Graph Machine Learning

​​Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problems guest post by Chendi Qian, Didier Chételat, Christopher Morris 📜 Paper: arxiv (accepted to AISTATS 2024) 🛠️ Code: https://github.com/chendiqian/IPM_MPNN Recent research shows growing interest in training message-passing graph neural networks (MPNNs) to mimic classical algorithms, particularly for solving linear optimization problems (LPs). For example, in integer linear optimization, state-of-the-art solvers rely on the branch-and-bound algorithm, in which one must repeatedly select variables, subdividing the search space. The best-known heuristic for variable selection is known as strong branching which entails solving LPs to score the variables. This heuristic is too computationally expensive to use in practice. However, in recent years, a collection of works, e.g., Gasse et al. (2019), have proposed using MPNNs to imitate strong branching with impressive success. However, it remained to be seen why such approaches work. Hence, our paper explores the intriguing possibility of MPNNs approximating general LPs by interpreting various interior-point methods (IPMs) as MPNNs with specific architectures and parameters. We prove that standard MPNN steps can emulate a single iteration of the IPM algorithm on the LP’s tripartite graph representation. This theoretical insight suggests that MPNNs may succeed in LP solving by effectively imitating IPMs. Despite our theoretical model, our empirical results indicate that MPNNs with fewer layers can approximate the output of practical IPMs for LP solving. Empirically, our approach reduces solving times compared to a state-of-the-art LP solver and other neural network-based methods. Our study enhances the theoretical understanding of data-driven optimization using MPNNs and highlights the potential of MPNNs as efficient proxies for solving LPs.

GraphML News (Jan 20th) - More Blogs, MACE pre-trained potentials, AlphaFold 🤝 Psychedelics ICLR 2024 announced the accepted papers together with orals and spotlights — we’ll probably make a rundown on the coolest papers but meanwhile you can check one-line tl;dr’s by the famous Compressor by Vitaly Kurin. See you in Vienna in May! 📝 In addition to the megapost on the state of affairs in Graph & Geometric ML, the community delivered two more reviews: - On Temporal Graph Learning by Shenyang Huang, Emanuele Rossi, Michael Galkin, Andrea Cini, Ingo Scholtes. - On AI 4 Science by the organizers of the AI for Science workshops (that you see at all major ML venues) including Sherry Lixue Cheng, Yuanqi Du, Chenru Duan, Ada Fang, Tianfan Fu, Wenhao Gao, Kexin Huang, Ziming Liu, Di Luo, and Lijing Wang ⚛️ The MACE team released two foundational ML potential checkpoints: MP for inorganic crystals from the Materials Project and OFF for organic materials and molecular liquids. We covered those in the previous posts — now you can run some MD simulations with them on a laptop. 🍭 AlphaFold discovers potentially new psychedelic molecules (thousands of candidates!) - practically, those can be new antidepressants (would some researchers be willing to try some just for the sake of science and scientific method?) Besides, the article mentions some works that apply AlphaFold to target G-protein-coupled receptors (GPCR). Apart from having its own Wiki page, GPCR was the main subject of the 2012 Nobel Prize in chemistry. The Nobel Prize for AlphaFold seems even closer? Weekend reading: You want to say you finished all those blogposts? 😉

​​Graph & Geometric ML in 2024: Where We Are and What’s Next 📣 Two new blog posts - a comprehensive review of Graph and Geometric ML in 2023 with predictions for 2024. Together with Michael Bronstein, we asked 30 academic and industrial experts about the most important things happened in their areas and open challenges to be solved. 1️⃣ Part I: https://towardsdatascience.com/graph-geometric-ml-in-2024-where-we-are-and-whats-next-part-i-theory-architectures-3af5d38376e1 2️⃣ Part II: https://medium.com/towards-data-science/graph-geometric-ml-in-2024-where-we-are-and-whats-next-part-ii-applications-1ed786f7bf63 Part I covers: theory of GNNs, new and exotic message passing, going beyong graphs (with Topology, Geometric Algebras, and PDEs), robustness, graph transformers, new datasets, community events, and, of course, top memes of 2023 (that’s what you are here for, right). Part II covers applications in structural biology, materials science, Molecular Dynamics and ML potentials, geometric generative models on manifolds, Very Large Graphs, algorithmic reasoning, knowledge graph reasoning, LLMs + Graphs, cool GNN applications, and The Geometric Wall Street Bulletin 💸 New things this year: - the industrial perspective on important problems in structural biology that are often overlooked by researchers; - The Geometric Wall Street Bulletin prepared with Nathan Benaich, the author of the State of AI report It was a huge community effort and we are very grateful to all our experts for their availability around winter holidays. Here is the slide with all the contributors, the best “thank you” would be to follow all of them on Twitter!

​​GraphML News (Jan 13th) - New material discovered by geometric models, LOWE What time could be better than the time in between ICLR announcements (Jan 15th) and the ICML deadline (Feb 1st) 🫠. As far as we know, the graph community is working on some huge blog posts - you can expect those coming in the next few days. The two big news from this week: Microsoft Azure Quantum together with Pacific Northwest National Lab announced successful synthesis and validation of a potentially new electrolyte candidate suitable for solid-state batteries. The fresh accompanying paper describes the pipeline from generating 32M candidates and stepwise filtering of those down to 500K, 800, 18, and 1 final candidate. The main bulk of the job of filtering millions of candidates was done by the geometric ML potential model M3GNet (published in 2022 in Nature Computational Science) while later stages with a dozen candidates included HPC simulations of molecular dynamics. Geometric DL for materials discovery is rising! 🚀 Valence & Recursion announced LOWE (LLM-orchestrated Workflow Engine). LOWE is an LLM agent that strives to do all things around drug discovery - from screening and running geometric generative models to the procurement of materials. Was ChemCrow🐦‍⬛ the inspiration for LOWE? Weekend reading: Accelerating computational materials discovery with artificial intelligence and cloud high-performance computing: from large-scale screening to experimental validation by Chen, Nguyen, et al - the paper behind the newly discovered material by Azure Quantum and PNNL. MACE-OFF23: Transferable Machine Learning Force Fields for Organic Molecules by Kovács, Moore, et al - similarly to MACE-MP-0 from the last week, MACE-OFF23 is a transferable ML potential for organic molecules but smaller - Medium and Large models were trained on a single A100 for 10/14 days. Improved motif-scaffolding with SE(3) flow matching by Yim et al - the improved version of FrameFlow (based on trendy flow matching), originally for protein backbone generation, to motif-scaffolding. On some benchmarks, new FrameFlow is on par or better than mighty RFDiffusion 💪

GraphML News (Jan 6th) - ICLR’24 workshops, new blog posts, MACE-MP-0 potential We are getting back with the weekly news, hope you had a nice winter holiday! 🎤 ICLR’24 started announcing accepted workshops, the list is (so far) incomplete, but we might expect some graph and geometric learning here: - AI for Differential Equations in Science - Generative and Experimental Perspectives for Biomolecular Design - Machine Learning for Genomics Explorations 📝 New blogposts! ▶️ Pat Walters started a massive series on AI in Drug Discovery in 2023: part 1 covers benchmarks, deep learning for docking, and AlphaFold for ligand discovery and design. Part 2 will focus on LLMs and generative models, Part 3 will be on review articles. ▶️ Zhaocheng Zhu, Michael Galkin, Abulhair Saparov, Shibo Hao, and Yihong Chen review the landscape of LLM reasoning approaches covering tool usage, retrieval, planning, and open reasoning problems. Lots of unsolved theoretical and practical problems to work on in 2024! ⚛️ Ilyes Batatia and a huge collab from Cambrige, Oxford, and EU universities announced MACE-MP-0: a foundational ML potentials model that can accurately approximate DFT calculations needed for molecular dynamics and atomistic simulations. The model is based on MACE (equivariant MPNN) and was trained on the Materials Project to predict forces, energy, and stress on 150k crystal structures for 200 epochs on 40-80 A100’s (definitely not a GPU-poor project, perhaps GPU-middle class). The authors ran about 30 experiments studying a single pre-trained model with different crystal structures and atomistic systems. The race for ML potentials has officially started 🏎️ Weekend reading: Learning Scalable Structural Representations for Link Prediction with Bloom Signatures by Zhang et al. feat Pan Li - hashing-based link prediction now with Bloom filters Scalable network reconstruction in subquadratic time by Tiago Peixoto (Mr. GraphTool) - present a O(N log^2 N) algorithm for network reconstruction A foundation model for atomistic materials chemistry by Batatia et al - MACE-MP-0

Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching Guest post by Federico Errica 📖 Blog post: link ⚗️ Paper: http://arxiv.org/abs/2312.16560 Long-range interactions are essential for the correct description of complex systems in many scientific fields. Recently, deep graph networks have been employed as efficient, data-driven surrogate models for predicting properties of complex systems represented as graphs. In practice, most deep graph networks cannot really model long-range dependencies due to the intrinsic limitations of (synchronous) message passing, namely oversmoothing, oversquashing, and underreaching. Motivated by these observations, we propose Adaptive Message Passing (AMP) to let the DGN decide how many messages each node should send -up to infinity! - and when to send them. In other words: 1️⃣ We learn the depth of the network during training (addressing underreaching) 2️⃣ We apply a differentiable, soft filter on messages sent by nodes, which in principle can completely shut down the propagation of a message (addressing oversmoothing and oversquashing). ❗️ AMP can easily and automatically improve the performances of your favorite message passing architecture, e.g., GCN/GIN. ❗️ We believe AMP will foster exciting research opportunities in the graph machine learning field and find successful applications in the fields of physics, chemistry, and material sciences.

​​Neural Algorithmic Reasoning Without Intermediate Supervision Guest post by Gleb Rodionov 📝 Paper: https://openreview.net/forum?id=vBwSACOB3x (NeurIPS 2023) 🛠️ Code: in the supplementary on OpenReview Algorithmic reasoning aims to capture computations with neural networks, imitating the execution of classical algorithms. Typically, the generalization abilities of such models are improved through various forms of intermediate supervision, which demonstrate a particular execution trajectory (a sequence of intermediate steps, called hints) that the model needs to follow. However, progress can also be made on the other side of the spectrum, where models are trained only with input-output pairs. Such models are not tied to any particular execution trajectory and are free to converge to the optimal execution flow for their own architecture. We demonstrate that models without hints can be competitive with hint-based models or even outperform them: 1️⃣ We propose several architectural modifications for models trained without intermediate supervision, that are aimed at making the comparison versus hint-based models clearer and fairer. 2️⃣ We build a self-supervised objective that can regularize intermediate computations of the model without access to the algorithm trajectory. We hope our work will encourage further investigation of neural algorithmic reasoners without intermediate supervision. For more details, see the blog post.

GraphML News (Dec 23rd) - Antibiotics discovered with GNNs, OpenCatalyst 23, TF GNN A group of MIT and Harvard researchers reported (in the recent Nature paper) the discovery of a new class of antibiotics. The screening process was supported by ChemProp, a suite of GNNs for molecular property prediction. The authors trained an ensemble of 10 models to filter down the initial space of 11M compounds to 1.5K compounds. Most of those models are 5-layer MPNNs with hidden size of 1600. Pre-trained checkpoints and notebooks are available in the GitHub repo of the project. Exciting times for the field (and many bio startups)! 👏 The Open Catalyst project announced the winners of the recent OCP 23 challenge (aka AdsorbML) - the top approaches build around Equiformer V2 with the best model reaching 46% success rate. It is likely that the numbers can be bumped even further by training on even larger OCP splits as demonstrated by eSCN Large and Equiformer V2 in the paper. Google released TensorFlow GNN v1.0, the library you can run in production on GPUs and TPUs. Heterogeneous graphs are of particular focus - have a look at the example notebooks to learn more. We’ll probably take a break with the news the next week to enjoy the holiday season and get back in January with the massive year-review post. 🥂 Weekend reading: Perspectives on the State and Future of Deep Learning - 2023 - opinions of prominent ML researchers (incl. Max Welling, Kyunghyun Cho, Andrew Gordon Wilson, and ChatGPT, lolz) on the current problems and challenges. High-quality holiday reading 👌 Graph Transformers for Large Graphs by Vijay Prakash Dwivedi feat. Xavier Bresson, Neil Shah. Scaling GTs to graphs of 100M nodes. Harmonics of Learning: Universal Fourier Features Emerge in Invariant Networks by Giovanni Luca Marchetti et al. Turns out Fourier features do emerge in neural networks and help to identify symmetries. The nature of the Fourier kernels looks quite similar to the steerable kernels for irreducible representations

GraphML News (Dec 17th) - The NeurIPS edition, TGB and TpuGraphs NeurIPS’23 happened this week in New Orleans with 3000+ papers, 50+ workshops and competitions, and 16000+ registered participants. The most important part of such enormous events is networking, and, based on my impressions, the Graph ML community is thriving with so many new ideas and projects (especially after attending the workshops). We will be reflecting on the hot trends, ideas that fell out of favor / are solved, and update the predictions in the annual 2023-2024 post which is already in the works (so stay tuned). PS > All the flow matching t-shirts found their owners 😉 New blogposts: - Temporal Graph Benchmark by Andy Huang and Emanuele Rossi - introduces TGB, its design principles and supported tasks - Advancements in ML for ML by Google on the new TpuGraphs dataset, Graph Segment Training for large graphs, and the recently finished Kaggle competition on the TpuGraphs dataset (GraphSAGE is in the most of the top winning solutions) Weekend reading: A Hitchhiker’s Guide to Geometric GNNs for 3D Atomic Systems by Alexandre Duval, Simon V. Mathis, Chaitanya K. Joshi, Victor Schmidt, et al - a handbook on geometric GNNs, see our previous post for more details Are Graph Neural Networks Optimal Approximation Algorithms? by Morris Yau feat. Stefanie Jegelka - introduces OptGNN that performs very competitively on a bunch of combinatorial optimization tasks TorchCFM, the main library for conditional flow matching, released a bunch of new tutorials in Jupyter notebooks - winter holidays are a perfect time to learn more about flow matching and optimal transport

A team including folks from Mila and Cambridge just released a “Hitchhiker’s Guide” for getting started with GNNs for 3D structural biology & chemistry -- we think it will be useful for newcomers to start their learning journey on the core architectures powering recent breakthroughs of graph ML in protein design, material discovery, molecular simulations, and more! A Hitchhiker’s Guide to Geometric GNNs for 3D Atomic Systems 👥 Alexandre Duval, Simon V. Mathis, Chaitanya K. Joshi, Victor Schmidt, Santiago Miret, Fragkiskos Malliaros, Taco Cohen, Pietro Liò, Yoshua Bengio, and Michael Bronstein 📝 PDF: https://arxiv.org/abs/2312.07511

GraphML News (Dec 9th) - NeurIPS’23, MatterGen, new blogs, PygHO 🎷 NeurIPS’23 starts on Sunday in jazzy New Orleans including tons of Graph ML papers and workshops that we covered in the previous articles (search by “NeurIPS workshop”). Find Michael (jetlagged from Dagstuhl) in the unique meme-designed t-shirt at two poster sessions (one, two) to chat about papers, graphs, or relay your POV on the diffusion vs flow matching feud of the year. ⚛️ Following the announcements of UniMat and GNoME from DeepMind, MSR AI 4 Science announced MatterGen, a new generative model for inorganic materials design. Practically, unconditional MatterGen is a diffusion model based on the GemNet backbone with both continuous and discrete diffusion components, ie, continuous diffusion is applied to lattice parameters and fractional coordinates, discrete diffusion (absorbing state with the MASK token) is applied to atom compositions. A pre-trained MatterGen can then be steered in many directions with classifier-free guidance, and the authors report conditioning on target chemistry, energy, magnetic properties, and on a practical use-case of designing magnets. Seems like big labs are picking up on materials science and it will be a key topic of generative models in 2024 along with molecules and proteins. Meanwhile, a few new blog posts have arrived: - Cooperative GNNs by Ben Finkelshtein, Ismail Ceylan, Xingyue Huang, and Michael Bronstein on the recently proposed GNN architecture; - Equivariant CNNs and steerable kernels - part 3 of the series based off the monumental book Equivariant CNN by Maurice Weiler Xiyuan Wang and Muhan Zhang published PyTorch Geometric Higher Order (PygHO), a library that implements a collection of primitives to create higher-order GNNs (like subgraph GNNs, PPGN, Nested GNNs) and data wrappers with proper graph transformations. Weekend reading: MatterGen: a generative model for inorganic materials design by Zeni et al. - the MatterGen paper Expressive Sign Equivariant Networks for Spectral Geometric Learning (NeurIPS’23) by Derek Lim, Joshua Robinson, Stefanie Jegelka, and Haggai Maron - extension of invariant SignNet to sign equivariance Recurrent Distance-Encoding Neural Networks for Graph Representation Learning by Yuhui Ding et al. - Linear Recurrent Units (LRUs) straight from NLP arrived to GNNs Variational Annealing on Graphs for Combinatorial Optimization by Sebastian Sanokowski feat. Sepp Hochreiter

Guest post by Maryan Ramezani: Joint Inference of Diffusion and Structure in Partially Observed Social Networks Using Coupled Matrix Factorization By Maryam Ramezani, Aryan Ahadinia, Amirmohammad Ziaei Bideh, and Hamid R Rabiee. Published in ACM Transactions on Knowledge Discovery from Data (TKDD). 🌐 ACM Digital Library: https://dl.acm.org/doi/abs/10.1145/3599237 🌐 GitHub: https://github.com/maryram/DiffStru 📢 Thrilled to unveil our latest research on #SocialNetworks! My paper dives into the challenges of missing data in large-scale networks from a novel point of view: partial observation of both the temporal cascades and the underlying structure. Introducing 'DiffStru,' a probabilistic generative model, we jointly uncover hidden diffusion activities and network structures through coupled matrix factorization. Excitingly, our approach not only fills gaps in data but also aids in network classification problems by learning coupled representations of temporal cascades and users. 🚀 Tested on synthetic and real datasets, the results are promising – detecting hidden behaviors and predicting links by unveiling latent features. 📊🔍 Our method uses the following input. ☝️ A partial observations of the underlying network as a graph: Nodes are representing users and directed links are corresponding to the following relations between users. All nodes are present but some links are omitted. ✌️ A partial sequential observation of user participations in information diffusion process, namely cascades: Users participate in cascades, e.g. retweeting a topic, in a social media. Our observation is a set of cascades with users participated in some of them in a specified timestamp. The output of our method is as follows. 1️⃣ Predictions of omitted links in the underlying network. 2️⃣ Predictions of users' participations in cascades, including their timestamps. 3️⃣ A coupled representation of users and cascades which can be used for further analysis, e.g. community detection.