arXiv:2607.14834 2026 Memory 2 ideas extracted · analyzed Aug 30, 2026
The paper provides a principled way to reinterpret edge weights as a graph signal: vertices of the line graph correspond to original edges, so incident edges become neighboring signal locations. This creates a spectral basis in which locally smooth edge parameters concentrate in low-frequency coefficients, enabling structured parameter sharing and transform-domain compression. The most promising neural transfers are compact spectral parameterizations for edge-conditioned GNNs and rate-distortion quantization of edge-dependent attention biases, while retaining the original graph topology exactly.
Compress a trained graph-attention model's edge-dependent logits or gates in the line-graph Fourier domain. Smooth edge values become concentrated in low-frequency coefficients, allowing low-frequency coefficients to retain more precision while high-frequency residuals use fewer bits or are discarded.
Replace one independently learned vector per graph edge with a truncated spectral expansion on the line graph. The model learns coefficients for low-frequency edge modes and reconstructs edge features before message passing, reducing parameters while imposing an inductive bias that incident edges should have correlated behavior.