Academic

k-Maximum Inner Product Attention for Graph Transformers and the Expressive Power of GraphGPS The Expressive Power of GraphGPS

arXiv:2604.03815v1 Announce Type: new Abstract: Graph transformers have shown promise in overcoming limitations of traditional graph neural networks, such as oversquashing and difficulties in modelling long-range dependencies. However, their application to large-scale graphs is hindered by the quadratic memory and computational complexity of the all-to-all attention mechanism. Although alternatives such as linearized attention and restricted attention patterns have been proposed, these often degrade performance or limit expressive power. To better balance efficiency and effectiveness, we introduce k-Maximum Inner Product (k-MIP) attention for graph transformers. k-MIP attention selects the most relevant key nodes per query via a top-k operation, yielding a sparse yet flexible attention pattern. Combined with an attention score computation based on symbolic matrices, this results in linear memory complexity and practical speedups of up to an order of magnitude compared to all-to-all at

J
Jonas De Schouwer, Haitz S\'aez de Oc\'ariz Borde, Xiaowen Dong · · 1 min read · 5 views
#cs.LG #cs.AI

arXiv:2604.03815v1 Announce Type: new Abstract: Graph transformers have shown promise in overcoming limitations of traditional graph neural networks, such as oversquashing and difficulties in modelling long-range dependencies. However, their application to large-scale graphs is hindered by the quadratic memory and computational complexity of the all-to-all attention mechanism. Although alternatives such as linearized attention and restricted attention patterns have been proposed, these often degrade performance or limit expressive power. To better balance efficiency and effectiveness, we introduce k-Maximum Inner Product (k-MIP) attention for graph transformers. k-MIP attention selects the most relevant key nodes per query via a top-k operation, yielding a sparse yet flexible attention pattern. Combined with an attention score computation based on symbolic matrices, this results in linear memory complexity and practical speedups of up to an order of magnitude compared to all-to-all attention, enabling the processing of graphs with over 500k nodes on a single A100 GPU. We provide a theoretical analysis of expressive power, showing that k-MIP attention does not compromise the expressiveness of graph transformers: specifically, we prove that k-MIP transformers can approximate any full-attention transformer to arbitrary precision. In addition, we analyze the expressive power of the GraphGPS framework, in which we integrate our attention mechanism, and establish an upper bound on its graph distinguishing capability in terms of the S-SEG-WL test. Finally, we validate our approach on the Long Range Graph Benchmark, the City-Networks benchmark, and two custom large-scale inductive point cloud datasets, consistently ranking among the top-performing scalable graph transformers.

Executive Summary

This article introduces a novel attention mechanism, k-Maximum Inner Product (k-MIP) attention, designed to improve the scalability of graph transformers by reducing the computational and memory complexity of the all-to-all attention mechanism. k-MIP attention selects the most relevant key nodes per query via a top-k operation, resulting in a sparse yet flexible attention pattern. The authors provide a theoretical analysis of expressive power, demonstrating that k-MIP transformers can approximate any full-attention transformer to arbitrary precision. The proposed approach is validated on several large-scale graph benchmarks, achieving state-of-the-art performance. The GraphGPS framework, which integrates k-MIP attention, is also analyzed in terms of expressive power and graph distinguishing capability.

Key Points

  • ▸ k-MIP attention mechanism reduces computational and memory complexity of graph transformers
  • ▸ Sparse and flexible attention pattern achieved through top-k operation
  • ▸ Theoretical analysis demonstrates k-MIP transformers can approximate any full-attention transformer
  • ▸ GraphGPS framework integrates k-MIP attention and is analyzed in terms of expressive power and graph distinguishing capability

Merits

Improved Scalability

The k-MIP attention mechanism enables the processing of large-scale graphs on a single A100 GPU, expanding the applicability of graph transformers.

Preservation of Expressive Power

Theoretical analysis demonstrates that k-MIP transformers can approximate any full-attention transformer, ensuring that the proposed approach does not compromise the expressiveness of graph transformers.

Demerits

Potential Overhead of Top-k Operation

The top-k operation required by k-MIP attention may introduce additional computational overhead, potentially affecting performance in certain scenarios.

Expert Commentary

The introduction of k-MIP attention is a significant advancement in the development of graph transformers. By reducing the computational and memory complexity of the all-to-all attention mechanism, the proposed approach enables the processing of large-scale graphs on a single A100 GPU. The theoretical analysis demonstrating the preservation of expressive power is also a notable aspect of this work. However, the potential overhead of the top-k operation should be carefully evaluated in future studies. Overall, this article makes a valuable contribution to the field of graph neural networks and has the potential to impact various industries and applications.

Recommendations

  • ✓ Further investigation of the k-MIP attention mechanism on more complex and diverse graph datasets is necessary to fully evaluate its effectiveness.
  • ✓ The impact of the top-k operation on performance should be carefully evaluated and addressed in future studies.

Sources

Original: arXiv - cs.LG

Related Articles