What Improves the Generalization of Graph Transformers? A Theoretical Dive into the Self-attention and Positional Encoding

• URL: http://arxiv.org/abs/2406.01977v1
• Date: Tue, 4 Jun 2024 05:30:16 GMT
• Title: What Improves the Generalization of Graph Transformers? A Theoretical Dive into the Self-attention and Positional Encoding
• Authors: Hongkang Li, Meng Wang, Tengfei Ma, Sijia Liu, Zaixi Zhang, Pin-Yu Chen,
• Abstract summary: 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.
• Score: 67.59552859593985
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions across layers and the recursive graph structure have made it challenging to establish a theoretical foundation for learning and generalization. This study introduces the first theoretical investigation of a shallow Graph Transformer for semi-supervised node classification, comprising a self-attention layer with relative positional encoding and a two-layer perceptron. Focusing on a graph data model with discriminative nodes that determine node labels and non-discriminative nodes that are class-irrelevant, we characterize the sample complexity required to achieve a desirable generalization error by training with stochastic gradient descent (SGD). This paper provides the quantitative characterization of the sample complexity and number of iterations for convergence dependent on the fraction of discriminative nodes, the dominant patterns, and the initial model errors. Furthermore, we demonstrate that self-attention and positional encoding enhance generalization by making the attention map sparse and promoting the core neighborhood during training, which explains the superior feature representation of Graph Transformers. Our theoretical results are supported by empirical experiments on synthetic and real-world benchmarks.

Related papers

• Transformers Provably Learn Directed Acyclic Graphs via Kernel-Guided Mutual Information [91.66597637613263]
  transformer-based models leveraging the attention mechanism have demonstrated strong empirical success in capturing complex dependencies within graphs.<n>We introduce a novel information-theoretic metric: the kernel-guided mutual information (KG-MI) based on the $f$-divergence.<n>We prove that, given sequences generated by a $K$-parent DAG, training a single-layer, multi-head transformer via a gradient ascent converges to the global optimum time.
  arXiv  Detail & Related papers  (2025-10-29T14:07:12Z)
• HeSRN: Representation Learning On Heterogeneous Graphs via Slot-Aware Retentive Network [22.60005673964228]
  HeSRN is a novel Heterogeneous Slot-aware Retentive Network for efficient and expressive heterogeneous graph representation learning.<n>HeSRN consistently outperforms state-of-the-art heterogeneous graph neural networks and Graph Transformer baselines on node classification tasks.
  arXiv  Detail & Related papers  (2025-10-10T18:18:06Z)
• GraphUniverse: Enabling Systematic Evaluation of Inductive Generalization [8.95975918626961]
  GraphUniverse is a framework for generating entire families of graphs.<n>It enables the first systematic evaluation of inductive generalization at scale.<n>Our core innovation is the generation of graphs with persistent semantic communities.
  arXiv  Detail & Related papers  (2025-09-25T12:46:01Z)
• Exploring Heterophily in Graph-level Tasks [9.539979711178416]
  We present the first analysis of heterophily in graph-level learning, combining theoretical insights with empirical validation.<n>We first introduce a taxonomy of graph-level labeling schemes, and focus on motif-based tasks within local structure labeling.<n>Using energy-based gradient flow analysis, we reveal a key insight: unlike frequency-dominated regimes in node-level tasks, motif detection requires mixed-frequency dynamics to remain flexible.
  arXiv  Detail & Related papers  (2025-09-23T11:07:16Z)
• Invariant Graph Transformer for Out-of-Distribution Generalization [21.60139614144787]
  We introduce Graph Out-Of-Distribution generalized Transformer (GOODFormer)<n>It aims to learn generalized graph representations by capturing invariant relationships between predictive graph structures and labels.<n>We design an evolving subgraph positional and structural encoder to effectively and efficiently capture the encoding information of dynamically changing subgraphs.
  arXiv  Detail & Related papers  (2025-08-01T04:11:53Z)
• Unitary convolutions for learning on graphs and groups [0.9899763598214121]
  We study unitary group convolutions, which allow for deeper networks that are more stable during training. The main focus of the paper are graph neural networks, where we show that unitary graph convolutions provably avoid over-smoothing. Our experimental results confirm that unitary graph convolutional networks achieve competitive performance on benchmark datasets.
  arXiv  Detail & Related papers  (2024-10-07T21:09:14Z)
• Gradformer: Graph Transformer with Exponential Decay [69.50738015412189]
  Self-attention mechanism in Graph Transformers (GTs) overlooks the graph's inductive biases, particularly biases related to structure. This paper presents Gradformer, a method innovatively integrating GT with the intrinsic inductive bias. Gradformer consistently outperforms the Graph Neural Network and GT baseline models in various graph classification and regression tasks.
  arXiv  Detail & Related papers  (2024-04-24T08:37:13Z)
• Deep Contrastive Graph Learning with Clustering-Oriented Guidance [61.103996105756394]
  Graph Convolutional Network (GCN) has exhibited remarkable potential in improving graph-based clustering. Models estimate an initial graph beforehand to apply GCN. Deep Contrastive Graph Learning (DCGL) model is proposed for general data clustering.
  arXiv  Detail & Related papers  (2024-02-25T07:03:37Z)
• Topology-Informed Graph Transformer [7.857955053895979]
  'Topology-Informed Graph Transformer (TIGT)' is a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs.
  arXiv  Detail & Related papers  (2024-02-03T03:17:44Z)
• Isomorphic-Consistent Variational Graph Auto-Encoders for Multi-Level Graph Representation Learning [9.039193854524763]
  We propose the Isomorphic-Consistent VGAE (IsoC-VGAE) for task-agnostic graph representation learning. We first devise a decoding scheme to provide a theoretical guarantee of keeping the isomorphic consistency. We then propose the Inverse Graph Neural Network (Inv-GNN) decoder as its intuitive realization.
  arXiv  Detail & Related papers  (2023-12-09T10:16:53Z)
• Advective Diffusion Transformers for Topological Generalization in Graph Learning [69.2894350228753]
  We show how graph diffusion equations extrapolate and generalize in the presence of varying graph topologies. We propose a novel graph encoder backbone, Advective Diffusion Transformer (ADiT), inspired by advective graph diffusion equations.
  arXiv  Detail & Related papers  (2023-10-10T08:40:47Z)
• A Theoretical Understanding of Shallow Vision Transformers: Learning, Generalization, and Sample Complexity [71.11795737362459]
  ViTs with self-attention modules have recently achieved great empirical success in many tasks. However, theoretical learning generalization analysis is mostly noisy and elusive. This paper provides the first theoretical analysis of a shallow ViT for a classification task.
  arXiv  Detail & Related papers  (2023-02-12T22:12:35Z)
• DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion [66.21290235237808]
  We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
  arXiv  Detail & Related papers  (2023-01-23T15:18:54Z)
• Optimal Propagation for Graph Neural Networks [51.08426265813481]
  We propose a bi-level optimization approach for learning the optimal graph structure. We also explore a low-rank approximation model for further reducing the time complexity.
  arXiv  Detail & Related papers  (2022-05-06T03:37:00Z)

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.