Spectral Neural Graph Sparsification
Angelica Liguori, Ettore Ritacco, Pietro Sabatino, Annalisa Socievole
TL;DR
This paper introduces the Spectral Preservation Network, a novel graph sparsification framework that adaptively reduces graph complexity while maintaining spectral properties, improving efficiency and performance in graph learning tasks.
Contribution
It proposes the Spectral Preservation Network with the Joint Graph Evolution layer and Spectral Concordance loss, enabling adaptive graph sparsification with spectral fidelity.
Findings
Outperforms state-of-the-art graph sparsification methods
Maintains spectral properties effectively during sparsification
Enhances downstream graph learning tasks efficiency
Abstract
Graphs are central to modeling complex systems in domains such as social networks, molecular chemistry, and neuroscience. While Graph Neural Networks, particularly Graph Convolutional Networks, have become standard tools for graph learning, they remain constrained by reliance on fixed structures and susceptibility to over-smoothing. We propose the Spectral Preservation Network, a new framework for graph representation learning that generates reduced graphs serving as faithful proxies of the original, enabling downstream tasks such as community detection, influence propagation, and information diffusion at a reduced computational cost. The Spectral Preservation Network introduces two key components: the Joint Graph Evolution layer and the Spectral Concordance loss. The former jointly transforms both the graph topology and the node feature matrix, allowing the structure and attributes to…
Peer Reviews
Decision·ICLR 2026 Conference Withdrawn Submission
1. Graph sparsification is indeed a practical problem when dealing with large graphs. 2. The writing of the proposal is easy to follow, which also applies to most parts of the paper.
1. The motivation is unclear and lacks real-world support. For instance, in line 42, the authors mention “evolve the graph.” However, if the graph encoder is already changing continuously, the extracted information from the graph would also change without needing to modify the graph structure itself. What is the deeper reason for evolving the graph structure? 2. Dropping nodes may limit the applicability of the proposed GNN. For example, link prediction would no longer be fully feasible. 3. Coul
1. Novel joint architecture that evolves structure and features instead of treating graphs as static. 2. Spectral-theoretic objective preserves global connectivity and dynamical properties. 3. Extensive evaluation across 5 datasets and multiple sparsity ratios
1. Experiments primarily assess spectral metrics (MASS, τc) rather than downstream performance. 2. Eigen-decomposition can be computationally costly for large graphs
1. The paper explores the idea of evolving the graph structure during training, a direction that has been relatively underexplored in existing research, highlighting its novel contribution. 2. The proposed method achieves superior performance compared to established baselines, demonstrating its effectiveness and supporting the originality of the approach.
1. The paper would benefit from additional comparisons with related works. For instance, graph pooling methods also dynamically compress graph structures for improved representation, often employing similar equations. A more apparent distinction and comparison with such approaches would strengthen the contribution. 2. Some key experiments, particularly an ablation study on the loss functions, are missing and should be included to clarify the contribution of each component. 3. Even though the aut
1. The paper attempts to couple structure learning and sparsification: it proposes a Joint Graph Evolution (JGE) layer that is intended to update both the graph connectivity ($Q_{t+1}$) and node features ($H_{t+1}$), together with a Spectral Concordance loss meant to preserve spectral properties (e.g., Laplacian behavior, global structure) after pruning nodes. 2. The experiments at least try to evaluate sparsification not only by edge count but also by higher-level structural indicators (larges
The paper would benefit from a substantial revision under the guidance of a more senior researcher. In its current form, it’s difficult to evaluate. The abstract and introduction together span only about one page, are very high-level, and begin describing the method almost immediately. There is no sufficiently developed background, related work section or problem formulation, and the motivation is unclear. As a result, it’s not clear what specific task the paper is targeting or what the concrete
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Taxonomy
TopicsAdvanced Graph Neural Networks · Machine Learning in Healthcare · Graph Theory and Algorithms