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On the Connection Between MPNN and Graph Transformer
Chen Cai · Truong Son Hy · Rose Yu · Yusu Wang

Wed Jul 26 02:00 PM -- 03:30 PM (PDT) @ Exhibit Hall 1 #325
Graph Transformer (GT) recently has emerged as a new paradigm of graph learning algorithms, outperforming the previously popular Message Passing Neural Network (MPNN) on multiple benchmarks. Previous work shows that with proper position embedding, GT can approximate MPNN arbitrarily well, implying that GT is at least as powerful as MPNN. In this paper, we study the inverse connection and show that MPNN with virtual node (VN), a commonly used heuristic with little theoretical understanding, is powerful enough to arbitrarily approximate the self-attention layer of GT. In particular, we first show that if we consider one type of linear transformer, the so-called Performer/Linear Transformer, then MPNN + VN with only $\mathcal{O}(1)$ depth and $\mathcal{O}(1)$ width can approximate a self-attention layer in Performer/Linear Transformer. Next, via a connection between MPNN + VN and DeepSets, we prove the MPNN + VN with $\mathcal{O}(n^d)$ width and $\mathcal{O}(1)$ depth can approximate the self-attention layer arbitrarily well, where $d$ is the input feature dimension. Lastly, under some assumptions, we provide an explicit construction of MPNN + VN with $\mathcal{O}(1)$ width and $\mathcal{O}(n)$ depth approximating the self-attention layer in GT arbitrarily well. On the empirical side, we demonstrate that 1) MPNN + VN is a surprisingly strong baseline, outperforming GT on the recently proposed Long Range Graph Benchmark (LRGB) dataset, 2) our MPNN + VN improves over early implementation on a wide range of OGB datasets and 3) MPNN + VN outperforms Linear Transformer and MPNN on the climate modeling task.

Author Information

Chen Cai (University of California, San Diego)
Truong Son Hy (Indiana State University)

Tenure-track Assistant Professor at Indiana State University

Rose Yu (University of California, San Diego)
Rose Yu

Dr. Rose Yu is an assistant professor at the University of California San Diego, Department of Computer Science and Engineering. She earned her Ph.D. in Computer Sciences at USC in 2017. She was subsequently a Postdoctoral Fellow at Caltech. Her research focuses on advancing machine learning techniques for large-scale spatiotemporal data analysis, with applications to sustainability, health, and physical sciences. A particular emphasis of her research is on physics-guided AI which aims to integrate first principles with data-driven models. Among her awards, she has won NSF CAREER Award, Faculty Research Award from JP Morgan, Facebook, Google, Amazon, and Adobe, Several Best Paper Awards, Best Dissertation Award at USC, and was nominated as one of the ’MIT Rising Stars in EECS’.

Yusu Wang (UC San Diego)

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