Graph Inductive Biases in Transformers without Message Passing (2305.17589v1)

Abstract: Transformers for graph data are increasingly widely studied and successful in numerous learning tasks. Graph inductive biases are crucial for Graph Transformers, and previous works incorporate them using message-passing modules and/or positional encodings. However, Graph Transformers that use message-passing inherit known issues of message-passing, and differ significantly from Transformers used in other domains, thus making transfer of research advances more difficult. On the other hand, Graph Transformers without message-passing often perform poorly on smaller datasets, where inductive biases are more crucial. To bridge this gap, we propose the Graph Inductive bias Transformer (GRIT) -- a new Graph Transformer that incorporates graph inductive biases without using message passing. GRIT is based on several architectural changes that are each theoretically and empirically justified, including: learned relative positional encodings initialized with random walk probabilities, a flexible attention mechanism that updates node and node-pair representations, and injection of degree information in each layer. We prove that GRIT is expressive -- it can express shortest path distances and various graph propagation matrices. GRIT achieves state-of-the-art empirical performance across a variety of graph datasets, thus showing the power that Graph Transformers without message-passing can deliver.

• The paper introduces GRIT, a Graph Transformer that bypasses message passing by integrating graph-specific inductive biases.
• It employs learned relative positional encodings from random walk probabilities, a flexible attention mechanism for node and node-pair updates, and degree information injection.
• Empirical results show GRIT achieves state-of-the-art performance on diverse graph datasets, offering a promising alternative for graph representation learning.

Graph Inductive Biases in Transformers without Message Passing

The paper "Graph Inductive Biases in Transformers without Message Passing" by Ma et al. introduces a novel approach to improve the performance of Graph Transformers without relying on traditional message-passing mechanisms. The paper addresses a notable challenge: while Graph Transformers incorporating message-passing techniques have achieved significant success in learning tasks, they also inherit limitations associated with message-passing and exhibit limited transferability from domain-agnostic Transformer advances. Conversely, Graph Transformers that forgo message-passing generally underperform on smaller datasets where inductive biases are crucial.

To overcome this dichotomy, the authors propose the Graph Inductive Bias Transformer (GRIT), a new architecture designed to leverage graph-specific inductive biases while eliminating the need for message-passing modules. GRIT is characterized by a trio of architectural innovations:

1. Learned Relative Positional Encodings: These are initialized using random walk probabilities, enabling the network to capture the relative positional information essential for meaningful graph processing.
2. Flexible Attention Mechanism: This mechanism updates both node and node-pair representations, facilitating a richer context and enhancing the expressive power of the model.
3. Injection of Degree Information: Degree information is embedded at each layer, enriching the model's ability to grasp inherent graph structures and relationships.

The paper provides both theoretical and empirical justifications for these architectural enhancements. Theoretically, GRIT is proven to be expressive enough to capture shortest path distances and various graph propagation matrices, which are pivotal for graph-based learning tasks. Empirically, GRIT demonstrates state-of-the-art performance across a diverse set of graph datasets, establishing the effectiveness of Graph Transformers without message-passing.

The implications of these findings are profound in the domain of graph representation learning. GRIT's architecture simplifies the transfer of advancements from traditional Transformers, potentially accelerating the pace of innovation in Graph Transformers. Practically, the paper expands the toolkit available for graph learning by offering an alternative path that circumvents the limitations of message-passing Graph Neural Networks (GNNs). Furthermore, the enhanced expressiveness and flexibility of GRIT could spur further research into scale-up graph learning applications, where large and complex graphs necessitate robust and efficient learning models.

Looking forward, this work opens up promising directions for future research. There is potential to further explore the scalability of GRIT on even larger real-world graph datasets. Additionally, understanding the interplay between the architectural changes proposed and other graph learning paradigms could lead to new hybrid models that further enhance performance and applicability. The paper sets a clear precedent for the benefit of integrating domain-specific inductive biases in Transformer architectures, an approach that could extend beyond the field of graph learning.