GRAMA: Adaptive Graph Autoregressive Moving Average Models
This work addresses the problem of improving long-range dependency modeling in graph neural networks for researchers and practitioners, representing an incremental advancement over prior methods.
The paper tackles the limitations of existing Graph State Space Models in modeling long-range interactions on graphs by introducing GRAMA, a learnable Autoregressive Moving Average framework that preserves permutation equivariance and handles sequential graph data, achieving competitive performance with state-of-the-art methods on 14 datasets.
Graph State Space Models (SSMs) have recently been introduced to enhance Graph Neural Networks (GNNs) in modeling long-range interactions. Despite their success, existing methods either compromise on permutation equivariance or limit their focus to pairwise interactions rather than sequences. Building on the connection between Autoregressive Moving Average (ARMA) and SSM, in this paper, we introduce GRAMA, a Graph Adaptive method based on a learnable Autoregressive Moving Average (ARMA) framework that addresses these limitations. By transforming from static to sequential graph data, GRAMA leverages the strengths of the ARMA framework, while preserving permutation equivariance. Moreover, GRAMA incorporates a selective attention mechanism for dynamic learning of ARMA coefficients, enabling efficient and flexible long-range information propagation. We also establish theoretical connections between GRAMA and Selective SSMs, providing insights into its ability to capture long-range dependencies. Extensive experiments on 14 synthetic and real-world datasets demonstrate that GRAMA consistently outperforms backbone models and performs competitively with state-of-the-art methods.