For absolute beginners with little or no experience, this series is a perfect introduction to Cunningham Technique, a form of training designed to create strength and flexibility of both the body and the mind. Clarity of movement in the torso and legs is emphasized with these areas of the body used either in coordination or opposition to one another. You will learn about spatial awareness through exercising changes of direction, rhythmic precision, and dynamic movement in a fun and non-competitive environment with live musical accompaniment.

For absolute beginners with little or no experience, this series is an introduction to ballet fundamentals, from developing skills at the barre and center, to traveling exercises across the floor. You will gain a better understanding of terminology, alignment, balance, artistry, sequencing, and space. This series is a perfect place to begin your education of the fundamentals of ballet in a non-competitive, fun environment with musical live accompaniment.

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For absolute beginners with little or no experience, this class is the perfect introduction to the fundamentals of contemporary dance; the beginning of an exploration of the totality of movement and form, as well as storytelling, dynamic rhythms and energetic release. This is a great series to develop your skill set in contemporary dance elements in a non-competitive, fun environment. 

For absolute beginners with little or no experience, this series is an introduction to Hip-Hop fundamentals. This is a great place to begin developing your skills in the basics of Hip-Hop dance including freestyle, popping, and locking in a non-competitive, fun environment.

Start your journey using Visual Studio Code with this set of introductory videos! These videos are designed to give you an overview of VS Code's various features and quickly get you familiar with them.

This tour takes you inside our Engadine or Galatea enclosure into a large viewing platform with one of our guides. Enjoy the opportunity to learn all about the Sanctuary and get an introduction to what wolfdogs are all about through our 30-minute presentation. This tour offers a "front row" viewing experience of the wolfdogs and the opportunity to photograph them without visual barriers. You will also have full access to your very own wolfdog expert!

The experience includes an introductory talk with one of our experienced staff members, to understand more about wolfdogs and what we do at the Sanctuary. Specifically, guests will be taken into a viewing platform inside the Engadine enclosure to view a pack of high content wolfdogs. In addition to the tour, guests will also be able to explore the entire Sanctuary to view the 40+ wolfdogs on site on our Sanctuary Walk.

A crack intro, also known as a cracktro, loader, or just intro, is a small introduction sequence added to cracked software. It aims to inform the user which "cracking crew" or individual cracker removed the software's copy protection and distributed the crack.[1][2][3]

Crack intros first appeared on Apple II computers in the late 1970s or early 1980s,[2][4][5] and then on ZX Spectrum, Commodore 64 and Amstrad CPC games that were distributed around the world via Bulletin Board Systems (BBSes) and floppy disk copying.[5] By 1985, when reviewing the commercially available ISEPIC cartridge which adds a custom crack intro to memory dumps of Commodore 64 software, Ahoy! wrote that such intros were "in the tradition of the true hacker".[6] Early crack intros resemble graffiti in many ways, although they invaded the private sphere and not the public space.[7][8]

As time went on, crack intros became a medium to demonstrate the purported superiority of a cracking group.[4] Such intros grew very complex, sometimes exceeding the size[9] and complexity[10] of the software itself. Crack intros only became more sophisticated on more advanced systems such as the Amiga, Atari ST, and some IBM PC compatibles with sound cards.[5] These intros feature big, colourful effects, music, and scrollers.[11]

Cracking groups would use the intros not just to gain credit for cracking, but to advertise their BBSes, greet friends, and gain themselves recognition.[4] Messages were frequently of a vulgar nature, and on some occasions made threats of violence against software companies or the members of some rival crack-group.[4]

Crack-intro programming eventually became an art form in its own right, and people started coding intros without attaching them to a crack just to show off how well they could program. This practice evolved into the demoscene.[1]

Crack intros and other small software created by software crackers such as keygens and patches that remove protection from commercial applications often use chiptunes in the form of background music. These chiptunes are now still accessible as downloadable musicdisks or musicpacks.[12]

Math 225 is a linear algebra course, and a part of our introductory sequence into the math major. In linear algebra, you will learn key language and concepts used throughout pure mathematics as well as in a wide variety of applications. Linear algebra starts by studying systems of equations with many variables, and it builds a detailed understanding of how to work in abstract n-dimensional space. This version of linear algebra focuses on concepts, and provides an introduction to writing mathematical proofs.

This course is an introduction to manifolds, which are low-dimensional shapes living in a higher dimensional universe (e.g., a one-dimensional coat hanger or a two-dimensional eggshell each living in a three-dimensional world), and it teaches how to do calculus in this abstract setting. Although the focus of this course will be on abstract mathematical objects and their properties, the material in this course also has applications to a broad range of topics including theoretical physics and machine learning.

Most students with integral calculus background will start with Math 120, to finish the calculus sequence, and gain more experience with mathematics before enrolling in proof-based courses. This choice is recommended particularly if you may need multivariable calculus for another major you are considering, or if it is needed for other courses you might like to take soon (such as in physics or economics). After Math 120, you would move to Math 225 or 226, and Math 255 or 256, which would complete your introductory sequence requirement.

Before getting started with The Basics, we recommend reading one of the following introductory pages. These introductions are intended to highlight key similarities and differences between TypeScript and your favored programming language, and clear up common misconceptions specific to those languages.

This is not an introductory document. It is a detailed technical description of the guidelines and their Success Criteria. See Web Content Accessibility Guidelines (WCAG) Overview for an introduction to WCAG, supporting technical documents, and educational material.

[["Monti2018-ov",{"title":"Dual-Primal Graph Convolutional Networks","author":"Monti, Federico and Shchur, Oleksandr and Bojchevski, Aleksandar and Litany, Or and Gunnemann, Stephan and Bronstein, Michael M","abstract":"In recent years, there has been a surge of interest in developing deep learning methods for non-Euclidean structured data such as graphs. In this paper, we propose Dual-Primal Graph CNN, a graph convolutional architecture that alternates convolution-like operations on the graph and its dual. Our approach allows to learn both vertex- and edge features and generalizes the previous graph attention (GAT) model. We provide extensive experimental validation showing state-of-the-art results on a variety of tasks tested on established graph benchmarks, including CORA and Citeseer citation networks as well as MovieLens, Flixter, Douban and Yahoo Music graph-guided recommender systems.","month":"jun","year":"2018","eprint":"1806.00770","type":"ARTICLE"}],["Battaglia2018-pi",{"title":"Relational inductive biases, deep learning, and graph networks","author":"Battaglia, Peter W and Hamrick, Jessica B and Bapst, Victor and Sanchez-Gonzalez, Alvaro and Zambaldi, Vinicius and Malinowski, Mateusz and Tacchetti, Andrea and Raposo, David and Santoro, Adam and Faulkner, Ryan and Gulcehre, Caglar and Song, Francis and Ballard, Andrew and Gilmer, Justin and Dahl, George and Vaswani, Ashish and Allen, Kelsey and Nash, Charles and Langston, Victoria and Dyer, Chris and Heess, Nicolas and Wierstra, Daan and Kohli, Pushmeet and Botvinick, Matt and Vinyals, Oriol and Li, Yujia and Pascanu, Razvan","abstract":"Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which have fit the natural strengths of deep learning. However, many defining characteristics of human intelligence, which developed under much different pressures, remain out of reach for current approaches. In particular, generalizing beyond one's experiences--a hallmark of human intelligence from infancy--remains a formidable challenge for modern AI. The following is part position paper, part review, and part unification. We argue that combinatorial generalization must be a top priority for AI to achieve human-like abilities, and that structured representations and computations are key to realizing this objective. Just as biology uses nature and nurture cooperatively, we reject the false choice between ``hand-engineering'' and ``end-to-end'' learning, and instead advocate for an approach which benefits from their complementary strengths. We explore how using relational inductive biases within deep learning architectures can facilitate learning about entities, relations, and rules for composing them. We present a new building block for the AI toolkit with a strong relational inductive bias--the graph network--which generalizes and extends various approaches for neural networks that operate on graphs, and provides a straightforward interface for manipulating structured knowledge and producing structured behaviors. We discuss how graph networks can support relational reasoning and combinatorial generalization, laying the foundation for more sophisticated, interpretable, and flexible patterns of reasoning. As a companion to this paper, we have released an open-source software library for building graph networks, with demonstrations of how to use them in practice.","month":"jun","year":"2018","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1806.01261","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Corso2020-py",{"title":"Principal Neighbourhood Aggregation for Graph Nets","author":"Corso, Gabriele and Cavalleri, Luca and Beaini, Dominique and Lio, Pietro and Velickovic, Petar","abstract":"Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.","month":"apr","year":"2020","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"2004.05718","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Poulovassilis1994-bt",{"title":"A nested-graph model for the representation and manipulation of complex objects","author":"Poulovassilis, Alexandra and Levene, Mark","journal":"ACM Transactions on Information Systems","volume":"12","number":"1","pages":"35--68","year":"1994","type":"MISC"}],["Gao2019-lf",{"title":"Graph U-Nets","author":"Gao, Hongyang and Ji, Shuiwang","abstract":"We consider the problem of representation learning for graph data. Convolutional neural networks can naturally operate on images, but have significant challenges in dealing with graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied on many image pixel-wise prediction tasks, similar methods are lacking for graph data. This is due to the fact that pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling (gPool) and unpooling (gUnpool) operations in this work. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. We further propose the gUnpool layer as the inverse operation of the gPool layer. The gUnpool layer restores the graph into its original structure using the position information of nodes selected in the corresponding gPool layer. Based on our proposed gPool and gUnpool layers, we develop an encoder-decoder model on graph, known as the graph U-Nets. Our experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.","month":"may","year":"2019","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1905.05178","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Pope2019-py",{"title":"Explainability Methods for Graph Convolutional Neural Networks","author":"Pope, Phillip E and Kolouri, Soheil and Rostami, Mohammad and Martin, Charles E and Hoffmann, Heiko","journal":"2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","year":"2019","type":"MISC"}],["Zachary1977-jg",{"title":"An Information Flow Model for Conflict and Fission in Small Groups","author":"Zachary, Wayne W","abstract":"Data from a voluntary association are used to construct a new formal model for a traditional anthropological problem, fission in small groups. The process leading to fission is viewed as an unequal flow of sentiments and information across the ties in a social network. This flow is unequal because it is uniquely constrained by the contextual range and sensitivity of each relationship in the network. The subsequent differential sharing of sentiments leads to the formation of subgroups with more internal stability than the group as a whole, and results in fission. The Ford-Fulkerson labeling algorithm allows an accurate prediction of membership in the subgroups and of the locus of the fission to be made from measurements of the potential for information flow across each edge in the network. Methods for measurement of potential information flow are discussed, and it is shown that all appropriate techniques will generate the same predictions.","journal":"J. Anthropol. Res.","publisher":"The University of Chicago Press","volume":"33","number":"4","pages":"452--473","month":"dec","year":"1977","type":"ARTICLE"}],["Duvenaud2015-yc",{"title":"Convolutional Networks on Graphs for Learning Molecular Fingerprints","author":"Duvenaud, David and Maclaurin, Dougal and Aguilera-Iparraguirre, Jorge and Gomez-Bombarelli, Rafael and Hirzel, Timothy and Aspuru-Guzik, Alan and Adams, Ryan P","abstract":"We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We show that these data-driven features are more interpretable, and have better predictive performance on a variety of tasks.","month":"sep","year":"2015","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1509.09292","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Pennington2014-kg",{"title":"Glove: Global Vectors for Word Representation","author":"Pennington, Jeffrey and Socher, Richard and Manning, Christopher","journal":"Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP)","year":"2014","type":"MISC"}],["Velickovic2017-hf",{"title":"Graph Attention Networks","author":"Velickovic, Petar and Cucurull, Guillem and Casanova, Arantxa and Romero, Adriana and Lio, Pietro and Bengio, Yoshua","abstract":"We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods' features, we enable (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of costly matrix operation (such as inversion) or depending on knowing the graph structure upfront. In this way, we address several key challenges of spectral-based graph neural networks simultaneously, and make our model readily applicable to inductive as well as transductive problems. Our GAT models have achieved or matched state-of-the-art results across four established transductive and inductive graph benchmarks: the Cora, Citeseer and Pubmed citation network datasets, as well as a protein-protein interaction dataset (wherein test graphs remain unseen during training).","month":"oct","year":"2017","eprint":"1710.10903","type":"ARTICLE"}],["Vaswani2017-as",{"title":"Attention Is All You Need","author":"Vaswani, Ashish and Shazeer, Noam and Parmar, Niki and Uszkoreit, Jakob and Jones, Llion and Gomez, Aidan N and Kaiser, Lukasz and Polosukhin, Illia","abstract":"The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.","month":"jun","year":"2017","eprint":"1706.03762","type":"ARTICLE"}],["Lample2019-jg",{"title":"Deep Learning for Symbolic Mathematics","author":"Lample, Guillaume and Charton, Francois","abstract":"Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.","month":"dec","year":"2019","eprint":"1912.01412","type":"ARTICLE"}],["McCloskey2018-ml",{"title":"Using Attribution to Decode Dataset Bias in Neural Network Models for Chemistry","author":"McCloskey, Kevin and Taly, Ankur and Monti, Federico and Brenner, Michael P and Colwell, Lucy","abstract":"Deep neural networks have achieved state of the art accuracy at classifying molecules with respect to whether they bind to specific protein targets. A key breakthrough would occur if these models could reveal the fragment pharmacophores that are causally involved in binding. Extracting chemical details of binding from the networks could potentially lead to scientific discoveries about the mechanisms of drug actions. But doing so requires shining light into the black box that is the trained neural network model, a task that has proved difficult across many domains. Here we show how the binding mechanism learned by deep neural network models can be interrogated, using a recently described attribution method. We first work with carefully constructed synthetic datasets, in which the 'fragment logic' of binding is fully known. We find that networks that achieve perfect accuracy on held out test datasets still learn spurious correlations due to biases in the datasets, and we are able to exploit this non-robustness to construct adversarial examples that fool the model. The dataset bias makes these models unreliable for accurately revealing information about the mechanisms of protein-ligand binding. In light of our findings, we prescribe a test that checks for dataset bias given a hypothesis. If the test fails, it indicates that either the model must be simplified or regularized and/or that the training dataset requires augmentation.","month":"nov","year":"2018","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1811.11310","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Rozemberczki2020-lq",{"title":"Little Ball of Fur","author":"Rozemberczki, Benedek and Kiss, Oliver and Sarkar, Rik","journal":"Proceedings of the 29th ACM International Conference on Information & Knowledge Management","year":"2020","type":"MISC"}],["Berge1976-ss",{"title":"Graphs and Hypergraphs","author":"Berge, Claude","publisher":"Elsevier","year":"1976","language":"en","type":"BOOK"}],["Harary1969-qo",{"title":"Graph Theory","author":"Harary, Frank","year":"1969","type":"MISC"}],["Zaheer2017-uc",{"title":"Deep Sets","author":"Zaheer, Manzil and Kottur, Satwik and Ravanbakhsh, Siamak and Poczos, Barnabas and Salakhutdinov, Ruslan and Smola, Alexander","abstract":"We study the problem of designing models for machine learning tasks defined on \\textbackslashemph\\{sets\\}. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics \\textbackslashcite\\{poczos13aistats\\}, to anomaly detection in piezometer data of embankment dams \\textbackslashcite\\{Jung15Exploration\\}, to cosmology \\textbackslashcite\\{Ntampaka16Dynamical,Ravanbakhsh16ICML1\\}. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.","month":"mar","year":"2017","eprint":"1703.06114","type":"ARTICLE"}],["Kunegis2013-er",{"title":"KONECT","author":"Kunegis, Jerome","journal":"Proceedings of the 22nd International Conference on World Wide Web - WWW '13 Companion","year":"2013","type":"MISC"}],["Zitnik2018-uk",{"title":"Modeling polypharmacy side effects with graph convolutional networks","author":"Zitnik, Marinka and Agrawal, Monica and Leskovec, Jure","abstract":"Motivation: The use of drug combinations, termed polypharmacy, is common to treat patients with complex diseases or co-existing conditions. However, a major consequence of polypharmacy is a much higher risk of adverse side effects for the patient. Polypharmacy side effects emerge because of drug-drug interactions, in which activity of one drug may change, favorably or unfavorably, if taken with another drug. The knowledge of drug interactions is often limited because these complex relationships are rare, and are usually not observed in relatively small clinical testing. Discovering polypharmacy side effects thus remains an important challenge with significant implications for patient mortality and morbidity. Results: Here, we present Decagon, an approach for modeling polypharmacy side effects. The approach constructs a multimodal graph of protein-protein interactions, drug-protein target interactions and the polypharmacy side effects, which are represented as drug-drug interactions, where each side effect is an edge of a different type. Decagon is developed specifically to handle such multimodal graphs with a large number of edge types. Our approach develops a new graph convolutional neural network for multirelational link prediction in multimodal networks. Unlike approaches limited to predicting simple drug-drug interaction values, Decagon can predict the exact side effect, if any, through which a given drug combination manifests clinically. Decagon accurately predicts polypharmacy side effects, outperforming baselines by up to 69\\%. We find that it automatically learns representations of side effects indicative of co-occurrence of polypharmacy in patients. Furthermore, Decagon models particularly well polypharmacy side effects that have a strong molecular basis, while on predominantly non-molecular side effects, it achieves good performance because of effective sharing of model parameters across edge types. Decagon opens up opportunities to use large pharmacogenomic and patient population data to flag and prioritize polypharmacy side effects for follow-up analysis via formal pharmacological studies. Availability and implementation: Source code and preprocessed datasets are at: ","journal":"Bioinformatics","volume":"34","number":"13","pages":"i457--i466","month":"jul","year":"2018","language":"en","type":"ARTICLE"}],["Kearnes2016-rl",{"title":"Molecular graph convolutions: moving beyond fingerprints","author":"Kearnes, Steven and McCloskey, Kevin and Berndl, Marc and Pande, Vijay and Riley, Patrick","abstract":"Molecular ``fingerprints'' encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular graph convolutions, a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph-atoms, bonds, distances, etc.-which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.","journal":"J. Comput. Aided Mol. Des.","volume":"30","number":"8","pages":"595--608","month":"aug","year":"2016","keywords":"Artificial neural networks; Deep learning; Machine learning; Molecular descriptors; Virtual screening;references.bib","language":"en","type":"ARTICLE"}],["Kipf2016-ky",{"title":"Variational Graph Auto-Encoders","author":"Kipf, Thomas N and Welling, Max","abstract":"We introduce the variational graph auto-encoder (VGAE), a framework for unsupervised learning on graph-structured data based on the variational auto-encoder (VAE). This model makes use of latent variables and is capable of learning interpretable latent representations for undirected graphs. We demonstrate this model using a graph convolutional network (GCN) encoder and a simple inner product decoder. Our model achieves competitive results on a link prediction task in citation networks. In contrast to most existing models for unsupervised learning on graph-structured data and link prediction, our model can naturally incorporate node features, which significantly improves predictive performance on a number of benchmark datasets.","month":"nov","year":"2016","eprint":"1611.07308","type":"ARTICLE"}],["You2018-vx",{"title":"GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models","author":"You, Jiaxuan and Ying, Rex and Ren, Xiang and Hamilton, William L and Leskovec, Jure","abstract":"Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due to the non-unique, high-dimensional nature of graphs and the complex, non-local dependencies that exist between edges in a given graph. Here we propose GraphRNN, a deep autoregressive model that addresses the above challenges and approximates any distribution of graphs with minimal assumptions about their structure. GraphRNN learns to generate graphs by training on a representative set of graphs and decomposes the graph generation process into a sequence of node and edge formations, conditioned on the graph structure generated so far. In order to quantitatively evaluate the performance of GraphRNN, we introduce a benchmark suite of datasets, baselines and novel evaluation metrics based on Maximum Mean Discrepancy, which measure distances between sets of graphs. Our experiments show that GraphRNN significantly outperforms all baselines, learning to generate diverse graphs that match the structural characteristics of a target set, while also scaling to graphs 50 times larger than previous deep models.","month":"feb","year":"2018","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1802.08773","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Devlin2018-mi",{"title":"BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding","author":"Devlin, Jacob and Chang, Ming-Wei and Lee, Kenton and Toutanova, Kristina","abstract":"We introduce a new language representation model called BERT, which stands for Bidirectional Encoder Representations from Transformers. Unlike recent language representation models, BERT is designed to pre-train deep bidirectional representations from unlabeled text by jointly conditioning on both left and right context in all layers. As a result, the pre-trained BERT model can be fine-tuned with just one additional output layer to create state-of-the-art models for a wide range of tasks, such as question answering and language inference, without substantial task-specific architecture modifications. BERT is conceptually simple and empirically powerful. It obtains new state-of-the-art results on eleven natural language processing tasks, including pushing the GLUE score to 80.5\\% (7.7\\% point absolute improvement), MultiNLI accuracy to 86.7\\% (4.6\\% absolute improvement), SQuAD v1.1 question answering Test F1 to 93.2 (1.5 point absolute improvement) and SQuAD v2.0 Test F1 to 83.1 (5.1 point absolute improvement).","month":"oct","year":"2018","eprint":"1810.04805","type":"ARTICLE"}],["Liao2019-kf",{"title":"Efficient Graph Generation with Graph Recurrent Attention Networks","author":"Liao, Renjie and Li, Yujia and Song, Yang and Wang, Shenlong and Nash, Charlie and Hamilton, William L and Duvenaud, David and Urtasun, Raquel and Zemel, Richard S","abstract":"We propose a new family of efficient and expressive deep generative models of graphs, called Graph Recurrent Attention Networks (GRANs). Our model generates graphs one block of nodes and associated edges at a time. The block size and sampling stride allow us to trade off sample quality for efficiency. Compared to previous RNN-based graph generative models, our framework better captures the auto-regressive conditioning between the already-generated and to-be-generated parts of the graph using Graph Neural Networks (GNNs) with attention. This not only reduces the dependency on node ordering but also bypasses the long-term bottleneck caused by the sequential nature of RNNs. Moreover, we parameterize the output distribution per block using a mixture of Bernoulli, which captures the correlations among generated edges within the block. Finally, we propose to handle node orderings in generation by marginalizing over a family of canonical orderings. On standard benchmarks, we achieve state-of-the-art time efficiency and sample quality compared to previous models. Additionally, we show our model is capable of generating large graphs of up to 5K nodes with good quality. To the best of our knowledge, GRAN is the first deep graph generative model that can scale to this size. Our code is released at: ","month":"oct","year":"2019","eprint":"1910.00760","type":"ARTICLE"}],["Dumoulin2018-tb",{"title":"Feature-wise transformations","author":"Dumoulin, Vincent and Perez, Ethan and Schucher, Nathan and Strub, Florian and Vries, Harm de and Courville, Aaron and Bengio, Yoshua","abstract":"A simple and surprisingly effective family of conditioning mechanisms.","journal":"Distill","volume":"3","number":"7","pages":"e11","month":"jul","year":"2018","type":"ARTICLE"}],["Lee2018-ti",{"title":"Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks","author":"Lee, Juho and Lee, Yoonho and Kim, Jungtaek and Kosiorek, Adam R and Choi, Seungjin and Teh, Yee Whye","abstract":"Many machine learning tasks such as multiple instance learning, 3D shape recognition, and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the order of elements of the set, models used to address them should be permutation invariant. We present an attention-based neural network module, the Set Transformer, specifically designed to model interactions among elements in the input set. The model consists of an encoder and a decoder, both of which rely on attention mechanisms. In an effort to reduce computational complexity, we introduce an attention scheme inspired by inducing point methods from sparse Gaussian process literature. It reduces the computation time of self-attention from quadratic to linear in the number of elements in the set. We show that our model is theoretically attractive and we evaluate it on a range of tasks, demonstrating the state-of-the-art performance compared to recent methods for set-structured data.","month":"oct","year":"2018","eprint":"1810.00825","type":"ARTICLE"}],["Skianis2019-ds",{"title":"Rep the Set: Neural Networks for Learning Set Representations","author":"Skianis, Konstantinos and Nikolentzos, Giannis and Limnios, Stratis and Vazirgiannis, Michalis","abstract":"In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this kind of representations, since sets may vary in cardinality and elements lack a meaningful ordering. In this paper, we present a new neural network architecture, called RepSet, that can handle examples that are represented as sets of vectors. The proposed model computes the correspondences between an input set and some hidden sets by solving a series of network flow problems. This representation is then fed to a standard neural network architecture to produce the output. The architecture allows end-to-end gradient-based learning. We demonstrate RepSet on classification tasks, including text categorization, and graph classification, and we show that the proposed neural network achieves performance better or comparable to state-of-the-art algorithms.","month":"apr","year":"2019","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1904.01962","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Gilmer2017-no",{"title":"Neural Message Passing for Quantum Chemistry","booktitle":"Proceedings of the 34th International Conference on Machine Learning","author":"Gilmer, Justin and Schoenholz, Samuel S and Riley, Patrick F and Vinyals, Oriol and Dahl, George E","editor":"Precup, Doina and Teh, Yee Whye","abstract":"Supervised learning on molecules has incredible potential to be useful in chemistry, drug discovery, and materials science. Luckily, several promising and closely related neural network models invariant to molecular symmetries have already been described in the literature. These models learn a message passing algorithm and aggregation procedure to compute a function of their entire input graph. At this point, the next step is to find a particularly effective variant of this general approach and apply it to chemical prediction benchmarks until we either solve them or reach the limits of the approach. In this paper, we reformulate existing models into a single common framework we call Message Passing Neural Networks (MPNNs) and explore additional novel variations within this framework. Using MPNNs we demonstrate state of the art results on an important molecular property prediction benchmark; these results are strong enough that we believe future work should focus on datasets with larger molecules or more accurate ground truth labels.","publisher":"PMLR","volume":"70","pages":"1263--1272","series":"Proceedings of Machine Learning Research","year":"2017","address":"International Convention Centre, Sydney, Australia","type":"INPROCEEDINGS"}],["Allamanis2017-kz",{"title":"Learning to Represent Programs with Graphs","author":"Allamanis, Miltiadis and Brockschmidt, Marc and Khademi, Mahmoud","abstract":"Learning tasks on source code (i.e., formal languages) have been considered recently, but most work has tried to transfer natural language methods and does not capitalize on the unique opportunities offered by code's known syntax. For example, long-range dependencies induced by using the same variable or function in distant locations are often not considered. We propose to use graphs to represent both the syntactic and semantic structure of code and use graph-based deep learning methods to learn to reason over program structures. In this work, we present how to construct graphs from source code and how to scale Gated Graph Neural Networks training to such large graphs. We evaluate our method on two tasks: VarNaming, in which a network attempts to predict the name of a variable given its usage, and VarMisuse, in which the network learns to reason about selecting the correct variable that should be used at a given program location. Our comparison to methods that use less structured program representations shows the advantages of modeling known structure, and suggests that our models learn to infer meaningful names and to solve the VarMisuse task in many cases. Additionally, our testing showed that VarMisuse identifies a number of bugs in mature open-source projects.","month":"nov","year":"2017","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1711.00740","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Mena2018-ce",{"title":"Learning Latent Permutations with Gumbel-Sinkhorn Networks","author":"Mena, Gonzalo and Belanger, David and Linderman, Scott and Snoek, Jasper","abstract":"Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collection of new methods for end-to-end learning in such models that approximate discrete maximum-weight matching using the continuous Sinkhorn operator. Sinkhorn iteration is attractive because it functions as a simple, easy-to-implement analog of the softmax operator. With this, we can define the Gumbel-Sinkhorn method, an extension of the Gumbel-Softmax method (Jang et al. 2016, Maddison2016 et al. 2016) to distributions over latent matchings. We demonstrate the effectiveness of our method by outperforming competitive baselines on a range of qualitatively different tasks: sorting numbers, solving jigsaw puzzles, and identifying neural signals in worms.","month":"feb","year":"2018","eprint":"1802.08665","type":"ARTICLE"}],["Scarselli2009-ku",{"title":"The Graph Neural Network Model","author":"Scarselli, F and Gori, M and Tsoi, Ah Chung and Hagenbuchner, M and Monfardini, G","journal":"IEEE Transactions on Neural Networks","volume":"20","number":"1","pages":"61--80","year":"2009","type":"MISC"}],["Krenn2019-gg",{"title":"Self-Referencing Embedded Strings (SELFIES): A 100% robust molecular string representation","author":"Krenn, Mario and Hase, Florian and Nigam, Akshatkumar and Friederich, Pascal and Aspuru-Guzik, Alan","abstract":"The discovery of novel materials and functional molecules can help to solve some of society's most urgent challenges, ranging from efficient energy harvesting and storage to uncovering novel pharmaceutical drug candidates. Traditionally matter engineering -- generally denoted as inverse design -- was based massively on human intuition and high-throughput virtual screening. The last few years have seen the emergence of significant interest in computer-inspired designs based on evolutionary or deep learning methods. The major challenge here is that the standard strings molecular representation SMILES shows substantial weaknesses in that task because large fractions of strings do not correspond to valid molecules. Here, we solve this problem at a fundamental level and introduce SELFIES (SELF-referencIng Embedded Strings), a string-based representation of molecules which is 100% robust. Every SELFIES string corresponds to a valid molecule, and SELFIES can represent every molecule. SELFIES can be directly applied in arbitrary machine learning models without the adaptation of the models; each of the generated molecule candidates is valid. In our experiments, the model's internal memory stores two orders of magnitude more diverse molecules than a similar test with SMILES. Furthermore, as all molecules are valid, it allows for explanation and interpretation of the internal working of the generative models.","month":"may","year":"2019","eprint":"1905.13741","type":"ARTICLE"}],["Goyal2020-wl",{"title":"GraphGen: A Scalable Approach to Domain-agnostic Labeled Graph Generation","author":"Goyal, Nikhil and Jain, Harsh Vardhan and Ranu, Sayan","abstract":"Graph generative models have been extensively studied in the data mining literature. While traditional techniques are based on generating structures that adhere to a pre-decided distribution, recent techniques have shifted towards learning this distribution directly from the data. While learning-based approaches have imparted significant improvement in quality, some limitations remain to be addressed. First, learning graph distributions introduces additional computational overhead, which limits their scalability to large graph databases. Second, many techniques only learn the structure and do not address the need to also learn node and edge labels, which encode important semantic information and influence the structure itself. Third, existing techniques often incorporate domain-specific rules and lack generalizability. Fourth, the experimentation of existing techniques is not comprehensive enough due to either using weak evaluation metrics or focusing primarily on synthetic or small datasets. In this work, we develop a domain-agnostic technique called GraphGen to overcome all of these limitations. GraphGen converts graphs to sequences using minimum DFS codes. Minimum DFS codes are canonical labels and capture the graph structure precisely along with the label information. The complex joint distributions between structure and semantic labels are learned through a novel LSTM architecture. Extensive experiments on million-sized, real graph datasets show GraphGen to be 4 times faster on average than state-of-the-art techniques while being significantly better in quality across a comprehensive set of 11 different metrics. Our code is released at -iitd/graphgen.","month":"jan","year":"2020","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"2001.08184","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Ying2019-gk",{"title":"GNNExplainer: Generating Explanations for Graph Neural Networks","booktitle":"Advances in Neural Information Processing Systems","author":"Ying, Zhitao and Bourgeois, Dylan and You, Jiaxuan and Zitnik, Marinka and Leskovec, Jure","editor":"Wallach, H and Larochelle, H and Beygelzimer, A and d\\textbackslashtextquotesingle Alche-Buc, F and Fox, E and Garnett, R","publisher":"Curran Associates, Inc.","volume":"32","pages":"9244--9255","year":"2019","type":"INPROCEEDINGS"}],["Sanchez-Lengeling2020-qq",{"title":"Leffingwell Odor Dataset","author":"Sanchez-Lengeling, Benjamin and Wei, Jennifer N and Lee, Brian K and Gerkin, Richard C and Aspuru-Guzik, Alan and Wiltschko, Alexander B","abstract":"Predicting properties of molecules is an area of growing research in machine learning, particularly as models for learning from graph-valued inputs improve in sophistication and robustness. A molecular property prediction problem that has received comparatively little attention during this surge in research activity is building Structure-Odor Relationships (SOR) models (as opposed to Quantitative Structure-Activity Relationships, a term from medicinal chemistry). This is a 70+ year-old problem straddling chemistry, physics, neuroscience, and machine learning. To spur development on the SOR problem, we curated and cleaned a dataset of 3523 molecules associated with expert-labeled odor descriptors from the Leffingwell PMP 2001 database. We provide featurizations of all molecules in the dataset using bit-based and count-based fingerprints, Mordred molecular descriptors, and the embeddings from our trained GNN model (Sanchez-Lengeling et al., 2019). This dataset is comprised of two files: leffingwell\\_data.csv: this contains molecular structures, and what they smell like, along with train, test, and cross-validation splits. More detail on the file structure is found in leffingwell\\_readme.pdf. leffingwell\\_embeddings.npz: this contains several featurizations of the molecules in the dataset. leffingwell\\_readme.pdf: a more detailed description of the data and its provenance, including expected performance metrics. LICENSE: a copy of the CC-BY-NC license language. The dataset, and all associated features, is freely available for research use under the CC-BY-NC license.","month":"oct","year":"2020","keywords":"machine learning; artificial intelligence; olfaction; neuroscience; chemistry; scent; fragrance","type":"MISC"}],["Hubler2008-us",{"title":"Metropolis Algorithms for Representative Subgraph Sampling","author":"Hubler, Christian and Kriegel, Hans-Peter and Borgwardt, Karsten and Ghahramani, Zoubin","journal":"2008 Eighth IEEE International Conference on Data Mining","year":"2008","type":"MISC"}],["Mikolov2013-vr",{"title":"Distributed Representations of Words and Phrases and their Compositionality","author":"Mikolov, Tomas and Sutskever, Ilya and Chen, Kai and Corrado, Greg and Dean, Jeffrey","abstract":"The recently introduced continuous Skip-gram model is an efficient method for learning high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships. In this paper we present several extensions that improve both the quality of the vectors and the training speed. By subsampling of the frequent words we obtain significant speedup and also learn more regular word representations. We also describe a simple alternative to the hierarchical softmax called negative sampling. An inherent limitation of word representations is their indifference to word order and their inability to represent idiomatic phrases. For example, the meanings of ``Canada'' and ``Air'' cannot be easily combined to obtain ``Air Canada''. Motivated by this example, we present a simple method for finding phrases in text, and show that learning good vector representations for millions of phrases is possible.","month":"oct","year":"2013","eprint":"1310.4546","type":"ARTICLE"}],["Xu2018-sf",{"title":"How Powerful are Graph Neural Networks?","author":"Xu, Keyulu and Hu, Weihua and Leskovec, Jure and Jegelka, Stefanie","abstract":"Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.","month":"oct","year":"2018","eprint":"1810.00826","type":"ARTICLE"}],["Liu2018-kf",{"title":"N-Gram Graph: Simple Unsupervised Representation for Graphs, with Applications to Molecules","author":"Liu, Shengchao and Demirel, Mehmet Furkan and Liang, Yingyu","abstract":"Machine learning techniques have recently been adopted in various applications in medicine, biology, chemistry, and material engineering. An important task is to predict the properties of molecules, which serves as the main subroutine in many downstream applications such as virtual screening and drug design. Despite the increasing interest, the key challenge is to construct proper representations of molecules for learning algorithms. This paper introduces the N-gram graph, a simple unsupervised representation for molecules. The method first embeds the vertices in the molecule graph. It then constructs a compact representation for the graph by assembling the vertex embeddings in short walks in the graph, which we show is equivalent to a simple graph neural network that needs no training. The representations can thus be efficiently computed and then used with supervised learning methods for prediction. Experiments on 60 tasks from 10 benchmark datasets demonstrate its advantages over both popular graph neural networks and traditional representation methods. This is complemented by theoretical analysis showing its strong representation and prediction power.","month":"jun","year":"2018","eprint":"1806.09206","type":"ARTICLE"}],["Zhou2019-ko",{"title":"Optimization of Molecules via Deep Reinforcement Learning","author":"Zhou, Zhenpeng and Kearnes, Steven and Li, Li and Zare, Richard N and Riley, Patrick","abstract":"We present a framework, which we call Molecule Deep Q-Networks (MolDQN), for molecule optimization by combining domain knowledge of chemistry and state-of-the-art reinforcement learning techniques (double Q-learning and randomized value functions). We directly define modifications on molecules, thereby ensuring 100\\% chemical validity. Further, we operate without pre-training on any dataset to avoid possible bias from the choice of that set. MolDQN achieves comparable or better performance against several other recently published algorithms for benchmark molecular optimization tasks. However, we also argue that many of these tasks are not representative of real optimization problems in drug discovery. Inspired by problems faced during medicinal chemistry lead optimization, we extend our model with multi-objective reinforcement learning, which maximizes drug-likeness while maintaining similarity to the original molecule. We further show the path through chemical space to achieve optimization for a molecule to understand how the model works.","journal":"Sci. Rep.","publisher":"Nature Publishing Group","volume":"9","number":"1","pages":"1--10","month":"jul","year":"2019","language":"en","type":"ARTICLE"}],["Sanchez-Lengeling2019-vs",{"title":"Machine Learning for Scent: Learning Generalizable Perceptual Representations of Small Molecules","author":"Sanchez-Lengeling, Benjamin and Wei, Jennifer N and Lee, Brian K and Gerkin, Richard C and Aspuru-Guzik, Alan and Wiltschko, Alexander B","abstract":"Predicting the relationship between a molecule's structure and its odor remains a difficult, decades-old task. This problem, termed quantitative structure-odor relationship (QSOR) modeling, is an important challenge in chemistry, impacting human nutrition, manufacture of synthetic fragrance, the environment, and sensory neuroscience. We propose the use of graph neural networks for QSOR, and show they significantly out-perform prior methods on a novel data set labeled by olfactory experts. Additional analysis shows that the learned embeddings from graph neural networks capture a meaningful odor space representation of the underlying relationship between structure and odor, as demonstrated by strong performance on two challenging transfer learning tasks. Machine learning has already had a large impact on the senses of sight and sound. Based on these early results with graph neural networks for molecular properties, we hope machine learning can eventually do for olfaction what it has already done for vision and hearing.","month":"oct","year":"2019","eprint":"1910.10685","type":"ARTICLE"}],["Murphy2018-fz",{"title":"Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs","author":"Murphy, Ryan L and Srinivasan, Balasubramaniam and Rao, Vinayak and Ribeiro, Bruno","abstract":"We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with $k$-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.","month":"nov","year":"2018","eprint":"1811.01900","type":"ARTICLE"}],["Leskovec2006-st",{"title":"Sampling from large graphs","author":"Leskovec, Jure and Faloutsos, Christos","journal":"Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '06","year":"2006","type":"MISC"}],["NEURIPS2020_6054",{"title":"Evaluating Attribution for Graph Neural Networks","author":"Benjamin Sanchez-Lengeling and Jennifer Wei and Brian Lee and Emily Reif and Wesley Qian and Yiliu Wang and Kevin James McCloskey and Lucy Colwell and Alexander B Wiltschko","booktitle":"Advances in Neural Information Processing Systems 33","year":"2020","url":" -Abstract.html","type":"article"}],["Joshi2020-ze",{"title":"Transformers are Graph Neural Networks","author":"Joshi, Chaitanya","abstract":"Engineer friends often ask me: Graph Deep Learning sounds great, but are there any big commercial success stories? Is it being deployed in practical applications? Besides the obvious ones--recommendation systems at Pinterest, Alibaba and Twitter--a slightly nuanced success story is the Transformer architecture, which has taken the NLP industry by storm. Through this post, I want to establish links between Graph Neural Networks (GNNs) and Transformers. I'll talk about the intuitions behind model architectures in the NLP and GNN communities, make connections using equations and figures, and discuss how we could work together to drive progress.","publisher":"NTU Graph Deep Learning Lab","month":"feb","year":"2020","howpublished":"\\url{ -are-gnns/}","note":"Accessed: 2021-7-19","type":"MISC"}],["Eksombatchai2017-il",{"title":"Pixie: A System for Recommending 3+ Billion Items to 200+ Million Users in {Real-Time}","author":"Eksombatchai, Chantat and Jindal, Pranav and Liu, Jerry Zitao and Liu, Yuchen and Sharma, Rahul and Sugnet, Charles and Ulrich, Mark and Leskovec, Jure","abstract":"User experience in modern content discovery applications critically depends on high-quality personalized recommendations. However, building systems that provide such recommendations presents a major challenge due to a massive pool of items, a large number of users, and requirements for recommendations to be responsive to user actions and generated on demand in real-time. Here we present Pixie, a scalable graph-based real-time recommender system that we developed and deployed at Pinterest. Given a set of user-specific pins as a query, Pixie selects in real-time from billions of possible pins those that are most related to the query. To generate recommendations, we develop Pixie Random Walk algorithm that utilizes the Pinterest object graph of 3 billion nodes and 17 billion edges. Experiments show that recommendations provided by Pixie lead up to 50\\% higher user engagement when compared to the previous Hadoop-based production system. Furthermore, we develop a graph pruning strategy at that leads to an additional 58\\% improvement in recommendations. Last, we discuss system aspects of Pixie, where a single server executes 1,200 recommendation requests per second with 60 millisecond latency. Today, systems backed by Pixie contribute to more than 80\\% of all user engagement on Pinterest.","month":"nov","year":"2017","archivePrefix":"arXiv","primaryClass":"cs.IR","eprint":"1711.07601","archiveprefix":"arXiv","primaryclass":"cs.IR","type":"ARTICLE"}],["undated-sy",{"title":"Traffic prediction with advanced Graph Neural Networks","author":"*, Oliver Lange and Perez, Luis","abstract":"Working with our partners at Google Maps, we used advanced machine learning techniques including Graph Neural Networks, to improve the accuracy of real time ETAs by up to 50\\%.","howpublished":"\\url{ -prediction-with-advanced-graph-neural-networks}","note":"Accessed: 2021-7-19","type":"MISC"}],["Monti2019-tf",{"title":"Fake News Detection on Social Media using Geometric Deep Learning","author":"Monti, Federico and Frasca, Fabrizio and Eynard, Davide and Mannion, Damon and Bronstein, Michael M","abstract":"Social media are nowadays one of the main news sources for millions of people around the globe due to their low cost, easy access and rapid dissemination. This however comes at the cost of dubious trustworthiness and significant risk of exposure to 'fake news', intentionally written to mislead the readers. Automatically detecting fake news poses challenges that defy existing content-based analysis approaches. One of the main reasons is that often the interpretation of the news requires the knowledge of political or social context or 'common sense', which current NLP algorithms are still missing. Recent studies have shown that fake and real news spread differently on social media, forming propagation patterns that could be harnessed for the automatic fake news detection. Propagation-based approaches have multiple advantages compared to their content-based counterparts, among which is language independence and better resilience to adversarial attacks. In this paper we show a novel automatic fake news detection model based on geometric deep learning. The underlying core algorithms are a generalization of classical CNNs to graphs, allowing the fusion of heterogeneous data such as content, user profile and activity, social graph, and news propagation. Our model was trained and tested on news stories, verified by professional fact-checking organizations, that were spread on Twitter. Our experiments indicate that social network structure and propagation are important features allowing highly accurate (92.7\\% ROC AUC) fake news detection. Second, we observe that fake news can be reliably detected at an early stage, after just a few hours of propagation. Third, we test the aging of our model on training and testing data separated in time. Our results point to the promise of propagation-based approaches for fake news detection as an alternative or complementary strategy to content-based approaches.","month":"feb","year":"2019","archivePrefix":"arXiv","primaryClass":"cs.SI","eprint":"1902.06673","archiveprefix":"arXiv","primaryclass":"cs.SI","type":"ARTICLE"}],["Sanchez-Gonzalez2020-yo",{"title":"Learning to simulate complex physics with graph networks","author":"Sanchez-Gonzalez, Alvaro and Godwin, Jonathan and Pfaff, Tobias and Ying, Rex and Leskovec, Jure and Battaglia, Peter W","abstract":"Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term ``Graph Network-based Simulators'' (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.","month":"feb","year":"2020","copyright":" -distrib/1.0/","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"2002.09405","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Stokes2020-az",{"title":"A Deep Learning Approach to Antibiotic Discovery","author":"Stokes, Jonathan M and Yang, Kevin and Swanson, Kyle and Jin, Wengong and Cubillos-Ruiz, Andres and Donghia, Nina M and MacNair, Craig R and French, Shawn and Carfrae, Lindsey A and Bloom-Ackermann, Zohar and Tran, Victoria M and Chiappino-Pepe, Anush and Badran, Ahmed H and Andrews, Ian W and Chory, Emma J and Church, George M and Brown, Eric D and Jaakkola, Tommi S and Barzilay, Regina and Collins, James J","journal":"Cell","volume":"181","number":"2","pages":"475--483","month":"apr","year":"2020","language":"en","type":"ARTICLE"}],["Dwivedi2020-xm",{"title":"Benchmarking Graph Neural Networks","author":"Dwivedi, Vijay Prakash and Joshi, Chaitanya K and Laurent, Thomas and Bengio, Yoshua and Bresson, Xavier","abstract":"Graph neural networks (GNNs) have become the standard toolkit for analyzing and learning from data on graphs. As the field grows, it becomes critical to identify key architectures and validate new ideas that generalize to larger, more complex datasets. Unfortunately, it has been increasingly difficult to gauge the effectiveness of new models in the absence of a standardized benchmark with consistent experimental settings. In this paper, we introduce a reproducible GNN benchmarking framework, with the facility for researchers to add new models conveniently for arbitrary datasets. We demonstrate the usefulness of our framework by presenting a principled investigation into the recent Weisfeiler-Lehman GNNs (WL-GNNs) compared to message passing-based graph convolutional networks (GCNs) for a variety of graph tasks, i.e. graph regression/classification and node/link prediction, with medium-scale datasets.","month":"mar","year":"2020","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"2003.00982","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["You2020-vk",{"title":"Design Space for Graph Neural Networks","author":"You, Jiaxuan and Ying, Rex and Leskovec, Jure","abstract":"The rapid evolution of Graph Neural Networks (GNNs) has led to a growing number of new architectures as well as novel applications. However, current research focuses on proposing and evaluating specific architectural designs of GNNs, as opposed to studying the more general design space of GNNs that consists of a Cartesian product of different design dimensions, such as the number of layers or the type of the aggregation function. Additionally, GNN designs are often specialized to a single task, yet few efforts have been made to understand how to quickly find the best GNN design for a novel task or a novel dataset. Here we define and systematically study the architectural design space for GNNs which consists of 315,000 different designs over 32 different predictive tasks. Our approach features three key innovations: (1) A general GNN design space; (2) a GNN task space with a similarity metric, so that for a given novel task/dataset, we can quickly identify/transfer the best performing architecture; (3) an efficient and effective design space evaluation method which allows insights to be distilled from a huge number of model-task combinations. Our key results include: (1) A comprehensive set of guidelines for designing well-performing GNNs; (2) while best GNN designs for different tasks vary significantly, the GNN task space allows for transferring the best designs across different tasks; (3) models discovered using our design space achieve state-of-the-art performance. Overall, our work offers a principled and scalable approach to transition from studying individual GNN designs for specific tasks, to systematically studying the GNN design space and the task space. Finally, we release GraphGym, a powerful platform for exploring different GNN designs and tasks. GraphGym features modularized GNN implementation, standardized GNN evaluation, and reproducible and scalable experiment management.","month":"nov","year":"2020","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"2011.08843","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Zhong2020-mv",{"title":"Hierarchical Message-Passing Graph Neural Networks","author":"Zhong, Zhiqiang and Li, Cheng-Te and Pang, Jun","abstract":"Graph Neural Networks (GNNs) have become a promising approach to machine learning with graphs. Since existing GNN models are based on flat message-passing mechanisms, two limitations need to be tackled. One is costly in encoding global information on the graph topology. The other is failing to model meso- and macro-level semantics hidden in the graph, such as the knowledge of institutes and research areas in an academic collaboration network. To deal with these two issues, we propose a novel Hierarchical Message-Passing Graph Neural Networks framework. The main idea is to generate a hierarchical structure that re-organises all nodes in a graph into multi-level clusters, along with intra- and inter-level edge connections. The derived hierarchy not only creates shortcuts connecting far-away nodes so that global information can be efficiently accessed via message passing but also incorporates meso- and macro-level semantics into the learning of node embedding. We present the first model to implement this hierarchical message-passing mechanism, termed Hierarchical Community-aware Graph Neural Network (HC-GNN), based on hierarchical communities detected from the graph. Experiments conducted on eight datasets under transductive, inductive, and few-shot settings exhibit that HC-GNN can outperform state-of-the-art GNN models in network analysis tasks, including node classification, link prediction, and community detection.","month":"sep","year":"2020","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"2009.03717","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Yadati2018-de",{"title":"HyperGCN: A New Method of Training Graph Convolutional Networks on Hypergraphs","author":"Yadati, Naganand and Nimishakavi, Madhav and Yadav, Prateek and Nitin, Vikram and Louis, Anand and Talukdar, Partha","abstract":"In many real-world network datasets such as co-authorship, co-citation, email communication, etc., relationships are complex and go beyond pairwise. Hypergraphs provide a flexible and natural modeling tool to model such complex relationships. The obvious existence of such complex relationships in many real-world networks naturaly motivates the problem of learning with hypergraphs. A popular learning paradigm is hypergraph-based semi-supervised learning (SSL) where the goal is to assign labels to initially unlabeled vertices in a hypergraph. Motivated by the fact that a graph convolutional network (GCN) has been effective for graph-based SSL, we propose HyperGCN, a novel GCN for SSL on attributed hypergraphs. Additionally, we show how HyperGCN can be used as a learning-based approach for combinatorial optimisation on NP-hard hypergraph problems. We demonstrate HyperGCN's effectiveness through detailed experimentation on real-world hypergraphs.","month":"sep","year":"2018","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1809.02589","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Stocker2020-tr",{"title":"Machine learning in chemical reaction space","author":"Stocker, Sina and Csanyi, Gabor and Reuter, Karsten and Margraf, Johannes T","abstract":"Chemical compound space refers to the vast set of all possible chemical compounds, estimated to contain 1060 molecules. While intractable as a whole, modern machine learning (ML) is increasingly capable of accurately predicting molecular properties in important subsets. Here, we therefore engage in the ML-driven study of even larger reaction space. Central to chemistry as a science of transformations, this space contains all possible chemical reactions. As an important basis for 'reactive' ML, we establish a first-principles database (Rad-6) containing closed and open-shell organic molecules, along with an associated database of chemical reaction energies (Rad-6-RE). We show that the special topology of reaction spaces, with central hub molecules involved in multiple reactions, requires a modification of existing compound space ML-concepts. Showcased by the application to methane combustion, we demonstrate that the learned reaction energies offer a non-empirical route to rationally extract reduced reaction networks for detailed microkinetic analyses.","journal":"Nat. Commun.","volume":"11","number":"1","pages":"5505","month":"oct","year":"2020","language":"en","type":"ARTICLE"}],["Chiang2019-yh",{"title":"Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks","author":"Chiang, Wei-Lin and Liu, Xuanqing and Si, Si and Li, Yang and Bengio, Samy and Hsieh, Cho-Jui","abstract":"Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at -research/google-research/tree/master/cluster\\_gcn.","month":"may","year":"2019","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1905.07953","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Zeng2019-eh",{"title":"GraphSAINT: Graph Sampling Based Inductive Learning Method","author":"Zeng, Hanqing and Zhou, Hongkuan and Srivastava, Ajitesh and Kannan, Rajgopal and Prasanna, Viktor","abstract":"Graph Convolutional Networks (GCNs) are powerful models for learning representations of attributed graphs. To scale GCNs to large graphs, state-of-the-art methods use various layer sampling techniques to alleviate the ``neighbor explosion'' problem during minibatch training. We propose GraphSAINT, a graph sampling based inductive learning method that improves training efficiency and accuracy in a fundamentally different way. By changing perspective, GraphSAINT constructs minibatches by sampling the training graph, rather than the nodes or edges across GCN layers. Each iteration, a complete GCN is built from the properly sampled subgraph. Thus, we ensure fixed number of well-connected nodes in all layers. We further propose normalization technique to eliminate bias, and sampling algorithms for variance reduction. Importantly, we can decouple the sampling from the forward and backward propagation, and extend GraphSAINT with many architecture variants (e.g., graph attention, jumping connection). GraphSAINT demonstrates superior performance in both accuracy and training time on five large graphs, and achieves new state-of-the-art F1 scores for PPI (0.995) and Reddit (0.970).","month":"jul","year":"2019","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1907.04931","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Markowitz2021-rn",{"title":"Graph Traversal with Tensor Functionals: A Meta-Algorithm for Scalable Learning","author":"Markowitz, Elan and Balasubramanian, Keshav and Mirtaheri, Mehrnoosh and Abu-El-Haija, Sami and Perozzi, Bryan and Ver Steeg, Greg and Galstyan, Aram","abstract":"Graph Representation Learning (GRL) methods have impacted fields from chemistry to social science. However, their algorithmic implementations are specialized to specific use-cases e.g.message passing methods are run differently from node embedding ones. Despite their apparent differences, all these methods utilize the graph structure, and therefore, their learning can be approximated with stochastic graph traversals. We propose Graph Traversal via Tensor Functionals(GTTF), a unifying meta-algorithm framework for easing the implementation of diverse graph algorithms and enabling transparent and efficient scaling to large graphs. GTTF is founded upon a data structure (stored as a sparse tensor) and a stochastic graph traversal algorithm (described using tensor operations). The algorithm is a functional that accept two functions, and can be specialized to obtain a variety of GRL models and objectives, simply by changing those two functions. We show for a wide class of methods, our algorithm learns in an unbiased fashion and, in expectation, approximates the learning as if the specialized implementations were run directly. With these capabilities, we scale otherwise non-scalable methods to set state-of-the-art on large graph datasets while being more efficient than existing GRL libraries - with only a handful of lines of code for each method specialization. GTTF and its various GRL implementations are on: -usc-edu/gttf.","month":"feb","year":"2021","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"2102.04350","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Du2019-hr",{"title":"Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels","author":"Du, Simon S and Hou, Kangcheng and Poczos, Barnabas and Salakhutdinov, Ruslan and Wang, Ruosong and Xu, Keyulu","abstract":"While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better practical performance, as GNNs use multi-layer architectures and non-linear activation functions to extract high-order information of graphs as features. However, due to the large number of hyper-parameters and the non-convex nature of the training procedure, GNNs are harder to train. Theoretical guarantees of GNNs are also not well-understood. Furthermore, the expressive power of GNNs scales with the number of parameters, and thus it is hard to exploit the full power of GNNs when computing resources are limited. The current paper presents a new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to infinitely wide multi-layer GNNs trained by gradient descent. GNTKs enjoy the full expressive power of GNNs and inherit advantages of GKs. Theoretically, we show GNTKs provably learn a class of smooth functions on graphs. Empirically, we test GNTKs on graph classification datasets and show they achieve strong performance.","month":"may","year":"2019","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1905.13192","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Xu2018-hq",{"title":"Representation Learning on Graphs with Jumping Knowledge Networks","author":"Xu, Keyulu and Li, Chengtao and Tian, Yonglong and Sonobe, Tomohiro and Kawarabayashi, Ken-Ichi and Jegelka, Stefanie","abstract":"Recent deep learning approaches for representation learning on graphs follow a neighborhood aggregation procedure. We analyze some important properties of these models, and propose a strategy to overcome those. In particular, the range of ``neighboring'' nodes that a node's representation draws from strongly depends on the graph structure, analogous to the spread of a random walk. To adapt to local neighborhood properties and tasks, we explore an architecture -- jumping knowledge (JK) networks -- that flexibly leverages, for each node, different neighborhood ranges to enable better structure-aware representation. In a number of experiments on social, bioinformatics and citation networks, we demonstrate that our model achieves state-of-the-art performance. Furthermore, combining the JK framework with models like Graph Convolutional Networks, GraphSAGE and Graph Attention Networks consistently improves those models' performance.","month":"jun","year":"2018","archivePrefix":"arXiv","primaryClass":"cs.LG","eprint":"1806.03536","archiveprefix":"arXiv","primaryclass":"cs.LG","type":"ARTICLE"}],["Velickovic2019-io",{"title":"Neural Execution of Graph Algorithms","author":"Velickovic, Petar and Ying, Rex and Padovano, Matilde and Hadsell, Raia and Blundell, Charles","abstract":"Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without explicit guidance on how to structure their problem-solving. Here, instead, we focus on learning in the space of algorithms: we train several state-of-the-art GNN architectures to imitate individual steps of classical graph algorithms, parallel (breadth-first search, Bellman-Ford) as well as sequential (Prim's algorithm). As graph algorithms usually rely on making discrete decisions within neighbourhoods, we hypothesise that maximisation-based message passing neural networks are best-suited for such objectives, and validate this claim empirically. We also demonstrate how learning in the space of algorithms can yield new opportunities for positive transfer between tasks---showing how learning a shortest-path algorithm can be substantially improved when simultaneously learning a reachability algorithm.","month":"oct","year":"2019","archivePrefix":"arXiv","primaryClass":"stat.ML","eprint":"1910.10593","archiveprefix":"arXiv","primaryclass":"stat.ML","type":"ARTICLE"}],["noauthor_undated-qq",{"author":"Tai-Danae Bradley","title":"Viewing matrices & probability as graphs","howpublished":"\\url{ -probability-graphs}","type":"MISC"}],["Bapat2014-fk",{"title":"Graphs and Matrices","author":"Bapat, Ravindra B","abstract":"This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail.Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph.Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book.In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized.Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.","publisher":"Springer","month":"sep","year":"2014","language":"en","type":"BOOK"}],["Bollobas2013-uk",{"title":"Modern Graph Theory","author":"Bollobas, Bela","abstract":"The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\\textbackslash'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.","publisher":"Springer Science & Business Media","month":"dec","year":"2013","language":"en","type":"BOOK"}],["Pattanaik2020-jj",{"title":"Message Passing Networks for Molecules with Tetrahedral Chirality","author":"Pattanaik, Lagnajit and Ganea, Octavian-Eugen and Coley, Ian and Jensen, Klavs F and Green, William H and Coley, Connor W","abstract":"Molecules with identical graph connectivity can exhibit different physical and biological properties if they exhibit stereochemistry-a spatial structural characteristic. However, modern neural architectures designed for learning structure-property relationships from molecular structures treat molecules as graph-structured data and therefore are invariant to stereochemistry. Here, we develop two custom aggregation functions for message passing neural networks to learn properties of molecules with tetrahedral chirality, one common form of stereochemistry. We evaluate performance on synthetic data as well as a newly-proposed protein-ligand docking dataset with relevance to drug discovery. Results show modest improvements over a baseline sum aggregator, highlighting opportunities for further architecture development.","month":"nov","year":"2020","archivePrefix":"arXiv","primaryClass":"q-bio.QM","eprint":"2012.00094","archiveprefix":"arXiv","primaryclass":"q-bio.QM","type":"ARTICLE"}],["daigavane2021understanding",{"author":"Daigavane, Ameya and Ravindran, Balaraman and Aggarwal, Gaurav","title":"Understanding Convolutions on Graphs","journal":"Distill","year":"2021","note":" -gnns","doi":"10.23915/distill.00032","type":"article"}]] e24fc04721

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