Lorentzian Graph Isomorphic Network

• URL: http://arxiv.org/abs/2504.00142v4
• Date: Sun, 25 May 2025 08:02:13 GMT
• Title: Lorentzian Graph Isomorphic Network
• Authors: Srinitish Srinivasan, Omkumar CU,
• Abstract summary: Lorentzian Graph Isomorphic Network (LGIN) is a novel HGNN designed for enhanced discrimination within the Lorentzian model.<n>LGIN is the first to adapt principles of powerful, highly discriminative GNN architectures to a Riemannian manifold.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While hyperbolic GNNs show promise for hierarchical data, they often have limited discriminative power compared to Euclidean counterparts or the WL test, due to non-injective aggregation. To address this expressivity gap, we propose the Lorentzian Graph Isomorphic Network (LGIN), a novel HGNN designed for enhanced discrimination within the Lorentzian model. LGIN introduces a new update rule that preserves the Lorentzian metric while effectively capturing richer structural information. This marks a significant step towards more expressive GNNs on Riemannian manifolds. Extensive evaluations across nine benchmark datasets demonstrate LGIN's superior performance, consistently outperforming or matching state-of-the-art hyperbolic and Euclidean baselines, showcasing its ability to capture complex graph structures. LGIN is the first to adapt principles of powerful, highly discriminative GNN architectures to a Riemannian manifold. The code for our paper can be found at https://github.com/Deceptrax123/LGIN

Related papers

• On the Expressive Power of Subgraph Graph Neural Networks for Graphs with Bounded Cycles [17.29046077604317]
  This work investigates $k$-hop subgraph GNNs that aggregate information from neighbors with distances up to $k$.<n>We prove that the $k$-hop subgraph GNNs can approximate any permutation-invariant/equivariant continuous function over graphs without cycles of length greater than $2k+1$ within any error tolerance.
  arXiv  Detail & Related papers  (2025-02-06T01:25:22Z)
• Redesigning graph filter-based GNNs to relax the homophily assumption [31.368672838207022]
  Graph neural networks (GNNs) have become a workhorse approach for learning from data defined over irregular domains. We present a simple yet effective architecture designed to mitigate the limitations of the homophily assumption. The proposed architecture reinterprets the role of graph filters in convolutional GNNs, resulting in a more general architecture.
  arXiv  Detail & Related papers  (2024-09-13T09:43:36Z)
• MAG-GNN: Reinforcement Learning Boosted Graph Neural Network [68.60884768323739]
  A particular line of work proposed subgraph GNNs that use subgraph information to improve GNNs' expressivity and achieved great success. Such effectivity sacrifices the efficiency of GNNs by enumerating all possible subgraphs. We propose Magnetic Graph Neural Network (MAG-GNN), a reinforcement learning (RL) boosted GNN, to solve the problem.
  arXiv  Detail & Related papers  (2023-10-29T20:32:21Z)
• 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)
• LSGNN: Towards General Graph Neural Network in Node Classification by Local Similarity [59.41119013018377]
  We propose to use the local similarity (LocalSim) to learn node-level weighted fusion, which can also serve as a plug-and-play module. For better fusion, we propose a novel and efficient Initial Residual Difference Connection (IRDC) to extract more informative multi-hop information. Our proposed method, namely Local Similarity Graph Neural Network (LSGNN), can offer comparable or superior state-of-the-art performance on both homophilic and heterophilic graphs.
  arXiv  Detail & Related papers  (2023-05-07T09:06:11Z)
• Rethinking the Expressive Power of GNNs via Graph Biconnectivity [45.4674360883544]
  We introduce a novel class of expressivity metrics via graph biconnectivity and highlight their importance in both theory and practice. We introduce a principled and more efficient approach, called the Generalized Distance Weisfeiler-Lehman (GD-WL) Practically, we show GD-WL can be implemented by a Transformer-like architecture that preserves and enjoys full parallelizability.
  arXiv  Detail & Related papers  (2023-01-23T15:58:59Z)
• A Comprehensive Study on Large-Scale Graph Training: Benchmarking and Rethinking [124.21408098724551]
  Large-scale graph training is a notoriously challenging problem for graph neural networks (GNNs) We present a new ensembling training manner, named EnGCN, to address the existing issues. Our proposed method has achieved new state-of-the-art (SOTA) performance on large-scale datasets.
  arXiv  Detail & Related papers  (2022-10-14T03:43:05Z)
• 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)
• Discovering the Representation Bottleneck of Graph Neural Networks from Multi-order Interactions [51.597480162777074]
  Graph neural networks (GNNs) rely on the message passing paradigm to propagate node features and build interactions. Recent works point out that different graph learning tasks require different ranges of interactions between nodes. We study two common graph construction methods in scientific domains, i.e., emphK-nearest neighbor (KNN) graphs and emphfully-connected (FC) graphs.
  arXiv  Detail & Related papers  (2022-05-15T11:38:14Z)
• ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network [72.16255675586089]
  We propose an Adaptive Curvature Exploration Hyperbolic Graph NeuralNetwork named ACE-HGNN to adaptively learn the optimal curvature according to the input graph and downstream tasks. Experiments on multiple real-world graph datasets demonstrate a significant and consistent performance improvement in model quality with competitive performance and good generalization ability.
  arXiv  Detail & Related papers  (2021-10-15T07:18:57Z)
• Graph Neural Networks with Local Graph Parameters [1.8600631687568656]
  Local graph parameters can be added to any Graph Neural Networks (GNNs) architecture. Our results connect GNNs with deep results in finite model theory and finite variable logics.
  arXiv  Detail & Related papers  (2021-06-12T07:43:51Z)
• Is Homophily a Necessity for Graph Neural Networks? [50.959340355849896]
  Graph neural networks (GNNs) have shown great prowess in learning representations suitable for numerous graph-based machine learning tasks. GNNs are widely believed to work well due to the homophily assumption ("like attracts like"), and fail to generalize to heterophilous graphs where dissimilar nodes connect. Recent works design new architectures to overcome such heterophily-related limitations, citing poor baseline performance and new architecture improvements on a few heterophilous graph benchmark datasets as evidence for this notion. In our experiments, we empirically find that standard graph convolutional networks (GCNs) can actually achieve better performance than
  arXiv  Detail & Related papers  (2021-06-11T02:44:00Z)
• Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs [77.33781731432163]
  We learn dynamic graph representation in hyperbolic space, for the first time, which aims to infer node representations. We present a novel Hyperbolic Variational Graph Network, referred to as HVGNN. In particular, to model the dynamics, we introduce a Temporal GNN (TGNN) based on a theoretically grounded time encoding approach.
  arXiv  Detail & Related papers  (2021-04-06T01:44:15Z)
• Parameterized Hypercomplex Graph Neural Networks for Graph Classification [1.1852406625172216]
  We develop graph neural networks that leverage the properties of hypercomplex feature transformation. In particular, in our proposed class of models, the multiplication rule specifying the algebra itself is inferred from the data during training. We test our proposed hypercomplex GNN on several open graph benchmark datasets and show that our models reach state-of-the-art performance.
  arXiv  Detail & Related papers  (2021-03-30T18:01:06Z)
• Counting Substructures with Higher-Order Graph Neural Networks: Possibility and Impossibility Results [58.277290855841976]
  We study tradeoffs of computational cost and expressive power of Graph Neural Networks (GNNs) We show that a new model can count subgraphs of size $k$, and thereby overcomes a known limitation of low-order GNNs. In several cases, the proposed algorithm can greatly reduce computational complexity compared to the existing higher-order $k$-GNNs.
  arXiv  Detail & Related papers  (2020-12-06T03:42:54Z)
• Data-Driven Learning of Geometric Scattering Networks [74.3283600072357]
  We propose a new graph neural network (GNN) module based on relaxations of recently proposed geometric scattering transforms. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations.
  arXiv  Detail & Related papers  (2020-10-06T01:20:27Z)
• The Surprising Power of Graph Neural Networks with Random Node Initialization [54.4101931234922]
  Graph neural networks (GNNs) are effective models for representation learning on relational data. Standard GNNs are limited in their expressive power, as they cannot distinguish beyond the capability of the Weisfeiler-Leman graph isomorphism. In this work, we analyze the expressive power of GNNs with random node (RNI) We prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties.
  arXiv  Detail & Related papers  (2020-10-02T19:53:05Z)
• Hierarchical Message-Passing Graph Neural Networks [12.207978823927386]
  We propose a novel Hierarchical Message-passing Graph Neural Networks framework. Key idea is generating a hierarchical structure that re-organises all nodes in a flat graph into multi-level super graphs. We present the first model to implement this framework, termed Hierarchical Community-aware Graph Neural Network (HC-GNN)
  arXiv  Detail & Related papers  (2020-09-08T13:11:07Z)
• A Novel Higher-order Weisfeiler-Lehman Graph Convolution [2.658812114255374]
  We propose a novel graph convolution operator that is based on the 2-dimensional Weisfeiler-Lehman test. We show that the resulting 2-WL-GNN architecture is more discriminative than existing GNN approaches.
  arXiv  Detail & Related papers  (2020-07-01T09:32:01Z)
• 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)

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.