Graph Machine Learning

Geometric and Relational Deep Learning A workshop on GML will be streamed tomorrow on YouTube. It will start at 9-20 and continue until 17-00. The list of speakers is great: Peter Battaglia, DeepMind Natalia Neverova, Facebook AI Research (FAIR) Stephan Günnemann, TU Munich Yaron Lipman, Weizmann Institute of Science Miltos Allamanis, Microsoft Research Qi Liu, University of Oxford Pim de Haan, University of Amsterdam & Qualcomm AI Research Noemi Montobbio, Italian Institute of Technology

A forgotten story of Soviet AI I found out about Weisfeiler-Leman algorithm about 5 years ago, and then sometime after I realized that both authors were from the USSR. That was quite unexpected. I started looking up information about the authors and found quite a good biography of Boris Weisfeiler, written by his sister, and not so much about Andrey Leman. About one year I was searching the people who knew him, one by one, who are now quite senior and don't use all fancy messengers, to find out more about his life. Finally, I gathered enough to write a post on his life, from interest in math olympiads to development of the first AI chess player, to working in Silicon Valley. His life is a symbol of generation of mathematicians of his time. Strong performance in math olympiads, competitive Moscow State University, working in the Institute of theoretical and experimental physics, and then emigration to the West, when the iron curtain collapsed. I like hearing these stories because it's reminiscent of stories of my parents and their friends-engineers. It's the voice of that time, that now is inevitably gone. Similar to the trip of Babai to the USSR, reading about these stories uncovers the foundations of graph theory, computer science and artificial intelligence that we study today and let us connect the dots between old and new approaches.

Fresh picks from ArXiv Ever wondered what color of the sofa to choose to be compatible with the rest of the furniture? 🛋 Today you will find an answer in one of the papers and of course with the help of GNN. Besides, there is a survey on 6G (!) technologies 📱, new theoretical result on graph isomorphism 🎓, and many applications of graphs. Applications The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case — quantum computation Recommendation system using a deep learning and graph analysis approach — recommendation Learning Furniture Compatibility with Graph Neural Networks — interior design Gumbel-softmax-based Optimization: A Simple General Framework for Optimization Problems on Graphs —combinatorial optimization Knowledge graphs DGL-KE: Training Knowledge Graph Embeddings at Scale Dynamic Knowledge Graph-based Dialogue Generation with Improved Adversarial Meta-Learning Layered Graph Embedding for Entity Recommendation using Wikipedia in the Yahoo! Knowledge Graph Survey A Survey of 6G Wireless Communications: Emerging Technologies Duplication Detection in Knowledge Graphs: Literature and Tools Graph theory Isomorphism Testing for Graphs Excluding Small Minors — on graph isomorphism Hitting forbidden induced subgraphs on bounded treewidth graphs — on treewidth Low-stretch spanning trees of graphs with bounded width Steiner Trees for Hereditary Graph Classes: a Treewidth Perspective

Web Conference 2020 This week, fully-virtual, the Web Conference 2020 will take place. It will last for 5 days, you can still register (~200 USD). There are tracks on social networks, semantics (KG), and user modeling, which often deal with graphs. About every third paper is on graphs. There will be 4 tutorials and 2 workshops on graphs (Monday-Tuesday), which I described in this post.

April Arxiv: how many graphs papers? From 18 March to 17 April there were 300 new and 108 updated papers in ArXiv CS section. This is around 50 papers less that in the previous period.

Discrete Differential Geometrical Course CS 15-458/858: Discrete Differential Geometry (Spring 2020) at Carnegie Mellon University. The lectures are available at YouTube. Discussions of Laplace operator, smooth and discrete surfaces, curvatures, etc.

Some notes on visualization of the graphs Stephen Wolfram, creator of Wolfram language, recently made a post Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful, where he discusses possible origins of how the universe operates. I think the crux of his idea is that if you consider interactions between objects as a graph and then say how from some interactions appear new interactions you can get beautifully looking graphs that look like some 3D shapes which can represent our universe in the limit and therefore you can analyze properties of these graphs such as diameter or curvature to find equivalent notions in physics. I won't speculate whether this post is theoretically-sound or not, let physicists debate, in the end any new theory should predict new facts which we need to wait, but one thing that is noticeable is that graphs that are drawn by Wolfram are beautiful. If you try to draw some big graphs you find that it very hard to draw it so that it does not look like a mess, but here you get pretty-looking networks that indeed remind you some known 3D shapes. Wolfram language has many layouts to draw graphs, which results in different images of the graph. From the shapes of the graphs in the post, it seems that he used SpectralEmbedding or SpringElectricalEmbedding layout. Daniel Spielman, professor at Yale and twice Turing award winner, has a nice popsci video where he discusses how these drawings are related to spectral graph theory and the conditions on the adjacency matrix to have a nice drawing. So maybe next time you will use some of these layouts to impress reviewers of your paper.

Discovering automorphism of a graph and its deck. My hypothesis was that if you take some hard graph for graph isomorphism problem and remove one vertex, then the resulted graph will be much easier because the symmetry of the original graph will be broken. So I took the hardest known graphs for graph isomorphism and checked how much time it takes for determining automorphism group (which is similar to how hard it would be to run isomorphism test). The results are quite interesting. Indeed for many subgraphs determining automorphism is 50-100 times easier. But surprisingly, there are subgraphs which are harder than the original graph. In the image below, you can see results for 6 graphs from cfi-rigid-z2 with ~1000-2000 vertices and checked the runtime for the original graph and all possible subgraphs by deleting one vertex. You can see that while for the first two graphs (first row), all subgraphs are easier, for the next 4 graphs, there are smaller subgraphs that take 5x more time to solve that the original graph. This could happen for three reasons: (1) nauty solver has some heuristics that worked better for the original graph than for the subgraphs (2) not stable running and rerunning it would result in different runtimes and (3) smaller graphs somehow indeed harder than the original graph. I think (2) is very unlikely and my guess is a combination of (1) and (3): removing a vertex makes equivalent vertices in the original graph to be non-equivalent in the subgraph which reduces the amount of pruning nauty does.

KDD Cup 2020 AutoGraph Challenge There is a kaggle-like challenge until 25th May on automl for graph embeddings. 5 datasets, $33.5K prize pool, node classification task, accuracy metric, time constraints on train and predict.

Fresh picks from ArXiv This week features SIDMOD and CVPR accepted papers + ICML submissions; graph embeddings for text classification and surveys on reconstruction conjecture and double descent. SIGMOD • Exact Single-Source SimRank Computation on Large Graphs • An Algorithm for Context-Free Path Queries over Graph Databases • A1: A Distributed In-Memory Graph Database — Bing's graph database GNN • Principal Neighbourhood Aggregation for Graph Nets with Petar Veličković; on the injection with continuous features • VGCN-BERT: Augmenting BERT with Graph Embedding for Text Classification — application to NLP CVPR • Semantic Image Manipulation Using Scene Graphs ICML • Learning to Recognize Spatial Configurations of Objects with Graph Neural Networks • Graph Highway Networks • The general theory of permutation equivarant neural networks and higher order graph variational encoders Graph Theory • On reconstruction of graphs from the multiset of subgraphs obtained by deleting ℓ vertices Survey • A Brief Prehistory of Double Descent

Online Math Seminars There is a list of upcoming math seminars around the world, that are due to the confinement will be organized online and can be accessed by anyone. Topics are broad, including combinatorics, group theory and graphs.