通过谱低秩修正延缓深度图网络的过度平滑问题
Laplacian-LoRA: Delaying Oversmoothing in Deep GCNs via Spectral Low-Rank Adaptation
- 在图传播算子中引入可学习的谱锚定修正项
- 使节点表示在更深网络中仍保持差异性，有效深度提升一倍
- 方法简单可解释，适合研究图神经网络泛化性的学者
过度平滑是深度图卷积网络的根本限制，导致节点表示随网络加深而坍缩。现有方法多通过结构改进或残差机制缓解，但未明确其谱学成因。本文提出Laplacian-LoRA，一种简单且可解释的谱低秩适应方法。不重构消息传递机制，而是对固定拉普拉斯传播算子引入可学习的谱锚定修正，选择性减弱收缩效应，同时保持稳定性和低通归纳偏置。在多个基准数据集与不同深度下，该方法均显著延迟过度平滑的发生，使图网络有效深度提升达两倍。嵌入方差诊断证实收益源于表示坍缩的延缓，谱分析表明修正项平滑、有界且行为良好。结果表明，过度平滑是依赖深度的谱现象，可通过轻微、低秩的图传播算子调整系统性延缓。
原文摘要 · Abstract (English)
Oversmoothing is a fundamental limitation of deep graph convolutional networks (GCNs), causing node representations to collapse as depth increases. While many prior approaches mitigate this effect through architectural modifications or residual mechanisms, the underlying spectral cause of oversmoothing is often left implicit. We propose Laplacian-LoRA, a simple and interpretable low-rank spectral adaptation of standard GCNs. Rather than redesigning message passing, Laplacian-LoRA introduces a learnable, spectrally anchored correction to the fixed Laplacian propagation operator, selectively weakening contraction while preserving stability and the low-pass inductive bias. Across multiple benchmark datasets and depths, Laplacian-LoRA consistently delays the onset of oversmoothing, extending the effective depth of GCNs by up to a factor of two. Embedding variance diagnostics confirm that these gains arise from delayed representational collapse, while learned spectral analysis demonstrates that the correction is smooth, bounded, and well behaved. Our results show that oversmoothing is a depth-dependent spectral phenomenon that can be systematically delayed through modest, low-rank adaptation of the graph propagation operator.
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