SemEval-2017 task 8 dataset (Derczynski et al., 2017). All tweets are relevant to the event “Ottawa Shooting”.

tweet contents and conversation structures into alatent space using a graph convolutional network(GCN) (Kipf and Welling, 2017), aiming to learnstance feature for each tweet by aggregating itsneighbors’ features. Compared with the sequentialand temporal based methods, our aggregation basedmethod leverages the intrinsic structural propertyin conversations to learn tweet representations.

After determining the stances of people’s re-actions, another challenge is how we can utilizepublic stances to predict rumor veracity accurately.We observe that the temporal dynamics of publicstances can indicate rumor veracity. Figure 2 illus-trates the stance distributions of tweets discussingtrue rumors, false rumors, and unverified ru-mors, respectively. As we can see, supportingstance dominates the inception phase of spread-ing. However, as time goes by, the proportion ofdenying tweets towards false rumors increasesquite significantly. Meanwhile, the proportion ofquerying tweets towards unverified rumors alsoshows an upward trend. Based on this observa-tion, we propose to model the temporal dynamicsof stance evolution with a recurrent neural network(RNN), capturing the crucial signals containing instance features for effective veracity prediction.

Further, most existing methods tackle stanceclassification and veracity prediction separately,which is suboptimal and limits the generalization ofmodels. As shown previously, they are two closelyrelated tasks in which stance classification can pro-vide indicative clues to facilitate veracity predic-tion. Thus, these two tasks can be jointly learnedto make better use of their interrelation.

Based on the above considerations, in this pa-per, we propose a hierarchical multi-task learningframework for jointly predicting rumor stance andveracity, which achieves deep integration betweenthe preceding task (stance classification) and the

subsequent task (veracity prediction). The bot-tom component of our framework classifies thestances of tweets in a conversation discussing arumor via aggregation-based structure modeling,and we design a novel graph convolution operationcustomized for conversation structures. The topcomponent predicts rumor veracity by exploitingthe temporal dynamics of stance evolution, takingboth content features and stance features learned bythe bottom component into account. Two compo-nents are jointly trained to utilize the interrelationbetween the two tasks for learning more powerfulfeature representations.

The contributions of this work are as follows.•We propose a hierarchical framework to tackle

rumor stance classification and veracity predictionjointly, exploiting both structural characteristic andtemporal dynamics in rumor spreading process.•We design a novel graph convolution operation

customized to encode conversation structures forlearning stance features. To our knowledge, we arethe first to employ graph convolution for modelingthe structural property of Twitter conversations.• Experimental results on two benchmark

datasets verify that our hierarchical framework per-forms better than existing methods in both rumorstance classification and veracity prediction.

2 Related Work

Rumor Stance Classification Stance analysishas been widely studied in online debate fo-rums (Somasundaran and Wiebe, 2009; Hasan andNg, 2013), and recently has attracted increasingattention in different contexts (Mohammad et al.,2016; Augenstein et al., 2016; Ferreira and Vla-chos, 2016; Mohtarami et al., 2018). After thepioneering studies on stance classification towardsrumors in social media (Mendoza et al., 2010;

4789

Qazvinian et al., 2011; Procter et al., 2013), linguis-tic feature (Hamidian and Diab, 2016; Zeng et al.,2016) and point process based methods (Lukasiket al., 2016, 2019) have been developed.

Recent work has focused on Twitter conversa-tions discussing rumors. Zubiaga et al. (2016a) pro-posed to capture the sequential property of con-versations with linear-chain CRF, and also used atree-structured CRF to consider the conversationstructure as a whole. Aker et al. (2017) developeda novel feature set that scores the level of users’confidence. Pamungkas et al. (2018) designed af-fective and dialogue-act features to cover variousfacets of affect. Giasemidis et al. (2018) proposed asemi-supervised method that propagates the stancelabels on similarity graph. Beyond feature-basedmethods, Kochkina et al. (2017) utilized an LSTMto model the sequential branches in a conversation,and their system ranked the first in SemEval-2017task 8. Veyseh et al. (2017) adopted attention tomodel the temporal property of a conversation andachieved the state-of-the-art performance.

Rumor Veracity Prediction Previous studieshave proposed methods based on various featuressuch as linguistics, time series and propagationstructures (Castillo et al., 2011; Kwon et al., 2013;Wu et al., 2015; Ma et al., 2017). Neural networksshow the effectiveness of modeling time series (Maet al., 2016; Ruchansky et al., 2017) and propaga-tion paths (Liu and Wu, 2018). Ma et al. (2018b)’smodel adopted recursive neural networks to incor-porate structure information into tweet representa-tions and outperformed previous methods.

Some studies utilized stance labels as the inputfeature of veracity classifiers to improve the per-formance (Liu et al., 2015; Enayet and El-Beltagy,2017). Dungs et al. (2018) proposed to recognizethe temporal patterns of true and false rumors’stances by two hidden Markov models (HMMs).Unlike their solution, our method learns discrim-inative features of stance evolution with an RNN.Moreover, our method jointly predicts stance andveracity by exploiting both structural and temporalcharacteristics, whereas HMMs need stance labelsas the input sequence of observations.

Joint Predictions of Rumor Stance and Ve-racity Several work has addressed the problem ofjointly predicting rumor stance and veracity. Thesestudies adopted multi-task learning to jointly traintwo tasks (Ma et al., 2018a; Kochkina et al., 2018;Poddar et al., 2018) and learned shared represen-

tations with parameter-sharing. Compared withsuch solutions based on “parallel” architectures,our method is deployed in a hierarchical fashionthat encodes conversation structures to learn morepowerful stance features by the bottom component,and models stance evolution by the top component,achieving deep integration between the two tasks’feature learning.

3 Problem Definition

Consider a Twitter conversation thread C whichconsists of a source tweet t1 (originating a rumor)and a number of reply tweets {t2, t3, . . . , t|C|} thatrespond t1 directly or indirectly, and each tweetti (i ∈ [1, |C|]) expresses its stance towards therumor. The thread C is a tree structure, in which thesource tweet t1 is the root node, and the replyingrelationships among tweets form the edges.1

This paper focuses on two tasks. The first taskis rumor stance classification, aiming to determinethe stance of each tweet in C, which belongs to{supporting, denying, querying, commenting}.The second task is rumor veracity prediction, withthe aim of identifying the veracity of the rumor,belonging to {true, false, unverified}.

4 Proposed Method

We propose a Hierarchical multi-task learningframework for jointly Predicting rumor Stance andVeracity (named Hierarchical-PSV). Figure 3 illus-trates its overall architecture that is composed oftwo components. The bottom component is to clas-sify the stances of tweets in a conversation thread,which learns stance features via encoding conver-sation structure using a customized graph convolu-tional network (named Conversational-GCN). Thetop component is to predict the rumor’s veracity,which takes the learned features from the bottomcomponent into account and models the temporaldynamics of stance evolution with a recurrent neu-ral network (named Stance-Aware RNN).

4.1 Conversational-GCN: Aggregation-basedStructure Modeling for Stance Prediction

Now we detail Conversational-GCN, the bottomcomponent of our framework. We first adopt abidirectional GRU (BGRU) (Cho et al., 2014) layerto learn the content feature for each tweet in thethread C. For a tweet ti (i ∈ [1, |C|]), we run the

1We consider each replying relationship between twotweets in a conversation as an undirected edge in the tree.

4790

Conversation Thread

Timeline

1

2

3

4

5

6

Structure Modeling for Stance Classification Temporal Modeling for Veracity Prediction

Hierarchical Multi-task Learning

1

2

3

4

5

6

1

2

3

4

5

6

Content Feature

StanceFeature

Content Feature

StanceFeature

Conversational-GCN Stance-Aware RNN

Softmax

Softmax

Softmax

Softmax

Softmax

Softmax

Source tweet (rumorous): 1. Reply tweets: 2, 3, 4, 5, and 6.

False<latexit sha1_base64="PhubaBmVWsqV6T7AWUdomK/U0xU=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNREI8VTFtoQ9lsJ+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBVcG9f9dkpr6xubW+Xtys7u3v5B9fCopZNMMfRZIhLVCalGwSX6hhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVby76jQ2K/W3Lo7B1klXkFqUKDZr371BgnLYpSGCap113NTE+RUGc4ETiu9TGNK2ZgOsWuppDHqIJ8fOyVnVhmQKFG2pCFz9fdETmOtJ3FoO2NqRnrZm4n/ed3MRNdBzmWaGZRssSjKBDEJmX1OBlwhM2JiCWWK21sJG1FFmbH5VGwI3vLLq6R1UffcuvdwWWvcFHGU4QRO4Rw8uIIG3EMTfGDA4Rle4c2Rzovz7nwsWktOMXMMf+B8/gCv1I6X</latexit><latexit sha1_base64="PhubaBmVWsqV6T7AWUdomK/U0xU=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNREI8VTFtoQ9lsJ+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBVcG9f9dkpr6xubW+Xtys7u3v5B9fCopZNMMfRZIhLVCalGwSX6hhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVby76jQ2K/W3Lo7B1klXkFqUKDZr371BgnLYpSGCap113NTE+RUGc4ETiu9TGNK2ZgOsWuppDHqIJ8fOyVnVhmQKFG2pCFz9fdETmOtJ3FoO2NqRnrZm4n/ed3MRNdBzmWaGZRssSjKBDEJmX1OBlwhM2JiCWWK21sJG1FFmbH5VGwI3vLLq6R1UffcuvdwWWvcFHGU4QRO4Rw8uIIG3EMTfGDA4Rle4c2Rzovz7nwsWktOMXMMf+B8/gCv1I6X</latexit><latexit sha1_base64="PhubaBmVWsqV6T7AWUdomK/U0xU=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNREI8VTFtoQ9lsJ+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBVcG9f9dkpr6xubW+Xtys7u3v5B9fCopZNMMfRZIhLVCalGwSX6hhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVby76jQ2K/W3Lo7B1klXkFqUKDZr371BgnLYpSGCap113NTE+RUGc4ETiu9TGNK2ZgOsWuppDHqIJ8fOyVnVhmQKFG2pCFz9fdETmOtJ3FoO2NqRnrZm4n/ed3MRNdBzmWaGZRssSjKBDEJmX1OBlwhM2JiCWWK21sJG1FFmbH5VGwI3vLLq6R1UffcuvdwWWvcFHGU4QRO4Rw8uIIG3EMTfGDA4Rle4c2Rzovz7nwsWktOMXMMf+B8/gCv1I6X</latexit><latexit sha1_base64="PhubaBmVWsqV6T7AWUdomK/U0xU=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNREI8VTFtoQ9lsJ+3SzSbsboQS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBVcG9f9dkpr6xubW+Xtys7u3v5B9fCopZNMMfRZIhLVCalGwSX6hhuBnVQhjUOB7XB8O/PbT6g0T+SjmaQYxHQoecQZNVby76jQ2K/W3Lo7B1klXkFqUKDZr371BgnLYpSGCap113NTE+RUGc4ETiu9TGNK2ZgOsWuppDHqIJ8fOyVnVhmQKFG2pCFz9fdETmOtJ3FoO2NqRnrZm4n/ed3MRNdBzmWaGZRssSjKBDEJmX1OBlwhM2JiCWWK21sJG1FFmbH5VGwI3vLLq6R1UffcuvdwWWvcFHGU4QRO4Rw8uIIG3EMTfGDA4Rle4c2Rzovz7nwsWktOMXMMf+B8/gCv1I6X</latexit>

Support<latexit sha1_base64="LmF7uylmEdUT0h/2SzQhZJC2F10=">AAAB7nicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48RzQOSJcxOZpMhszPDTK8QQj7CiwdFvPo93vwbJ8keNLGgoajqprsr1oJbDIJvr7C2vrG5Vdwu7ezu7R+UD4+aVmWGsgZVQpl2TCwTXLIGchSsrQ0jaSxYKx7dzvzWEzOWK/mIY82ilAwkTzgl6KTWQ6a1MtgrV4JqMIe/SsKcVCBHvVf+6vYVzVImkQpibScMNEYTYpBTwaalbmaZJnREBqzjqCQps9Fkfu7UP3NK30+UcSXRn6u/JyYktXacxq4zJTi0y95M/M/rZJhcRxMudYZM0sWiJBM+Kn/2u9/nhlEUY0cINdzd6tMhMYSiS6jkQgiXX14lzYtqGFTD+8tK7SaPowgncArnEMIV1OAO6tAACiN4hld487T34r17H4vWgpfPHMMfeJ8/nimPvQ==</latexit><latexit sha1_base64="LmF7uylmEdUT0h/2SzQhZJC2F10=">AAAB7nicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48RzQOSJcxOZpMhszPDTK8QQj7CiwdFvPo93vwbJ8keNLGgoajqprsr1oJbDIJvr7C2vrG5Vdwu7ezu7R+UD4+aVmWGsgZVQpl2TCwTXLIGchSsrQ0jaSxYKx7dzvzWEzOWK/mIY82ilAwkTzgl6KTWQ6a1MtgrV4JqMIe/SsKcVCBHvVf+6vYVzVImkQpibScMNEYTYpBTwaalbmaZJnREBqzjqCQps9Fkfu7UP3NK30+UcSXRn6u/JyYktXacxq4zJTi0y95M/M/rZJhcRxMudYZM0sWiJBM+Kn/2u9/nhlEUY0cINdzd6tMhMYSiS6jkQgiXX14lzYtqGFTD+8tK7SaPowgncArnEMIV1OAO6tAACiN4hld487T34r17H4vWgpfPHMMfeJ8/nimPvQ==</latexit><latexit sha1_base64="LmF7uylmEdUT0h/2SzQhZJC2F10=">AAAB7nicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48RzQOSJcxOZpMhszPDTK8QQj7CiwdFvPo93vwbJ8keNLGgoajqprsr1oJbDIJvr7C2vrG5Vdwu7ezu7R+UD4+aVmWGsgZVQpl2TCwTXLIGchSsrQ0jaSxYKx7dzvzWEzOWK/mIY82ilAwkTzgl6KTWQ6a1MtgrV4JqMIe/SsKcVCBHvVf+6vYVzVImkQpibScMNEYTYpBTwaalbmaZJnREBqzjqCQps9Fkfu7UP3NK30+UcSXRn6u/JyYktXacxq4zJTi0y95M/M/rZJhcRxMudYZM0sWiJBM+Kn/2u9/nhlEUY0cINdzd6tMhMYSiS6jkQgiXX14lzYtqGFTD+8tK7SaPowgncArnEMIV1OAO6tAACiN4hld487T34r17H4vWgpfPHMMfeJ8/nimPvQ==</latexit><latexit sha1_base64="LmF7uylmEdUT0h/2SzQhZJC2F10=">AAAB7nicbVDLSgNBEOyNrxhfUY9eFoPgKeyKoMegF48RzQOSJcxOZpMhszPDTK8QQj7CiwdFvPo93vwbJ8keNLGgoajqprsr1oJbDIJvr7C2vrG5Vdwu7ezu7R+UD4+aVmWGsgZVQpl2TCwTXLIGchSsrQ0jaSxYKx7dzvzWEzOWK/mIY82ilAwkTzgl6KTWQ6a1MtgrV4JqMIe/SsKcVCBHvVf+6vYVzVImkQpibScMNEYTYpBTwaalbmaZJnREBqzjqCQps9Fkfu7UP3NK30+UcSXRn6u/JyYktXacxq4zJTi0y95M/M/rZJhcRxMudYZM0sWiJBM+Kn/2u9/nhlEUY0cINdzd6tMhMYSiS6jkQgiXX14lzYtqGFTD+8tK7SaPowgncArnEMIV1OAO6tAACiN4hld487T34r17H4vWgpfPHMMfeJ8/nimPvQ==</latexit>


Query<latexit sha1_base64="tcn3XJLk8U1N6KP5fFc5SCaEEKE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cWTFtoQ9lsp+3SzSbsboQQ+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dkobm1vbO+Xdyt7+weFR9fikreNUMfRZLGLVDalGwSX6hhuB3UQhjUKBnXB6P/c7T6g0j+WjyRIMIjqWfMQZNVbyWymqbFCtuXV3AbJOvILUoEBzUP3qD2OWRigNE1TrnucmJsipMpwJnFX6qcaEsikdY89SSSPUQb44dkYurDIko1jZkoYs1N8TOY20zqLQdkbUTPSqNxf/83qpGd0GOZdJalCy5aJRKoiJyfxzMuQKmRGZJZQpbm8lbEIVZcbmU7EheKsvr5P2Vd1z617ruta4K+IowxmcwyV4cAMNeIAm+MCAwzO8wpsjnRfn3flYtpacYuYU/sD5/AHxWY7C</latexit><latexit sha1_base64="tcn3XJLk8U1N6KP5fFc5SCaEEKE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cWTFtoQ9lsp+3SzSbsboQQ+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dkobm1vbO+Xdyt7+weFR9fikreNUMfRZLGLVDalGwSX6hhuB3UQhjUKBnXB6P/c7T6g0j+WjyRIMIjqWfMQZNVbyWymqbFCtuXV3AbJOvILUoEBzUP3qD2OWRigNE1TrnucmJsipMpwJnFX6qcaEsikdY89SSSPUQb44dkYurDIko1jZkoYs1N8TOY20zqLQdkbUTPSqNxf/83qpGd0GOZdJalCy5aJRKoiJyfxzMuQKmRGZJZQpbm8lbEIVZcbmU7EheKsvr5P2Vd1z617ruta4K+IowxmcwyV4cAMNeIAm+MCAwzO8wpsjnRfn3flYtpacYuYU/sD5/AHxWY7C</latexit><latexit sha1_base64="tcn3XJLk8U1N6KP5fFc5SCaEEKE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cWTFtoQ9lsp+3SzSbsboQQ+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dkobm1vbO+Xdyt7+weFR9fikreNUMfRZLGLVDalGwSX6hhuB3UQhjUKBnXB6P/c7T6g0j+WjyRIMIjqWfMQZNVbyWymqbFCtuXV3AbJOvILUoEBzUP3qD2OWRigNE1TrnucmJsipMpwJnFX6qcaEsikdY89SSSPUQb44dkYurDIko1jZkoYs1N8TOY20zqLQdkbUTPSqNxf/83qpGd0GOZdJalCy5aJRKoiJyfxzMuQKmRGZJZQpbm8lbEIVZcbmU7EheKsvr5P2Vd1z617ruta4K+IowxmcwyV4cAMNeIAm+MCAwzO8wpsjnRfn3flYtpacYuYU/sD5/AHxWY7C</latexit><latexit sha1_base64="tcn3XJLk8U1N6KP5fFc5SCaEEKE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cWTFtoQ9lsp+3SzSbsboQQ+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8MBFcG9f9dkobm1vbO+Xdyt7+weFR9fikreNUMfRZLGLVDalGwSX6hhuB3UQhjUKBnXB6P/c7T6g0j+WjyRIMIjqWfMQZNVbyWymqbFCtuXV3AbJOvILUoEBzUP3qD2OWRigNE1TrnucmJsipMpwJnFX6qcaEsikdY89SSSPUQb44dkYurDIko1jZkoYs1N8TOY20zqLQdkbUTPSqNxf/83qpGd0GOZdJalCy5aJRKoiJyfxzMuQKmRGZJZQpbm8lbEIVZcbmU7EheKsvr5P2Vd1z617ruta4K+IowxmcwyV4cAMNeIAm+MCAwzO8wpsjnRfn3flYtpacYuYU/sD5/AHxWY7C</latexit>


Max-Pooling

FNN

+ SoftmaxDeny

<latexit sha1_base64="8ekNGixclA8ONaWdNJoQQqMbz68=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNRDx4r2A9oQ9lsJ+3SzSbsboRQ+he8eFDEq3/Im//GTZuDtj4YeLw3w8y8IBFcG9f9dkpr6xubW+Xtys7u3v5B9fCoreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJbe53nlBpHstHkyXoR3QkecgZNbl0hzIbVGtu3Z2DrBKvIDUo0BxUv/rDmKURSsME1brnuYnxp1QZzgTOKv1UY0LZhI6wZ6mkEWp/Or91Rs6sMiRhrGxJQ+bq74kpjbTOosB2RtSM9bKXi/95vdSE1/6UyyQ1KNliUZgKYmKSP06GXCEzIrOEMsXtrYSNqaLM2HgqNgRv+eVV0r6oe27de7isNW6KOMpwAqdwDh5cQQPuoQktYDCGZ3iFNydyXpx352PRWnKKmWP4A+fzB/9tjjI=</latexit><latexit sha1_base64="8ekNGixclA8ONaWdNJoQQqMbz68=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNRDx4r2A9oQ9lsJ+3SzSbsboRQ+he8eFDEq3/Im//GTZuDtj4YeLw3w8y8IBFcG9f9dkpr6xubW+Xtys7u3v5B9fCoreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJbe53nlBpHstHkyXoR3QkecgZNbl0hzIbVGtu3Z2DrBKvIDUo0BxUv/rDmKURSsME1brnuYnxp1QZzgTOKv1UY0LZhI6wZ6mkEWp/Or91Rs6sMiRhrGxJQ+bq74kpjbTOosB2RtSM9bKXi/95vdSE1/6UyyQ1KNliUZgKYmKSP06GXCEzIrOEMsXtrYSNqaLM2HgqNgRv+eVV0r6oe27de7isNW6KOMpwAqdwDh5cQQPuoQktYDCGZ3iFNydyXpx352PRWnKKmWP4A+fzB/9tjjI=</latexit><latexit sha1_base64="8ekNGixclA8ONaWdNJoQQqMbz68=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNRDx4r2A9oQ9lsJ+3SzSbsboRQ+he8eFDEq3/Im//GTZuDtj4YeLw3w8y8IBFcG9f9dkpr6xubW+Xtys7u3v5B9fCoreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJbe53nlBpHstHkyXoR3QkecgZNbl0hzIbVGtu3Z2DrBKvIDUo0BxUv/rDmKURSsME1brnuYnxp1QZzgTOKv1UY0LZhI6wZ6mkEWp/Or91Rs6sMiRhrGxJQ+bq74kpjbTOosB2RtSM9bKXi/95vdSE1/6UyyQ1KNliUZgKYmKSP06GXCEzIrOEMsXtrYSNqaLM2HgqNgRv+eVV0r6oe27de7isNW6KOMpwAqdwDh5cQQPuoQktYDCGZ3iFNydyXpx352PRWnKKmWP4A+fzB/9tjjI=</latexit><latexit sha1_base64="8ekNGixclA8ONaWdNJoQQqMbz68=">AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GNRDx4r2A9oQ9lsJ+3SzSbsboRQ+he8eFDEq3/Im//GTZuDtj4YeLw3w8y8IBFcG9f9dkpr6xubW+Xtys7u3v5B9fCoreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJbe53nlBpHstHkyXoR3QkecgZNbl0hzIbVGtu3Z2DrBKvIDUo0BxUv/rDmKURSsME1brnuYnxp1QZzgTOKv1UY0LZhI6wZ6mkEWp/Or91Rs6sMiRhrGxJQ+bq74kpjbTOosB2RtSM9bKXi/95vdSE1/6UyyQ1KNliUZgKYmKSP06GXCEzIrOEMsXtrYSNqaLM2HgqNgRv+eVV0r6oe27de7isNW6KOMpwAqdwDh5cQQPuoQktYDCGZ3iFNydyXpx352PRWnKKmWP4A+fzB/9tjjI=</latexit>


Stance1

2

3

4

5

6

Veracity

L = Lveracity + �Lstance<latexit sha1_base64="sbqJozHT2fE18V3V5hcP/cKaKb8=">AAACMnicbVBNS8NAEN34WetX1aOXxSIIQklE0ItQ9KLgoYJVoSllsp3apZtNyE7EEvKbvPhLBA96UMSrP8JtLfhRHyw83puZnXlBrKQh131yJianpmdmC3PF+YXFpeXSyuqFidJEYF1EKkquAjCopMY6SVJ4FScIYaDwMugdDfzLG0yMjPQ59WNshnCtZUcKICu1Sid+CNQVoPjpwTdtZT7hLWW2E4Skfp5v+8oObcN4jSHQAvO8VSq7FXcIPk68ESmzEWqt0oPfjkQaoiahwJiG58bUzCAhKRTmRT81GIPowTU2LNUQomlmw5NzvmmVNu9EiX2a+FD92ZFBaEw/DGzlYGPz1xuI/3mNlDr7zUzqOCXU4uujTqo4RXyQH2/LBAWpviUgEml35aILNiayKRdtCN7fk8fJxU7Fcyve2W65ejiKo8DW2QbbYh7bY1V2zGqszgS7Y4/shb06986z8+a8f5VOOKOeNfYLzscnxbCsVQ==</latexit><latexit sha1_base64="sbqJozHT2fE18V3V5hcP/cKaKb8=">AAACMnicbVBNS8NAEN34WetX1aOXxSIIQklE0ItQ9KLgoYJVoSllsp3apZtNyE7EEvKbvPhLBA96UMSrP8JtLfhRHyw83puZnXlBrKQh131yJianpmdmC3PF+YXFpeXSyuqFidJEYF1EKkquAjCopMY6SVJ4FScIYaDwMugdDfzLG0yMjPQ59WNshnCtZUcKICu1Sid+CNQVoPjpwTdtZT7hLWW2E4Skfp5v+8oObcN4jSHQAvO8VSq7FXcIPk68ESmzEWqt0oPfjkQaoiahwJiG58bUzCAhKRTmRT81GIPowTU2LNUQomlmw5NzvmmVNu9EiX2a+FD92ZFBaEw/DGzlYGPz1xuI/3mNlDr7zUzqOCXU4uujTqo4RXyQH2/LBAWpviUgEml35aILNiayKRdtCN7fk8fJxU7Fcyve2W65ejiKo8DW2QbbYh7bY1V2zGqszgS7Y4/shb06986z8+a8f5VOOKOeNfYLzscnxbCsVQ==</latexit><latexit sha1_base64="sbqJozHT2fE18V3V5hcP/cKaKb8=">AAACMnicbVBNS8NAEN34WetX1aOXxSIIQklE0ItQ9KLgoYJVoSllsp3apZtNyE7EEvKbvPhLBA96UMSrP8JtLfhRHyw83puZnXlBrKQh131yJianpmdmC3PF+YXFpeXSyuqFidJEYF1EKkquAjCopMY6SVJ4FScIYaDwMugdDfzLG0yMjPQ59WNshnCtZUcKICu1Sid+CNQVoPjpwTdtZT7hLWW2E4Skfp5v+8oObcN4jSHQAvO8VSq7FXcIPk68ESmzEWqt0oPfjkQaoiahwJiG58bUzCAhKRTmRT81GIPowTU2LNUQomlmw5NzvmmVNu9EiX2a+FD92ZFBaEw/DGzlYGPz1xuI/3mNlDr7zUzqOCXU4uujTqo4RXyQH2/LBAWpviUgEml35aILNiayKRdtCN7fk8fJxU7Fcyve2W65ejiKo8DW2QbbYh7bY1V2zGqszgS7Y4/shb06986z8+a8f5VOOKOeNfYLzscnxbCsVQ==</latexit><latexit sha1_base64="sbqJozHT2fE18V3V5hcP/cKaKb8=">AAACMnicbVBNS8NAEN34WetX1aOXxSIIQklE0ItQ9KLgoYJVoSllsp3apZtNyE7EEvKbvPhLBA96UMSrP8JtLfhRHyw83puZnXlBrKQh131yJianpmdmC3PF+YXFpeXSyuqFidJEYF1EKkquAjCopMY6SVJ4FScIYaDwMugdDfzLG0yMjPQ59WNshnCtZUcKICu1Sid+CNQVoPjpwTdtZT7hLWW2E4Skfp5v+8oObcN4jSHQAvO8VSq7FXcIPk68ESmzEWqt0oPfjkQaoiahwJiG58bUzCAhKRTmRT81GIPowTU2LNUQomlmw5NzvmmVNu9EiX2a+FD92ZFBaEw/DGzlYGPz1xuI/3mNlDr7zUzqOCXU4uujTqo4RXyQH2/LBAWpviUgEml35aILNiayKRdtCN7fk8fJxU7Fcyve2W65ejiKo8DW2QbbYh7bY1V2zGqszgS7Y4/shb06986z8+a8f5VOOKOeNfYLzscnxbCsVQ==</latexit>

Figure 3: Overall architecture of our proposed framework for joint predictions of rumor stance and veracity. Inthis illustration, the number of GCN layers is one. The information aggregation process for the tweet t2 based onoriginal graph convolution operation (Eq. (1)) is detailed.

BGRU over its word embedding sequence, and usethe final step’s hidden vector to represent the tweet.The content feature representation of ti is denotedas ci ∈ Rd, where d is the output size of the BGRU.

As we mentioned in Section 1, the stance expres-sions of a tweet ti’s nearer neighbors can providemore informative signals than farther neighbors forlearning ti’s stance feature. Based on the aboveintuition, we model the structural property of theconversation thread C to learn stance feature rep-resentation for each tweet in C. To this end, weencode structural contexts to improve tweet repre-sentations by aggregating information from neigh-boring tweets with a graph convolutional network(GCN) (Kipf and Welling, 2017).

Formally, the conversation C’s structure can berepresented by a graph CG = 〈T , E〉, where T =

{ti}|C|i=1 denotes the node set (i.e., tweets in theconversation), and E denotes the edge set composedof all replying relationships among the tweets. Wetransform the edge set E to an adjacency matrixA ∈ R|C|×|C|, where Aij = Aji = 1 if the tweetti directly replies the tweet tj or i = j. In oneGCN layer, the graph convolution operation forone tweet ti on CG is defined as:

houti = tanh

∑j∈{j|Aij 6=0}

AijW>hin

j + b

,

(1)where hin

i ∈ Rdin and houti ∈ Rdout denote the input

and output feature representations of the tweet tirespectively. The convolution filter W ∈ Rdin×dout

and the bias b ∈ Rdout are shared over all tweets

in a conversation. We apply symmetric normal-ized transformation A = D−

12AD−

12 to avoid the

scale changing of feature representations, whereD is the degree matrix of A, and {j | Aij 6= 0}contains ti’s one-hop neighbors and ti itself.

In this original graph convolution operation,given a tweet ti, the receptive field for ti containsits one-hop neighbors and ti itself, and the aggre-gation level of two tweets ti and tj is dependent onAij . In the context of encoding conversation struc-tures, we observe that such operation can be furtherimproved for two issues. First, a tree-structuredconversation may be very deep, which means thatthe receptive field of a GCN layer is restricted inour case. Although we can stack multiple GCNlayers to expand the receptive field, it is still diffi-cult to handle conversations with deep structuresand increases the number of parameters. Second,the normalized matrix A partly weakens the im-portance of the tweet ti itself. To address theseissues, we design a novel graph convolution oper-ation which is customized to encode conversationstructures. Formally, it is implemented by modify-ing the matrix A in Eq. (1):

A← AA+ I , (2)

where the multiplication operation expands the re-ceptive field of a GCN layer, and adding an identitymatrix elevates the importance of ti itself.

After defining the above graph convolution op-eration, we adopt an L-layer GCN to model con-versation structures. The lth GCN layer (l ∈ [1, L])computed over the entire conversation structure can

4791

be written as an efficient matrix operation:

H(l) = tanh(AH(l−1)W (l) + b(l)) , (3)

where H(l−1) ∈ R|C|×dl−1 and H(l) ∈ R|C|×dldenote the input and output features of all tweetsin the conversation C respectively.

Specifically, the first GCN layer takes the con-tent features of all tweets as input, i.e., H(0) =(c1, c2, . . . , c|C|)

> ∈ R|C|×d. The output of thelast GCN layer represents the stance featuresof all tweets in the conversation, i.e., H(L) =(s1, s2, . . . , s|C|)

> ∈ R|C|×4, where si is the un-normalized stance distribution of the tweet ti.

For each tweet ti in the conversation C, we applysoftmax to obtain its predicted stance distribution:

si = softmax(si) ∈ R4 , i ∈ [1, |C|] . (4)

The ground-truth labels of stance classificationsupervise the learning process of Conversational-GCN. The loss function of C for stance classifica-tion is computed by cross-entropy criterion:

Lstance =1

|C|

|C|∑i=1

(−s>i log si

), (5)

where si is a one-hot vector that denotes the stancelabel of the tweet ti. For batch-wise training, theobjective function for a batch is the averaged cross-entropy loss of all tweets in these conversations.

In previous studies, GCNs are used to en-code dependency trees (Marcheggiani and Titov,2017; Zhang et al., 2018) and cross-document rela-tions (Yasunaga et al., 2017; De Cao et al., 2019)for downstream tasks. Our work is the first to lever-age GCNs for encoding conversation structures.

4.2 Stance-Aware RNN: Temporal DynamicsModeling for Veracity Prediction

The top component, Stance-Aware RNN, aims tocapture the temporal dynamics of stance evolutionin a conversation discussing a rumor. It integratesboth content features and stance features learnedfrom the bottom Conversational-GCN to facilitatethe veracity prediction of the rumor.

Specifically, given a conversation thread C ={t1, t2, . . . , t|C|} (where the tweets t∗ are orderedchronologically), we combine the content featureand the stance feature for each tweet, and adopt aGRU layer to model the temporal evolution:

vi = GRU([ci; si],vi−1) , i ∈ [1, |C|] , (6)

where [·; ·] denotes vector concatenation, and(v1,v2, . . . ,v|C|) is the output sequence that rep-resents the temporal feature. We then transformthe sequence to a vector v by a max-pooling func-tion that captures the global information of stanceevolution, and feed it into a one-layer feed-forwardneural network (FNN) with softmax normalizationto produce the predicted veracity distribution v:

v = max-pooling(v1,v2, . . . ,v|C|) ,

v = softmax(FNN(v)) .(7)

The loss function of C for veracity prediction isalso computed by cross-entropy criterion:

Lveracity = −v> log v , (8)

where v denotes the veracity label of C.

4.3 Jointly Learning Two TasksTo leverage the interrelation between the precedingtask (stance classification) and the subsequent task(veracity prediction), we jointly train two compo-nents in our framework. Specifically, we add twotasks’ loss functions to obtain a joint loss functionL (with a trade-off parameter λ), and optimize Lto train our framework:

L = Lveracity + λLstance . (9)

In our Hierarchical-PSV, the bottom componentConversational-GCN learns content and stance fea-tures, and the top component Stance-Aware RNNtakes the learned features as input to further exploittemporal evolution for predicting rumor veracity.Our multi-task framework achieves deep integra-tion of the feature representation learning processfor the two closely related tasks.

5 Experiments

In this section, we first evaluate the performanceof Conversational-GCN on rumor stance classifi-cation and evaluate Hierarchical-PSV on veracityprediction (Section 5.3). We then give a detailedanalysis of our proposed method (Section 5.4).

5.1 Data & Evaluation MetricTo evaluate our proposed method, we conduct ex-periments on two benchmark datasets.

The first is SemEval-2017 task 8 (Derczynskiet al., 2017) dataset. It includes 325 rumorous con-versation threads, and has been split into training,development and test sets. These threads cover ten

4792

Dataset # Thread Depth # Tweet Stance Labels Veracity Labels

# support # deny # query # comment # true # false # unverified

SemEval 325 3.5 5,568 1,004 415 464 3,685 145 74 106PHEME 2,402 2.8 105,354 – 1,067 638 697

Table 1: Statistics of two datasets. The column “Depth” denotes the average depth of all conversation threads.

Method Evaluation MetricMacro-F1 FS FD FQ FC Acc.

Affective Feature + SVM (Pamungkas et al., 2018) 0.470 0.410 0.000 0.580 0.880 0.795BranchLSTM (Kochkina et al., 2017) 0.434 0.403 0.000 0.462 0.873 0.784TemporalAttention (Veyseh et al., 2017) 0.482 – – – – 0.820Conversational-GCN (Ours, L = 2) 0.499 0.311 0.194 0.646 0.847 0.751

Table 2: Results of rumor stance classification. FS, FD, FQ and FC denote the F1 scores of supporting, denying,querying and commenting classes respectively. “–” indicates that the original paper does not report the metric.

events, and two events of that only appear in thetest set. This dataset is used to evaluate both stanceclassification and veracity prediction tasks.

The second is PHEME dataset (Zubiaga et al.,2016b). It provides 2,402 conversations coveringnine events. Following previous work, we conductleave-one-event-out cross-validation: in each fold,one event’s conversations are used for testing, andall the rest events are used for training. The evalu-ation metric on this dataset is computed after inte-grating the outputs of all nine folds. Note that onlya subset of this dataset has stance labels, and allconversations in this subset are already containedin SemEval-2017 task 8 dataset. Thus, PHEMEdataset is used to evaluate veracity prediction task.

Table 1 shows the statistics of two datasets. Be-cause of the class-imbalanced problem, we usemacro-averaged F1 as the evaluation metric fortwo tasks. We also report accuracy for reference.

5.2 Implementation Details

In all experiments, the number of GCN layers isset to L = 2. We list the implementation details inAppendix A.

5.3 Experimental Results

5.3.1 Results: Rumor Stance ClassificationBaselines We compare our Conversational-GCNwith the following methods in the literature:• Affective Feature + SVM (Pamungkas et al.,

2018) extracts affective and dialogue-act featuresfor individual tweets, and then trains an SVM forclassifying stances.• BranchLSTM (Kochkina et al., 2017) is the

winner of SemEval-2017 shared task 8 subtask A. It

adopts an LSTM to model the sequential branchesin a conversation thread. Before feeding branchesinto the LSTM, some additional hand-crafted fea-tures are used to enrich the tweet representations.

• TemporalAttention (Veyseh et al., 2017) isthe state-of-the-art method. It uses a tweet’s “neigh-bors in the conversation timeline” as the context,and utilizes attention to model such temporal se-quence for learning the weight of each neighbor.Extra hand-crafted features are also used.

Performance Comparison Table 2 shows theresults of different methods for rumor stance clas-sification. Clearly, the macro-averaged F1 ofConversational-GCN is better than all baselines.

Especially, our method shows the effectivenessof determining denying stance, while other meth-ods can not give any correct prediction for denyingclass (the FD scores of them are equal to zero).Further, Conversational-GCN also achieves higherF1 score for querying stance (FQ). Identifyingdenying and querying stances correctly is crucialfor veracity prediction because they play the roleof indicators for false and unverified rumorsrespectively (see Figure 2). Meanwhile, the class-imbalanced problem of data makes this a challenge.Conversational-GCN effectively encodes structuralcontext for each tweet via aggregating informationfrom its neighbors, learning powerful stance fea-tures without feature engineering. It is also morecomputationally efficient than sequential and tem-poral based methods. The information aggregationsfor all tweets in a conversation are worked in par-allel and thus the running time is not sensitive toconversation’s depth.

4793

Setting Method SemEval dataset PHEME dataset

Macro-F1 Acc. Macro-F1 Acc.

Single-task TD-RvNN (Ma et al., 2018b) 0.509 0.536 0.264 0.341Hierarchical GCN-RNN (Ours) 0.540 0.536 0.317 0.356

Multi-taskBranchLSTM+NileTMRG (Kochkina et al., 2018) 0.539 0.570 0.297 0.360MTL2 (Veracity+Stance) (Kochkina et al., 2018) 0.558 0.571 0.318 0.357Hierarchical-PSV (Ours, λ = 1) 0.588 0.643 0.333 0.361

Table 3: Results of veracity prediction. Single-task setting means that stance labels cannot be used to train models.

5.3.2 Results: Rumor Veracity PredictionTo evaluate our framework Hierarchical-PSV, weconsider two groups of baselines: single-task andmulti-task baselines.

Single-task Baselines In single-task setting,stance labels are not available. Only veracity labelscan be used to supervise the training process.• TD-RvNN (Ma et al., 2018b) models the top-

down tree structure using a recursive neural net-work for veracity classification.• Hierarchical GCN-RNN is the single-task

variant of our framework: we optimize Lveracity(i.e., λ = 0 in Eq. (9)) during training. Thus, thebottom Conversational-GCN only has indirect su-pervision (veracity labels) to learn stance features.

Multi-task Baselines In multi-task setting,both stance labels and veracity labels are availablefor training.• BranchLSTM+NileTMRG (Kochkina et al.,

2018) is a pipeline method, combining the winnersystems of two subtasks in SemEval-2017 sharedtask 8. It first trains a BranchLSTM for stanceclassification, and then uses the predicted stancelabels as extra features to train an SVM for veracityprediction (Enayet and El-Beltagy, 2017).• MTL2 (Veracity+Stance) (Kochkina et al.,

2018) is a multi-task learning method that adoptsBranchLSTM as the shared block across tasks.Then, each task has a task-specific output layer,and two tasks are jointly learned.2

Performance Comparison Table 3 shows thecomparisons of different methods. By comparingsingle-task methods, Hierarchical GCN-RNN per-forms better than TD-RvNN, which indicates thatour hierarchical framework can effectively modelconversation structures to learn high-quality tweetrepresentations. The recursive operation in TD-

2Kochkina et al. (2018) also proposed MTL3 that jointlytrains three tasks (plus rumor detection (Zubiaga et al., 2017)).In our framework, we do not utilize data and labels from rumordetection task, and thus we choose MTL2 (Veracity+Stance)as the state-of-the-art method for comparison.

RvNN is performed in a fixed direction and runsover all tweets, thus may not obtain enough use-ful information. Moreover, the training speed ofHierarchical GCN-RNN is significantly faster thanTD-RvNN: in the condition of batch-wise optimiza-tion for training one step over a batch containing 32conversations, our method takes only 0.18 seconds,while TD-RvNN takes 5.02 seconds.

Comparisons among multi-task methods showthat two joint methods outperform the pipelinemethod (BranchLSTM+NileTMRG), indicatingthat jointly learning two tasks can improve the gen-eralization through leveraging the interrelation be-tween them. Further, compared with MTL2 whichuses a “parallel” architecture to make predictionsfor two tasks, our Hierarchical-PSV performs bet-ter than MTL2. The hierarchical architecture ismore effective to tackle the joint predictions ofrumor stance and veracity, because it not only pos-sesses the advantage of parameter-sharing but alsooffers deep integration of the feature representationlearning process for the two tasks. Compared withHierarchical GCN-RNN that does not use the super-vision from stance classification task, Hierarchical-PSV provides a performance boost, which demon-strates that our framework benefits from the jointlearning scheme.

5.4 Further Analysis and Discussions

We conduct additional experiments to furtherdemonstrate the effectiveness of our model.

5.4.1 Effect of Customized GraphConvolution

To show the effect of our customized graph convo-lution operation (Eq. (2)) for modeling conversa-tion structures, we further compare it with the orig-inal graph convolution (Eq. (1), named Original-GCN) on stance classification task.

Specifically, we cluster tweets in the test set ac-cording to their depths in the conversation threads(e.g., the cluster “depth = 0” consists of all source

4794

0 1 2 3 4 5 6+Depth

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mac

ro-F

1

BranchLSTMOriginal-GCNConversational-GCN

Figure 4: Stance classification results w.r.t. differentdepths (see Appendix B for exact numerical numbers).

Method Macro-F1 Acc.

Hierarchical-PSV (full model) 0.333 0.361– stance features 0.299 0.338

– GRU, + CNN 0.312 0.328– GRU 0.288 0.326

Table 4: Ablation tests of stance features and temporalmodeling for veracity prediction on PHEME dataset.

tweets in the test set). For BranchLSTM, Original-GCN and Conversational-GCN, we report theirmacro-averaged F1 on each cluster in Figure 4.

We observe that our Conversational-GCN out-performs Original-GCN and BranchLSTM signifi-cantly in most levels of depth. BranchLSTM mayprefer to “shallow” tweets in a conversation be-cause they often occur in multiple branches (e.g.,in Figure 1, the tweet “2” occurs in two branchesand thus it will be modeled twice). The resultsindicate that Conversational-GCN has advantage toidentify stances of “deep” tweets in conversations.

5.4.2 Ablation TestsEffect of Stance Features To understand the im-portance of stance features for veracity prediction,we conduct an ablation study: we only input thecontent features of all tweets in a conversation tothe top component RNN. It means that the RNNonly models the temporal variation of tweet con-tents during spreading, but does not consider theirstances and is not “stance-aware”. Table 4 showsthat “– stance features” performs poorly, and thusthe temporal modeling process benefits from the in-dicative signals provided by stance features. Hence,combining the low-level content features and thehigh-level stance features is crucial to improve ru-mor veracity prediction.

Effect of Temporal Evolution Modeling Wemodify the Stance-Aware RNN by two ways: (i)we replace the GRU layer by a CNN that only cap-

0.0 0.2 0.4 0.6 0.8 1.00.000.050.100.150.200.250.300.35

F F

FF

0.0

0.1

0.2

0.3

0.4

F U

FU

Figure 5: Veracity prediction results v.s. various val-ues of λ on PHEME dataset. FF and FU denote the F1

scores of false and unverified classes respectively.

supporting<latexit sha1_base64="5tnQ7qkx5YWeDPu4yoHLyufwt9Y=">AAAB8XicbVDLSgMxFL1TX7W+Rl26CRbBVZkRQZdFNy4r2Ae2Q8mkmTY0k4QkI5Shf+HGhSJu/Rt3/o1pOwttPRA4nHPvzb0nVpwZGwTfXmltfWNzq7xd2dnd2z/wD49aRmaa0CaRXOpOjA3lTNCmZZbTjtIUpzGn7Xh8O/PbT1QbJsWDnSgapXgoWMIItk56NJlSUlsmhn2/GtSCOdAqCQtShQKNvv/VG0iSpVRYwrEx3TBQNsqxm0Y4nVZ6maEKkzEe0q6jAqfURPl84yk6c8oAJVK7Jyyaq787cpwaM0ljV5liOzLL3kz8z+tmNrmOciZUZqkgi4+SjCMr0ex8NGCaEssnjmCimdsVkRHWmFgXUsWFEC6fvEpaF7UwqIX3l9X6TRFHGU7gFM4hhCuowx00oAkEBDzDK7x5xnvx3r2PRWnJK3qO4Q+8zx8q+5E5</latexit><latexit sha1_base64="5tnQ7qkx5YWeDPu4yoHLyufwt9Y=">AAAB8XicbVDLSgMxFL1TX7W+Rl26CRbBVZkRQZdFNy4r2Ae2Q8mkmTY0k4QkI5Shf+HGhSJu/Rt3/o1pOwttPRA4nHPvzb0nVpwZGwTfXmltfWNzq7xd2dnd2z/wD49aRmaa0CaRXOpOjA3lTNCmZZbTjtIUpzGn7Xh8O/PbT1QbJsWDnSgapXgoWMIItk56NJlSUlsmhn2/GtSCOdAqCQtShQKNvv/VG0iSpVRYwrEx3TBQNsqxm0Y4nVZ6maEKkzEe0q6jAqfURPl84yk6c8oAJVK7Jyyaq787cpwaM0ljV5liOzLL3kz8z+tmNrmOciZUZqkgi4+SjCMr0ex8NGCaEssnjmCimdsVkRHWmFgXUsWFEC6fvEpaF7UwqIX3l9X6TRFHGU7gFM4hhCuowx00oAkEBDzDK7x5xnvx3r2PRWnJK3qO4Q+8zx8q+5E5</latexit><latexit sha1_base64="5tnQ7qkx5YWeDPu4yoHLyufwt9Y=">AAAB8XicbVDLSgMxFL1TX7W+Rl26CRbBVZkRQZdFNy4r2Ae2Q8mkmTY0k4QkI5Shf+HGhSJu/Rt3/o1pOwttPRA4nHPvzb0nVpwZGwTfXmltfWNzq7xd2dnd2z/wD49aRmaa0CaRXOpOjA3lTNCmZZbTjtIUpzGn7Xh8O/PbT1QbJsWDnSgapXgoWMIItk56NJlSUlsmhn2/GtSCOdAqCQtShQKNvv/VG0iSpVRYwrEx3TBQNsqxm0Y4nVZ6maEKkzEe0q6jAqfURPl84yk6c8oAJVK7Jyyaq787cpwaM0ljV5liOzLL3kz8z+tmNrmOciZUZqkgi4+SjCMr0ex8NGCaEssnjmCimdsVkRHWmFgXUsWFEC6fvEpaF7UwqIX3l9X6TRFHGU7gFM4hhCuowx00oAkEBDzDK7x5xnvx3r2PRWnJK3qO4Q+8zx8q+5E5</latexit><latexit sha1_base64="5tnQ7qkx5YWeDPu4yoHLyufwt9Y=">AAAB8XicbVDLSgMxFL1TX7W+Rl26CRbBVZkRQZdFNy4r2Ae2Q8mkmTY0k4QkI5Shf+HGhSJu/Rt3/o1pOwttPRA4nHPvzb0nVpwZGwTfXmltfWNzq7xd2dnd2z/wD49aRmaa0CaRXOpOjA3lTNCmZZbTjtIUpzGn7Xh8O/PbT1QbJsWDnSgapXgoWMIItk56NJlSUlsmhn2/GtSCOdAqCQtShQKNvv/VG0iSpVRYwrEx3TBQNsqxm0Y4nVZ6maEKkzEe0q6jAqfURPl84yk6c8oAJVK7Jyyaq787cpwaM0ljV5liOzLL3kz8z+tmNrmOciZUZqkgi4+SjCMr0ex8NGCaEssnjmCimdsVkRHWmFgXUsWFEC6fvEpaF7UwqIX3l9X6TRFHGU7gFM4hhCuowx00oAkEBDzDK7x5xnvx3r2PRWnJK3qO4Q+8zx8q+5E5</latexit>

querying<latexit sha1_base64="glzlt6zjq/sNECJ1l+RRW2Y5yIw=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymY7aZduNunuRgihf8KLB0W8+ne8+W/ctjlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dJwqhk0Wi1h1AqpRcIlNw43ATqKQRoHAdjC+m/ntJ1Sax/LRZAn6ER1KHnJGjZU6kxRVxuWwX6m6NXcOskq8glShQKNf+eoNYpZGKA0TVOuu5ybGz6kynAmclnupxoSyMR1i11JJI9R+Pr93Ss6tMiBhrGxJQ+bq74mcRlpnUWA7I2pGetmbif953dSEN37OZZIalGyxKEwFMTGZPU8GXCEzIrOEMsXtrYSNqKLM2IjKNgRv+eVV0rqseW7Ne7iq1m+LOEpwCmdwAR5cQx3uoQFNYCDgGV7hzZk4L86787FoXXOKmRP4A+fzB3sqkD4=</latexit><latexit sha1_base64="glzlt6zjq/sNECJ1l+RRW2Y5yIw=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymY7aZduNunuRgihf8KLB0W8+ne8+W/ctjlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dJwqhk0Wi1h1AqpRcIlNw43ATqKQRoHAdjC+m/ntJ1Sax/LRZAn6ER1KHnJGjZU6kxRVxuWwX6m6NXcOskq8glShQKNf+eoNYpZGKA0TVOuu5ybGz6kynAmclnupxoSyMR1i11JJI9R+Pr93Ss6tMiBhrGxJQ+bq74mcRlpnUWA7I2pGetmbif953dSEN37OZZIalGyxKEwFMTGZPU8GXCEzIrOEMsXtrYSNqKLM2IjKNgRv+eVV0rqseW7Ne7iq1m+LOEpwCmdwAR5cQx3uoQFNYCDgGV7hzZk4L86787FoXXOKmRP4A+fzB3sqkD4=</latexit><latexit sha1_base64="glzlt6zjq/sNECJ1l+RRW2Y5yIw=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymY7aZduNunuRgihf8KLB0W8+ne8+W/ctjlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dJwqhk0Wi1h1AqpRcIlNw43ATqKQRoHAdjC+m/ntJ1Sax/LRZAn6ER1KHnJGjZU6kxRVxuWwX6m6NXcOskq8glShQKNf+eoNYpZGKA0TVOuu5ybGz6kynAmclnupxoSyMR1i11JJI9R+Pr93Ss6tMiBhrGxJQ+bq74mcRlpnUWA7I2pGetmbif953dSEN37OZZIalGyxKEwFMTGZPU8GXCEzIrOEMsXtrYSNqKLM2IjKNgRv+eVV0rqseW7Ne7iq1m+LOEpwCmdwAR5cQx3uoQFNYCDgGV7hzZk4L86787FoXXOKmRP4A+fzB3sqkD4=</latexit><latexit sha1_base64="glzlt6zjq/sNECJ1l+RRW2Y5yIw=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymY7aZduNunuRgihf8KLB0W8+ne8+W/ctjlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dJwqhk0Wi1h1AqpRcIlNw43ATqKQRoHAdjC+m/ntJ1Sax/LRZAn6ER1KHnJGjZU6kxRVxuWwX6m6NXcOskq8glShQKNf+eoNYpZGKA0TVOuu5ybGz6kynAmclnupxoSyMR1i11JJI9R+Pr93Ss6tMiBhrGxJQ+bq74mcRlpnUWA7I2pGetmbif953dSEN37OZZIalGyxKEwFMTGZPU8GXCEzIrOEMsXtrYSNqKLM2IjKNgRv+eVV0rqseW7Ne7iq1m+LOEpwCmdwAR5cQx3uoQFNYCDgGV7hzZk4L86787FoXXOKmRP4A+fzB3sqkD4=</latexit>

denying<latexit sha1_base64="V12bKXEB6EpPBRFHn+6mJrWSs3k=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymYzaZduNmF3I4TQH+HFgyJe/T3e/Ddu2xy09cHA470ZZuYFqeDauO63s7a+sbm1Xdmp7u7tHxzWjo47OskUwzZLRKJ6AdUouMS24UZgL1VI40BgN5jczfzuEyrNE/lo8hT9mI4kjzijxkrdEGXO5WhYq7sNdw6ySryS1KFEa1j7GoQJy2KUhgmqdd9zU+MXVBnOBE6rg0xjStmEjrBvqaQxar+Ynzsl51YJSZQoW9KQufp7oqCx1nkc2M6YmrFe9mbif14/M9GNX3CZZgYlWyyKMkFMQma/k5ArZEbkllCmuL2VsDFVlBmbUNWG4C2/vEo6lw3PbXgPV/XmbRlHBU7hDC7Ag2towj20oA0MJvAMr/DmpM6L8+58LFrXnHLmBP7A+fwBh4aPrg==</latexit><latexit sha1_base64="V12bKXEB6EpPBRFHn+6mJrWSs3k=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymYzaZduNmF3I4TQH+HFgyJe/T3e/Ddu2xy09cHA470ZZuYFqeDauO63s7a+sbm1Xdmp7u7tHxzWjo47OskUwzZLRKJ6AdUouMS24UZgL1VI40BgN5jczfzuEyrNE/lo8hT9mI4kjzijxkrdEGXO5WhYq7sNdw6ySryS1KFEa1j7GoQJy2KUhgmqdd9zU+MXVBnOBE6rg0xjStmEjrBvqaQxar+Ynzsl51YJSZQoW9KQufp7oqCx1nkc2M6YmrFe9mbif14/M9GNX3CZZgYlWyyKMkFMQma/k5ArZEbkllCmuL2VsDFVlBmbUNWG4C2/vEo6lw3PbXgPV/XmbRlHBU7hDC7Ag2towj20oA0MJvAMr/DmpM6L8+58LFrXnHLmBP7A+fwBh4aPrg==</latexit><latexit sha1_base64="V12bKXEB6EpPBRFHn+6mJrWSs3k=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymYzaZduNmF3I4TQH+HFgyJe/T3e/Ddu2xy09cHA470ZZuYFqeDauO63s7a+sbm1Xdmp7u7tHxzWjo47OskUwzZLRKJ6AdUouMS24UZgL1VI40BgN5jczfzuEyrNE/lo8hT9mI4kjzijxkrdEGXO5WhYq7sNdw6ySryS1KFEa1j7GoQJy2KUhgmqdd9zU+MXVBnOBE6rg0xjStmEjrBvqaQxar+Ynzsl51YJSZQoW9KQufp7oqCx1nkc2M6YmrFe9mbif14/M9GNX3CZZgYlWyyKMkFMQma/k5ArZEbkllCmuL2VsDFVlBmbUNWG4C2/vEo6lw3PbXgPV/XmbRlHBU7hDC7Ag2towj20oA0MJvAMr/DmpM6L8+58LFrXnHLmBP7A+fwBh4aPrg==</latexit><latexit sha1_base64="V12bKXEB6EpPBRFHn+6mJrWSs3k=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymYzaZduNmF3I4TQH+HFgyJe/T3e/Ddu2xy09cHA470ZZuYFqeDauO63s7a+sbm1Xdmp7u7tHxzWjo47OskUwzZLRKJ6AdUouMS24UZgL1VI40BgN5jczfzuEyrNE/lo8hT9mI4kjzijxkrdEGXO5WhYq7sNdw6ySryS1KFEa1j7GoQJy2KUhgmqdd9zU+MXVBnOBE6rg0xjStmEjrBvqaQxar+Ynzsl51YJSZQoW9KQufp7oqCx1nkc2M6YmrFe9mbif14/M9GNX3CZZgYlWyyKMkFMQma/k5ArZEbkllCmuL2VsDFVlBmbUNWG4C2/vEo6lw3PbXgPV/XmbRlHBU7hDC7Ag2towj20oA0MJvAMr/DmpM6L8+58LFrXnHLmBP7A+fwBh4aPrg==</latexit>

querying<latexit sha1_base64="glzlt6zjq/sNECJ1l+RRW2Y5yIw=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymY7aZduNunuRgihf8KLB0W8+ne8+W/ctjlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dJwqhk0Wi1h1AqpRcIlNw43ATqKQRoHAdjC+m/ntJ1Sax/LRZAn6ER1KHnJGjZU6kxRVxuWwX6m6NXcOskq8glShQKNf+eoNYpZGKA0TVOuu5ybGz6kynAmclnupxoSyMR1i11JJI9R+Pr93Ss6tMiBhrGxJQ+bq74mcRlpnUWA7I2pGetmbif953dSEN37OZZIalGyxKEwFMTGZPU8GXCEzIrOEMsXtrYSNqKLM2IjKNgRv+eVV0rqseW7Ne7iq1m+LOEpwCmdwAR5cQx3uoQFNYCDgGV7hzZk4L86787FoXXOKmRP4A+fzB3sqkD4=</latexit><latexit sha1_base64="glzlt6zjq/sNECJ1l+RRW2Y5yIw=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymY7aZduNunuRgihf8KLB0W8+ne8+W/ctjlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dJwqhk0Wi1h1AqpRcIlNw43ATqKQRoHAdjC+m/ntJ1Sax/LRZAn6ER1KHnJGjZU6kxRVxuWwX6m6NXcOskq8glShQKNf+eoNYpZGKA0TVOuu5ybGz6kynAmclnupxoSyMR1i11JJI9R+Pr93Ss6tMiBhrGxJQ+bq74mcRlpnUWA7I2pGetmbif953dSEN37OZZIalGyxKEwFMTGZPU8GXCEzIrOEMsXtrYSNqKLM2IjKNgRv+eVV0rqseW7Ne7iq1m+LOEpwCmdwAR5cQx3uoQFNYCDgGV7hzZk4L86787FoXXOKmRP4A+fzB3sqkD4=</latexit><latexit sha1_base64="glzlt6zjq/sNECJ1l+RRW2Y5yIw=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymY7aZduNunuRgihf8KLB0W8+ne8+W/ctjlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dJwqhk0Wi1h1AqpRcIlNw43ATqKQRoHAdjC+m/ntJ1Sax/LRZAn6ER1KHnJGjZU6kxRVxuWwX6m6NXcOskq8glShQKNf+eoNYpZGKA0TVOuu5ybGz6kynAmclnupxoSyMR1i11JJI9R+Pr93Ss6tMiBhrGxJQ+bq74mcRlpnUWA7I2pGetmbif953dSEN37OZZIalGyxKEwFMTGZPU8GXCEzIrOEMsXtrYSNqKLM2IjKNgRv+eVV0rqseW7Ne7iq1m+LOEpwCmdwAR5cQx3uoQFNYCDgGV7hzZk4L86787FoXXOKmRP4A+fzB3sqkD4=</latexit><latexit sha1_base64="glzlt6zjq/sNECJ1l+RRW2Y5yIw=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymY7aZduNunuRgihf8KLB0W8+ne8+W/ctjlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dJwqhk0Wi1h1AqpRcIlNw43ATqKQRoHAdjC+m/ntJ1Sax/LRZAn6ER1KHnJGjZU6kxRVxuWwX6m6NXcOskq8glShQKNf+eoNYpZGKA0TVOuu5ybGz6kynAmclnupxoSyMR1i11JJI9R+Pr93Ss6tMiBhrGxJQ+bq74mcRlpnUWA7I2pGetmbif953dSEN37OZZIalGyxKEwFMTGZPU8GXCEzIrOEMsXtrYSNqKLM2IjKNgRv+eVV0rqseW7Ne7iq1m+LOEpwCmdwAR5cQx3uoQFNYCDgGV7hzZk4L86787FoXXOKmRP4A+fzB3sqkD4=</latexit>

commenting<latexit sha1_base64="xoQaQ3Om1v8PnJj0zeiDzda5pR8=">AAAB8XicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiG5cV7APboWTSTBuax5BkhDL0L9y4UMStf+POvzHTzkJbDwQO59xD7j1Rwpmxvv/tldbWNza3ytuVnd29/YPq4VHbqFQT2iKKK92NsKGcSdqyzHLaTTTFIuK0E01uc7/zRLVhSj7YaUJDgUeSxYxg66RHooSg0jI5GlRrft2fA62SoCA1KNAcVL/6Q0XSPE44NqYX+IkNM6wtI5zOKv3U0ASTCR7RnqMSC2rCbL7xDJ05ZYhipd2TFs3V34kMC2OmInKTAtuxWfZy8T+vl9r4OsyYTFJLJVl8FKccWYXy89GQaUosnzqCiWZuV0TGWGNiXUkVV0KwfPIqaV/UA78e3F/WGjdFHWU4gVM4hwCuoAF30IQWEJDwDK/w5hnvxXv3PhajJa/IHMMfeJ8/6huRDw==</latexit><latexit sha1_base64="xoQaQ3Om1v8PnJj0zeiDzda5pR8=">AAAB8XicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiG5cV7APboWTSTBuax5BkhDL0L9y4UMStf+POvzHTzkJbDwQO59xD7j1Rwpmxvv/tldbWNza3ytuVnd29/YPq4VHbqFQT2iKKK92NsKGcSdqyzHLaTTTFIuK0E01uc7/zRLVhSj7YaUJDgUeSxYxg66RHooSg0jI5GlRrft2fA62SoCA1KNAcVL/6Q0XSPE44NqYX+IkNM6wtI5zOKv3U0ASTCR7RnqMSC2rCbL7xDJ05ZYhipd2TFs3V34kMC2OmInKTAtuxWfZy8T+vl9r4OsyYTFJLJVl8FKccWYXy89GQaUosnzqCiWZuV0TGWGNiXUkVV0KwfPIqaV/UA78e3F/WGjdFHWU4gVM4hwCuoAF30IQWEJDwDK/w5hnvxXv3PhajJa/IHMMfeJ8/6huRDw==</latexit><latexit sha1_base64="xoQaQ3Om1v8PnJj0zeiDzda5pR8=">AAAB8XicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiG5cV7APboWTSTBuax5BkhDL0L9y4UMStf+POvzHTzkJbDwQO59xD7j1Rwpmxvv/tldbWNza3ytuVnd29/YPq4VHbqFQT2iKKK92NsKGcSdqyzHLaTTTFIuK0E01uc7/zRLVhSj7YaUJDgUeSxYxg66RHooSg0jI5GlRrft2fA62SoCA1KNAcVL/6Q0XSPE44NqYX+IkNM6wtI5zOKv3U0ASTCR7RnqMSC2rCbL7xDJ05ZYhipd2TFs3V34kMC2OmInKTAtuxWfZy8T+vl9r4OsyYTFJLJVl8FKccWYXy89GQaUosnzqCiWZuV0TGWGNiXUkVV0KwfPIqaV/UA78e3F/WGjdFHWU4gVM4hwCuoAF30IQWEJDwDK/w5hnvxXv3PhajJa/IHMMfeJ8/6huRDw==</latexit><latexit sha1_base64="xoQaQ3Om1v8PnJj0zeiDzda5pR8=">AAAB8XicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiG5cV7APboWTSTBuax5BkhDL0L9y4UMStf+POvzHTzkJbDwQO59xD7j1Rwpmxvv/tldbWNza3ytuVnd29/YPq4VHbqFQT2iKKK92NsKGcSdqyzHLaTTTFIuK0E01uc7/zRLVhSj7YaUJDgUeSxYxg66RHooSg0jI5GlRrft2fA62SoCA1KNAcVL/6Q0XSPE44NqYX+IkNM6wtI5zOKv3U0ASTCR7RnqMSC2rCbL7xDJ05ZYhipd2TFs3V34kMC2OmInKTAtuxWfZy8T+vl9r4OsyYTFJLJVl8FKccWYXy89GQaUosnzqCiWZuV0TGWGNiXUkVV0KwfPIqaV/UA78e3F/WGjdFHWU4gVM4hwCuoAF30IQWEJDwDK/w5hnvxXv3PhajJa/IHMMfeJ8/6huRDw==</latexit>

NEWS: 'Emergency Emergency' was the final distress call that was sent from the cockpit of flight #4U9525 - @PollyR_Aviation

@airlivenet @PollyR_Aviation is that a normal call in this situation?

@airlivenet I doubt any pilot would say 'Emergency', but rather 'Mayday'

@PascalSyn @airlivenet but isn’t declaring an emergency the proper procedure if you still have control of the situation?

@damienramage @airlivenet Plus they stayed more or less constant speed, which means they reduced throttle, so they were in control #u4u9525

Conversation Thread Stance EvolutionMar 24 12:55:38

Mar 24 12:56:53

Mar 24 13:03:53

Mar 24 13:13:17

Mar 24 13:20:03





Figure 6: Case study: a false rumor. Each tweet iscolored by the number of dimensions it contributes tov in the max-pooling operation (Eq. (7)). We show im-portant tweets in the conversation and truncate others.

tures local temporal information; (ii) we remove theGRU layer. Results in Table 4 verify that replacingor removing the GRU block hurts the performance,and thus modeling the stance evolution of publicreactions towards a rumorous message is indeednecessary for effective veracity prediction.

5.4.3 Interrelation of Stance and VeracityWe vary the value of λ in the joint loss L and trainmodels with various λ to show the interrelationbetween stance and veracity in Figure 5. As λincreases from 0.0 to 1.0, the performance of iden-tifying false and unverified rumors generallygains. Therefore, when the supervision signal ofstance classification becomes strong, the learnedstance features can produce more accurate cluesfor predicting rumor veracity.

5.5 Case Study

Figure 6 illustrates a false rumor identified byour model. We can observe that the stances ofreply tweets present a typical temporal pattern“supporting → querying → denying”. Our

4795

model captures such stance evolution with RNNand predicts its veracity correctly. Further, the vi-sualization of tweets shows that the max-poolingoperation catches informative tweets in the conver-sation. Hence, our framework can notice salienceindicators of rumor veracity in the spreading pro-cess and combine them to give correct prediction.

6 Conclusion

We propose a hierarchical multi-task learningframework for jointly predicting rumor stance andveracity on Twitter. We design a new graph con-volution operation, Conversational-GCN, to en-code conversation structures for classifying stance,and then the top Stance-Aware RNN combines thelearned features to model the temporal dynamicsof stance evolution for veracity prediction. Experi-mental results verify that Conversational-GCN canhandle deep conversation structures effectively, andour hierarchical framework performs much betterthan existing methods. In future work, we shallexplore to incorporate external context (Derczyn-ski et al., 2017; Popat et al., 2018), and extendour model to multi-lingual scenarios (Wen et al.,2018). Moreover, we shall investigate the diffu-sion process of rumors from social science perspec-tive (Vosoughi et al., 2018), draw deeper insightsfrom there and try to incorporate them into themodel design.

Acknowledgments

This work was supported in part by the Na-tional Key R&D Program of China under Grant#2016QY02D0305, NSFC Grants #71621002,#71472175, #71974187 and #71602184, andMinistry of Health of China under Grant#2017ZX10303401-002. We thank all the anony-mous reviewers for their valuable comments. Wealso thank Qianqian Dong for her kind assistance.

ReferencesAhmet Aker, Leon Derczynski, and Kalina Bontcheva.

2017. Simple open stance classification for rumouranalysis. In Proceedings of RANLP, pages 31–39.

Isabelle Augenstein, Tim Rocktaschel, Andreas Vla-chos, and Kalina Bontcheva. 2016. Stance detectionwith bidirectional conditional encoding. In Proceed-ings of EMNLP, pages 876–885.

Carlos Castillo, Marcelo Mendoza, and BarbaraPoblete. 2011. Information credibility on Twitter.In Proceedings of WWW, pages 675–684.

Kyunghyun Cho, Bart van Merrienboer, Caglar Gul-cehre, Dzmitry Bahdanau, Fethi Bougares, HolgerSchwenk, and Yoshua Bengio. 2014. Learningphrase representations using RNN encoder–decoderfor statistical machine translation. In Proceedings ofEMNLP, pages 1724–1734.

Nicola De Cao, Wilker Aziz, and Ivan Titov. 2019.Question answering by reasoning across documentswith graph convolutional networks. In Proceedingsof NAACL-HLT, pages 2306–2317.

Leon Derczynski, Kalina Bontcheva, Maria Liakata,Rob Procter, Geraldine Wong Sak Hoi, and ArkaitzZubiaga. 2017. SemEval-2017 task 8: RumourEval:Determining rumour veracity and support for ru-mours. In Proceedings of SemEval, pages 69–76.

Sebastian Dungs, Ahmet Aker, Norbert Fuhr, andKalina Bontcheva. 2018. Can rumour stance alonepredict veracity? In Proceedings of COLING, pages3360–3370.

Omar Enayet and Samhaa R El-Beltagy. 2017.NileTMRG at SemEval-2017 task 8: Determiningrumour and veracity support for rumours on Twitter.In Proceedings of SemEval, pages 470–474.

William Ferreira and Andreas Vlachos. 2016. Emer-gent: A novel data-set for stance classification. InProceedings of NAACL-HLT, pages 1163–1168.

Georgios Giasemidis, Nikolaos Kaplis, Ioannis Agrafi-otis, and Jason Nurse. 2018. A semi-supervisedapproach to message stance classification. IEEETransactions on Knowledge and Data Engineering(TKDE).

Maria Glenski, Tim Weninger, and Svitlana Volkova.2018. Identifying and understanding user reactionsto deceptive and trusted social news sources. In Pro-ceedings of ACL, pages 176–181.

Sardar Hamidian and Mona Diab. 2016. Rumor identi-fication and belief investigation on Twitter. In Pro-ceedings of NAACL-HLT, pages 3–8.

Kazi Saidul Hasan and Vincent Ng. 2013. Extra-linguistic constraints on stance recognition in ideo-logical debates. In Proceedings of ACL, pages 816–821.

Zhiwei Jin, Juan Cao, Yongdong Zhang, and Jiebo Luo.2016. News verification by exploiting conflictingsocial viewpoints in microblogs. In Proceedings ofAAAI, pages 2972–2978.

Yoon Kim. 2014. Convolutional neural networks forsentence classification. In Proceedings of EMNLP,pages 1746–1751.

Diederik Kingma and Jimmy Ba. 2015. Adam: Amethod for stochastic optimization. In Proceedingsof ICLR.

http://www.acl-bg.org/proceedings/2017/RANLP%202017/pdf/RANLP005.pdf

http://www.acl-bg.org/proceedings/2017/RANLP%202017/pdf/RANLP005.pdf

http://www.aclweb.org/anthology/D16-1084


https://dl.acm.org/citation.cfm?id=1963500

http://anthology.aclweb.org/D/D14/D14-1179.pdf



https://aclweb.org/anthology/papers/N/N19/N19-1240/

https://aclweb.org/anthology/papers/N/N19/N19-1240/

http://aclweb.org/anthology/S17-2006



http://www.aclweb.org/anthology/C18-1284


http://www.aclweb.org/anthology/S17-2082


http://www.aclweb.org/anthology/N16-1138


https://ieeexplore.ieee.org/abstract/document/8528884


http://www.aclweb.org/anthology/P18-2029


http://www.aclweb.org/anthology/W16-0403

http://www.aclweb.org/anthology/W16-0403




https://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12128


https://www.aclweb.org/anthology/D14-1181


https://arxiv.org/pdf/1412.6980.pdf%20%22%20entire%20document

https://arxiv.org/pdf/1412.6980.pdf%20%22%20entire%20document

4796

Thomas N Kipf and Max Welling. 2017. Semi-supervised classification with graph convolutionalnetworks. In Proceedings of ICLR.

Elena Kochkina, Maria Liakata, and Isabelle Augen-stein. 2017. Turing at SemEval-2017 task 8: Sequen-tial approach to rumour stance classification withbranch-LSTM. In Proceedings of SemEval, pages475–480.

Elena Kochkina, Maria Liakata, and Arkaitz Zubiaga.2018. All-in-one: Multi-task learning for rumourverification. In Proceedings of COLING, pages3402–3413.

Sejeong Kwon, Meeyoung Cha, Kyomin Jung, WeiChen, and Yajun Wang. 2013. Prominent featuresof rumor propagation in online social media. In Pro-ceedings of ICDM, pages 1103–1108.

Xiaomo Liu, Armineh Nourbakhsh, Quanzhi Li, RuiFang, and Sameena Shah. 2015. Real-time rumor de-bunking on Twitter. In Proceedings of CIKM, pages1867–1870.

Yang Liu and Yi-fang Brook Wu. 2018. Early detectionof fake news on social media through propagationpath classification with recurrent and convolutionalnetworks. In Proceedings of AAAI, pages 354–361.

Michal Lukasik, Kalina Bontcheva, Trevor Cohn,Arkaitz Zubiaga, Maria Liakata, and Rob Procter.2019. Gaussian processes for rumour stance clas-sification in social media. ACM Transactions on In-formation Systems (TOIS), 37(2):20.

Michal Lukasik, PK Srijith, Duy Vu, Kalina Bontcheva,Arkaitz Zubiaga, and Trevor Cohn. 2016. Hawkesprocesses for continuous time sequence classifica-tion: An application to rumour stance classificationin Twitter. In Proceedings of ACL, pages 393–398.

Jing Ma, Wei Gao, Prasenjit Mitra, Sejeong Kwon,Bernard J Jansen, Kam-Fai Wong, and MeeyoungCha. 2016. Detecting rumors from microblogs withrecurrent neural networks. In Proceedings of IJCAI,pages 3818–3824.

Jing Ma, Wei Gao, and Kam-Fai Wong. 2017. Detectrumors in microblog posts using propagation struc-ture via kernel learning. In Proceedings of ACL,pages 708–717.

Jing Ma, Wei Gao, and Kam-Fai Wong. 2018a. Detectrumor and stance jointly by neural multi-task learn-ing. In Proceedings of WWW Companion, pages585–593.

Jing Ma, Wei Gao, and Kam-Fai Wong. 2018b. Ru-mor detection on Twitter with tree-structured recur-sive neural networks. In Proceedings of ACL, pages1980–1989.

Diego Marcheggiani and Ivan Titov. 2017. Encodingsentences with graph convolutional networks for se-mantic role labeling. In Proceedings of EMNLP,pages 1506–1515.

Marcelo Mendoza, Barbara Poblete, and CarlosCastillo. 2010. Twitter under crisis: Can we trustwhat we RT? In Proceedings of the 1st Workshop onSocial Media Analytics (SOMA), pages 71–79.

Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg Cor-rado, and Jeff Dean. 2013. Distributed representa-tions of words and phrases and their compositional-ity. In Proceedings of NIPS, pages 3111–3119.

Saif Mohammad, Svetlana Kiritchenko, Parinaz Sob-hani, Xiaodan Zhu, and Colin Cherry. 2016.SemEval-2016 task 6: Detecting stance in tweets. InProceedings of SemEval, pages 31–41.

Mitra Mohtarami, Ramy Baly, James Glass, PreslavNakov, Lluıs Marquez, and Alessandro Moschitti.2018. Automatic stance detection using end-to-endmemory networks. In Proceedings of NAACL-HLT,pages 767–776.

Ray Oshikawa, Jing Qian, and William Yang Wang.2018. A survey on natural language process-ing for fake news detection. arXiv preprintarXiv:1811.00770.

Endang Wahyu Pamungkas, Valerio Basile, and Vi-viana Patti. 2018. Stance classification for rumouranalysis in Twitter: Exploiting affective informationand conversation structure. In Proceedings of the2nd International Workshop on Rumours and Decep-tion in Social Media (RDSM).

Lahari Poddar, Wynne Hsu, Mong Li Lee, and ShrutiSubramaniyam. 2018. Predicting stances in Twit-ter conversations for detecting veracity of rumors:A neural approach. In Proceedings of ICTAI, pages65–72.

Kashyap Popat, Subhabrata Mukherjee, Andrew Yates,and Gerhard Weikum. 2018. DeClarE: Debunkingfake news and false claims using evidence-awaredeep learning. In Proceedings of EMNLP, pages 22–32.

Rob Procter, Farida Vis, and Alex Voss. 2013. Readingthe riots on Twitter: Methodological innovation forthe analysis of big data. International Journal ofSocial Research Methodology, 16(3):197–214.

Vahed Qazvinian, Emily Rosengren, Dragomir RRadev, and Qiaozhu Mei. 2011. Rumor has it: Iden-tifying misinformation in microblogs. In Proceed-ings of EMNLP, pages 1589–1599.

Natali Ruchansky, Sungyong Seo, and Yan Liu. 2017.CSI: A hybrid deep model for fake news detection.In Proceedings of CIKM, pages 797–806.

Karishma Sharma, Feng Qian, He Jiang, NataliRuchansky, Ming Zhang, and Yan Liu. 2019. Com-bating fake news: A survey on identification and mit-igation techniques. ACM Transactions on IntelligentSystems and Technology (TIST).

https://openreview.net/pdf?id=SJU4ayYgl






http://aclweb.org/anthology/C18-1288

http://aclweb.org/anthology/C18-1288









https://dl.acm.org/citation.cfm?id=3295823&picked=formats

https://dl.acm.org/citation.cfm?id=3295823&picked=formats





https://www.ijcai.org/Proceedings/16/Papers/537.pdf

https://www.ijcai.org/Proceedings/16/Papers/537.pdf















http://papers.nips.cc/paper/5021-distributed-representations-of-words-and-phrases-and-their-compositionality.pdf






https://arxiv.org/pdf/1811.00770.pdf


https://arxiv.org/abs/1901.01911






http://aclweb.org/anthology/D18-1003



https://www.tandfonline.com/doi/abs/10.1080/13645579.2013.774172









4797

Kai Shu, Amy Sliva, Suhang Wang, Jiliang Tang, andHuan Liu. 2017. Fake news detection on social me-dia: A data mining perspective. ACM SIGKDD Ex-plorations Newsletter, 19(1):22–36.

Swapna Somasundaran and Janyce Wiebe. 2009. Rec-ognizing stances in online debates. In Proceedingsof ACL-IJCNLP, pages 226–234.

Amir Pouran Ben Veyseh, Javid Ebrahimi, Dejing Dou,and Daniel Lowd. 2017. A temporal attentionalmodel for rumor stance classification. In Proceed-ings of CIKM, pages 2335–2338.

Soroush Vosoughi, Deb Roy, and Sinan Aral. 2018.The spread of true and false news online. Science,359(6380):1146–1151.

Weiming Wen, Songwen Su, and Zhou Yu. 2018.Cross-lingual cross-platform rumor verification piv-oting on multimedia content. In Proceedings ofEMNLP, pages 3487–3496.

Ke Wu, Song Yang, and Kenny Q Zhu. 2015. False ru-mors detection on Sina weibo by propagation struc-tures. In Proceedings of ICDE, pages 651–662.

Michihiro Yasunaga, Rui Zhang, Kshitijh Meelu,Ayush Pareek, Krishnan Srinivasan, and DragomirRadev. 2017. Graph-based neural multi-documentsummarization. In Proceedings of CoNLL, pages452–462.

Li Zeng, Kate Starbird, and Emma S Spiro. 2016.#unconfirmed: Classifying rumor stance in crisis-related social media messages. In Proceedings ofICWSM, pages 747–750.

Yuhao Zhang, Peng Qi, and Christopher D Manning.2018. Graph convolution over pruned dependencytrees improves relation extraction. In Proceedingsof EMNLP, pages 2205–2215.

Zhe Zhao, Paul Resnick, and Qiaozhu Mei. 2015. En-quiring minds: Early detection of rumors in socialmedia from enquiry posts. In Proceedings of WWW,pages 1395–1405.

Xinyi Zhou and Reza Zafarani. 2018. Fake news: Asurvey of research, detection methods, and opportu-nities. arXiv preprint arXiv:1812.00315.

Arkaitz Zubiaga, Ahmet Aker, Kalina Bontcheva,Maria Liakata, and Rob Procter. 2018. Detectionand resolution of rumours in social media: A survey.ACM Computing Surveys (CSUR), 51(2):32.

Arkaitz Zubiaga, Elena Kochkina, Maria Liakata, RobProcter, and Michal Lukasik. 2016a. Stance classifi-cation in rumours as a sequential task exploiting thetree structure of social media conversations. In Pro-ceedings of COLING, pages 2438–2448.

Arkaitz Zubiaga, Maria Liakata, and Rob Procter. 2017.Exploiting context for rumour detection in social me-dia. In Proceedings of SocInfo, pages 109–123.

Arkaitz Zubiaga, Maria Liakata, Rob Procter, Geral-dine Wong Sak Hoi, and Peter Tolmie. 2016b.Analysing how people orient to and spread rumoursin social media by looking at conversational threads.PloS one, 11(3):e0150989.

A Implementation Details

A.1 HyperparametersSemEval-2017 task 8 dataset We pretrain 200-dimensional word embeddings by Skip-gram withnegative sampling (Mikolov et al., 2013), and theyare fixed during the training process. We set thedimension of content feature to 200. We use a two-layer GCN, and the output sizes of two layers are200 and 4, respectively. The max-pooling functionin Eq. (7) is to select the maximum value of eachdimension, and thus the size of v is equal to that ofvi. The trade-off parameter λ is set to 1. We adddropout with 0.5 ratio to all but the last GCN layersand the FNN layer (used for veracity prediction).We train our model with 0.001 learning rate and32 batch size using Adam (Kingma and Ba, 2015).For this dataset, after tuning hyperparameters onthe development set, we merge the training andthe development sets and re-train our model on themerged set.PHEME dataset We set the learning rate to0.005 for accelerating the training process. Otherconfigurations are same to that of SemEval dataset.Because only a subset of PHEME dataset containsstance labels, if a training conversation does nothave stance labels, we will not compute its lossfunction of rumor stance classification task duringthe training process.

A.2 The CNN Layer in Ablation StudyIn Section 5.4.2, to demonstrate the effectivenessof modeling the temporal dynamics of stance evolu-tion, we replace the GRU layer by a CNN layer thatonly captures local temporal information. Specifi-cally, this CNN layer consists of a 1D convolutionlayer and a max-pooling function (Kim, 2014). Weuse three different filter windows: 2, 3 and 4. Eachfilter window has 100 feature maps. The outputvector of this CNN layer is then fed into an FNNlayer with softmax function to obtain the predictedveracity distribution.

B Numerical Results of Figure 4

Table 5 shows the exact numerical numbers of theresults in Figure 4.







https://science.sciencemag.org/content/359/6380/1146






http://www.aclweb.org/anthology/K17-1045

http://www.aclweb.org/anthology/K17-1045

https://www.aaai.org/ocs/index.php/ICWSM/ICWSM16/paper/viewPaper/13075

https://www.aaai.org/ocs/index.php/ICWSM/ICWSM16/paper/viewPaper/13075














https://link.springer.com/chapter/10.1007/978-3-319-67217-5_8

https://link.springer.com/chapter/10.1007/978-3-319-67217-5_8

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0150989

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0150989

4798

Depth MethodBranchLSTM Original-GCN Ours

0 0.481 0.481 0.3811 0.348 0.363 0.4682 0.233 0.297 0.4673 0.232 0.300 0.4804 0.481 0.548 0.6725 0.321 0.292 0.321

6+ 0.223 0.337 0.438

Table 5: Stance classification results w.r.t. differentdepths.

modeling conversation structure and temporal dynamics for ...4789 qazvinian et al.,2011;procter et...

Documents