Laplacian-LoRA: Delaying Oversmoothing in Deep GCNs via Spectral Low-Rank Adaptation

TL;DR

Laplacian-LoRA introduces a spectral low-rank adaptation to deep GCNs, effectively delaying oversmoothing by modifying the Laplacian operator, which extends the networks' effective depth and preserves node representation quality.

Contribution

This paper presents Laplacian-LoRA, a novel spectral low-rank correction method that systematically delays oversmoothing in deep GCNs without redesigning message passing mechanisms.

Findings

Laplacian-LoRA extends GCN depth by up to two times before oversmoothing occurs.

The spectral correction is smooth, bounded, and maintains stability.

Empirical results confirm delayed representational collapse across multiple datasets.

Abstract

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.