Rethinking Parameter Sharing as Graph Coloring for Structured Compression

Parameter sharing is a key model compression technique, yet existing methods overlook the geometric properties of the loss landscape, often causing severe accuracy degradation under high compression ratios. Inspired by second-order optimization, we propose Curvature-aware Graph Coloring (CGC), a cross-layer parameter sharing framework that treats each network layer as a graph node, with each node assigned to a shared low-rank basis. CGC leverages Hessian eigenspace information to group layers with similar curvature profiles, aligning the perturbations introduced by parameter sharing with the low-curvature (flat) directions of the loss ellipsoid. This effectively mitigates performance loss while enabling flexible, global cross-layer sharing. Experiments on LLaMA-7B and Swin Transformer show that CGC achieves 28\%–50\% parameter compression with Top-1 accuracy loss no more than 0.01\% on Swin—or even accuracy gains on LLaMA—while delivering over 60\% higher inference throughput, significantly outperforming SVD-based and heuristic-based methods. This work demonstrates that curvature-guided, geometry-aware sharing is essential for efficient, stable, and high-ratio model compression.