Learning From Graph-Structured Data: Addressing Design Issues and Exploring Practical Applications in Graph Representation Learning

TL;DR

This work delves into the capabilities of GNNs, examining their foundational designs and their application in addressing real-world challenges, and introduces a GNN equipped with an advanced high-order pooling function, adept at capturing complex node interactions within graph-structured data.

Abstract

Graphs serve as fundamental descriptors for systems composed of interacting elements, capturing a wide array of data types, from molecular interactions to social networks and knowledge graphs. In this paper, we present an exhaustive review of the latest advancements in graph representation learning and Graph Neural Networks (GNNs). GNNs, tailored to handle graph-structured data, excel in deriving insights and predictions from intricate relational information, making them invaluable for tasks involving such data. Graph representation learning, a pivotal approach in analyzing graph-structured data, facilitates numerous downstream tasks and applications across machine learning, data mining, biomedicine, and healthcare. Our work delves into the capabilities of GNNs, examining their foundational designs and their application in addressing real-world challenges. We introduce a GNN equipped with an advanced high-order pooling function, adept at capturing complex node interactions within graph-structured data. This pooling function significantly enhances the GNN's efficacy in both node- and graph-level tasks. Additionally, we propose a molecular graph generative model with a GNN as its core framework. This GNN backbone is proficient in learning invariant and equivariant molecular characteristics. Employing these features, the molecular graph generative model is capable of simultaneously learning and generating molecular graphs with atom-bond structures and precise atom positions. Our models undergo thorough experimental evaluations and comparisons with established methods, showcasing their superior performance in addressing diverse real-world challenges with various datasets.

Figures (5)

• Figure 1: Example of a rank $R$ symmetric CP decomposition of a symmetric $3$-order tensor $\boldsymbol{\mathcal{T}}\in \mathbb{R}^{N\times N \times N}$ such that $\boldsymbol{\mathcal{T}}=\Sigma_{r=1}^R \mathbf{v}_r\circ \mathbf{v}_r\circ \mathbf{v}_r$.
• Figure 2: (Left) Sum pooling followed by a FC layer: the output takes individual components of the input into account. (Right) The CP layer can be interpreted as a combination of product pooling with linear layers (with weight matrices $\mathbf{{W}}$ and $\mathbf{{M}}$) and non-linearities. The weight matrices of a CP layer corresponds to a partially symmetric CP decomposition of a weight tensor $\boldsymbol{\mathcal{T}} = [\![\mathbf{{W}},\mathbf{{W}},\mathbf{{W}},\mathbf{{M}}]\!]$. It shows that the output of a CP layer takes high-order multiplicative interactions of the inputs' components into account (in contrast with sum pooling that only considers 1st order terms).
• Figure 3: Visualization of relations of {permutation-invariant function space} $\supseteq$ {CP function space} $\supseteq$ {permutation-invariant multilinear polynomial space} $\supseteq$ {sum and mean aggregation functions}.
• Figure 4: Results of node classification with increasing rank dimension on three citation datasets. Left Figure: Left axis shows accuracy, right axis shows #training epochs second, and horizontal axis indicates rank dim of tGNN or hidden dim of baselines. Right Figure: Left axis shows accuracy, right axis shows #training epochs second, and horizontal axis indicates rank dim of tGNN.
• Figure 5: The figure showcases our MUformer for processing 2D and 3D molecular data. Within the Transformer backbone, two channels exist: purple for 2D data and brown for 3D data. The blue part encodes 2D molecular structures, while the green part handles atom-level information and the red part processes 3D geometric structures. With missing 2D or 3D structures, the model activates either the invariant (purple) or equivariant (brown) channel. The invariant channel predicts atom and edge features, while the equivariant channel offers geometric transformation robustness and predicts atom features and positions. When both channels are operational, the model maintains robustness to geometric transformations and predicts a complete molecule, and final atom features are derived by merging outputs from both channels and feeding the combined data through an output network.

Theorems & Definitions (10)

• Lemma 1
• proof
• Definition 1
• Definition 2
• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof