CS 520: Knowledge Graphs

Today starts a Stanford course on knowledge graphs. It's available for everyone for free via Zoom (although there is no guarantee to have the videos afterwards).

Graph Isomorphism Software

Open-source software for finding isomorphism or canonical forms of graphs.

* Nauty/Traces
* Bliss
* saucy
* conauto
* Gi-ext

CS 520: Knowledge Graphs

There is no promise for the materials afterwards, but here is a page where presentations can be stored (so far there is a single presentation from Michael Galkin).

​Deep Graph Library v0.4.3

In version 0.4.3, a popular GNN library DGL has now support for TensorFlow (originally supported PyTorch only), spin-off packages for Knowledge Graphs and Life Sciences (DGL-KE and DGL-LifeSci) and more flexible distributed training.

For me it's really interesting to see a big uplift in training time against PyTorch-BigGraph library, this looks great.

Knowledge Graph course 2019

Michael Galkin had a course on knowledge graphs in 2019 and there are presentations of the course (though most in Russian) if you are interested.

Network Epidemiology Online Workshop Series

In April, there are seminars, tutorials, and discussion groups organized by University of Maryland to study how network science can help fighting virus contamination. It's for free, although there is a limitation on the number of participants (~150). There are two tracks: just listen to the tutorials or additionally participate in the groups. Lectures through Zoom. Deadline for application: tomorrow, 7th April.

CS 520 Knowledge Graphs Video Materials

It seems that they will make the lectures available on YouTube 👍

Fresh picks from ArXiv
This week is full of CVPR papers with graphs, surveys on recommendation, and a historical note of the discovery of TSP algorithm is USSR 👨‍🚀

CVPR
• HOPE-Net: A Graph-based Model for Hand-Object Pose Estimation
• Graph Structured Network for Image-Text Matching
• Spatio-Temporal Graph for Video Captioning with Knowledge Distillation
• Multi-Modal Graph Neural Network for Joint Reasoning on Vision and Scene Text
• Disentangling and Unifying Graph Convolutions for Skeleton-Based Action Recognition
• Deep Homography Estimation for Dynamic Scenes
• Iterative Context-Aware Graph Inference for Visual Dialog
• Geometrically Principled Connections in Graph Neural Networks with Michael Bronstein
• LiDAR-based Online 3D Video Object Detection with Graph-based Message Passing and Spatiotemporal Transformer Attention

WebConf
• Graph Enhanced Representation Learning for News Recommendation

Survey
• Deep Learning on Knowledge Graph for Recommender System: A Survey
• Heterogeneous Network Representation Learning: Survey, Benchmark, Evaluation, and Beyond — essentially a survey on KG
• A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem — show that Christofides algorithm used for TSP was discovered in USSR around the same time
• A Survey on Conversational Recommender Systems

Graph Theory
• Longest paths in random hypergraphs
• A Fast Algorithm for the Product Structure of Planar Graphs
• Counterexamples to "A Conjecture on Induced Subgraphs of Cayley Graphs"

RL for TSP

There is already a rich literature on applying RL methods for Traveling Salesman Problem (TSP). In one line of research the solution is built incrementally, one node at a time. This is for example in a popular paper, Attention, Learn to Solve Routing Problems!. Recently another approach appeared: start with some solution to TSP and update this solution by swapping nodes. For example, Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning uses policy gradient method and shows that it significantly outperforms incremental approaches.

Graph Representation Learning Workshop ICML 20

One of the places that gather a lot of researchers in GML is the workshop on Graph Representation Learning. This year it will appear at ICML 20. You can submit short papers (4 pages), including the works that you can resubmit later to a full conference elsewhere. This year there will be a separate track on using graphs for COVID-19 resolution. Deadline: 29th May.

Some notes on reconstruction conjecture

Studying reconstruction conjecture is going down the rabbit hole 🐇 It seems so simple, but after a few steps its complexity unfolds and you find yourself reading another paper that provides some extra insights which only steer you away from the target.

Formulation. You have a graph. You delete one vertex from it, and put obtained subgraph to a list, called deck. Then you return to the original graph, delete another vertex and again add obtained subgraph to the deck. And so on, for all n different vertices. The main question is whether there are two non-isomorphic graphs that have the same deck.

Difficulty. I already wrote about this conjecture, showing that if you delete more than 1 vertex then there are indeed two different graphs with the same decks. That's the fact that you delete only one vertex makes it more difficult. Now think, you have n subgraphs, each has (n-1) original vertices, it seems you just have so much information as an input, O(n^3), to say everything about the original graph, which has only O(n^2). But no, it's still very hard to solve it.

So what if we have a deck instead and try to recover original graph. Can we do it fast? I'm maybe wrong, but it seems there is no known polynomial-time algorithms and even the complexity of this problem is not clear. This paper, for specific type of graphs, shows an algorithm O(n^8), which is the biggest factor I've seen for poly-time algorithms. This paper studies some similar problems related to reconstruction conjecture, showing that just checking that a graph has specific deck is already equivalent to graph isomorphism. Finally, there is a manual 1991 on all major achievements to date showing that reconstruction conjecture is solved for some families of graphs such as regular graphs.

Insights. After reading all this, I have the following thoughts.

* It would be cool to write a paper on the algorithm for reconstruction of the graph from its deck. I have some trivial idea how to do it via graph isomorphism solver and some heuristics. Actually the problem is not purely abstract and has a lot of important applications to chemoinformatics for example, so it's interesting.

* It would be cool to write a follow-up paper which uses RL to improve heuristics. Graph reconstruction is under radar compared to TSP, so it would be first-of-its-kind RL algorithm for such problem.

* Initially I had the idea that if I take hard instances for graph isomorphism and compute decks for such graphs then I would get the same decks for non-isomorphic graphs, solving reconstruction conjecture. The reason why I thought this was that hard non-isomorphic graphs are very similar to each other, so their subgraphs would be identical. But, regular graphs are already proved to be reconstructible, so many hard instances won't work (such as SRG or Miyazaki graphs). Then, there are "very hard" graphs, which are half-regular (there are only two values for degrees across all nodes). I tried those, but found that decks are completely different for non-isomorphic graphs. So my idea failed and I spent two days reading, thinking, and implementing it 😀

Graph Machine Learning research groups: Karsten Borgwardt

I do a series of posts on the groups in graph research. The third is Karsten Borgwardt. His group at ETH Zurich is working on computational biology and his lab is well known for development of some of commonly used graph kernels (e.g. Weisfeiler-Leman, graphlet, shortest path).

Karsten Borgwardt (1980)
- Affiliation: ETH Zurich;
- Education: Ph.D. at Ludwig-​Maximilians-University in Munich in 2007 (supervised by Hans-​Peter Kriegel);
- h-index: 47;
- Awards: Krupp Award, best papers at NeurIPS;
- Interests: graph kernels; molecular graph representation; computational biology

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.

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

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.

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.

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.

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.

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.

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.