Cayley Graph Propagation

• URL: http://arxiv.org/abs/2410.03424v1
• Date: Fri, 4 Oct 2024 13:32:34 GMT
• Title: Cayley Graph Propagation
• Authors: JJ Wilson, Maya Bechler-Speicher, Petar Veličković,
• Abstract summary: We show that truncation is detrimental to the expansion properties of Cayley graph structures. Instead, we propose CGP, a method to propagate information over a complete Cayley graph structure.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In spite of the plethora of success stories with graph neural networks (GNNs) on modelling graph-structured data, they are notoriously vulnerable to over-squashing, whereby tasks necessitate the mixing of information between distance pairs of nodes. To address this problem, prior work suggests rewiring the graph structure to improve information flow. Alternatively, a significant body of research has dedicated itself to discovering and precomputing bottleneck-free graph structures to ameliorate over-squashing. One well regarded family of bottleneck-free graphs within the mathematical community are expander graphs, with prior work$\unicode{x2014}$Expander Graph Propagation (EGP)$\unicode{x2014}$proposing the use of a well-known expander graph family$\unicode{x2014}$the Cayley graphs of the $\mathrm{SL}(2,\mathbb{Z}_n)$ special linear group$\unicode{x2014}$as a computational template for GNNs. However, in EGP the computational graphs used are truncated to align with a given input graph. In this work, we show that truncation is detrimental to the coveted expansion properties. Instead, we propose CGP, a method to propagate information over a complete Cayley graph structure, thereby ensuring it is bottleneck-free to better alleviate over-squashing. Our empirical evidence across several real-world datasets not only shows that CGP recovers significant improvements as compared to EGP, but it is also akin to or outperforms computationally complex graph rewiring techniques.

Related papers

• NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification [70.51126383984555]
  We introduce a novel all-pair message passing scheme for efficiently propagating node signals between arbitrary nodes. The efficient computation is enabled by a kernerlized Gumbel-Softmax operator. Experiments demonstrate the promising efficacy of the method in various tasks including node classification on graphs.
  arXiv  Detail & Related papers  (2023-06-14T09:21:15Z)
• Unlearnable Graph: Protecting Graphs from Unauthorized Exploitation [68.59161853439339]
  We propose a novel method for generating unlearnable graph examples. By injecting delusive but imperceptible noise into graphs using our Error-Minimizing Structural Poisoning (EMinS) module, we are able to make the graphs unexploitable.
  arXiv  Detail & Related papers  (2023-03-05T03:30:22Z)
• FoSR: First-order spectral rewiring for addressing oversquashing in GNNs [0.0]
  Graph neural networks (GNNs) are able to leverage the structure of graph data by passing messages along the edges of the graph. We propose a computationally efficient algorithm that prevents oversquashing by systematically adding edges to the graph. We find experimentally that our algorithm outperforms existing graph rewiring methods in several graph classification tasks.
  arXiv  Detail & Related papers  (2022-10-21T07:58:03Z)
• Expander Graph Propagation [0.0]
  We propose an elegant approach based on propagating information over expander graphs. We show that EGP is able to address all of the above concerns, while requiring minimal effort to set up. We believe our analysis paves the way to a novel class of scalable methods to counter oversquashing in GNNs.
  arXiv  Detail & Related papers  (2022-10-06T15:36:37Z)
• SPGP: Structure Prototype Guided Graph Pooling [1.3764085113103217]
  We propose Structure Prototype Guided Pooling (SPGP) for learning graph-level representations. SPGP formulates graph structures as learnable prototype vectors and computes the affinity between nodes and prototype vectors. Our experimental results show that SPGP outperforms state-of-the-art graph pooling methods on graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2022-09-16T09:33:09Z)
• Graph Neural Network Bandits [89.31889875864599]
  We consider the bandit optimization problem with the reward function defined over graph-structured data. Key challenges in this setting are scaling to large domains, and to graphs with many nodes. We show that graph neural networks (GNNs) can be used to estimate the reward function.
  arXiv  Detail & Related papers  (2022-07-13T18:12:36Z)
• AnchorGAE: General Data Clustering via $O(n)$ Bipartite Graph Convolution [79.44066256794187]
  We show how to convert a non-graph dataset into a graph by introducing the generative graph model, which is used to build graph convolution networks (GCNs) A bipartite graph constructed by anchors is updated dynamically to exploit the high-level information behind data. We theoretically prove that the simple update will lead to degeneration and a specific strategy is accordingly designed.
  arXiv  Detail & Related papers  (2021-11-12T07:08:13Z)
• Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction [123.20238648121445]
  We propose a new self-supervised learning framework, Graph Information Aided Node feature exTraction (GIANT) GIANT makes use of the eXtreme Multi-label Classification (XMC) formalism, which is crucial for fine-tuning the language model based on graph information. We demonstrate the superior performance of GIANT over the standard GNN pipeline on Open Graph Benchmark datasets.
  arXiv  Detail & Related papers  (2021-10-29T19:55:12Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.