Grothendieck Graph Neural Networks Framework: An Algebraic Platform for Crafting Topology-Aware GNNs

• URL: http://arxiv.org/abs/2412.08835v1
• Date: Thu, 12 Dec 2024 00:25:48 GMT
• Title: Grothendieck Graph Neural Networks Framework: An Algebraic Platform for Crafting Topology-Aware GNNs
• Authors: Amirreza Shiralinasab Langari, Leila Yeganeh, Kim Khoa Nguyen,
• Abstract summary: This paper investigates graph structure in message passing, aimed to incorporate topological characteristics. We design the Grothendieck Graph Neural Networks (GGNN) framework, offering an algebraic platform for creating and refining diverse covers for graphs. Based on the GGNN framework, we propose Sieve Neural Networks (SNN), a new GNN model that leverages the notion of sieves from category theory.
• Score: 5.582101184758528
• License:
• Abstract: Due to the structural limitations of Graph Neural Networks (GNNs), in particular with respect to conventional neighborhoods, alternative aggregation strategies have recently been investigated. This paper investigates graph structure in message passing, aimed to incorporate topological characteristics. While the simplicity of neighborhoods remains alluring, we propose a novel perspective by introducing the concept of 'cover' as a generalization of neighborhoods. We design the Grothendieck Graph Neural Networks (GGNN) framework, offering an algebraic platform for creating and refining diverse covers for graphs. This framework translates covers into matrix forms, such as the adjacency matrix, expanding the scope of designing GNN models based on desired message-passing strategies. Leveraging algebraic tools, GGNN facilitates the creation of models that outperform traditional approaches. Based on the GGNN framework, we propose Sieve Neural Networks (SNN), a new GNN model that leverages the notion of sieves from category theory. SNN demonstrates outstanding performance in experiments, particularly on benchmarks designed to test the expressivity of GNNs, and exemplifies the versatility of GGNN in generating novel architectures.

Related papers

• Graph Neural Networks at a Fraction [1.8175282137722093]
  This paper introduces Quaternion Message Passing Neural Networks (QMPNNs), a framework that leverages quaternion space to compute node representations. We present a novel perspective on Graph Lottery Tickets, redefining their applicability within the context of GNNs and QMPNNs.
  arXiv  Detail & Related papers  (2025-02-10T03:55:09Z)
• Towards Understanding Graph Neural Networks: An Algorithm Unrolling Perspective [9.426760895586428]
  We introduce a class of unrolled networks built on truncated optimization algorithms for graph signal denoising problems. The training process of a GNN model can be seen as solving a bilevel optimization problem with a GSD problem at the lower level. An expressive model named UGDGNN, i.e., unrolled gradient descent GNN, is proposed which inherits appealing theoretical properties.
  arXiv  Detail & Related papers  (2022-06-09T12:54:03Z)
• EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networks [51.42338058718487]
  Graph Neural Networks (GNNs) have received extensive research attention for their promising performance in graph machine learning. Existing approaches, such as GCN and GPRGNN, are not robust in the face of homophily changes on test graphs. We propose EvenNet, a spectral GNN corresponding to an even-polynomial graph filter.
  arXiv  Detail & Related papers  (2022-05-27T10:48:14Z)
• A Variational Edge Partition Model for Supervised Graph Representation Learning [51.30365677476971]
  This paper introduces a graph generative process to model how the observed edges are generated by aggregating the node interactions over a set of overlapping node communities. We partition each edge into the summation of multiple community-specific weighted edges and use them to define community-specific GNNs. A variational inference framework is proposed to jointly learn a GNN based inference network that partitions the edges into different communities, these community-specific GNNs, and a GNN based predictor that combines community-specific GNNs for the end classification task.
  arXiv  Detail & Related papers  (2022-02-07T14:37:50Z)
• Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks [11.857894213975644]
  We propose a hybrid graph neural network (GNN) framework that combines traditional GCN filters with band-pass filters defined via the geometric scattering transform. Our theoretical results establish the complementary benefits of the scattering filters to leverage structural information from the graph, while our experiments show the benefits of our method on various learning tasks.
  arXiv  Detail & Related papers  (2022-01-22T00:47:41Z)
• Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks [61.17075071853949]
  Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. The purpose of this study is to establish a unified framework that integrates GNNs based on spectral graph and approximation theory.
  arXiv  Detail & Related papers  (2021-07-21T17:34:33Z)
• A Unified View on Graph Neural Networks as Graph Signal Denoising [49.980783124401555]
  Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. In this work, we establish mathematically that the aggregation processes in a group of representative GNN models can be regarded as solving a graph denoising problem. We instantiate a novel GNN model, ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across nodes.
  arXiv  Detail & Related papers  (2020-10-05T04:57:18Z)
• Architectural Implications of Graph Neural Networks [17.01480604968118]
  Graph neural networks (GNN) represent an emerging line of deep learning models that operate on graph structures. GNN is not as well understood in the system and architecture community as its counterparts such as multi-layer perceptrons and convolutional neural networks.
  arXiv  Detail & Related papers  (2020-09-02T03:36:24Z)
• Eigen-GNN: A Graph Structure Preserving Plug-in for GNNs [95.63153473559865]
  Graph Neural Networks (GNNs) are emerging machine learning models on graphs. Most existing GNN models in practice are shallow and essentially feature-centric. We show empirically and analytically that the existing shallow GNNs cannot preserve graph structures well. We propose Eigen-GNN, a plug-in module to boost GNNs ability in preserving graph structures.
  arXiv  Detail & Related papers  (2020-06-08T02:47:38Z)
• Binarized Graph Neural Network [65.20589262811677]
  We develop a binarized graph neural network to learn the binary representations of the nodes with binary network parameters. Our proposed method can be seamlessly integrated into the existing GNN-based embedding approaches. Experiments indicate that the proposed binarized graph neural network, namely BGN, is orders of magnitude more efficient in terms of both time and space.
  arXiv  Detail & Related papers  (2020-04-19T09:43:14Z)

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.