Holographic Node Representations: Pre-training Task-Agnostic Node Embeddings

Large general purpose pre-trained models have revolutionized computer vision and natural language understanding. However, the development of general purpose pre-trained Graph Neural Networks (GNNs) lags behind other domains due to the lack of suitable generalist node representations. Existing GNN architectures are often tailored to specific task orders, such as node-level, link-level, or higher-order tasks, because different tasks require distinct permutation symmetries, which are difficult to reconcile within a single model. In this paper, we propose holographic node representations, a new blueprint for node representations capable of solving tasks of any order. Holographic node representations have two key components: (1) a task-agnostic expansion map, which produces highly expressive, high-dimensional embeddings, free from node-permutation symmetries, to be fed into (2) a reduction map that carefully reintroduces the relevant permutation symmetries to produce low-dimensional, task-specific embeddings. We show that well-constructed expansion maps enable simple and efficient reduction maps, which can be adapted for any task order. Empirical results show that holographic node representations can be effectively pre-trained and reused across tasks of varying orders, yielding up to 100% relative performance improvement, including in cases where prior methods fail entirely.