GRAMA: Adaptive Graph Autoregressive Moving Average Models

TL;DR

GRAMA introduces a learnable ARMA-based graph model that effectively captures long-range dependencies while maintaining permutation equivariance, outperforming existing methods on diverse datasets.

Contribution

It presents a novel adaptive ARMA framework for graph modeling that preserves permutation equivariance and enhances long-range interaction learning.

Findings

Outperforms baseline models on 14 datasets

Effectively captures long-range dependencies

Maintains permutation equivariance

Abstract

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.