Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactions

• URL: http://arxiv.org/abs/2402.06908v1
• Date: Sat, 10 Feb 2024 08:26:06 GMT
• Title: Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactions
• Authors: Lorenzo Giusti
• Abstract summary: This work starts with a theoretical framework to reveal the impact of network's width, depth, and graph topology on the over-squashing phenomena in message-passing neural networks. The work drifts towards, higher-order interactions and multi-relational inductive biases via Topological Neural Networks. Inspired by Graph Attention Networks, two topological attention networks are proposed: Simplicial and Cell Attention Networks.
• Score: 1.994307489466967
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is remarkable, the implications associated with long-range and higher-order dependencies pose considerable challenges to such models. This work starts with a theoretical framework to reveal the impact of network's width, depth, and graph topology on the over-squashing phenomena in message-passing neural networks. Then, the work drifts towards, higher-order interactions and multi-relational inductive biases via Topological Neural Networks. Such models propagate messages through higher-dimensional structures, providing shortcuts or additional routes for information flow. With this construction, the underlying computational graph is no longer coupled with the input graph structure, thus mitigating the aforementioned bottlenecks while accounting also for higher-order interactions. Inspired by Graph Attention Networks, two topological attention networks are proposed: Simplicial and Cell Attention Networks. The rationale behind these architecture is to leverage the extended notion of neighbourhoods provided by the arrangement of groups of nodes within a simplicial or cell complex to design anisotropic aggregations able to measure the importance of the information coming from different regions of the domain. By doing so, they capture dependencies that conventional Graph Neural Networks might miss. Finally, a multi-way communication scheme is introduced with Enhanced Cellular Isomorphism Networks, which augment topological message passing schemes to enable a direct interactions among groups of nodes arranged in ring-like structures.

Related papers

• NetDiff: Deep Graph Denoising Diffusion for Ad Hoc Network Topology Generation [1.6768151308423371]
  We introduce NetDiff, a graph denoising diffusion probabilistic architecture that generates wireless ad hoc network link topologies. Our results show that the generated links are realistic, present structural properties similar to the dataset graphs', and require only minor corrections and verification steps to be operational.
  arXiv  Detail & Related papers  (2024-10-09T15:39:49Z)
• Harnessing Collective Structure Knowledge in Data Augmentation for Graph Neural Networks [25.12261412297796]
  Graph neural networks (GNNs) have achieved state-of-the-art performance in graph representation learning. We propose a novel approach, namely collective structure knowledge-augmented graph neural network (CoS-GNN)
  arXiv  Detail & Related papers  (2024-05-17T08:50:00Z)
• Unsupervised Graph Attention Autoencoder for Attributed Networks using K-means Loss [0.0]
  We introduce a simple, efficient, and clustering-oriented model based on unsupervised textbfGraph Attention textbfAutotextbfEncoder for community detection in attributed networks. The proposed model adeptly learns representations from both the network's topology and attribute information, simultaneously addressing dual objectives: reconstruction and community discovery.
  arXiv  Detail & Related papers  (2023-11-21T20:45:55Z)
• Topology-guided Hypergraph Transformer Network: Unveiling Structural Insights for Improved Representation [1.1606619391009658]
  We propose a Topology-guided Hypergraph Transformer Network (THTN) In this model, we first formulate a hypergraph from a graph while retaining its structural essence to learn higher-order relations within the graph. We present a structure-aware self-attention mechanism that discovers the important nodes and hyperedges from both semantic and structural viewpoints.
  arXiv  Detail & Related papers  (2023-10-14T20:08:54Z)
• Simple and Efficient Heterogeneous Graph Neural Network [55.56564522532328]
  Heterogeneous graph neural networks (HGNNs) have powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations. Existing HGNNs inherit many mechanisms from graph neural networks (GNNs) over homogeneous graphs, especially the attention mechanism and the multi-layer structure. This paper conducts an in-depth and detailed study of these mechanisms and proposes Simple and Efficient Heterogeneous Graph Neural Network (SeHGNN)
  arXiv  Detail & Related papers  (2022-07-06T10:01:46Z)
• BScNets: Block Simplicial Complex Neural Networks [79.81654213581977]
  Simplicial neural networks (SNN) have recently emerged as the newest direction in graph learning. We present Block Simplicial Complex Neural Networks (BScNets) model for link prediction. BScNets outperforms state-of-the-art models by a significant margin while maintaining low costs.
  arXiv  Detail & Related papers  (2021-12-13T17:35:54Z)
• Reinforced Neighborhood Selection Guided Multi-Relational Graph Neural Networks [68.9026534589483]
  RioGNN is a novel Reinforced, recursive and flexible neighborhood selection guided multi-relational Graph Neural Network architecture. RioGNN can learn more discriminative node embedding with enhanced explainability due to the recognition of individual importance of each relation.
  arXiv  Detail & Related papers  (2021-04-16T04:30:06Z)
• Learning Connectivity of Neural Networks from a Topological Perspective [80.35103711638548]
  We propose a topological perspective to represent a network into a complete graph for analysis. By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner. This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks.
  arXiv  Detail & Related papers  (2020-08-19T04:53:31Z)
• Towards Deeper Graph Neural Networks [63.46470695525957]
  Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Several recent studies attribute this performance deterioration to the over-smoothing issue. We propose Deep Adaptive Graph Neural Network (DAGNN) to adaptively incorporate information from large receptive fields.
  arXiv  Detail & Related papers  (2020-07-18T01:11:14Z)
• Graph Structure of Neural Networks [104.33754950606298]
  We show how the graph structure of neural networks affect their predictive performance. A "sweet spot" of relational graphs leads to neural networks with significantly improved predictive performance. Top-performing neural networks have graph structure surprisingly similar to those of real biological neural networks.
  arXiv  Detail & Related papers  (2020-07-13T17:59:31Z)

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.