Figure 2: These two graphs cannot be distinguished by 1-WL-test. The COMBINE step takes the result of AGGREGATE and the previous representation of current node asinput. Wereduce theFFN inner-layer dimension of4din [47] tod, which does not appreciably hurt the performance but significantly save the parameters. The embedding dropout ratio is set to 0.1 by default in many previous Transformer works[11,34]. The rest of hyper-parameters remain unchanged. Table 8 summarizes the hyper-parameters used for fine-tuning Graphormer on OGBGMolPCBA.

The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared to mainstream GNN variants. Therefore, it remains a mystery how Transformers could perform well for graph representation learning. In this paper, we solve this mystery by presenting Graphormer, which is built upon the standard Transformer architecture, and could attain excellent results on a broad range of graph representation learning tasks, especially on the recent OGB Large-Scale Challenge. Our key insight to utilizing Transformer in the graph is the necessity of effectively encoding the structural information of a graph into the model. To this end, we propose several simple yet effective structural encoding methods to help Graphormer better model graph-structured data. Besides, we mathematically characterize the expressive power of Graphormer and exhibit that with our ways of encoding the structural information of graphs, many popular GNN variants could be covered as the special cases of Graphormer.

There are many attempts of leveraging Transformer into the graph domain, but the only effective way is replacing some key modules (e.g., feature aggregation) in classic GNN variants by the softmax attention

Textual Attribute Graphs (TAGs) are critical for modeling complex networks like citation networks, but effective node classification remains challenging due to difficulties in integrating rich semantics from text with structural graph information. Existing methods often struggle with capturing nuanced domain-specific terminology, modeling long-range dependencies, adapting to temporal evolution, and scaling to massive datasets. To address these issues, we propose a novel framework that integrates TAPE (Text-Attributed Graph Representation Enhancement) with Graphormer. Our approach leverages a large language model (LLM), specifically ChatGPT, within the TAPE framework to generate semantically rich explanations from paper content, which are then fused into enhanced node representations. These embeddings are combined with structural features using a novel integration layer with learned attention weights. Graphormer's path-aware position encoding and multi-head attention mechanisms are employed to effectively capture long-range dependencies across the citation network. We demonstrate the efficacy of our framework on the challenging ogbn-arxiv dataset, achieving state-of-the-art performance with a classification accuracy of 0.772, significantly surpassing the best GCN baseline of 0.713. Our method also yields strong results in precision (0.671), recall (0.577), and F1-score (0.610). We validate our approach through comprehensive ablation studies that quantify the contribution of each component, demonstrating the synergy between semantic and structural information. Our framework provides a scalable and robust solution for node classification in dynamic TAGs, offering a promising direction for future research in knowledge systems and scientific discovery.

Recent advancements in large language models (LLMs) have expanded their role in robotic task planning. However, while LLMs have been explored for generating feasible task sequences, their ability to ensure safe task execution remains underdeveloped. Existing methods struggle with structured risk perception, making them inadequate for safety-critical applications where low-latency hazard adaptation is required. To address this limitation, we propose a Graphormer-enhanced risk-aware task planning framework that combines LLM-based decision-making with structured safety modeling. Our approach constructs a dynamic spatio-semantic safety graph, capturing spatial and contextual risk factors to enable online hazard detection and adaptive task refinement. Unlike existing methods that rely on predefined safety constraints, our framework introduces a context-aware risk perception module that continuously refines safety predictions based on real-time task execution. This enables a more flexible and scalable approach to robotic planning, allowing for adaptive safety compliance beyond static rules. To validate our framework, we conduct experiments in the AI2-THOR environment. The experiments results validates improvements in risk detection accuracy, rising safety notice, and task adaptability of our framework in continuous environments compared to static rule-based and LLM-only baselines. Our project is available at https://github.com/hwj20/GGTP

In recent years, machine learning has profoundly reshaped the field of chemistry, facilitating significant advancements across various applications, including the prediction of molecular properties and the generation of molecular structures. Language models and graph-based models are extensively utilized within this domain, consistently achieving state-of-the-art results across an array of tasks. However, the prevailing practice of representing chemical compounds in the SMILES format -- used by most datasets and many language models -- presents notable limitations as a training data format. In contrast, chemical fingerprints offer a more physically informed representation of compounds, thereby enhancing their suitability for model training. This study aims to develop a language model that is specifically trained on fingerprints. Furthermore, we introduce a bimodal architecture that integrates this language model with a graph model. Our proposed methodology synthesizes these approaches, utilizing RoBERTa as the language model and employing Graph Isomorphism Networks (GIN), Graph Convolutional Networks (GCN) and Graphormer as graph models. This integration results in a significant improvement in predictive performance compared to conventional strategies for tasks such as Quantitative Structure-Activity Relationship (QSAR) and the prediction of nuclear magnetic resonance (NMR) spectra, among others.

Graph neural networks (GNNs) have been widely used in graph-related contexts. It is known that the separation power of GNNs is equivalent to that of the Weisfeiler-Lehman (WL) test; hence, GNNs are imperfect at identifying all non-isomorphic graphs, which severely limits their expressive power. This work investigates $k$-hop subgraph GNNs that aggregate information from neighbors with distances up to $k$ and incorporate the subgraph structure. We prove that under appropriate assumptions, 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. We also provide an extension to $k$-hop GNNs without incorporating the subgraph structure. Our numerical experiments on established benchmarks and novel architectures validate our theory on the relationship between the information aggregation distance and the cycle size.

The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared to mainstream GNN variants. Therefore, it remains a mystery how Transformers could perform well for graph representation learning. In this paper, we solve this mystery by presenting Graphormer, which is built upon the standard Transformer architecture, and could attain excellent results on a broad range of graph representation learning tasks, especially on the recent OGB Large-Scale Challenge. Our key insight to utilizing Transformer in the graph is the necessity of effectively encoding the structural information of a graph into the model. To this end, we propose several simple yet effective structural encoding methods to help Graphormer better model graph-structured data.