​​Monday Theory: Logical Expressiveness of Hypergraph GNNs

A prominent spotlight ICLR'20 paper by Barcelo et al proved several important expressiveness boundaries for message passing GNNs on graphs with normal binary edges, ie, an edge connects two nodes. Using a well-known mapping of classifying First Order Logic formulae to the WL-test, the authors show that Aggregate-Combine GNNs are bounded by ALCQ - a common Denoscription Logic fragment of FOL. And Aggregate-Combine-Readout (GNNs with global pooling) are bounded by FOC-2 subset for FOL, i.e., First Order Logic with counting quantifiers and at most 2 variables.

A new anonymous ICLR'22 submission extends this framework to hypergraphs, ie, the graphs where (hyper)edges are constructed from B > 2 nodes. This time, the authors resort to higher-order k-WL tests and find a natural connection between k-WL and expressiveness of hypergraph networks. Three cool contributions:

1. Hypergraphs with B-ary hyperedges are bounded by FOC-B subset of FOL. That is, a logical formula can have up to B variables now.
2. The framework includes several relational architetures such as Neural Logic Machines, Deep Sets, Transformers, and GNNs
3. The authors estimate theoretical bounds on min depth and arity of hypergraph architectures for common GRL tasks. For instance, identifying bipartiteness of n-nodes graph requires log(n) layers of 3-ary GNNs (or 2-WL kernels)

Experiments were conducted on rather toy graphs of 10-80 nodes which is explained by the need to train hypergraph nets on all possible permutations of nodes in hyperedges (and this at the moment has bad scaling properties). Still, most of the hypotheses are confirmed by the experiments, so check out the full paper if you're into logic+GNN studies!

Fresh picks from ArXiv
This week on ArXiv: uncertainty for node classification, GNNs for tabular data, and cryptocurrency graph 🤑

If I forgot to mention your paper, please shoot me a message and I will update the post.

GNNs
* A Scalable AutoML Approach Based on Graph Neural Networks
* Optimizing Sparse Matrix Multiplications for Graph Neural Networks
* Graph Embedding with Hierarchical Attentive Membership WSDM 2022
* Unbiased Graph Embedding with Biased Graph Observations
* Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification with Stephan Günnemann
* Robustness of Graph Neural Networks at Scale with Stephan Günnemann
* VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization
* Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods
* Nested Graph Neural Networks with Pan Li
* Convergent Boosted Smoothing for Modeling Graph Data with Tabular Node Features
* Tackling Oversmoothing of GNNs with Contrastive Learning
* On the Power of Edge Independent Graph Models
* On Provable Benefits of Depth in Training Graph Convolutional Networks
* UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation CIKM'2021
* Finding a Concise, Precise, and Exhaustive Set of Near Bi-Cliques in Dynamic Graphs WSDM 2022
* How to transfer algorithmic reasoning knowledge to learn new algorithms? with Petar Velickovic and Jian Tang


Software
* retworkx: A High-Performance Graph Library for Python
* NeuroComb: Improving SAT Solving with Graph Neural Networks
* Graph? Yes! Which one? Help!

Datasets
* Towards a Taxonomy of Graph Learning Datasets
* Cryptocurrencies Activity as a Complex Network: Analysis of Transactions Graphs

Graph papers at NeurIPS 2021

There are ~140 graph papers which can be found here, which is about 6% of all 2334 papers. More statistics can be found here.

Papers with Code newsletter: GNN

The 19th issue of the Papers with Code newsletter covers a brief update of the latest developments in graph neural networks (GNNs), a list of recent applications of GNNs, top trending papers for October 2021 on Papers with Code.

Graph Databases Blog Posts

4 blog posts exploring different ideas behind graph databases:

* Graph Fundamentals — Part 1: RDF
* Graph Fundamentals — Part 2: Labelled Property Graphs
* Graph Fundamentals — Part 3: Graph Schema Languages
* Graph Fundamentals — Part 4: Linked Data

Graph papers and reviews at ICLR 2022

Here is a list of reviews on graph papers at ICLR 2022. Three papers received the average score of 8. For more stats refer here.

COLLOQUIUM PRAIRIE

A colloquium on AI, which among others talks about graph ML. Next talk will be on "Exploiting Graph Invariants in Deep Learning" by Marc Lelarge (Inria).

From Mila with 💌 and graphs

A prolific week for Mila researchers:

- Michael Galkin released a new review of Knowledge Graph papers from EMNLP 2021. For those of us who didn't make it to Dominical Republic, you can experience the premium Punta Cana content about applications of graphs in language modeling, KG construction, entity linking, and question answering.
- Best Long Paper award at EMNLP 2021 went to Visually Grounded Reasoning across Languages and Cultures by the team from Cambridge, Copenhagen, and Mila

Mila and Mila-affiliated folks run a good bunch of reading groups you might find useful: in addition to the GRL Reading Group and LoGaG Reading group, there exist ones on Neural AI, Out-of-Distribution Generalization, Quantum & AI , ML4Code

Fresh picks from ArXiv
This week on ArXiv: knowledge distillation, robustness benchmark, and SVD instead of learning ✒️

If I forgot to mention your paper, please shoot me a message and I will update the post.

GNNs
* On Representation Knowledge Distillation for Graph Neural Networks
* Can Graph Neural Networks Learn to Solve MaxSAT Problem?
* DropGNN: Random Dropouts Increase the Expressiveness of Graph Neural Networks NeurIPS 2021
* An Interpretable Graph Generative Model with Heterophily
* Convolutional Neural Network Dynamics: A Graph Perspective with Danai Koutra

Benchmarks
* Graph Robustness Benchmark: Benchmarking the Adversarial Robustness of Graph Machine Learning

GRL
* Implicit SVD for Graph Representation Learning NeurIPS 2021
* Multi-task Learning of Order-Consistent Causal Graphs with Le Song
* Adversarial Attacks on Graph Classification via Bayesian Optimisation
* Conditional Attention Networks for Distilling Knowledge Graphs in Recommendation CIKM 2021

Complex and Simple Models of Multidimensional Data : from graphs to neural networks

A mini-workshop on applications of graphs in biology. 1 December, free, but registration is mandatory.

Introducing TensorFlow Graph Neural Networks

A new API for TF2 to build GNNs. It would be interesting to see how it compares to PyG and DGL libraries.

Graph Neural Networks through the lens of Differential Geometry and Algebraic Topology

And Michael is back with a first post in the series of posts on the connection between GML and differential geometry and algebraic topology. We've been waiting for this!

Fresh picks from ArXiv
This week on ArXiv: generalization guarantees, explaining bio recommendations, and learning over cosmos data 🌕

If I forgot to mention your paper, please shoot me a message and I will update the post.

GNNs
* Generalizing Graph Neural Networks on Out-Of-Distribution Graphs
* Federated Social Recommendation with Graph Neural Network with Philip S. Yu
* Pre-training Graph Neural Network for Cross Domain Recommendation with Philip S. Yu
* Inferring halo masses with Graph Neural Networks
* Explainable Biomedical Recommendations via Reinforcement Learning Reasoning on Knowledge Graphs

Benchmark
* GRecX: An Efficient and Unified Benchmark for GNN-based Recommendation

Hardware
* QGTC: Accelerating Quantized GNN via GPU Tensor Core

Successful Phase I Cancer Vaccine Trials Powered by Graph ML

Transgene and NEC Corporation published a press release on the successful Phase I trials of TG4050, neoantigen cancer vaccine, tested on ovarian cancer, head and neck cancer. The release outlines the NEC's Neoantigen Prediction System based on Graph ML algorithms.

We reached out to Mathias Niepert, Chief Research Scientist of NEC Labs, to shed a bit more light on the graph ml setup and he kindly provided a few interesting details! Mathias says:

The main graph ML method is derived from Embedding Propagation which is a GNN that’s trained in an unsupervised way and, crucially, is able to handle / impute missing data in embedding space. The most relevant papers are Learning Graph Representations with Embedding Propagation (NeurIPS 2017) and Learning Representations of Missing Data for Predicting Patient Outcomes

A major challenge is that for each neoantigen we have some measurements but not all. Obtaining some of these requires expensive tests and some have to be collected from previous biomedical studies. One ends up with several very different feature types (requiring different ML encoders) and, for each such feature type, we only sometimes have a value. The graph-based ML method helps to impute and learn a unifying embedding space.

The graph itself is created based on specific similarity measures between proteins and is not given a-priori. Having a general graph, the task is to rank peptide candidates which would be most efficient for a given patient.

From a probe of a patient's cancer and healthy cells, you get several tens of thousands of neoantigen candidates. To manufacture a personalized vaccine, you have to narrow this down to several dozen candidates. These candidates should have two properties (1) likelihood to elicit immune response (2) different from healthy cell antigen. You end up scoring the neoantigens with the ML method, take the top K, and based on these you synthesize the vaccine. Graph ML is one component of a pretty complex system.

Mathias would like to emphasize that this is based on the work of several people at NEC and most credit should go to the domain experts who have collected the data and adapted and applied the graph ML methods to this problem.

Fresh picks from ArXiv
This week on ArXiv: feature propagation to alleviate missing node features, new sota for molecular prediction, and benchmarks on GNN explanations 👴
If I forgot to mention your paper, please shoot me a message and I will update the post.

GNNs
* Multi-fidelity Stability for Graph Representation Learning with Joan Bruna
* AutoHEnsGNN: Winning Solution to AutoGraph Challenge for KDD Cup 2020
* Demystifying Graph Neural Network Explanations
* Unsupervised Learning for Identifying High Eigenvector Centrality Nodes: A Graph Neural Network Approach
* On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features with Michael Bronstein
* Directional Message Passing on Molecular Graphs via Synthetic Coordinates with Stephan Günnemann

Over-squashing, Bottlenecks, and Graph Ricci curvature

A second post by Michael Bronstein about over-squashing effect, when exponentially many neighbors aggregate their information into a fix-sized vector, causing the loss of the information. In this post, Michael connects over-squashing effect with Ricci flow — a well-studied notion of the space curvature that is used in differential geometry.

Connected Data World 2021

Today at 14-00 (Paris time), I will be in the panel at Connected Data World conference, with a great line of graph ML researchers to talk about applications of GNNs. Besides there are many other interesting talks talking about ML, knowledge graphs, graph databases, and more. If you want to attend, you need to register (there is a free streaming track and also a discount code CDW21SPEAKERA20 for a full program).

Mathematical discoveries take intuition and creativity – and now a little help from AI

A new work published in Nature with Petar Veličković and his colleagues shows how GNNs can guide the intuition of mathematicians in both representation theory & knot theory. In a more mathematical manunoscript they prove a combinatorial conjecture from 80s with the help of GNNs. This article also describes their discovery.

Tutorial: Message Passing In Machine Learning

At NeurIPS 2021, there is a tutorial Message Passing In Machine Learning by Wee Sun Lee. It discusses in depth probabilistic graphical models (belief propagation, variational inference, mean field), markov decision processes (value iteration networks), GNNs and attention networks. It will be live today for registered people. Slides are available online.

Fresh picks from ArXiv
This week on ArXiv: library for graph recommendations, embeddings for molecules, and self-explaining GNNs 🦜
If I forgot to mention your paper, please shoot me a message and I will update the post.

GNNs
* Fast Graph Neural Tangent Kernel via Kronecker Sketching AAAI 22
* ProtGNN: Towards Self-Explaining Graph Neural Networks AAAI 22
* Graph4Rec: A Universal Toolkit with Graph Neural Networks for Recommender Systems
* Imbalanced Graph Classification via Graph-of-Graph Neural Networks
* Molecular Contrastive Learning with Chemical Element Knowledge Graph AAAI 22
* Learning Large-Time-Step Molecular Dynamics with Graph Neural Networks

Open PhD/PostDoc Positions on GML

Aleksandar Bojchevski, whom you may know by his works on robustness, adversarial attacks, generative models on graphs, hires PhDs and PostDocs to work on trustworthy machine learning research. The position is at CISPA Helmholtz Center for Information Security, in Saarland, Germany and is well paid (for PhDs around 4K euros per month before taxes). Apply here.