How Do Graph Signals Affect Recommendation: Unveiling the Mystery of Low and High-Frequency Graph Signals

2025-12-10

AI Summary

This work investigates how spectral characteristics of graph signals affect recommendation performance, revealing theoretical equivalence between low- and high-frequency components in smoothing user–item similarity. To exploit this insight, we propose a plug-and-play Frequency Signal Scaler (FSS) that enables differentiable control over smoothness, and a Spatial Flip (SF) technique to compensate for the limited high-frequency expressivity of standard graph embeddings. Our approach is fully compatible with arbitrary GNN-based recommendation models without modifying their backbone architectures. Extensive experiments on four public benchmark datasets demonstrate that using only a single frequency band—either low- or high-frequency—achieves state-of-the-art performance, validating both the sufficiency and complementarity of spectral information. The implementation is publicly available, supporting seamless integration into existing frameworks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Recommender Systems
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Spectral graph neural networks (GNNs) are highly effective in modeling graph signals, with their success in recommendation often attributed to low-pass filtering. However, recent studies highlight the importance of high-frequency signals. The role of low-frequency and high-frequency graph signals in recommendation remains unclear. This paper aims to bridge this gap by investigating the influence of graph signals on recommendation performance. We theoretically prove that the effects of low-frequency and high-frequency graph signals are equivalent in recommendation tasks, as both contribute by smoothing the similarities between user-item pairs. To leverage this insight, we propose a frequency signal scaler, a plug-and-play module that adjusts the graph signal filter function to fine-tune the smoothness between user-item pairs, making it compatible with any GNN model. Additionally, we identify and prove that graph embedding-based methods cannot fully capture the characteristics of graph signals. To address this limitation, a space flip method is introduced to restore the expressive power of graph embeddings. Remarkably, we demonstrate that either low-frequency or high-frequency graph signals alone are sufficient for effective recommendations. Extensive experiments on four public datasets validate the effectiveness of our proposed methods. Code is avaliable at https://github.com/mojosey/SimGCF.

Problem

• Investigates the unclear role of low and high-frequency graph signals in recommendation tasks.
• Proves low and high-frequency graph signals equivalently smooth user-item similarities for recommendations.
• Addresses limitations of graph embeddings in capturing graph signal characteristics for recommendations.

Innovation

• Frequency signal scaler adjusts graph signal filter function
• Space flip method restores graph embedding expressive power
• Low or high-frequency graph signals alone enable effective recommendations