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1. Motif-Based Graph Representation Learning with Application to Chemical Molecules

   https://doi.org/10.3390/informatics10010008  

   Wang, Yifei; Chen, Shiyang; Chen, Guobin; Shurberg, Ethan; Liu, Hang; Hong, Pengyu (March 2023, Informatics)

   This work considers the task of representation learning on the attributed relational graph (ARG). Both the nodes and edges in an ARG are associated with attributes/features allowing ARGs to encode rich structural information widely observed in real applications. Existing graph neural networks offer limited ability to capture complex interactions within local structural contexts, which hinders them from taking advantage of the expression power of ARGs. We propose motif convolution module (MCM), a new motif-based graph representation learning technique to better utilize local structural information. The ability to handle continuous edge and node features is one of MCM’s advantages over existing motif-based models. MCM builds a motif vocabulary in an unsupervised way and deploys a novel motif convolution operation to extract the local structural context of individual nodes, which is then used to learn higher level node representations via multilayer perceptron and/or message passing in graph neural networks. When compared with other graph learning approaches to classifying synthetic graphs, our approach is substantially better at capturing structural context. We also demonstrate the performance and explainability advantages of our approach by applying it to several molecular benchmarks. 

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2. Graph Regression and Classification using Permutation Invariant Representations

   Haghani, Naveed; Singh, Maneesh; Balan, Radu (February 2022, AAAI/Graphs and more Complex structures for Learning and Reasoning Workshop)

   We address the problem of graph regression using graph convolutional neural networks and permutation invariant representation. Many graph neural network algorithms can be abstracted as a series of message passing functions between the nodes, ultimately producing a set of latent features for each node. Processing these latent features to produce a single estimate over the entire graph is dependent on how the nodes are ordered in the graph’s representation. We propose a permutation invariant mapping that produces graph representations that are invariant to any ordering of the nodes. This mapping can serve as a pivotal piece in leveraging graph convolutional networks for graph classification and graph regression problems. We tested out this method and validated our solution on the QM9 dataset. 

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3. Molecular Graph Generation via Geometric Scattering

   https://doi.org/https://doi.org/10.48550/arXiv.2110.06241  

   Dhananjay Bhaskar, Jackson D. (July 2022, IEEE Machine Learning for Signal Processing)

   Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements and bonds respectively. Although existing deep learning models perform remarkably well at predicting physicochemical properties and binding affinities, the generation of new molecules with optimized properties remains challenging. Inherently, most GNNs perform poorly in whole-graph representation due to the limitations of the message-passing paradigm. Furthermore, step-by-step graph generation frameworks that use reinforcement learning or other sequential processing can be slow and result in a high proportion of invalid molecules with substantial post-processing needed in order to satisfy the principles of stoichiometry. To address these issues, we propose a representation-first approach to molecular graph generation. We guide the latent representation of an autoencoder by capturing graph structure information with the geometric scattering transform and apply penalties that structure the representation also by molecular properties. We show that this highly structured latent space can be directly used for molecular graph generation by the use of a GAN. We demonstrate that our architecture learns meaningful representations of drug datasets and provides a platform for goal-directed drug synthesis. 

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4. Graph Compression Networks

   https://doi.org/10.1109/BigData52589.2021.9671652  

   Guo, Ting; Zhu, Xingquan; Wang, Yang; Chen, Fang (December 2021, Proc. of the 2021 IEEE International Conference on Big Data (Big Data))

   Graphs/Networks are common in real-world applications where data have rich content and complex relationships. The increasing popularity also motivates many network learning algorithms, such as community detection, clustering, classification, and embedding learning, etc.. In reality, the large network volumes often hider a direct use of learning algorithms to the graphs. As a result, it is desirable to have the flexibility to condense a network to an arbitrary size, with well-preserved network topology and node content information. In this paper, we propose a graph compression network (GEN) to achieve network compression and embedding at the same time. Our theme is to leverage the network topology to find node mappings, such that densely connected nodes, including their node content, are compressed as a new node, with a latent vector (i.e. embedding) being learned to represent the compressed node. In addition to compression learning, we also develop a novel encoding-decoding framework, using feature diffusion process, to "decompress" the condensed network. Different from traditional graph convolution which uses direct-neighbor message passing, our decompression advocates high-order message passing within compressed nodes to learning feature representation for all nodes in the network. A unique strength of GEN is that it leverages the graph neural network principle to learn mapping automatically, so one can compress a network to an arbitrary size, and also decompress it to the original node space with minimum information loss. Experiments and comparisons confirm that GEN can automatically find clusters and communities, and compress them as new nodes. Results also show that GEN achieves improved performance for numerous tasks, including graph classification and node clustering. 

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5. Half-Hop: A graph upsampling approach for slowing down message passing

   Mehdi Azabou, Venkataramana Ganesh (January 2023, Proceedings of the 40th International Conference on Machine Learning)

   Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding “slow nodes” at each edge that can mediate com- munication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths. 

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