Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models

• URL: http://arxiv.org/abs/2506.14291v2
• Date: Sun, 29 Jun 2025 21:47:57 GMT
• Title: Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models
• Authors: Ben Finkelshtein, İsmail İlkan Ceylan, Michael Bronstein, Ron Levie,
• Abstract summary: We present a recipe for designing graph foundation models for node-level tasks from first principles.<n>The key ingredient underpinning our study is a systematic investigation of the symmetries that a graph foundation model must respect.<n>We validate our approach through extensive experiments on 29 real-world node classification datasets.
• Score: 13.053266613831447
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: how to build graph foundation models capable of generalizing across arbitrary graphs and features? In this work, we present a recipe for designing graph foundation models for node-level tasks from first principles. The key ingredient underpinning our study is a systematic investigation of the symmetries that a graph foundation model must respect. In a nutshell, we argue that label permutation-equivariance alongside feature permutation-invariance are necessary in addition to the common node permutation-equivariance on each local neighborhood of the graph. To this end, we first characterize the space of linear transformations that are equivariant to permutations of nodes and labels, and invariant to permutations of features. We then prove that the resulting network is a universal approximator on multisets that respect the aforementioned symmetries. Our recipe uses such layers on the multiset of features induced by the local neighborhood of the graph to obtain a class of graph foundation models for node property prediction. We validate our approach through extensive experiments on 29 real-world node classification datasets, demonstrating both strong zero-shot empirical performance and consistent improvement as the number of training graphs increases.

Related papers

• Towards Graph Foundation Models: Learning Generalities Across Graphs via Task-Trees [50.78679002846741]
  We propose a novel approach to cross-task generalization in graphs via task-trees.<n>We show that pretraining a graph neural network (GNN) on diverse task-trees with a reconstruction objective induces transferable knowledge.<n>This enables efficient adaptation to downstream tasks with minimal fine-tuning.
  arXiv  Detail & Related papers  (2024-12-21T02:07:43Z)
• GraphFM: A Scalable Framework for Multi-Graph Pretraining [2.882104808886318]
  We introduce a scalable multi-graph multi-task pretraining approach specifically tailored for node classification tasks across diverse graph datasets from different domains. We demonstrate the efficacy of our approach by training a model on 152 different graph datasets comprising over 7.4 million nodes and 189 million edges. Our results show that pretraining on a diverse array of real and synthetic graphs improves the model's adaptability and stability, while performing competitively with state-of-the-art specialist models.
  arXiv  Detail & Related papers  (2024-07-16T16:51:43Z)
• What Improves the Generalization of Graph Transformers? A Theoretical Dive into the Self-attention and Positional Encoding [67.59552859593985]
  Graph Transformers, which incorporate self-attention and positional encoding, have emerged as a powerful architecture for various graph learning tasks. This paper introduces first theoretical investigation of a shallow Graph Transformer for semi-supervised classification.
  arXiv  Detail & Related papers  (2024-06-04T05:30:16Z)
• Discrete Graph Auto-Encoder [52.50288418639075]
  We introduce a new framework named Discrete Graph Auto-Encoder (DGAE) We first use a permutation-equivariant auto-encoder to convert graphs into sets of discrete latent node representations. In the second step, we sort the sets of discrete latent representations and learn their distribution with a specifically designed auto-regressive model.
  arXiv  Detail & Related papers  (2023-06-13T12:40:39Z)
• GrannGAN: Graph annotation generative adversarial networks [72.66289932625742]
  We consider the problem of modelling high-dimensional distributions and generating new examples of data with complex relational feature structure coherent with a graph skeleton. The model we propose tackles the problem of generating the data features constrained by the specific graph structure of each data point by splitting the task into two phases. In the first it models the distribution of features associated with the nodes of the given graph, in the second it complements the edge features conditionally on the node features.
  arXiv  Detail & Related papers  (2022-12-01T11:49:07Z)
• Node Copying: A Random Graph Model for Effective Graph Sampling [35.957719744856696]
  We introduce the node copying model for constructing a distribution over graphs. We show the usefulness of the copying model in three tasks. We employ our proposed model to mitigate the effect of adversarial attacks on the graph topology.
  arXiv  Detail & Related papers  (2022-08-04T04:04:49Z)
• Similarity-aware Positive Instance Sampling for Graph Contrastive Pre-training [82.68805025636165]
  We propose to select positive graph instances directly from existing graphs in the training set. Our selection is based on certain domain-specific pair-wise similarity measurements. Besides, we develop an adaptive node-level pre-training method to dynamically mask nodes to distribute them evenly in the graph.
  arXiv  Detail & Related papers  (2022-06-23T20:12:51Z)
• Permutation-Invariant Variational Autoencoder for Graph-Level Representation Learning [0.0]
  We propose a permutation-invariant variational autoencoder for graph structured data. Our model indirectly learns to match the node ordering of input and output graph, without imposing a particular node ordering. We demonstrate the effectiveness of our proposed model on various graph reconstruction and generation tasks.
  arXiv  Detail & Related papers  (2021-04-20T09:44:41Z)
• Building powerful and equivariant graph neural networks with structural message-passing [74.93169425144755]
  We propose a powerful and equivariant message-passing framework based on two ideas. First, we propagate a one-hot encoding of the nodes, in addition to the features, in order to learn a local context matrix around each node. Second, we propose methods for the parametrization of the message and update functions that ensure permutation equivariance.
  arXiv  Detail & Related papers  (2020-06-26T17:15:16Z)
• Permutation Invariant Graph Generation via Score-Based Generative Modeling [114.12935776726606]
  We propose a permutation invariant approach to modeling graphs, using the recent framework of score-based generative modeling. In particular, we design a permutation equivariant, multi-channel graph neural network to model the gradient of the data distribution at the input graph. For graph generation, we find that our learning approach achieves better or comparable results to existing models on benchmark datasets.
  arXiv  Detail & Related papers  (2020-03-02T03:06:14Z)

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.