Graph filter design is central to spectral collaborative filtering, yet most existing methods rely on manually tuned hyperparameters rather than fully learnable filters. We show that this challenge stems from a bias in traditional recommendation objectives, which induces a spectral phenomenon termed low-frequency explosion, thereby fundamentally hindering the effective learning of graph filters. To overcome this limitation, we propose a novel adaptive spectral graph collaborative filtering framework (ASPIRE) based on a bi-level optimization objective. Guided by our theoretical analysis, we disentangle the filter learning objective, which in turn leads to excellent recommendation performance, spectral adaptivity, and training stability in practice. Extensive experiments show our learned filters match the performance of carefully engineered task-specific designs. Furthermore, ASPIRE is equally effective in LLM-powered collaborative filtering. Our findings demonstrate that graph filter learning is viable and generalizable, paving the way for more expressive graph neural networks in collaborative filtering.

翻译：图滤波器设计是谱协同过滤的核心，然而现有方法大多依赖手动调节的超参数而非完全可学习的滤波器。我们证明，这一挑战源于传统推荐目标中存在的偏差，该偏差会引发电磁现象——低频爆炸，从而从根本上阻碍图滤波器的有效学习。为克服此限制，我们提出一种基于双层优化目标的新型自适应谱图协同过滤框架（ASPIRE）。在理论分析的指导下，我们解耦了滤波器学习目标，从而在实践中实现了卓越的推荐性能、谱自适应性和训练稳定性。大量实验表明，我们学到的滤波器可媲美精心设计的任务特定方案。此外，ASPIRE在大语言模型赋能的协同过滤中同样有效。我们的发现证实了图滤波器学习的可行性与泛化性，为协同过滤中更具表达力的图神经网络铺平了道路。