LINK PREDICTION USING NEUMANN EIGENVALUES
Primary Area: learning on graphs and other geometries & topologies
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: graph neural network, link prediction
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Abstract: Recently, graph-structured data benefits from the advent of Graph Neural Networks (GNNs). Link prediction (LP) is a crucial task in graph-structured data, aiming to estimate the likelihood of non-observable links based on known graph structure and node/edge features. Despite GNN's success in solving graph-level tasks, their results, compared to classical methods, are worse in solving node-level tasks (e.g., LP). The main reason lies in the limitations of Message Passing GNNs (MPNNs), the most common technique used in GNNs. One of the main limitations of MPNNs is their inability to distinguish between some graphs, e.g., k-regular graphs. Discriminating between k-regular graphs lets us count the sub-structures and triangles, which are crucial in the success of classical methods for the LP task. Encoding Link representation instead of node representation can solve this problem, but the previous methods are prohibitively expensive and thus impractical. We propose a novel light learnable eigenbasis to encode the link representation and induced subgraphs efficiently and explicitly. Specifically, we introduce Neumann eigenvalues and encode its corresponding constraints to the eigenbasis. Given the Neumann constraints, the Neumann basis splits the nodes into two (one-hop and two-hop away nodes) and efficiently encodes the relation between them. By formulating the eigenvalue problem with linear constraints, we efficiently implement our proposed convolutional layer with a novel learnable Lanczos algorithm with linear constraints LLwLC. We also conducted experiments investigating the effect of encoding different linear constraints (subgraphs). Although our theoretical results apply to many problem settings, we report our results on link prediction tasks achieving state-of-the-art in benchmark datasets.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 185
Loading