Graph Machine Learning

Fresh picks from ArXiv This week ranges applications of graphs from social studies to astrophysics to robotics 🤖 Also checkout latest survey of deep learning impact on scientific discovery by Eric Schmidt, ex-Google CEO 🎓 And lots of other coolest graph papers from last week. Applications • Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers — combinatorial optimization • A Heterogeneous Dynamical Graph Neural Networks Approach to Quantify Scientific Impact — scientific impact • Investigating Software Usage in the Social Sciences: A Knowledge Graph Approach — social sciences • Graph Neural Networks for Particle Reconstruction in High Energy Physics detectors — physics • Representing Multi-Robot Structure through Multimodal Graph Embedding for the Selection of Robot Teams — robotics • Identification of Patterns in Cosmic-Ray Arrival Directions using Dynamic Graph Convolutional Neural Networks — astrophysics Survey • word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings of Structured Data by Martin Grohe • A Survey of Deep Learning for Scientific Discovery by Eric Schmidt (ex-Google CEO) • COVID-19 and Computer Audition: An Overview on What Speech & Sound Analysis Could Contribute in the SARS-CoV-2 Corona Crisis CVPR • Distillating Knowledge from Graph Convolutional Networks GNN • Bridging the Gap Between Spectral and Spatial Domains in Graph Neural Networks Graph Theory • The 1-2-3 Conjecture holds for graphs with large enough minimum degree • Bounds for the rainbow disconnection number of graphs

Chess is the Drosophila of Artificial Intelligence While writing another post on the life of Andrei Leman, I found that John McCarthy, the creator of Lisp, author of the term Artificial Intelligence, and one of the first and most influential programmers has an interesting remark, where he discusses the importance of long-term research. Apparently this saying, Chess is the Drosophila of Artificial Intelligence, is attributed to a legendary Soviet scientist, Alexander Kronrod, who arguably founded the first AI lab in the USSR. Back in '70s there were some huge ICL machines (analog of IBM machines), people used punch cards to provide the input, and calculations lasted for days, without the possibility to run a program in parallel. Yet, Kronrod's lab, which included Weisfeiler, Leman, and many other famous CS scientists and engineers, were working among others on the development of the chess programs, which in 1974, by the name Kaissa, won the first international chess tournament among machines.

Graph Machine Learning research groups: Le Song I do a series of posts on the groups in graph research. The second is Le Song. His group had 7 accepted papers at ICLR 2020. The top-2 result after Sergey Levine. Le Song (~1981) - Affiliation: Georgia Institute of Technology; - Education: Ph.D. at U. of Sydney in 2008 (supervised by Alex Smola); - h-index: 59; - Awards: best papers at ICML, NeurIPS, AISTATS; - Interests: generative and adversarial graph models, social network analysis, diffusion models.

Limitations of GNN A compiled version of the recent insights I gained from the recent studies on theoretical properties of GNN.

Deep Weisfeiler Leman Surprisingly this paper is not about applying deep neural networks to Weisfeiler Lehman algorithm. It's quite technical but well-written and I could understand the main results and ideas of the paper. They propose an extension of k-WL algorithm, when instead of adding all k-tuples to the input graph at each iteration, they add only a subset of k-tuples. Because you reduce the size of the graph comparing to the original k-WL algorithm, your DeepWL algorithm becomes more efficient, and hence they show that it can solve some graphs in polynomial time that original k-WL algorithm cannot (in particular CFI graphs).

Fresh picks from ArXiv This week presents a new challenge on the computing of triangles, connection between graphs and prime numbers, and as usual submissions to ICML 📕 Survey • Pre-trained Models for Natural Language Processing: A Survey • Survey of Privacy-Preserving Collaborative Filtering WebConf 20 • What is Normal, What is Strange, and What is Missing in a Knowledge Graph: Unified Characterization via Inductive Summarization ICML 20 • Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks • Probabilistic Dual Network Architecture Search on Graphs Applications • GFTE: Graph-based Financial Table Extraction • GraphChallenge.org Triangle Counting Performance Graph Theory • Classification of vertex-transitive digraphs via automorphism group • A Graph Theoretic Formula for the Number of Primes π(n) • Large cycles in essentially 4-connected graphs • Countable graphs are majority 3-choosable

GraphChallenge Challenges such as YOHO, MNIST, HPC Challenge, ImageNet, and VAST have played important roles in driving progress in fields as diverse as machine learning, high performance computing, and visual analytics. GraphChallenge encourages community approaches to developing new solutions for analyzing graphs and sparse data derived from social media, sensor feeds, and scientific data to enable relationships between events to be discovered as they unfold in the field.

This first X (which is in latex \mathcal{X}) is the set of all input features. What this theorem says is that you need to have input features that are countable. Countable means rational or categorical, but not irrational numbers. So this condition "prohibits" any "continuous" features such as real numbers (e.g. degrees). If your set of features is uncountable then the sum is not injective anymore and hence GNN becomes less powerful than 1-WL test. So that's why if you use one-hot encoding of features your GNN becomes theoretically more powerful.

​How powerful are graph neural networks? Part II This is the second insight I recently got from the paper, How powerful are graph neural networks. It's about the initial node features. In the paper they write:

The forbidden sidetrip by László Babai. László Babai, the top mathematician in the field of graph isomorphism, turns out, has a zingy autobiographical story called "The forbidden sidetrip" about his trip to Minsk, Moscow, and Leningrad, when it was 1978 and he was 28. It's just fun on its own, but it also contains lots of names of Soviet mathematicians and references about the places where and how math was being built in the late USSR. To my surprise, he knows (knew?) Russian quite well (originally Hungarian) to listen to lectures in the universities. There are stories about how he generally despises anti-semitism by another talented Russian mathematician Pontryagin, and how he was getting into the soviet queues before knowing what they sell, and how you can give "chervonets sverhu" (i.e. greasing the palm) to get the ticket when they are sold out, and lots of other soviet-related stuff that I really love asking older generation about. But among others, it's just interesting to look at the young, not-yet-famous guy who will then climb to the olymp of mathematics. I wish there was a movie about it.

Applications of graphs in NLP In addition to computer vision, there are many applications of graphs to NLP too. For example, knowledge graphs have been used extensively in research to bring fact knowledge to dialogue and question-answering systems, besides approaches for commonsense reasoning and named entity recognition (see these conference reviews of NLP+KG domains by Michael Galkin). And sometimes you even get more technical papers in this domain, like in this video Relation Embedding with Dihedral Group in Knowledge Graph of ACL '19 paper, where the authors model composition of relationships with some group theory.

​Scene Graph Generation by Iterative Message Passing There are numerous applications of graphs in computer vision, which usually boil down to reduction of the image to a sparse graph. This has found applications in image captioning, human action identification, predicting trajectories, or transferring knowledge to new data sets, among others (see Applications section from this survey). One of the recent interesting advancements is from 2017 CVPR paper (a group of Fei-Fei Li), Scene Graph Generation by Iterative Message Passing, where the authors proposed an image encoder that produces essentially a knowledge graph of objects in the image and their relationships, which can be then used for downstream tasks.