Rethinking Graph Super-resolution: Dual Frameworks for Topological Fidelity

TL;DR

Graph SR aims to recover high-resolution graphs $(oldsymbol{A}_h,oldsymbol{X}_h)$ from low-resolution inputs $(oldsymbol{A}_l,oldsymbol{X}_l)$, but existing methods suffer from permutation-variant node inference and limited, edge-focused learning. The authors introduce Bi-SR, a structure-aware, permutation-invariant node super-resolution framework using a bipartite LR–HR graph, and DEFEND, a dual-graph edge learning approach that maps HR edges to dual nodes for expressive inference via standard GNNs. Across twelve simulated datasets with diverse topologies and LR–HR mappings and a real brain connectome, Bi-SR and DEFEND achieve state-of-the-art performance on seven topological measures, highlighting the importance of structural inductive bias in graph SR. The work also provides a broad benchmarking pipeline and paves the way for scalable SR in neuroscience and other domains, with future directions including larger-scale graphs and standardized SR benchmarks, all while carefully preserving mathematical structure in the formulations.

Abstract

Graph super-resolution, the task of inferring high-resolution (HR) graphs from low-resolution (LR) counterparts, is an underexplored yet crucial research direction that circumvents the need for costly data acquisition. This makes it especially desirable for resource-constrained fields such as the medical domain. While recent GNN-based approaches show promise, they suffer from two key limitations: (1) matrix-based node super-resolution that disregards graph structure and lacks permutation invariance; and (2) reliance on node representations to infer edge weights, which limits scalability and expressivity. In this work, we propose two GNN-agnostic frameworks to address these issues. First, Bi-SR introduces a bipartite graph connecting LR and HR nodes to enable structure-aware node super-resolution that preserves topology and permutation invariance. Second, DEFEND learns edge representations by mapping HR edges to nodes of a dual graph, allowing edge inference via standard node-based GNNs. We evaluate both frameworks on a real-world brain connectome dataset, where they achieve state-of-the-art performance across seven topological measures. To support generalization, we introduce twelve new simulated datasets that capture diverse topologies and LR-HR relationships. These enable comprehensive benchmarking of graph super-resolution methods.

Figures (4)

• Figure 1: Comparison of image and graph super-resolution (SR). (A) and (C) illustrate image SR as a special case of graph SR, where the graph topology is fixed to a regular grid and node features correspond to pixel values. (B) and (D) represent the general case of graph SR considered in this work, which involves learning both the topology and edge features in addition to node features, without assuming spatial locality between LR and HR nodes.
• Figure 2: Limitations of existing brain graph super-resolution methods. (A) Current approaches to node super-resolution rely on a matrix transpose operation, which ignores graph structure and yields HR node features that are sensitive to LR node permutations. (B) GNN-based edge learning uses node representations to encode all incident edges, making them computationally expensive and limiting its capacity to model edges.
• Figure 3: Overview of the Bi-SR framework. Given a low-resolution (LR) graph, Bi-SR constructs a bipartite graph between LR and high-resolution (HR) nodes, enabling each HR node to aggregate information from all LR nodes through message passing. HR nodes are initialized with fixed random features to break symmetry. Optional representation learning steps refine LR and HR features before and after bipartite propagation. This structure-aware formulation preserves the graph topology and ensures permutation invariance with respect to LR node ordering.
• Figure 4: Overview of the DEFEND framework. Starting from HR node features, DEFEND initializes edge features (e.g., via dot product) and constructs a dual graph by mapping each HR edge to a dual node. Message passing is then performed on the dual graph to learn refined edge representations. These are mapped back to HR edges and used to infer the HR graph topology (e.g., via normalization). The primal-to-dual mapping is invertible and enables efficient edge inference using node-based GNNs.