Sai Vamsi Alisetti | Searcharxiv

arXiv2026

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

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.

cs.LG↗

arXiv2025

Beyond Attention: Learning Spatio-Temporal Dynamics with Emergent Interpretable Topologies

Spatio-temporal forecasting is critical in applications such as traffic prediction, energy demand modeling, and weather monitoring. While Graph Attention Networks (GATs) are popular for modeling spatial dependencies, they rely on predefined adjacency structures and dynamic attention scores, introducing inductive biases and computational overhead that can obscure interpretability. We propose InterGAT, a simplified alternative to GAT that replaces masked attention with a fully learnable, symmetric node interaction matrix, capturing latent spatial relationships without relying on fixed graph topologies. Our framework, InterGAT-GRU, which incorporates a GRU-based temporal decoder, outperforms the baseline GAT-GRU in forecasting accuracy, achieving at least a 21% improvement on the SZ-Taxi dataset and a 6% improvement on the Los-Loop dataset across all forecasting horizons (15 to 60 minutes). Additionally, we observed reduction in training time by 60-70% compared to GAT-GRU baseline. Crucially, the learned interaction matrix reveals interpretable structure: it recovers sparse, topology-aware attention patterns that align with community structure. Spectral and clustering analyses show that the model captures both localized and global dynamics, offering insights into the functional topology driving predictions. This highlights how structure learning can simultaneously support prediction, computational efficiency, and topological interpretabil-ity in dynamic graph-based domains.

cs.LG↗