HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations
arXiv:2505.15405v3 Announce Type: replace Abstract: While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations--such as simplicial or cellular complexes--to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical scalability challenges due to the steep complex
The increasing complexity of real-world data necessitates more sophisticated AI models that can capture multi-way relationships beyond simple pairwise connections, pushing the boundaries of current GNNs.
Scalable higher-order graph representations are crucial for developing more powerful and accurate AI models across various complex domains, from drug discovery to social network analysis, impacting the future capabilities of AI.
This research introduces a more efficient method (HOPSE) to handle higher-order interactions in AI models, potentially overcoming scalability bottlenecks that have limited the application of Topological Deep Learning.
- · AI researchers and developers
- · Sectors with complex relational data (e.g., life sciences, social media)
- · Companies building TDL-based AI systems
- · AI models reliant solely on traditional GNNs for complex tasks
Improved performance and broader application of AI in domains requiring complex relational understanding.
Accelerated discovery and design in fields like materials science and drug development due to enhanced modeling capabilities.
The democratization of advanced topological deep learning techniques as computational barriers are reduced, fostering new AI innovations.
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Read at arXiv cs.LG