A Gentle Introduction To Graph Neural Networks In Python

Crandi Man
-
a gentle introduction to graph neural networks in python

A Gentle Introduction to Graph Neural Networks in Python Graph neural networks (GNNs) can be pictured as a special class of neural network models where data are structured as graphs — both training data used to train the model and real-world data used... While conventional neural network architectures like feed-forward models excel in modeling predictive problems like classification on structured, tabular data or images, GNNs are designed to accommodate problems where the relationships between data entities are... Take for instance social networks, molecular structures, and knowledge graphs. Like in any graph, the input data used for training and inference in GNNs is represented as a graph, with nodes representing entities (e.g. users in a social network) and edges representing relationships (e.g.

friendships or follows between users). Interested in better understanding how GNNs work through a gentle practical example in Python? Then keep reading. In this introductory example of building a GNN, we will consider a small graph dataset associated with a social media platform, where each node represents a person and each edge connecting any two nodes... Furthermore, each node (person) has associated features like the person’s age, their interests, etc. Neural networks have been adapted to leverage the structure and properties of graphs.

We explore the components needed for building a graph neural network - and motivate the design choices behind them. This article is one of two Distill publications about graph neural networks. Take a look at Understanding Convolutions on Graphs to understand how convolutions over images generalize naturally to convolutions over graphs. Graphs are all around us; real world objects are often defined in terms of their connections to other things. A set of objects, and the connections between them, are naturally expressed as a graph. Researchers have developed neural networks that operate on graph data (called graph neural networks, or GNNs) for over a decade.

Recent developments have increased their capabilities and expressive power. We are starting to see practical applications in areas such as antibacterial discovery , physics simulations , fake news detection , traffic prediction and recommendation systems . This article explores and explains modern graph neural networks. We divide this work into four parts. First, we look at what kind of data is most naturally phrased as a graph, and some common examples. Second, we explore what makes graphs different from other types of data, and some of the specialized choices we have to make when using graphs.

Third, we build a modern GNN, walking through each of the parts of the model, starting with historic modeling innovations in the field. We move gradually from a bare-bones implementation to a state-of-the-art GNN model. Fourth and finally, we provide a GNN playground where you can play around with a real-word task and dataset to build a stronger intuition of how each component of a GNN model contributes to... To start, let’s establish what a graph is. A graph represents the relations (edges) between a collection of entities (nodes). Creating a GNN with Pytorch Geometric and OGB

Deep learning has opened a whole new world of possibilities for making predictions on non-structured data. Today it is common to use Convolutional Neural Networks (CNNs) on image data, Recurrent Neural Networks (RNNs) for text, and so on. Over the last years, a new exciting class of neural networks has emerged: Graph Neural Networks (GNNs). As the name implies, this network class focuses on working with graph data. In this post, you will learn the basics of how a Graph Neural Network works and how one can start implementing it in Python using the Pytorch Geometric (PyG) library and the Open Graph... The notebook with the codes for this post is available on my Github and Kaggle.

Graph Neural Networks (GNNs) are a class of artificial neural networks designed to process data that can be represented as graphs. Unlike traditional neural networks that operate on Euclidean data (like images or text), GNNs are tailored to handle non-Euclidean data structures, making them highly versatile for various applications. This article provides an introduction to GNNs, their architecture, and practical examples of their use. A graph is a data structure consisting of nodes (vertices) and edges (links) that connect pairs of nodes. Graphs can be directed or undirected, weighted or unweighted, and can represent a wide range of real-world data, such as social networks, molecular structures, and transportation systems. Traditional neural networks, such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), are not well-suited for graph data due to its irregular structure.

GNNs, however, are specifically designed to capture the dependencies and relationships between nodes in a graph, making them ideal for tasks that involve graph-structured data. A Graph Neural Network typically consists of three components: H = \sigma \left( \tilde{D}^{-\frac{1}{2}} \tilde{A} \tilde{D}^{-\frac{1}{2}} X \Theta \right) Indeed, traditional deep learning models, like Convolutional Neural Networks and Recurrent Neural Networks, are well adapted to data organized in grids, such as images, or sequences, such as text. They are not designed to process graphs, since intrinsic relationships between nodes are not considered. Graph Neural Networks (GNNs) have emerged as a powerful tool for machine learning, particularly when it comes to data structured as graphs.

Unlike traditional neural networks, GNNs are specially designed to learn from the relationships and structures inherent in graph data. This case study will guide you through the concept of GNNs, implementing one in Python, and understanding their practical applications. Graphs are composed of nodes (or vertices) and edges (connections between nodes). This structure allows GNNs to exploit the relationships interacting across the nodes for various applications in social networks, recommendation systems, biological networks, and more. In this tutorial, we will focus on implementing a simple Graph Neural Network using the PyTorch Geometric library, which provides various utilities for working with graph data. The objectives of this case study include:

To begin, ensure you have Python 3.6 or higher installed on your machine. This case study will utilize the PyTorch framework alongside PyTorch Geometric, which is the main library for implementing GNNs. You can install these libraries using the following commands in your terminal or command prompt: Note that PyTorch Geometric has some additional dependencies, which you can also install. Please refer to the official documentation here for guidance based on your platform. Welcome to the complete code implementation for the book Hands-On Graph Neural Networks Using Python.

This repository contains all the code examples from the book, organized into chapters for easy navigation, with each chapter provided in both `.py` and `.ipynb` formats. A `README.md` file accompanies each chapter to guide users through the respective code implementations. This repository is an excellent resource for learners, researchers, and developers interested in exploring and building powerful graph neural networks. Graph Neural Networks (GNNs) have quickly emerged as a cutting-edge technology in deep learning, only a decade after their inception. They are transforming industries worth billions, such as drug discovery, where they played a pivotal role in predicting a novel antibiotic named Halicin. Today, tech companies are exploring their applications in various fields, including recommender systems for food, videos, and romantic partners, as well as fake news detection, chip design, and 3D reconstruction.

In this book, "Graph Neural Networks," we will delve into the core principles of graph theory and learn how to create custom datasets from raw or tabular data. We will explore key graph neural network architectures to grasp essential concepts like graph convolution and self-attention. This foundational knowledge will then be used to understand and implement specialized models tailored for specific tasks such as link prediction and graph classification, as well as various contexts including spatio-temporal data and heterogeneous... Ultimately, we will apply these techniques to solve real-world problems and begin building a professional portfolio. Here’s a summary of the chapters implemented in this repository, along with a brief description of each: Before running the code, make sure you have the following tools and libraries installed:

ۓ�>(��JD&c����E�A���#$�i#t��+�!7/j���8oi� �.��i�S��w�n�!�=��+���J�6zw�%�u?�P�q�i���>ڝ|}-�kٱo�}�}Whw���EK���^h����y�8��p���F���4��#"`t=G�1��wzT؏5�TB;գF��<*���=G�?��������?#'��\9?�_c�#{�>��!G�s��[�U��W˧�d��ϣ�s.����䡡>���>q~�˽���j���������/�y�������3xo��|�x��5�`7?�l��Зo�v�/ B�����q&���FS}�D��'W6l�9 �WC]��E-��:���@�e��쮟TkD�������W`9�^C7�Ax�Q�{[N|[�3(v@����/ԢrW�����ĥ#|��w.�&9 T�}�[ u�$O��EQ2p�^Z���d���/���x��< $*jp9R����A(�xO��RԻL���C�}F$�c��cDu�,�0���̷d8lM��R��(#��r��j��> endobj 150 0 obj << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs1 6 0 R >> /Font << /TT2 8 0 R /TT17 126 0 R... 6�2ߝX���:�|o{�zo��Ӆ�E3�;u�Y�r���v- ��~�6��r����� �vu{�vl��_���ӐzS�_�?!x��U�V��>x}���_��ϡ�K����ת�o�ߵ_T)�9��k�,`m|���O� �x�� endstream endobj 165 0 obj << /Type /Page /Parent 157 0 R /Resources 167 0 R /Contents 166 0 R >> endobj 167 0 obj << /ProcSet [ /PDF /Text... ����� M�ى� H_�����p9% h�h��T4;������5j�eiZ�5��ק�~���p]��ɽw͑���H���\��)�h�*� ��d�=ҕI9\!��P5���s�9���xX��d�4�x*����]��\����4-ɚ�����d?��m��*�9&�?��5��K.r8��d����Aؒ�H�Ng��"ݵWC�=���<�dʢ��՞�`7ƹ��,�4'.nx"G��Q uI c��Z%#P�۳��m�B�q���}S0},+�,*�|h�tɕ3�d���,j8E"�4_��q$�5�6s���q�����xN6,� (�("�8��Qj .L�:��e�c�J1g��s҇������1 u�tI���BǴa�"V�=�B~5_���L��b���{�k�wd� ���q �nK�rLf&N����@�@䝪 2�qt/�i��w#s�Tʪ*�,j��ڜfU��$G�N���5�{{���e �'G͊�аzΒ�3���*H����Q��b�^��9e��=+�u�T�N�椫q`�sTг����s��t�5.Z: �E�M� �PtMڼp8�ӑ@/�\�$� Mk؍��[B�W*��O2�H:�ޒ7�ы!�0�]�n؝�B1��n;��UtVW�4[6�Д�� ����n��3d�������(?"�t��Á�q�f����|��Hd=\Z�3��F:PKt7yR2n]����Y^��!2���t�Y y�Q��Y����c�T�A�dN��wM�T�6�ч�/Gl�Kur$������HC"��(E�Z!J�6�]ĵ�h��:�fV2�qhT�@H��1�$t׆��%�bb�u�E����)���q���.-�ۥ�A�F,T0���tqA4صB�}�F�6��1��*���X$ZhS���i�a��A��-ɨ^ρ8 >$�›��`6�3,���B��Cj�{�BT��HX4?�����Ph�~(2�.��'�J�� aY�F#K�BYDI���Ƹz�O��8@��实/���\�w?�����"�d�C��� �"L|��<��52b���"�k��$k���PB��W�K�����h��Qy�W�D�,�u�)��)4$����2F�.`�)YM�x ��ߚZ4�q>��W���M� �%�ŖյjIȸyH`* �8�LTsC�R�ۡ�a�(Z��mg<�Ŷ#��yh�"S�XF53fчM<��> tB�5N�I�M,��p[�h���`Jɼl�8]yuٌ�:=K̫��8��L։֒�D$J��_2�$��x;9J���/��cy�uN�B"/�J$S�j\�#�i�Q�I���Lo�i ��a�c�:�#�&�A��U1��Κl��J�"����4��LWۿ*1#��U���>�*���⸬c'E�ͣDVE�+��1r�$��*�̛h�ȣ�I,�7� fI�N �%��\�I��\̡Q2�&b,�V�K&t[aϖ ��L7�*��C5�fm*ڙ�%�s :�i ڲY�V���9h�6���z|�ܾj%ؗ�V���t��P'*�j6��'��b�`:Q^0�JkH��D��R��,� �g-����ơ��$ `���Ʉ�@��/Kepx�9�zȌǁ�x,�j��]�7������[��px@FH�|d... D3� Ҝj��X���V0��*�q0����0�U�$� D�ƈ��%X���kR � �w�T �'y�Q�AP ⱹI$�-�:�H��zD ��8��@�}�h#��m0({T��s�YуĿ�By ��y0dL��>�<�/q��<(�F��L�%O��(e�C������G��N)� �|����w��MB~��6|2&؆CF���C  ������P1��9�P͗Ja^(r�z����]��U�o�zo > �SOƇ�?��|�K'�����&�p`JY�� �+,T4�e���*�e�p�k��3��t!�#B�8ۛw��|�G>���߹:����_F�$���%�9��zBT���~���Y��j�Hl��%�B��L�.�����JH��W>��0'ץ��>�C��C�1։"!?1��R)�!<#�Xp�2n��CB�w G1�|H�2�5 GA���C�1&���5��R>�LB�h͇�L� Q�C�(���N ���5r��7E���>\���}�@N�r Sa9J�|���ŵ� ����dm ��0��c��[̇X�8�W>��o��%k>TS��a�c[k>��p)�3kR��|��>s>��pĕd��=��4y������;>L"|�i߱�Ä;aLJ�S ���aƱs]� �U�T����K�F���ޢIZ2��Υ���7Ƈ���!���S�3e'?��|�_HP>h���C�xH r��������*��a�t��7��!rB8!��N�N��V��{ܫ;���ޖ? h������ v^�e. �.]���a�yo��!K�x�2�C�#0(�D�j� )j��U�|(F�#�+�<��P�I�8{��!˔+y� �����ʇ�߸�Cd���!K�|(2�:Q$�'�X>�J� WFcD n�CQ�-|�x0��%��;3����I;>T�!~�@�#� �ձ�S>,�ۆ R�y�?T��Ș�D���[�!�I qSD n��U?����Et���-&C�C�q�xˇ*c>��~��>���̇��nŇ��� �d͇*c�S=L~lk͇Z)%�M"����9�o��R����A�n��"����w��C�U��BԶ�C�G^W O�:8��5�@�Pe u��YP���TI�Pk͊Tr=껿1:����({��x����J����0)~�Y��4 endstream endobj 173 0 obj << /Type /Page /Parent 157 0 R /Resources 175 0 R /Contents 174 0 R >> endobj...

.1�����Ր���� M[�Y?l�/b�쐭Ռ�f��Rm/ -�$�� �%<�?�>� 6A��K K�I\�N[ :�� �R5� A��#l�RPn�I�1���O��j:�Q�ѩ��S�����ǂ�����Px����l�o��Vr��7q�{ʛ9vON���� ���7�GN�[��}!k}hC�S���=�`��EVt �3���t��Y�ݺ��a��{�S2�~X2�o���T�$�5,�q�d�'�������a����.��o��A1{��&ϐ̙[%���2�z�v�3��E��t�lq�$��b�OJ����0�Ax���`�: �Xя�W�Iźi�� qM���R��6oW/Z<�s�M���fHJ�d�T7�zXA�;���$�r1b}��̐�\_3���2nxW�G �9] ���{gbe _��h����^$�}Q4;ox�@�.����⥸�,П �����>�G:x�K��˫3��K����@�D�u�3Es&�c��O�7�$����A�I�q|���g�;��"�����a��|��$�9_�N?ѫ���DF�}�Tt�U�0�Y��V o4����U��� �l��tM��bm;�\��)DVAưX[��*t�k2�_6R�|�9��嫼�J%�_|�e�3e������A�3i�����5`�R:䊍�"��ɳ���[�������G:U��5���T�Z�X�ˆ��Q���+�@'N^1�c:d&�=&�j�Ǩ5�T�!�Q :`���*��4����L��q ���`��B��F�Hk��m��g���!�'v�E��KV)w���ПQ�@W 'T��<ɜ�:���L�_`K�rUi)Ě�?�Tw��c� ��p?�d�$�_"�;S�S��<ڀ�3-��MrI܋�7���$4�\�9�:�4�운���Y��ԉe&-���m�9ӯe��Y�6�Έ�:W �NM�Ef��3�uj��x�L�17�h%� ��w���/,I�b2��d`7B{���[7��lN�3ی�\���@��l|�UC�2V�����8�)���]� endstream endobj 177 0 obj << /Type /Page /Parent... ��X���x��u�h�ާ{�FG I�0��8Ȗ��~�Ѳ���t�X��igj��u��=--�# ~��0V�B��1���t�Z������-u��٠�yL�X��M#5���'k�3����Ât q ��z�PX5�ߥ��j 2l�_E��B�X���կ�z����|��z�����>>#4��z�P�]�L �BƷ�X��@�69����X�vW�8�#�����W��*��F�Ig��~�\�?�CΝ� -r�]j� �����_f�ؙ��Oi*'�@5?�3 %"�}� �� �nx|��%@���#�(�T�#�tL�;k�H-cc��[qM�3z��;�Za���6�l�t�M��]s��:�g�d��&(�� ���l x�v�����/��h�K�Z��;ř�l�X�`� ��e�HqU�Gs<�e���"��ĸhC��Z���x�\x$�KXos��$��H�Z:F�5�G1<�K\���/�����kc�b�'�҄��7v�;��57/X�����C� �i>x<��bs"/,2 Gx�w� �����nS�C�*��%�#��R*y��9�O�\��� ,��Q��i�|aQ�����wIRV� >N�Z�*Sq�� ��O&!�N����;���zZ��?6�f&7����ėM‡��$ۋ�5>(!#g#U�� ��~���J�ˉ�^p�P%N�w�(�\§n��6�j@>Ӈ��%�5{�<��-_�+e�N�Z�jx�ʣSt��QwL���#�gz<�%�� ��v���G���}sXo>�v���(�Ux-� �A�ƫe�w�_�x+�� ��7�+��� endstream endobj 181 0 obj << /Type /Page /Parent... H@��$ ��P�.B�f$  H@��j"�pn���{lذa�ׯ� '�p�7�K?�?��O=�ԡC��3f�ԩ�5���w��7�# H@��$����wM��$  H@��ژ#�Q��x� �s�s�9���P��������N��N:��o��vI���٢"sI@��$  ���wl�. H@��$�q(�'N�����:묒�]Mꮲ��~_t�Eo�[ݻh����$  H@�F@ݻ㡒%$  H@��ڒ+T�����?�7�0������ ����/g�﶐�ս�EE撀$  H@(uﶌ�tZ��$  H��>��&�4hP͊wYg�o����t���{-~�>���E�믿f�1:�É�f��<�΃��s����I�y�צr%��� ᇇ��$  H@h"bU�y�|��LЍ�]�������[2���9Qp+Q� �s �4.�: dW����s?��Su���-K�+���kS�62l��V9�x���w��� +�0}���|�l'0x���H��?<��>����n���w�e�%�vԽ;AY@��$  H�0���;�D�\�q{Ȑ!/��{Q��a��ʔ)&L��;�;�,#�Qѯ�����9K��n�M���NY7���\0hP6�tӜЬ>��,����rbŋA��sϜ����Y H�����$  H@�@�HO�}R �1�������#���I!����$... �F=�来�������������j� �@ P��h�c~ H@��$ �V#�����3*�4I�xo{����j����0�N�����-�� @$��{d�.�䒜�1�6�x`Nh���򫯶�v��F� ���w_�xD��^����=�p@��@�Խk��,% H@��$�"Х_���g D�T�K���?�|�ЯS��a�x��Q��;�Ҿj#0k֬ 7�0Up��w�3jԨ�.��a���Ku� �w^ؔ{%P��{���Yd�q���v�p)��{����;_~�M�WhM��-��$  H@�@m����������L{r��vtf���h�R�ޭ��&M��� +� n ,���ロ.�[k��R@xg��<ЦƏ߽{��F��j�M�6=\L_��B �:�Ү,i��ڔ��&��ݚ�^I@��$  d!�H�x >һ4�{��o��V�����ѲyԽ󎧴/���3�G�����g3?���RH��.�h���;/wѰ)�J�67�t+��p뭷F����R�=��\s͕���+��*!aSZ���w�):& H@��$&����o�q�Uu��?�q�HF�;KI��Y��{�f�W>|x��F��v��믿�=��ސ�ê���dy8�M ���/�����Ή��_�ŁM7�4��0�ziV(P��/�G��$  H� ̜9��oD�ftw<��e=+Z�`}kpIݻ��C-E�[V���������gq���t���9��ٮL1j�}��� ��#�8"����osr@��@�Խk," H@��$�����+����};.z��IN����<� �H�;�xJ����{�*�1D~��!���~����VAKI L��]7�|��F�U��C�Mն�!�;�c�d8��3k;��$ �N'����!�H@��$  t�S�L�>���YV�͊�W^y%»�$'PU���K$'��������3I�x�[�3l�喩 9�u�Y�N ��8`��]�\rI��f�/����YV�D�ޝ�yt... �-��ϔ�T�X �������j#�*��D���$��a� ��H�ȟ�U�\�|ROl'���-�I����O���y��d��d@`w].�@ W��X��#��^� %8{���,K��7V7FUN���0ˑ����_~yVH)�^�z����PI�ޙn��l����MîLl� |(�TZ����UW]�W��i���bP٪Z� �^���?�/����w�m7$����e4^�i���I ��Do��6�dz��[�޽���?�Ӟ{�T|=z�6 i�m��n����N"U��чE6��i�v�M���_��y䑤�c���vo�,%n�}�M����~�l�T�#Ӳ�5%��l$������j��"U�攔��I: ����{��{&�?�����I����_g���$���>��K/E�H��o�1 ��T5a�;�)‡��SN9�ԄD�(�-�%�� ��r�Fd�>hР�o���8!��#�.�HԚn�R���˙l >�7��d+�:�Dҵ׆�@S�3�ƀ�U���*��P�$mI ��x4��HE�R� X��DW ͕.�xb;{U(�G�"~�����}�W�NA� ���QU�5��V:�x�=���ܗ�YNO>��Sc�<��Ӵ����y$g9�[ٱI�&���*��BJq��>M^c�.F,s�r�I ��*`a�'�&L�@�vՄ�JOe� �3�:CK�7�o,���+��H�����Be�f�7�X�˪�4zwQ.��ɽ���y��˰Ѯ5����+�k���ˇ+n�q�sD�5��H;�>���1Tn�M�2a�����Ve��o,p��@�D�+'�S�~�Z�CD�c#�ĭ)�p�<����� ��x��L�#�� $_J��_��{�uK8���G��&�IT��m�� ���b�,���D�;�Ÿ�V[e9.1,����)�ei��&���`?^�w $�,�����~�3�Ǎ�E '���>��Sy9�����W,������ӟ�~p��R�[�LP��*�G~�"���@@)��q���Bۉ��9bĈ�h�^& �_� ����>���ݻGZ�'Ze�P�� 0�2�7��y �Z�<�7�t�x��nswCSM�h�1ux�tu�ۓ����_#6�W�VRJp8DՂ��� ��jU\&���-�X��Fm���H,���@qv�eD@�'ʠw l!��R��e�Y&`�k��+� �U^w�u��좓?�2d#'�>����o��U�@�{����z%�(���o�g2rRK�+�&z���&"�)�"�j�����q���XAs X�����t5Q��@qv�; h� ܯ8SIg����~:��@(K��2����^�Y(��p�BW#�\5U�"���f���D�+7�6�|��B)g��R/d�_$��... �!Gܮ��{�|����;|á3�������Vy��o���U�� R$�'K��+���yГßOr��G���'�v�D[a�\V�EW��f�NX�Jm����.�"��?y=F�����^b�����Oѡn�U��FF��F�4�M��Ko�5�K���l�G��Y���C���u:�d�CE�%�\�4���ؙe7�Ŝ����y�%�#���DK����{,�^Q�����D�����G~����R[�И�j�� ����$��M�U�+��T�H����ԫ���ɓD��ԑյP�#�{�e�* �U�Ni# �'����E�̐o�ʉ��&Q���%�����F��q~���e�@�� �u�7Q-U`0�(EU����� ������ �/ 6RZ y�<=-�m�2��� [E�Y5�C�� T�]���jb\��$ �*0�3+J5*h)Q;����ȥD������������{x��."��/��lx S\�c��9PզH�q���<����ƣ�%U�ub��P�h`��lD��1�Ot�����V��eV7��O��e��T0��Z��*�H��O��|# �$�?\|�Yه^���œ�$����p��I�R�Ǥܳ�X�*�������-k��6#'ݗ�NI� ԃ���S�^$O�9�&�N��zJ���������m3�1����G�"+��// ���˙�@b�̤�@��%P�ʬ��֞����r�]�H�1L:�<����-�P�)%4�$�瑆�m�o��?]�����ǁ�^M�:���LJt�O�8�لo<��tq��OJ�#��(�� $��'�G�W U@2MJtVrCH��g��� #���� d�'Y@Za~*����ˬ�P���ɪz���M���x'f�w�~ް���9�,��G�k����7�K�z<�!�{s�?1)a0�{Ӑ��ѐ"����1I�����o# ������\���Vo��ü-s��>Sy���爫���r;�l���t!� �J�3���M�����h��Υߥ�g�S,�'V������Nݛ� �R*�~�����1ŸOB�+:`��Ϩ@-Q�ȋw݀��º7�W�8�����.�na ���HH�����ȥ�K r�$U� �����0�hKI(�Yf} �-�+I��| }� �>`�� seB�gq4�p��pӦG�l���e�/V��HM��v�@�OW#O≞Jr�$�G,���Q�jb�0�� �AGWfy]��|,Ɵt�$=���,O�No&"d<�� ӼH3��VAx��) d#������e��9�\�x1�ȕ/��ܲ_܋x.�.J<2v�8�z9J���=��`�5x��v�m��f�L�zz�r��q...

�����i����ۦ~q����6^p���+$(+%�V ��ݾQ��K@��$ ��@���{Ru��;��nsQ���= C�B0�H"P����{���If�^'Ʋ��Ņ;���rP�����/^���G]u�x��杨:�D9ێ;�v2�I�ϫ��:nv�u�M�ˢ�7�o,U���%��LiRn��;��SjA3H@�P��5�S��$  H 'h\��{3 C�Խ��u�ڢ$Ku:����(��.�,����t� ��'�|��k����&I�uU����������f��6#���'����/Y����p�i},G_V�ΑaÆ�:O�\�9��ᄅ�  �F@�;{�`N H@��$ ��0uɅ^ֽQ���i��rr�xfսk��,��:�{�3�< �d\�Rd�'��_�+~s�9'�ͽ�O�>q��c��D��g� ���_9Vꟴ��B�G�Z� E%�����@�M2�s�=�2�i� 6��O�V��+ �L@ݻxэ5��$  H@�E����8p �V�%%t�3�<��?vr���Wݻ�@ɂ�K ���� ��.�mҜ�u����'�`z��ܷ7�pø�G�geAnY?���l�o�sd�c�*���77۵�^;rt\z�Y���� i���2�05}���ʽ� +��><\н�@�Խ�G 攀$  H@ȃSe�?��OF�N�َ*>t�PF���CQm�{�(Y�s dѽ��Zj��;��v��?���j��k0�I��Ѣ�.)ˠ�� �ӦM�Z$[C�\b�%>��ð��&M�ٳg�$�G}4��-]����i�ɲ��ߛ<��Ӭ);��s��� ]�Ք@� �{5Ʊ^��$  H�]0_��1c�?�����.2�u�]���iU�n~��B... v�:�… #���ٳS^�D���Q�q � �� �{Xq(@@Ce��ғ�m��[��>\�N�k8�f���.��Z�E_�=Z�<;n�:ګ��N_ؼys:��ɽ���h� � ���q� �D@Ȩ���%K�t��1�do��ݺu��� v6u '� Z�*++sE���=cƌ3gΤpL�]�������[�u��5Mr����8 @@�dȽ=�B@Ȑ��I����V���5�y���---�ΦN�t���m �]����k�;]'��X�������+rO'�'�N�>�= � �@~�{�P��  � �@:Jw������h7:뎾��{����ʩ�Yc�r+��[C�ܹ�={� �cǣi�555�\��ӛZ�\V�b[�C�Ug� � ����a�@3@@���뢖Z�#:莾�,�Q[[l�����{Ϝ9ӵ$�FXZZz�ĉtB���/�!�\�R�Lsr�d�#�#� ���wl��= � �Ь�����Π�Dߚ�=x���f����AK�����%Y4S}ԨQ�/â�Μ9�����2��Zj����Q�q � �� �{g���� � ���լ+B*܎ݮ �/^� ��5�[+l���˵$�F8{��`G��Z[[��KFo =z4�.Ƚ���h� � ��ޱ��... (�>v옮b�L[�0ٵkW� '���l���o��������J�A� � �� ��庆�!� � -��{ǎZ�[+�(�V���߮�������}��U0�,�]__o�ܠ_@@��{G��F@@ ��{/]�TK�h"�2��kמ>}�5`�ٽ{��q�Q�=`����z�J�A� � �� �v� |� � �@� hv����B�nݺ:t�uEK�\���ի����)S�Z�o�����~@@Ȳ�w�5 @@�h-`r�ĉ��2��V�=x����f�"'j�$����ɽ 6nܨCS��=z�ܹ,�t� � ��r��R�� � �䬀����w�.�={vl�{Z�[������Ze߾}ڱ��j�ȑ'O��Rt�) � �Y ��ٺ��!� � -���-Z�@[��h��� b�Vĭ�OJJJ�F�{���iIp�3z�h��Y.7�@@+��ѥ�@@�e�q��i�gqog"�k�Zܻ������ɽ}+���A�i�+�"� � �}roW��� � �䠀�j?~�W�^�­�޽{�֢%��hxee�(�v��]��;V���_k�# � ��Ƚs��aH �... ,)�R�r��AC�|�͗�V��B�/���ɚ1-�'�~M(/����^���}G��F���{�������_�WpP���|J+|�cC���DlW�j؀���cǎD#� �j������d f@` B�y�-�P�`� ��� �!u���� ��~��~�3����$�o����3fLXL�T�x��.v�k��!м�dQ;~=W�9�;�4�"]E�_��FA9nܸ��&P�#u�.�d����tE~M�`��Ԓ�X������l���?ފ���Pn�O��U�&к��)��� lN��`?� M���n�ނ�1x�����F�|)~29��?��-lH4M ¯����+<����������T�-Ū���!�$Y�����1��5���2��SyO !1[r䀬t�M7y��HY�8r`qL���c�9�� ��k�pL�X�L��zp�m�^� i���~�[�0�nFb�\�3t@� �� d+���Vb�54�ưX��-�A��o���`옚���a�rYƳ��Y��7�Ե@�ߒ���fm��ҟĺ��r�ͼw�>V�6���+��ܼ7�����>����{cQ`%�n��fɝ�+��9�+���_�7��́_:T�?�u ��/�~�3:d��ĺ����ϰ �'}����X��L((g�-@�Ї�$�[&e�M���?x GA9+�C~׏>�h0�� (������=��G#����� s���;�_�u�~��-!g+h ��ĺeH k��I؂c%��� S[G�(P�I�kan]䃕ĺu mn%�߂0<@��s��.��X����/�a�_b� ����>_�$��H`��c�_��_���`��O"�����k����&0�� ��0\@W�}�a�[��3�N>�Ћ�����F=]���f+�r��ګ�a*�f��&��D�j�T�,e9@V� ���e� \�g��ȁ j/��ר2!��y���Q@�V���Dhtglzr�@��� ��X��uU ט.0�2};r`̡��Y��^��4* ��0��fl�#��lC�c�q�Ȑ�*�r����"9_�Q^�Zƒě.�u�����, �U�+��[d�H6��,�O��5�\�He[%�o1������^��f�&P�tB�u�ϑ�P�va<��� T����%:r`&b��C��w$�͘UVw���YW`�m�ޞ�... �7]��� Ë�7�oy�=�W3�h��e��Y}}����W )j%�n ���Jb�Bۺs�`%�ߚu�#�>/�sG,ì$�-�FG�;�y��X��LzN����`�q�@�~���kC�����>�KE�D��ȁ�G�Zs�,�M����H�e �9�K�L��{9� �K �57��\�M�k� o�������s[��\��P( ܠ����[�&����" H��PB!P^�f�+�/ˌ�6D� @4���(6�;/�'2�H�� ��(�%�#9�0��"saY�2ZX�8��%g`��2��78f:����2ߑ�W����8r�i���X&s����w䀓7�E�w$�U�y��j�ʍ&�9�h.:���bps��t{�P�6�ޛV��T�Ř���Ms��"yo~V���H�;��5Sد� )�"�h]3,84 V*�-�V7�՜?~�Q1� f�r6�0��:h.��3����@��{c�֑��ճg��������:x���{9�[G�L�Y��ܬ59�䭸u쬄��&8�G`�` I��=��>�́p�@�!�a���yE�Xx{ ��8�f�����l|yo7�X�� T�bS�����>����Ԋ�-ƥ,~�8"d�^��^&O�R���S���Kŗ��c?�~{] �9N��sZ��/��� �j������~��� �M`��,��N �I ����a 9��2v2�W$�W��U�.f��RlD=� ����g?s�\ԍ&��u>�� ����`3�,��s������AB=*����`/�o<�#� ��� ����i(s�͘��ˁ�fy���ݾp����t�\�1�ҁk �(�z2M@ �#�8��<,�� ��� �J��.x ~��B��� �I�g�d]�ل֦��... ��cr�D�\�؛�������� l00-`O(,7N����`�cCh�<,9����zܐ�~ڜk$bl6�H����� �B@!�m�2Wй�����l�����R�:H6�b89i���7�])�y��!�;K�[U���C�s�X%{�[x�w��6� >n��h5��9�Z��K��i�Ԡb�e+ ��X�E��6G��kbiQ�p��B@R�{�-80�� ����(l����*^���.���M �� �r�c`7�nT�p��B�n� !

��H-L|�(3�dX��j_g���Уξ~v���m�Dj�kt8�4�9�u�-��B@@+ĝo,����=9��A ���1��x��HU*������=�#�<���EoW~"`^z�n��z O�������Tp���G��������_�1E��YxGZ��|�pb���ݷ�ʂ!��P� �1�;���#�s��!̴�7oN�4>R��<� �#��e���93�9N�LL$h�?�h��8��+�%��=gZ=B@!�%�q�\A�7��k�f� Tj[�9,������s-7o��F�T���x� �l�ل2���W���#�Ӄ�݆IX�îc�dN��\���uTI���B@�f.4��b6�O�)����PK1�e�*V���K�.���(�x��0a݌`�ۜ����.c--1�ݪU�'�xb�Ν��q�ȑ1��<��~����8�Ԃ�bl7~�/~� N��Mt����]j��'?6mڄ~ʏy�5��(,�+E�����s y<�5ʆ `��_�{Ϝ9���(%���0��5~���Ǹ?z�(�Lp�y�GI��B@� � w��{3A�g���3at���rὧM��{�e�[U'Jy�Z�w�d��jK�x���?�*���G�J3�k׮�\I�1~��Y��� w��i�<>+Yq*�?��0�s>��ɮ]��(NIb"��k7�|�;���_���P��1QU4!�m�{�!>�%1~Q �1�ƫ �OV�X�x�b�zsaܘ�Lˢwa��P�%�dL���j���x�� �xδz(��B m0�1bJ�Bo��s9}�ڦ ��ڇ�ÇG���ڵc����W'Jy�Z�w��� ��4��e�]���|���R`�n��(���\r &��oNѻ.M�G����'��D@�Σ,�w�9�m�C�M��$(R�� �����8��~��T��'UK�)A@�w�# "� �aʃ�ƽ �C�����,갋��������p�o.�a��B@� �<Ft�Ld�Ԗ� �bW� :m�f�>|VM�{�v�޸�F��Z@ڊ��� 鯔�Y�F������>�M/v�V�4��[Rӡ&��{���Q�*��:��w�}�W��Ą+��g�9lohh@'���Ɩ��믿�꫃o��_�Eg�&�+Xa�xk� ���']y�/�@��_jhiL$8�f�vO�>=''�`�+<��󡬖�P�B@$��[}ͱ9g��?dz�(��+ۖ"��\�u��婧�����<�m�~�����쉏�x��KX*�($�{�t�M]jk!ЊR��d��ќ�'NV��������w���]y|�I�&�ǟۅ^x�u�}�����8��O��k��|��<�R�l �f�_�0�d�����:nq�q�F�Cp��_��r�Ý?����("��K �DpcH\�jVg�71<�8��xΆq���z��)�dHH���V! �@Lؑ���-�d��Ξ,͘1�f���[����E����PK���+�����+����ʅ@r�7�B��bpR@�Z��r1r��>. ����o&4���Ċ�OҢkN��@O����G>�Dߢ|Ld&#�>�qxr���ci߷o_6ǎ�����7��8�rذay��$�@�a��^o��u��m>���u�5\<�g?�ٷ��-�&�C��T:�O~�A��Y�Fɳ�Ԋ�! ޻� 1kDo,���8�rɒ%���38�9�Op�8u���v6����-?TyJ�/��U��Ռ.��)Ϟ27 L��̕���R�v,�X�@k;Ho^�n��oDNU�S^��i��T��$�{c���"^Ŭ���AQ�gϞ��3�_mm-��I{����˖0����߿��oz�^AxW̙V��3f�EDs����q�o�a��������~��;���ݧ�R�-�h��¨[Ž��o�?�GՆ@]�:6�\�н�N�p8� V�1�<��׾6mڴb��� |�W8�Q���f�U��C�v����� ,�0Hc�d�VU^�?����4���z����SM"��p�s! ��H3�1+A2�����@}�L�%�a�(���-�"yo �X!��Y1�{;D!�J3I������� (���X7N^��}\��AD��D�\SS�i��������_����������W� ���O�'+���|�r?��e�����h�~/�.� ���~��V��7��4b�͏�z����ɪ��Sc�@���N�4��g�<8ps,&���I�n�:���M��;w.�hм3�9r �T�T�B@�j@�� �,���<ڹ��[�ne���OP)md�3|�p�soHo̥��JiW�)�;iyJ�'�@qy� .��3��̐!C��p5g{���[$�ϋ-b���׿n� ��|�͋.�C:��`�#F��#Orc�v$D�ƫ�U�G?�Q�:@��+�&a�mu �WE%t�m�Y��_��*�ЁlV�.��N�<���7sF��n:��+?��&�}�d�� ���<�t!��%F�w�E�Io*��:��}�]�t�x�t;��Ƿ*�w�wg��~�{gCj��V�����8���>2�L�#��[n���+���[�n���'��ۯ~�����Ր=��:���A+� ݩ:v�l�?��?�S�m��԰U�VV�`����_o=tߢ��8qb��Rӄ@��� *�я1v֬Y��� (�#�ŬĆ��B@!P0O��m��E�h�V �P�I������46»y�mێ7��i���#޻��J, ����̱q��,J��I6v]s�5���b����o/��iS���dǎW]u����W_�k׮8�[ ����߬����/٢|9KpR[�����p@*���?�i��ۿ�[�������pw�Y�Vm" �;�Jd����9�]6��l%�7� \㗌��n�(���j(�B@�0�b�5���N�1��K����/U��l g%ñ�n޻M��:�2�o$޻@qI�˅@�7�(�7����߀D?"�ۓ |��>�!�=� ���?�c��=�P~�J� ���O}���m?���;��_ms������ +T6�.a�0�x�x�8p ���6���1����s�uסK�����B ����C|H[vu��0�o߾v�ZXnp��{�-[�����\ yn|�� H��U}��@�i�5�ҥK���x{EP.�#�Fg��5���������`�9��w��]�H�E��/���9(���P���8eʔOK�Y7=�#0v�ؠ�k����mo���?���}oРAs�́����߿�?��?�4���P��3�y �d��;b�?ڡC��-`��g?���Y �@��l�����o���&��}�k�T�4X0[�u+�@���NT�(Y��&�]�����6h�1lc���۰���}D�߷o+�3���� aI�\! �@K`Z9p�V.]� Ho����8�b�n-�p%��5iҤ֭[�I���Z��[�_��V\�������{_y����w0*o��t�� wǓ /���_���O?��G��U0I֭[�n���/���i�&��"�`i4�}��ߏZdZE�*�����hC8��1�[�>L(�Y�'jWY�]q‹���l���c84ۺu+׎T�®��ӧ�y����0h��!?��M���B��0A1��X��u~) ���0�Ѥ���U��� ��2d��ޛ��с�y|��e�Th���{cx�я~=���� ��r�D�����w��bn��a9L�<�8����VƽW��=��̪�k\tXRd�cǎYeŹ����>�O t�I�8�C���p�����g?p�@��`0!Q���Z$ʅ�x�<ć�Hb�o�"�;*�zO�0��AA��������n�qdLGz%��B >LL��D `�s���Lj���ٳG�w�oT�t �꺹�{�{O�:O�%�^��].9K��@�7<*�G��/��ҕ<&���� w��������DI>C� �R���Ȏ��#�\q��:�{シ KȎ�g�y�*+�m�v�e�" �*q�8eG��h9Oq���ѕ�z���Իw�7J�A@�węB����z�j|��ɇ����!%�-[��x!E(�B@?L=���\k�…(^�t�sP�q���J�� �:U@m�ҀFp89��8>���{Ӌ��O��ޙܪ�!-����w�ߐ�����w��]q�[����ka���J�-��Y ;u��V�'x�ʊs��o;X�O<'��dv2^r�%V�@ W__�no���qg��B@��_�dL\y���� A�'P�!����QB@!P�V0�f��t�9(?��e�f��<������V�O�P�|�=��Snޛ�������\��t!|DZY>����S'O���9x� [�[�g��!��/�躂h�}���?���hT+��٨*���?�|��dﰻ�a�7������1ض�/�-��Ghw���!�l�y`?�E>`��>��: !

�@�`"�K�N��-���o�؍7"J�F�({KU7�p��p;���ׯ���uQ�[�4_ my g�������]���!;��D�oq��)޻p�I9�����y�w��7���ߌe�g�ڧO� ������y���i�F��� >��O���(�A���6Xm(tv$�I�8�D�-i�y����{���P�P�SSGa�3�[! ���.P�@r�,�o��b,��U��s�{�E�=�D,d�'� B@��#`��ia�W����Smc��4Dp[}{q N9�1�=J���k��J�5�+�f�M�6{o�r����RCJoӦ-�;�<� G0hNǎ1S>|x�}���Y7���5�㭚���# G�wPғ�@��^Σ���ҥ�^��/�����?TD��Wɟ��'�/b����/b��n�U��|V� /��yܟ����/�����[na��/+�5�ɠ%� \y���틓\q����}��gu nx�^�ۋ�;���k��4wg��B@����TJ&�>}�`�֭+W��@�F�hK֜a�%Ucc#�<&X�F���B@!P)�9��� Sm� �W�3g�,{� ���H �EQ�k��0g1;v̜_I����*�'_ N g(\� ɌR�,ν�!�D������R[�*��v� ���Ϣġ�bT�C����ĉqrۡC�`YP�,�G�=i�$~/��$��/�躂��9��G]�n]5*cU}�7���_ w?��O#[�؅��������iq��f���o�伿&暉 �� ��G0��T�������`'da����u��t'�L�B@�D@��CL��W�\fm$/���m���I�ڼy3��5��]Vz.��n�g�s#s�]X�Á�^��rJ��5����~�z�lRf�z[��]�ަ x-��0�A��<���/��)K�Y����m����٪3�t�.�EݘT�Ǭ61YGHŚ�%L��L��pAD��)�Q�x�b��� � �������V���#"H�1HF�йs�`���y'*NZ�����lx�$ �\p��}�<�z�żf� V;? =f���rX��3���Qhv"k��#�X ���7��P�����xo��Pͯ {���ֈÆ\�����}�fe�4N,��zD�f �v! ���3Awp�L65�p��Მ�5:Y� ����'�Ӑ*�a�f�c����ɐ �{�拗�+�n�_ý�^��&Xg��Ǝ����&a|����8{�,Z)\w�� rv@��x�E���/)f��q�q�]wav�o$U��� ���]ﲈ;8gv���`\��w�c%����\C@*�mD�8F���8R�:�%�9y��ܛj�IZeq��_���^��0�O�袋�^�lݭ�;ӝw�i%��n�z+�@���� a�k�]�vy�W��sv�c���z���ܑ�^ ! ��xo�Nt��h�9�c�̅P�t��Y6�n��Ot[��8�`Ց�����&L��w���� ��g �19f�� ���-�9=���������4�S�j� #^��ή�l��7��v[��cPu' ��6mZ�����p��(���n�ɪ6 2$FjE�&�惿<�@���!Ǎ7�hu'nǍ�N��B@���1EE "��ǩ��=��G}sa�oܱ�jrÆ �~�B@�H`�D���l�:u۶m([��wdZE�൦N��>�#j<۔��IN$�>���68 �°��9v���O�j߾=���Z��x� G����w�V�~��_2���U^�^�zY;<���v#�����}VZ���-g�ڵkg��-�-�qw}b�ݻw���n������8a����e �+t6�Kp��/})�G7g�KН8�=c(�9B�����)��a$�h0��f[Cw��o� �W���"! �������3�U��D�J`c��� +ݦt�lQwj ߋG�e����s�~`}mQ�4d�[�K��Ld��y>� |zc�G���+m�������Jo{�۸�k4���3T¢#��� ��}��_�䜑"����_|qKO)e|{衇�|����xh�� �T��3j����}D���%#�L��O}�SW_}�O~򓆆�T�M�d���A�n������׿&䌿��6<[ne�6��"���x�x�Ǭ����\�lK��L|vf]z�V��s�+��.�o}+�P<3�!B�4���O�P*?������~�zD3�1 ����)��П����B@x�^���{s��f � \�%��0�P�~�ۺ��{�r��h�}�,�����u���Q͚ ��&s���I!~DȔF�R)EG��ƒ>رcG6�=seX89�����ή���>�*���?�aK�իW��`�n� �r���� �`���Z1u[=�<����/g��~w�qG�;�r'�[!

Z��x�� JY-��)�5jw,�֮]�5O���R0�sGs�WB@!�U�1)�����E}}} �Ϭ�_�v�5��L���7�/��Y*��Ҟ�+ �o��RaҲ����i6���oq��b!��[*)~J�w��������>�����wbN��D+�u���yn��~ �V��[����`���ޖ���ĉ��G��@5e�䊓Iz��iu no��F�rw{1 nU ��Q�� �V��" ޻b]U�2����KGÉé4�fQ�b�!���^ ! ��E,Z����2~N�RT�X���ɬЏ��2����P�� ���ik ]W$��r Mݾ}�M�6�MS�-��Æ �`�����R�H����[���i���8p�UWYi9�"ݝ0��7�����?��σ1 ��z�%�X�����̕C�"�裏Z]�[�D6��A)l�X�jUdZEB�E��N���� ��ET�:,�1 4p��ɘ۷oG�úϝ0��B@!���9s��yohF�ޑ�UJ�{ ��M��-�ػ啱�La��P7x`�jkxo��+Wb��_��q&+���6���x� G�,�@L�����o~����9��~�J��w���.��[��o|�V>�2rZ1�r��,���tQ�W&��o�q�=�{�O<��A�c�}�{���(2�"!�"�{�'�(U��f �6��ȉ;v�8~�����Ur! �@�#��t0s�L����{�0-��tX�T,�q�Ѯ];8ޜ�p����� �۽z��\��n�}M~���o߾޽{�'�?�:.� o�x� G�,�@8��3�����q��_�*2��q� [�jŠ������o���QG{�V������z+~��U��,�;�3y�r;bĈȆ��-���,�ȴ� �@��%�R������a. �={�lܷ�e�w��H�B@��"�L������� _�[I�VXDϟ?�"��8"!�[S� ��?-�rn�y��Z��!CK�7��|"�J�� �{�H8Rd! � �Fݫ��:H܍3&2yN�$��i(n��~a܉[u��+v��i�,��#���EC5�E@��%��Zp�%��9@h�o���y��.K�-T�B �0Sp������m� ,b444�:yJ�w:�WKk�wdcW�~�����1��ݻwO��?r+��6m��+ojN�Z�W�|�� ���?Dʂ xHh)����S+��bB�r@�w�y�Y��>�܍B��ٗVBnql�N|�A� ��&�nG����,^�o��`��~+�'U�@N�7to&b7,����;�8q�;�� !�⽃ҁ��#�y�e���/�߲(�^ ڢ"��B ���%p�������eɓϊF�&8^?i�]C&O�4�,u�_(����:� ZTSS�2�6�ϊȜ�ݡC�Ü��E98���$B@�����/�������B!�N�gϞk���J��,�~� �o��'p<�Y��5k�\v�eV���w`�Ux�ʡB�����V!��-–��Vw������N��B@䁀xo���WI#��l������򌽓.]� ! �@!

eh}�Ȫb��q�i�Q�<�[��(^>"+�wxi���r[�=�ߴiS�ʓ��Ç  dեK\��OY��y�HJ"��眾J~��E2~˗/�.�?\�0�9J,���S�=Z\w�ulL+{�T�� ����n�z2�O>�dd}�&L���E�U! Z��x�HaA�F����5�U���OZj%�t ��B@!PD`z�O����@)��sk�ϊ "*{�-ޛ�eK���Ln:��Ielm(��G�wK�#�B��#�'>� qףGwBގ;6��U�V8�L[�lP V���oGGY�Z��2"�������{��E�j�ĉ�w�O���?��n���(��6���ˈ���8���Ӡ�����Q$,c�U�B@��B���t������ޘ=s�i��|$�-+�~��[��։��f�8E#8�عg�dB�۷���v��ٖ��:!Pz�p��g횯wӨ#+�AA���?�1K"Ӗ1������o~S�*���"�Q�������Y�C��^���b�P�����qD�)��wqA1�� (�A��\�B@!  G���x���9�焇���D(.�[x��r?~�u�%������ԟ5*�;��,9�mٲeq�U&�s��y�HJ"����k����{� �̑ʼ��� ���Ȅ����j�I���R�B@!��x���$D��͚5�^�) k�'N�����B@!`!�ö9Hz�x„ ���Z��ʶ,�pԬIZ�n�o M:th��i$_�~�9�@F�͎��7\�w�@�B@! ���D@�wY�$�7MMM+V���%G~�̙���v�]N̻�J(��B@�!ًso���\���؛c"7l؀MxX�T=��,K,��gϞ��v�LxK�#F�������$.�;�B�%��B@!��x�TIO��$D�^a� ��L��X�`�"�c�������B@! 2�@ө���yo,�G�E7c�p�]߼y�����ݻ7�c ��9sfB���{G D� ��B@!�I�{�GtRM"@ĺ��{{�7��K/���56G�B@!�r� ���B��ҔT*eƳG�.��5.P"�┴�jPU�m�[��a�6ovo����1 o6�~������6����Τ�F ! ��B@D" �;=��j�R!���y��~��D}}$�=�7*x�Q�rf%��i��h�1N{��, P��-�;R R!

��B@�L" ��/��0��ÇO�����*j�Y!P ���ɉ9�col�q!޻�'Z_��{�����=w��e��͉��H�i� ��߹�a�;w�k�.�e��q�S�Lc��z��*)�;�B�%��B@!��x�D e[b�% �By mr��!���c:2�+! ��Hh@�yO�>���� [��;i��Z{ٲe� E ���rggz,n�jkk��C��kv���|b��8K���A! ��B �����]d�|l�[�nɒ%�/njj��ϭ� !P�0>����~{o��n�*|V�#G����@�����6%0{N�CP���FZaQ�mڴY�|9.�M� ���#F�Xqx�-[��Y�G��3)ĩQB@! �����NN�P��Aa���_�H��͛��NO�T! �������㽹�C�q/�.*^��t���2��ر�+*���[�9�P�mڴ�{;iݺ�̙3��m����ڵ|Jf�.�;R R! ��B@�L" ޻�Gչ�`a����ɮy�B�â`]��������B@�D`KΜ9s̈͠ �i�&�Չb^������7��3�<��MXu� ���7�;v����{�޽� '��߿�&��3)ĩQB@!

�����.���Rʋ6= �P��.Z�۳S�N�N)��Q�B@d4�s��}��o�R���f���(|�.��� �ݺu����a��A��ٳ'���gQ��"�u\~�h�Ϝ>�g���K/�T�V����A! ��B ����[�S�JA�}�� ¢ �� ���� SG�}��Ji��)���2�'N����ڵkW�Z�{dt��.%I�e|[�6���Z8p ?�|S�ߩS��ia����������{��Oz޻�k��c����b�s����4|ԨQ@ ,-�y��I!N�B@! ���D@�w�"��Uucڍ�X -�o��Y�СC��@+ :?"�H�+f6�qǎ�۷�S�4�� `���,�t�.�4�Yz-�))�B@! �@&�� ��0��>x� �X�f� R߈�-�3 ��&��(;���P��Ta������9���*���Mqcc��4q0!&��������8��8�7-]�f ��-O�M�V��E�{gR�S���B@! "�GjS�l ���UCC������N8��B�f��j�B@���e'ԤI�`nak��qN��*���<'^6[�3�����4љ!������ ����7\���>�)�<'���k�޽�o�x�H�H��B@! 2��x�C%�,�L�ؗ-[6s�L�K�s,��y^Y Qm��B@$�s"�`�H�������ś�ȑ#�.]�V��Ǐ�e�\�!�ϫW�6l�?p�0 9�ʗ%[��x��۶m뇋���ĸ@��p�B^�%�x�L qj�B@!

�@$��"��2"��I@g�1>Kw���m룢��B@� �E����۲�6�.a�q~2|�p4�+W�lؼ��cf�nݺ��dٽ{wbz�p1h� �f��6ߎF�E �0~�����ߨ ��v�ޑ�"! ��B@d�ީ�4U��!�P�1:6i%+T ! ��H9̏ǎ�5�e��s�ryX׵�O߾C�=z4Ϙ�0����R�Wce1x.毿�:;Ȃ����q�ͩ�%>��k�x�L qj�B@! �@$�=�@Ն�=!��q�Df�B@! *�������c��.`� ���Kb�s�e�Io������ׅ�z �.�s<Ϝ>S��x�H�H��B@! 2��x�BU�r!`<��&�\��\!

��(1������i����/ �O�͛77+�c��K��b�-��mۂ�a �{��Q^���3)ĩQB@! �����.���|2���K/��s��ӧOgXZ��S����PΑ�ћq*�u�6���Y�Z�n��� �ݡC��l߾=��-��� �|�G(�B�w�@�B@! ���D@�w�%Pհ, �:th�…�=��+�����T^��,8�P! �@�@�x��a����m�)�VA�{��u;�#��ϱs�ҥ �=8J�,�9Z�J����gϞ4�Ák��}����-�z�5ܘ{�78t�ؑ�\^��{G D� ��B@!�I�{�T Ra�����mܸѐ��ކ��9s�ڵk�;V)�P=���� N��O����� /0�Ο?�!W�Ʋ|�%K��ãp���ā�%`�=f̘5k�`�_vʷ���W'N�ئM[�q���b�3)ĩQB@! �����.�@��*��W_}��s����5T̪U��B��h�*)��� H7l؀k)3�r� ���x��A0� ��� 7�m�N�:a�̇�b�L��|K��;� ݻw߱c���X%S�x�H�H��B@! 2��x� #�@:�@ ��H�� L�����MX�l�����{6�N�B�r�����f����\_�kmv9�?�[�n�ڵ3�vοp����+�m۶U�������W�\ɑ�FS0gΜ�0��3)ĩQB@!

People Also Search

A Gentle Introduction To Graph Neural Networks In Python Graph

A Gentle Introduction to Graph Neural Networks in Python Graph neural networks (GNNs) can be pictured as a special class of neural network models where data are structured as graphs — both training data used to train the model and real-world data used... While conventional neural network architectures like feed-forward models excel in modeling predictive problems like classification on structured,...

Friendships Or Follows Between Users). Interested In Better Understanding How

friendships or follows between users). Interested in better understanding how GNNs work through a gentle practical example in Python? Then keep reading. In this introductory example of building a GNN, we will consider a small graph dataset associated with a social media platform, where each node represents a person and each edge connecting any two nodes... Furthermore, each node (person) has assoc...

We Explore The Components Needed For Building A Graph Neural

We explore the components needed for building a graph neural network - and motivate the design choices behind them. This article is one of two Distill publications about graph neural networks. Take a look at Understanding Convolutions on Graphs to understand how convolutions over images generalize naturally to convolutions over graphs. Graphs are all around us; real world objects are often defined...

Recent Developments Have Increased Their Capabilities And Expressive Power. We

Recent developments have increased their capabilities and expressive power. We are starting to see practical applications in areas such as antibacterial discovery , physics simulations , fake news detection , traffic prediction and recommendation systems . This article explores and explains modern graph neural networks. We divide this work into four parts. First, we look at what kind of data is mo...

Third, We Build A Modern GNN, Walking Through Each Of

Third, we build a modern GNN, walking through each of the parts of the model, starting with historic modeling innovations in the field. We move gradually from a bare-bones implementation to a state-of-the-art GNN model. Fourth and finally, we provide a GNN playground where you can play around with a real-word task and dataset to build a stronger intuition of how each component of a GNN model contr...